As I was walking to work this morning, I was thinking about Hilbert space. Specifically, that the Dirac formulation of QM doesn't really work in normal Hilbert space, because a lot of the operators have no spectra or eigenfunctions there. You require either a "rigged Hilbert space" which has extra structure that allows the Dirac delta to exist there, or you need to move the analysis to the space of tempered distributions.
Now tempered distributions raise an interesting point about the Born interpretation of QM. In this standard interpretation, Hermitian operators correspond to observables, eigenvalues to measurement outcomes, and component amplitudes to probabilities of outcomes. As long as the eigenvalue spectrum is discrete, there is no interpretation problem with this, and in fact you can use the Hilbert space l_2 of square summable sequences to represent the theory. However, when the spectrum is continuous, you need both stronger mathematics and a slightly different interpretation.
In this case, (especially for the Schrodinger wave function) the interpretation of the amplitude (squared, of course) is usually as a probability density. This has always bothered me somewhat at a philosophical level, because the probability density is a point function. That is, it assigns to each point in space a numerical density, which can be integrated to find the probability that the particle will be found within a given search region. Mathematically, this presents no difficulty, but points are not phenomenologically fundamental. No conceivable experiment or set of experiments can actually verify the probability density at a given single point. Therefore, it always seemed to me to be inappropriate to formulate the Born intepretation as a probability density; on the other hand, it works in a practical sense, so it cannot be utterly wrong.
What struck me this morning was that both the Born interpretation and the mathematics were unproblematic for the same cases, namely discrete spectra. So perhaps the mathematical niceties of making the continuous spectrum case rigorous have some bearing on the philosophical niceties of interpreting such a spectrum. It occured to me that, since the tempered distributions are not actually point functions, but linear operators on a space of test functions that vanish at infinity, this might resolve my objections to the probability density interpretation. The new interpretation is that each test function represents an experiment; for instance a test function with compact support represents a search for a particle within a confined location. The wavefunction, considered as a tempered distribution, is a linear functional that assigns to each experiment a probability of finding the particle in the area being searched.
This nicely resolves my philosophical objection, because every assertion made by the theory is now experimentally accessible in principle. The price of this is that the wavefunction is now one step more abstract than before. Not only are observables operators, but the state itself is an operator on the space of measurements, which are represented by the test functions. This idea also breaks with the traditional Kolmogorov foundation of probability theory as a branch of measure theory, since it does not assign probability measures to point sets but to test functions.
Well, those were my thoughts this morning. I'm just posting them here in case they might be interesting, and because I ran out of people around here that will hold still to be told about it. Any comments?
--Stuart Anderson
hej Mr. homm
I agree very generally,
Probability in principle can be only attributed to discrete events, so fundamentally continuous probability density is not possible.
But in my opinion, in math we are just scratching the surface. I mean, continuous functions and infinite differentiation as such are valid concepts, but they miss the reference point, and the reference point is discreteness.
We are missing nuances in infinities in math by using only one infinity. We miss infinity of infinities , figuratively speaking, and we miss infinity of operations as well.
Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete- a physical analogy would be a looping of (imaginary) time.
Before this looping, we will have discrete structures as well - half loops etc- infinity of them- but in math they are all hidden in one infinity.
Now, if we think about continuous probability functions in general, physically they would be applicable to such infinitesimal discrete structures, and only.
That is obviously below quantum scale. Quantum scale should be deterministic not probabilistic as it is discrete, however its behavior can be driven by probabilistic SQ events that all have continuous character from today's math point of view as 1 infinity does not discern between them.
I am trying to think about vortex of imaginary time. Once time loops, it makes a vortex in time. If this loop is = smallest possible wavelength of de broglie waves (probably around 10-58 m), than after ( difficult to say what is after here) it forms, it will have a structure inside it with fractional debroglie wavelentghs. These fractional ones will have finite dimensions, and be localized, and interact with infinitesimal non-looped time structures which will behave in probabilistic way, via distributions, so we will always get when interfering the probability distribution width in our hands.
If ht <E gives quantum uncertainty that means that h as such is linked to the probability distribution of these SQ things in electron time vortex, or Kolmogorov Vortex of Time (which equals electron black hole radius).
I agree very generally,
Probability in principle can be only attributed to discrete events, so fundamentally continuous probability density is not possible.
But in my opinion, in math we are just scratching the surface. I mean, continuous functions and infinite differentiation as such are valid concepts, but they miss the reference point, and the reference point is discreteness.
We are missing nuances in infinities in math by using only one infinity. We miss infinity of infinities , figuratively speaking, and we miss infinity of operations as well.
Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete- a physical analogy would be a looping of (imaginary) time.
Before this looping, we will have discrete structures as well - half loops etc- infinity of them- but in math they are all hidden in one infinity.
Now, if we think about continuous probability functions in general, physically they would be applicable to such infinitesimal discrete structures, and only.
That is obviously below quantum scale. Quantum scale should be deterministic not probabilistic as it is discrete, however its behavior can be driven by probabilistic SQ events that all have continuous character from today's math point of view as 1 infinity does not discern between them.
I am trying to think about vortex of imaginary time. Once time loops, it makes a vortex in time. If this loop is = smallest possible wavelength of de broglie waves (probably around 10-58 m), than after ( difficult to say what is after here) it forms, it will have a structure inside it with fractional debroglie wavelentghs. These fractional ones will have finite dimensions, and be localized, and interact with infinitesimal non-looped time structures which will behave in probabilistic way, via distributions, so we will always get when interfering the probability distribution width in our hands.
If ht <E gives quantum uncertainty that means that h as such is linked to the probability distribution of these SQ things in electron time vortex, or Kolmogorov Vortex of Time (which equals electron black hole radius).
hej mr. homm
The idea being, that inside Kolmogorov vortex of imaginary time, fractional wave can form a standing wave system- I do not know how, but If I knew, it would be too easy.
Similar things must happen in Navier stokes equations and in superfluids, perhaps even water. Vortexes must be possible to Fourier decompose in rotating fractional (imaginary?) de Broglie waves that are fractions of their OWN circumference length.
This relates only to finite speeds. In case of Kolmogorov vortex of time, these finite speeds would be rational multiples of c, in other vortexes- related to their rotation speed in media.
The idea being, that inside Kolmogorov vortex of imaginary time, fractional wave can form a standing wave system- I do not know how, but If I knew, it would be too easy.
Similar things must happen in Navier stokes equations and in superfluids, perhaps even water. Vortexes must be possible to Fourier decompose in rotating fractional (imaginary?) de Broglie waves that are fractions of their OWN circumference length.
This relates only to finite speeds. In case of Kolmogorov vortex of time, these finite speeds would be rational multiples of c, in other vortexes- related to their rotation speed in media.
mr homm - Ivars
I would like to take it a step further -
QUOTE: Ivars "Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete-"
Well - and if not - then it is just to acknowledge that continuous simply is not a viable concept - continuous is not part of "existance" in physical world -
And it calls for a definition - What IS physical world ?
I imagine that physical world - Our Universe - best can be envisaged as how information express itsself in a physical form.
And I further imagine that information best can be seen as a binary system - a binary math system - that mathematics in its very essence is binary. Universe is a binary system, characterized by dynamic dimensionalities in a 3D space.
Origin conditions are simplest possible - namely a dimension (3D)to which a binary principle is being applied.
Dimension is without any defined size - meaning infinite - no form - just space - and when the binary principle is being applied - "the unfolding of physical" - that is the very moment where space - dimension is being divided in two - two dimensions - no size - just a ratio of two.
When this principle is working on space - the result is, that space is being segregated in more and more ratios - presenting as dimensions in space - and the binary principle place the dimensions after a system in 3D, so each ratio of space is being defined by its exact position relative to neighboring ratios - it is not only a ratio - it is also a position.
Each and any ratio is the equivalent to a number in our math system, and each and any number in our math system represents a dimension with its corresponding position in 3D space.
Physical Universe is such dimensions arranged in configurations according to math system, in scales - more and more complex as the binary system grows - and the positioning becomes more and more complex in russian doll like configurations - inwards - fractal - everything we already know about in space - manifolds and and ---and possibly a lot more complexion that we have no insight into as yet. Universe is oscillating flash expressions of dimensional configurations in 3D space. Universe exists once only. The only difference between potential and kietic is the way that the kinetic is being played - when in repetitions - it is seen as potential, when not repeating it is seen as kinetic.
Anyhow - this leads to the insight that there exist no such thing as infinite - every thing is discrete - all numbers are discrete and represented by a dimension - there exist no sucg thing as "point-particles" - there exist no such thing as a continuity - and numbers are constantly developing into smaller and smaller dimensions - bigger and bigger ratios - everything IS ratios, and it is meaningless to talk about seize of Universe - or whether it is expanding - decreasing or steady - because universe has no zize - it has the size that universe shall have and it is all about ratios - everything is relative.
Popularly Universe is expanding inwards - and the smallest dimensionality we can define as physical is made of a PATTERN - a repeating pattern of smallest dimensionalities which relates to said SCALE. Physical scale is human scale - and lower scales belong to subquantum - but subquantum is scaled smallwise, stepwise - and according to math development -
Always with a dimensionality linked to a number - always with discrete numbers - continuity simply cannot be part of physical Universe - if we define physical universe as the "reality" that we humans percept and imagine with our mind.
I would like to take it a step further -
QUOTE: Ivars "Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete-"
Well - and if not - then it is just to acknowledge that continuous simply is not a viable concept - continuous is not part of "existance" in physical world -
And it calls for a definition - What IS physical world ?
I imagine that physical world - Our Universe - best can be envisaged as how information express itsself in a physical form.
And I further imagine that information best can be seen as a binary system - a binary math system - that mathematics in its very essence is binary. Universe is a binary system, characterized by dynamic dimensionalities in a 3D space.
Origin conditions are simplest possible - namely a dimension (3D)to which a binary principle is being applied.
Dimension is without any defined size - meaning infinite - no form - just space - and when the binary principle is being applied - "the unfolding of physical" - that is the very moment where space - dimension is being divided in two - two dimensions - no size - just a ratio of two.
When this principle is working on space - the result is, that space is being segregated in more and more ratios - presenting as dimensions in space - and the binary principle place the dimensions after a system in 3D, so each ratio of space is being defined by its exact position relative to neighboring ratios - it is not only a ratio - it is also a position.
Each and any ratio is the equivalent to a number in our math system, and each and any number in our math system represents a dimension with its corresponding position in 3D space.
Physical Universe is such dimensions arranged in configurations according to math system, in scales - more and more complex as the binary system grows - and the positioning becomes more and more complex in russian doll like configurations - inwards - fractal - everything we already know about in space - manifolds and and ---and possibly a lot more complexion that we have no insight into as yet. Universe is oscillating flash expressions of dimensional configurations in 3D space. Universe exists once only. The only difference between potential and kietic is the way that the kinetic is being played - when in repetitions - it is seen as potential, when not repeating it is seen as kinetic.
Anyhow - this leads to the insight that there exist no such thing as infinite - every thing is discrete - all numbers are discrete and represented by a dimension - there exist no sucg thing as "point-particles" - there exist no such thing as a continuity - and numbers are constantly developing into smaller and smaller dimensions - bigger and bigger ratios - everything IS ratios, and it is meaningless to talk about seize of Universe - or whether it is expanding - decreasing or steady - because universe has no zize - it has the size that universe shall have and it is all about ratios - everything is relative.
Popularly Universe is expanding inwards - and the smallest dimensionality we can define as physical is made of a PATTERN - a repeating pattern of smallest dimensionalities which relates to said SCALE. Physical scale is human scale - and lower scales belong to subquantum - but subquantum is scaled smallwise, stepwise - and according to math development -
Always with a dimensionality linked to a number - always with discrete numbers - continuity simply cannot be part of physical Universe - if we define physical universe as the "reality" that we humans percept and imagine with our mind.
hej bukh,
Continuous is the single cause of existence of the physical world. And so via this it is also part of it.
As to infinity , there can be discrete infinities, and infinite amount of them. The problem is , math does not recognize them. The only truly continuous "number" is imaginary unit, and , perhaps, 0.
Fractions and discrete fractality alone, without infinities and continuous does not posses the needed uniqueness which we observe in Nature. Fractals are in fact boring, while Nature is not.
So what You call inwards expansion (of a Kolmogorov vortex of time) must interact with "outwardly" expanding infinitesimal information flows to create what we see as Universe, including life.
To summarize, if there exists true continuity in mathematics ( imaginary unit) or a mix of continuity and discrete infinitesimals ( complex numbers) , there exists one in Universe. There can not be 2 truths- either math fits Universe fully, or it does not fit to describe it. I consider first version to be more economical.
You are right about ratios, though. 2 Dimensions mean that ratios are "free flying", 3rd dimension fixes these ratios. It is like integration, where normally between 2 scales ( infinitesimal and integrated infinitesimal) You have an arbitrary integration constant- that means these 2 dimensions of space time can be positioned in ANY of infinity of posotions vs. each other. That is what I call ABSOLUTE relativity. Once the integration constant is fixed, or some ratio between integration constants of all 2D in all combinations is fixed ( e.g. equals speed of light as integration constant ratio between TIME and SPACE) we get Special relativity and 3rd dimension.
Continuous is the single cause of existence of the physical world. And so via this it is also part of it.
As to infinity , there can be discrete infinities, and infinite amount of them. The problem is , math does not recognize them. The only truly continuous "number" is imaginary unit, and , perhaps, 0.
Fractions and discrete fractality alone, without infinities and continuous does not posses the needed uniqueness which we observe in Nature. Fractals are in fact boring, while Nature is not.
So what You call inwards expansion (of a Kolmogorov vortex of time) must interact with "outwardly" expanding infinitesimal information flows to create what we see as Universe, including life.
To summarize, if there exists true continuity in mathematics ( imaginary unit) or a mix of continuity and discrete infinitesimals ( complex numbers) , there exists one in Universe. There can not be 2 truths- either math fits Universe fully, or it does not fit to describe it. I consider first version to be more economical.
You are right about ratios, though. 2 Dimensions mean that ratios are "free flying", 3rd dimension fixes these ratios. It is like integration, where normally between 2 scales ( infinitesimal and integrated infinitesimal) You have an arbitrary integration constant- that means these 2 dimensions of space time can be positioned in ANY of infinity of posotions vs. each other. That is what I call ABSOLUTE relativity. Once the integration constant is fixed, or some ratio between integration constants of all 2D in all combinations is fixed ( e.g. equals speed of light as integration constant ratio between TIME and SPACE) we get Special relativity and 3rd dimension.
Hej Ivars
I think that we are more in agreement than you think
QUOTE: "As to infinity , there can be discrete infinities, and infinite amount of them. The problem is , math does not recognize them. The only truly continuous "number" is imaginary unit, and , perhaps, 0."
Imaginary unit and 0 is the same - just being expressed differently - space without form - pure kinetic information - infinite number of formless informational bits - zero number of forms -
And imaginary unit and 0 is according to my definition OUTSIDE physical world - it is before physical world - it is the pre-origin conditions -
QUOTE: "Fractions and discrete fractality alone, without infinities and continuous does not posses the needed uniqueness which we observe in Nature. Fractals are in fact boring, while Nature is not."
Nature inhabit the potential to go as big as it wants - it is an open system - however with the little limitation that once TRUE INFINITY is being reached - the physical universe vanish - because true infinity indicate infinite number of FORMLESS informational bits - we are back at scratch - back at zero - back at origin conditions - or may be as I have indicated earlier - formless informational bits or kinetic information - perhaps ??? have "learned" something that can be translated to the next Universe.
QUOTE: "So what You call inwards expansion (of a Kolmogorov vortex of time) must interact with "outwardly" expanding infinitesimal information flows to create what we see as Universe, including life."
YES YES YES - Of Course - that is the principle behind everything and all of physical expressions (irrespective of scale) - and the only principle that is holy - is that speed - defined as reconfigurational rate x dimension of informational unit = "c" must be highest in lowest dimensional scale - in order to be translatable upwards - and so on in every upscaling step - because retrocausality is only relative from one scale to the next - true retrocausality is NOT an option. So speed must be increasingly more rapid in each downscaling.
QUOTE: "To summarize, if there exists true continuity in mathematics ( imaginary unit) or a mix of continuity and discrete infinitesimals ( complex numbers) , there exists one in Universe. There can not be 2 truths- either math fits Universe fully, or it does not fit to describe it. I consider first version to be more economical."
Right if you include imaginary unit to be part of physical universe - but then you have to be very cautious about the fit between math and physical universe - it HAS to be one to one fit - and it means that math will NOT include continuos except at very very last tick (infinite minus 1) before it vanish into formlessness.
QUOTE: "You are right about ratios, though. 2 Dimensions mean that ratios are "free flying", 3rd dimension fixes these ratios. It is like integration, where normally between 2 scales ( infinitesimal and integrated infinitesimal) You have an arbitrary integration constant- that means these 2 dimensions of space time can be positioned in ANY of infinity of posotions vs. each other. That is what I call ABSOLUTE relativity. Once the integration constant is fixed, or some ratio between integration constants of all 2D in all combinations is fixed ( e.g. equals speed of light as integration constant ratio between TIME and SPACE) we get Special relativity and 3rd dimension.
I think that the above nicely express what and where we seemingly "disagree"
You allow for infinity during the period where latest and smallest scale is "under construction" - In as much as dimensions = numbers are constantly expanding, new numbers are constantly being created, means that during this construction phase, dimensions = numbers are being calculated as per their being born - if you follow me - so in a sense each following number is being taken from "infinity" - albeit the infinity which is the existing infinity at that very moment - the next following moment still another number is being added into the calculation, and that number is being taken from "latest infinity plus 1"
The translation from 2D to 3D has not to do with the dimension of numbers = dimensions - because any number - irrespective of its smallness has a dimension, no, it has to do with the creation of a "PARTICLE" in that said scale - it has to do with the repetition that sooner or later will emerge when increasingly more and more numbers are being added to the operations that the math. system put onto said respective "new" numbers.
I think that we are more in agreement than you think
QUOTE: "As to infinity , there can be discrete infinities, and infinite amount of them. The problem is , math does not recognize them. The only truly continuous "number" is imaginary unit, and , perhaps, 0."
Imaginary unit and 0 is the same - just being expressed differently - space without form - pure kinetic information - infinite number of formless informational bits - zero number of forms -
And imaginary unit and 0 is according to my definition OUTSIDE physical world - it is before physical world - it is the pre-origin conditions -
QUOTE: "Fractions and discrete fractality alone, without infinities and continuous does not posses the needed uniqueness which we observe in Nature. Fractals are in fact boring, while Nature is not."
Nature inhabit the potential to go as big as it wants - it is an open system - however with the little limitation that once TRUE INFINITY is being reached - the physical universe vanish - because true infinity indicate infinite number of FORMLESS informational bits - we are back at scratch - back at zero - back at origin conditions - or may be as I have indicated earlier - formless informational bits or kinetic information - perhaps ??? have "learned" something that can be translated to the next Universe.
QUOTE: "So what You call inwards expansion (of a Kolmogorov vortex of time) must interact with "outwardly" expanding infinitesimal information flows to create what we see as Universe, including life."
YES YES YES - Of Course - that is the principle behind everything and all of physical expressions (irrespective of scale) - and the only principle that is holy - is that speed - defined as reconfigurational rate x dimension of informational unit = "c" must be highest in lowest dimensional scale - in order to be translatable upwards - and so on in every upscaling step - because retrocausality is only relative from one scale to the next - true retrocausality is NOT an option. So speed must be increasingly more rapid in each downscaling.
QUOTE: "To summarize, if there exists true continuity in mathematics ( imaginary unit) or a mix of continuity and discrete infinitesimals ( complex numbers) , there exists one in Universe. There can not be 2 truths- either math fits Universe fully, or it does not fit to describe it. I consider first version to be more economical."
Right if you include imaginary unit to be part of physical universe - but then you have to be very cautious about the fit between math and physical universe - it HAS to be one to one fit - and it means that math will NOT include continuos except at very very last tick (infinite minus 1) before it vanish into formlessness.
QUOTE: "You are right about ratios, though. 2 Dimensions mean that ratios are "free flying", 3rd dimension fixes these ratios. It is like integration, where normally between 2 scales ( infinitesimal and integrated infinitesimal) You have an arbitrary integration constant- that means these 2 dimensions of space time can be positioned in ANY of infinity of posotions vs. each other. That is what I call ABSOLUTE relativity. Once the integration constant is fixed, or some ratio between integration constants of all 2D in all combinations is fixed ( e.g. equals speed of light as integration constant ratio between TIME and SPACE) we get Special relativity and 3rd dimension.
I think that the above nicely express what and where we seemingly "disagree"
You allow for infinity during the period where latest and smallest scale is "under construction" - In as much as dimensions = numbers are constantly expanding, new numbers are constantly being created, means that during this construction phase, dimensions = numbers are being calculated as per their being born - if you follow me - so in a sense each following number is being taken from "infinity" - albeit the infinity which is the existing infinity at that very moment - the next following moment still another number is being added into the calculation, and that number is being taken from "latest infinity plus 1"
The translation from 2D to 3D has not to do with the dimension of numbers = dimensions - because any number - irrespective of its smallness has a dimension, no, it has to do with the creation of a "PARTICLE" in that said scale - it has to do with the repetition that sooner or later will emerge when increasingly more and more numbers are being added to the operations that the math. system put onto said respective "new" numbers.
hej bukh
I think we stole the thread... Not good. I hope at least some of the ideas may have been interesting to mr.homm.
I think we stole the thread... Not good. I hope at least some of the ideas may have been interesting to mr.homm.
An interesing link:
Time scales Hilger complex plane
Excerpt:
In Laplace transforms of continuous time signals, we have the s plane. In the ztransform of discrete time signals, there is the unit circle. In time scales, both are special cases of the Hilger circle shown here.
The Hilger circle hass a diameter equal to the reciprical of graininess and is tangent to the imaginary axis.
For discrete time, the graininess is one.
Time scales Hilger complex plane
Excerpt:
In Laplace transforms of continuous time signals, we have the s plane. In the ztransform of discrete time signals, there is the unit circle. In time scales, both are special cases of the Hilger circle shown here.
The Hilger circle hass a diameter equal to the reciprical of graininess and is tangent to the imaginary axis.
For discrete time, the graininess is one.
Hi mr_homm, Ivars, bukh et al,
I have only the highest regard for Stuart... that is no joke. But I would like a light hearted discussion of Quantum Principles and how they may fit with the Mathematical Theory you have outlined here in a rather abstract and circuitous way. That does not mean I am 'cold" to the pristine beauty of "pure mathematics" but I would like the maths to be pitched to the Physics of our Universe and how this mathematics actually then describe this "real experimental" physics. For my part you will find some of these points placed in a rather complex way (in engineering terms rather than philosophical terms) in this thread ... In fact I have outlined much of it in a couple of threads previously.
Light, compostion of light good Elf
or in this place...
Problem with the two slit experiment, Observing later Good Elf
This is no "battle of the brains" since I will shurely lose...
but humor me for what it is worth and we can both have a little good hearted "fun".
I have only the highest regard for Stuart... that is no joke. But I would like a light hearted discussion of Quantum Principles and how they may fit with the Mathematical Theory you have outlined here in a rather abstract and circuitous way. That does not mean I am 'cold" to the pristine beauty of "pure mathematics" but I would like the maths to be pitched to the Physics of our Universe and how this mathematics actually then describe this "real experimental" physics. For my part you will find some of these points placed in a rather complex way (in engineering terms rather than philosophical terms) in this thread ... In fact I have outlined much of it in a couple of threads previously.
Light, compostion of light good Elf
or in this place...
Problem with the two slit experiment, Observing later Good Elf
This is no "battle of the brains" since I will shurely lose...
but humor me for what it is worth and we can both have a little good hearted "fun".QUOTE (Stuart Anderson+)
As I was walking to work this morning, I was thinking about Hilbert space. Specifically, that the Dirac formulation of QM doesn't really work in normal Hilbert space, because a lot of the operators have no spectra or eigenfunctions there. You require either a "rigged Hilbert space" which has extra structure that allows the Dirac delta to exist there, or you need to move the analysis to the space of tempered distributions.
If you really think about it the Dirac delta functions can exist "nowhere" in any real universe since the energy under the curve must be infinite while the duration is zero. The delta function is an "idealization" that has some valid basis but it also has some invalid consequences. The same as would occur with the distribution of any "point function" which all mathematical functions really are. At every point in some three dimensional space the function must have a value to be analytic. This illustrates where mathematics as a philosophy can diverge from the real Universe. Mathematics is a way of collecting very useful ideas that have taken a very long time to develop into a "system" in which there is no room for discussion anymore. The axioms, theorems and the formalism can lead to viewing the physical world as a mathematical construct rather than the other way around. Our world is not a mathematical entity that must conform to our formal forms of analysis since those forms are of a purely human construct abstracted from the laws which govern our world. To give an example it is assumed that mathematical deconstruction can be used to solve much bigger problems by starting from the simple and then moving one layer at a time up to the "big picture". The basic idea is also that each individual step must be the simplest step possible. Our small brains have used this method to solve a lot of medium sized problems quite successfully. The compartmentalization of knowledge and the compartmentalization of physical theories has resulted in a decentralized view of our Universe and to a formal denial that solutions in a physical world are possible through blending concepts from say the quantum realm and the classical realm. It is a worry that anyone at all really understands what are and how are all those compartments connected in some kind of "Theory of Everything".
It is my "pet conspiracy theory" that there is a very tiny "Ministry of Information" or Government Department inside the upper Cryptrocracy of our Planet that actually think they know "everything that is needed to be known" and it is their avowed intention to protect that little connection between all science to a real "Theory of Everything" at all cost... maybe even at "extreme" cost to some individuals. A kind of "Star Trek Principle" similar to "The Prime Directive" where essential science (star travel and warp drive) is denied even the worthiest and noblest civilization on the basis that it will "stunt their growth" although we all know it is a way to continue to monopolize the power inherent in Federation "Galactic Control". Returning to this Cryptocracy point of view... This "little Ministry" would have, at most, only one individual that "formally" knows "everything" ... sort of like the Pope in the Catholic Church at the top of this "structure" in order that the "right stuff" is known by that one and only one person and the "underlings" and "functionaries" vow never to attempt to "join the dots" about this "information" about everything.
At any time if it happens that one of these "underlings" does inadvertently manage to "join the dots" they are required to terminate themselves with extreme prejudice to maintain the purity of the structure... "there can be only one"... he he he! Of course the joke on all of them is this is a "religion" after all (no peer review and no experiments), no different to the Catholic Church and the information they are guarding is "scientifically worthless"... all these "guardians" have done is terminate a lot of good and honest people who were "getting close" to actually making a major advance that would have taken science to the next level. A real story "exists" behind Dan Brown's Book "The Da Vinci Code" which has had so much of an attraction for those "who want to know" the "real" truth behind it all. We all know Brown's Book is nonsense but we are also strangely attracted by some "group consciousness" to a conspiracy that that we know does exist in the top levels of Government.... the Compartmentalization of Government Scientific Knowledge and to any number of Black Projects that have occurred in the past and continue to this day. I could go on and say how "worthless" this pursuit can and will be for those who engage in it... but why should I ... you all don't have a "need to know" so as scientists you should all "shut up and continue calculating".... Thank you for this "rant" ... I knew you would all like that eh?
Getting back to the main game...
Please forgive me for putting it this way but you are not the first and you will not be the last to do this... Here you have seen that this idea does not work and you have taken to "adding on a little modification" to the basic theory "ad hoc" to "solve" your immediate philosophical dilemma.
It is my "pet conspiracy theory" that there is a very tiny "Ministry of Information" or Government Department inside the upper Cryptrocracy of our Planet that actually think they know "everything that is needed to be known" and it is their avowed intention to protect that little connection between all science to a real "Theory of Everything" at all cost... maybe even at "extreme" cost to some individuals. A kind of "Star Trek Principle" similar to "The Prime Directive" where essential science (star travel and warp drive) is denied even the worthiest and noblest civilization on the basis that it will "stunt their growth" although we all know it is a way to continue to monopolize the power inherent in Federation "Galactic Control". Returning to this Cryptocracy point of view... This "little Ministry" would have, at most, only one individual that "formally" knows "everything" ... sort of like the Pope in the Catholic Church at the top of this "structure" in order that the "right stuff" is known by that one and only one person and the "underlings" and "functionaries" vow never to attempt to "join the dots" about this "information" about everything.
At any time if it happens that one of these "underlings" does inadvertently manage to "join the dots" they are required to terminate themselves with extreme prejudice to maintain the purity of the structure... "there can be only one"... he he he! Of course the joke on all of them is this is a "religion" after all (no peer review and no experiments), no different to the Catholic Church and the information they are guarding is "scientifically worthless"... all these "guardians" have done is terminate a lot of good and honest people who were "getting close" to actually making a major advance that would have taken science to the next level. A real story "exists" behind Dan Brown's Book "The Da Vinci Code" which has had so much of an attraction for those "who want to know" the "real" truth behind it all. We all know Brown's Book is nonsense but we are also strangely attracted by some "group consciousness" to a conspiracy that that we know does exist in the top levels of Government.... the Compartmentalization of Government Scientific Knowledge and to any number of Black Projects that have occurred in the past and continue to this day. I could go on and say how "worthless" this pursuit can and will be for those who engage in it... but why should I ... you all don't have a "need to know" so as scientists you should all "shut up and continue calculating"....
Thank you for this "rant" ... I knew you would all like that eh?Getting back to the main game...
Please forgive me for putting it this way but you are not the first and you will not be the last to do this... Here you have seen that this idea does not work and you have taken to "adding on a little modification" to the basic theory "ad hoc" to "solve" your immediate philosophical dilemma.QUOTE (Stuart Anderson+)
The wavefunction, considered as a tempered distribution, is a linear functional that assigns to each experiment a probability of finding the particle in the area being searched.
This nicely resolves my philosophical objection, because every assertion made by the theory is now experimentally accessible in principle. The price of this is that the wavefunction is now one step more abstract than before. Not only are observables operators, but the state itself is an operator on the space of measurements, which are represented by the test functions. This idea also breaks with the traditional Kolmogorov foundation of probability theory as a branch of measure theory, since it does not assign probability measures to point sets but to test functions.
This nicely resolves my philosophical objection, because every assertion made by the theory is now experimentally accessible in principle. The price of this is that the wavefunction is now one step more abstract than before. Not only are observables operators, but the state itself is an operator on the space of measurements, which are represented by the test functions. This idea also breaks with the traditional Kolmogorov foundation of probability theory as a branch of measure theory, since it does not assign probability measures to point sets but to test functions.
A cozy idea... But what about the Physics?? Being "ad hoc" and because this is "mathematics" then this approach is quite defensible. I can "create" a mathematical rule which says 1 + 1 = 3... and because it is a rule makes perfectly good philosophical sense. I also see that Bukh and Ivars are thinking you are referring to actual physics but in fact you are solving a "procedural problem" in mathematics. Your colleagues at your workplace may have missed your point too. What I am really saying is the basic problem has gone unresolved and the real problem about the "Theory of Everything" you are trying to get a handle on is as distant as ever but you may have some kudos for your efforts from the Cryptrocracy... another piece for a "very large jigsaw" of globally unconnected facts. It is very much like the closing scene of "Indiana Jones and the Lost Ark of the Covenant" where "some of the best people are now working on the problem" (if you can all remember that humorous though unsatisfying ending?).
To put all this into some perspective I was able to reference this statement of the Born Interpretation from a Web Page (... after your reference to the Born Interpretation earlier in your thread).
Minimal Quantum Theory PJ Fimmel
The interesting thing about this is it is a "philosophical discussion" without reference to experiment or to a concrete theory. Yet he does attempt to bring it together into a philosophical context in his paper...
On the Electrodynamics of Motionless Events
This is actually very "perceptual" and is very close to my view of how things actually operate. Not "exactly" but close enough to be able to create a view that pulls a few threads together.
To put all this into some perspective I was able to reference this statement of the Born Interpretation from a Web Page (... after your reference to the Born Interpretation earlier in your thread).
Minimal Quantum Theory PJ Fimmel
The interesting thing about this is it is a "philosophical discussion" without reference to experiment or to a concrete theory. Yet he does attempt to bring it together into a philosophical context in his paper...
On the Electrodynamics of Motionless Events
This is actually very "perceptual" and is very close to my view of how things actually operate. Not "exactly" but close enough to be able to create a view that pulls a few threads together.
QUOTE
Discrete Electrodynamics
One of the most remarkable achievements of the project to develop quantum theory in the first three decades of the twentieth century was Dirac's relativistic equations for the electron. Like so many of the foundations of quantum mechanics, those equations were full of surprises at the time and remain, eighty years later, a mine whose ore is yet to be fully worked out. One of the ore bodies still to be extracted is an interpretation of particles with negative energy which is consistent with phenomena.
There are also the problems of how to give equal roles for time and space in the description of the electron and how the electron moves at the speed of light while complying with the rules of special relativity. Both are consequences of the Dirac equations for the electron.
Special relativity arose from the requirement that the laws of nature should be independent of the position and motion (rectilinear) of the observer. A double assumption arises when applying that principle to the components of the atom: the first is that there is something significant that is actually observable at the atomic scale and second that anything which is observable should include concepts such as position and motion.
It does not follow that special relativity is not applicable to a theory of quantum electrodynamics in which nothing is observable as it happens. The concept of mass and the absolute nature of the speed of light are also central to special relativity.
The present approach to electrodynamics begins with a minimum of assumptions and seeks to find a new dynamical system in which the electron and the nucleon behave both quantum mechanically and gravitationally while their behavior is consistent with observed phenomena.
The following are the first two in a series of papers on the theory of the discrete electron.
Title
On the Electrodynamics of Motionless Events
Abstract
The problem of electrodynamics among charged particles is analyzed by a physical interpretation of the consequences of the Dirac relativistic equation for the electron. By replacing the mathematical opposites of positive and negative energies with the physical opposites of actual and potential energies and serially coupling them in an oscillation the electron becomes fully discrete in both space and time. When the oscillations of individual charged particles and photons are suitably geometrically related their classical aspects reduce to motionless events whose genesis and interactions form a seamless union of quantum mechanics and special relativity. The model is simply particulate, fields and waves play no role. The logical development of the extension of the model among electrons and protons leads naturally to the electromagnetic interaction of the components of the helium atom.
http://pjfimmel.id.au/electrodynamics.htm
I would say it has "gone too far" simply because it neglects the experimental sciences and has no formalism. In as much as you have presented a similar philosophical argument at this stage this is a context which has relevance until something more concrete is presented. Would you like to comment further on your ideas with reference to the concepts in the primary reference above (The Born Interpretation) in being a "minimalist quantum theory"? I think this Interpretation is too "spartan"and is far too minimal to encapsulate the "real theory" required to explain all the "real" experimental results which any "real theory" must include... One of the most remarkable achievements of the project to develop quantum theory in the first three decades of the twentieth century was Dirac's relativistic equations for the electron. Like so many of the foundations of quantum mechanics, those equations were full of surprises at the time and remain, eighty years later, a mine whose ore is yet to be fully worked out. One of the ore bodies still to be extracted is an interpretation of particles with negative energy which is consistent with phenomena.
There are also the problems of how to give equal roles for time and space in the description of the electron and how the electron moves at the speed of light while complying with the rules of special relativity. Both are consequences of the Dirac equations for the electron.
Special relativity arose from the requirement that the laws of nature should be independent of the position and motion (rectilinear) of the observer. A double assumption arises when applying that principle to the components of the atom: the first is that there is something significant that is actually observable at the atomic scale and second that anything which is observable should include concepts such as position and motion.
It does not follow that special relativity is not applicable to a theory of quantum electrodynamics in which nothing is observable as it happens. The concept of mass and the absolute nature of the speed of light are also central to special relativity.
The present approach to electrodynamics begins with a minimum of assumptions and seeks to find a new dynamical system in which the electron and the nucleon behave both quantum mechanically and gravitationally while their behavior is consistent with observed phenomena.
The following are the first two in a series of papers on the theory of the discrete electron.
Title
On the Electrodynamics of Motionless Events
Abstract
The problem of electrodynamics among charged particles is analyzed by a physical interpretation of the consequences of the Dirac relativistic equation for the electron. By replacing the mathematical opposites of positive and negative energies with the physical opposites of actual and potential energies and serially coupling them in an oscillation the electron becomes fully discrete in both space and time. When the oscillations of individual charged particles and photons are suitably geometrically related their classical aspects reduce to motionless events whose genesis and interactions form a seamless union of quantum mechanics and special relativity. The model is simply particulate, fields and waves play no role. The logical development of the extension of the model among electrons and protons leads naturally to the electromagnetic interaction of the components of the helium atom.
http://pjfimmel.id.au/electrodynamics.htm
QUOTE (->
| QUOTE |
| Discrete Electrodynamics One of the most remarkable achievements of the project to develop quantum theory in the first three decades of the twentieth century was Dirac's relativistic equations for the electron. Like so many of the foundations of quantum mechanics, those equations were full of surprises at the time and remain, eighty years later, a mine whose ore is yet to be fully worked out. One of the ore bodies still to be extracted is an interpretation of particles with negative energy which is consistent with phenomena. There are also the problems of how to give equal roles for time and space in the description of the electron and how the electron moves at the speed of light while complying with the rules of special relativity. Both are consequences of the Dirac equations for the electron. Special relativity arose from the requirement that the laws of nature should be independent of the position and motion (rectilinear) of the observer. A double assumption arises when applying that principle to the components of the atom: the first is that there is something significant that is actually observable at the atomic scale and second that anything which is observable should include concepts such as position and motion. It does not follow that special relativity is not applicable to a theory of quantum electrodynamics in which nothing is observable as it happens. The concept of mass and the absolute nature of the speed of light are also central to special relativity. The present approach to electrodynamics begins with a minimum of assumptions and seeks to find a new dynamical system in which the electron and the nucleon behave both quantum mechanically and gravitationally while their behavior is consistent with observed phenomena. The following are the first two in a series of papers on the theory of the discrete electron. Title On the Electrodynamics of Motionless Events Abstract The problem of electrodynamics among charged particles is analyzed by a physical interpretation of the consequences of the Dirac relativistic equation for the electron. By replacing the mathematical opposites of positive and negative energies with the physical opposites of actual and potential energies and serially coupling them in an oscillation the electron becomes fully discrete in both space and time. When the oscillations of individual charged particles and photons are suitably geometrically related their classical aspects reduce to motionless events whose genesis and interactions form a seamless union of quantum mechanics and special relativity. The model is simply particulate, fields and waves play no role. The logical development of the extension of the model among electrons and protons leads naturally to the electromagnetic interaction of the components of the helium atom. http://pjfimmel.id.au/electrodynamics.htm |
I would say it has "gone too far" simply because it neglects the experimental sciences and has no formalism. In as much as you have presented a similar philosophical argument at this stage this is a context which has relevance until something more concrete is presented. Would you like to comment further on your ideas with reference to the concepts in the primary reference above (The Born Interpretation) in being a "minimalist quantum theory"? I think this Interpretation is too "spartan"and is far too minimal to encapsulate the "real theory" required to explain all the "real" experimental results which any "real theory" must include...
The present event scheme adopts a minimalist interpretation of quantum mechanics in which nothing classical is attributed to the domain of quantum objects. Nothing meaningful can be inferred about that domain, and isolated evolving quantum objects have no properties—properties only appear at measurements (or unmeasured interactions). And the properties which appear are relevant to the interaction or type of instrument the system collides with. Quantum mechanics is consistent with evolving systems, such as an electron, not being at any particular position, even though there is some probability that it might be observed at every point in space. That is sometimes interpreted to mean that the system is really at all the positions, and when observed, its being at all positions reduces instantly to being at just one of them. The evolving quantum system is somehow smeared out among all possible positions, and they mathematically all contribute to their being finally at one position.
That is not the present analysis, according to which, if it is not at a particular or definite position the electron might as well be at no position and we have no reason to go beyond that conclusion. We need to set aside all reliance upon classicality, which is sometimes called common sense. Being at no particular or definite position does not warrant any conclusion as to where the system is; or whether it is anywhere! The minimalist analysis adopted here agrees that the electron is at no definite or particular position and draws no conclusions beyond that fact. Of course, this runs counter to commonsense--but then common-sense is what tells us the earth is flat!
The analysis of the logic underlying the electron being smeared out among all the positions, at which there is some probability of its being found, depends upon two implied propositions: One is that the world contains the electron and the other is that the world includes all the positions at which it might be found in the future. However, if we adopt the mode of coupling space and time in the formation of spacetime which does not reduce the time axis to a space-like axis, and separate the concept of action from its representation, then we can question the idea that future spacetime loci are present before they occur! Put simply, if space and time are merely relations among objects and if the object has not yet arrived then perhaps neither has the space and time which relate it to other objects. If the world is discrete instead of continuous, then perhaps it only sometimes “includes all the positions at which the electron might be found.” If the positions at which the electron might be found are not in existence in the intervening period--what then? Such an analysis of spacetime is consistent with the electron being at no definite or particular position during the intervening period.
The evolution of the quantum system is inscrutable—it is private because it has no extrinsic or classical aspect. And theory says nothing about what is going on in the quantum domain. It only predicts what happens when quantum objects interact with the classical domain—when what happens is always classical. The simplest position to take is that nothing classical is going on in the quantum domain—nothing that can be counted, measured or observed.
http://pjfimmel.id.au/interpretation.htm
See the drift I am coming from? Would you like to discuss this "problem"?
One "aspect" of this problem is in the "inner product's" inability to be "reversible" when in actual fact any "resonance" or cavity "phase accumulation" has a certain "Quantum Zeno Property" which is for a short time capable of reversal, a phenomenon found in Cavity Quantum Electrodynamics. So instead of the "square of the modulus of the wave function" it is simply the square of the wave function alone which has a vectorial phase which is lost on the action of projection and not recoverable. All quantum theory seem to be related to uncorrelated quantized phenomena leading only to statistical properties in a cavity (or perhaps defined by the incomplete cavity boundaries). This is easily handled by Feynman QED. To me a single photon may progress through several cavities as a wave which may be "quantum stationary states" and solutions of open forms of the Dirac Wave Equation and involve a "resonance" in the Wheeler-Feynman Absorber Context.
Cheers
The present event scheme adopts a minimalist interpretation of quantum mechanics in which nothing classical is attributed to the domain of quantum objects. Nothing meaningful can be inferred about that domain, and isolated evolving quantum objects have no properties—properties only appear at measurements (or unmeasured interactions). And the properties which appear are relevant to the interaction or type of instrument the system collides with. Quantum mechanics is consistent with evolving systems, such as an electron, not being at any particular position, even though there is some probability that it might be observed at every point in space. That is sometimes interpreted to mean that the system is really at all the positions, and when observed, its being at all positions reduces instantly to being at just one of them. The evolving quantum system is somehow smeared out among all possible positions, and they mathematically all contribute to their being finally at one position.
That is not the present analysis, according to which, if it is not at a particular or definite position the electron might as well be at no position and we have no reason to go beyond that conclusion. We need to set aside all reliance upon classicality, which is sometimes called common sense. Being at no particular or definite position does not warrant any conclusion as to where the system is; or whether it is anywhere! The minimalist analysis adopted here agrees that the electron is at no definite or particular position and draws no conclusions beyond that fact. Of course, this runs counter to commonsense--but then common-sense is what tells us the earth is flat!
The analysis of the logic underlying the electron being smeared out among all the positions, at which there is some probability of its being found, depends upon two implied propositions: One is that the world contains the electron and the other is that the world includes all the positions at which it might be found in the future. However, if we adopt the mode of coupling space and time in the formation of spacetime which does not reduce the time axis to a space-like axis, and separate the concept of action from its representation, then we can question the idea that future spacetime loci are present before they occur! Put simply, if space and time are merely relations among objects and if the object has not yet arrived then perhaps neither has the space and time which relate it to other objects. If the world is discrete instead of continuous, then perhaps it only sometimes “includes all the positions at which the electron might be found.” If the positions at which the electron might be found are not in existence in the intervening period--what then? Such an analysis of spacetime is consistent with the electron being at no definite or particular position during the intervening period.
The evolution of the quantum system is inscrutable—it is private because it has no extrinsic or classical aspect. And theory says nothing about what is going on in the quantum domain. It only predicts what happens when quantum objects interact with the classical domain—when what happens is always classical. The simplest position to take is that nothing classical is going on in the quantum domain—nothing that can be counted, measured or observed.
http://pjfimmel.id.au/interpretation.htm
See the drift I am coming from? Would you like to discuss this "problem"?
One "aspect" of this problem is in the "inner product's" inability to be "reversible" when in actual fact any "resonance" or cavity "phase accumulation" has a certain "Quantum Zeno Property" which is for a short time capable of reversal, a phenomenon found in Cavity Quantum Electrodynamics. So instead of the "square of the modulus of the wave function" it is simply the square of the wave function alone which has a vectorial phase which is lost on the action of projection and not recoverable. All quantum theory seem to be related to uncorrelated quantized phenomena leading only to statistical properties in a cavity (or perhaps defined by the incomplete cavity boundaries). This is easily handled by Feynman QED. To me a single photon may progress through several cavities as a wave which may be "quantum stationary states" and solutions of open forms of the Dirac Wave Equation and involve a "resonance" in the Wheeler-Feynman Absorber Context.
Cheers
hi Good Elf, mr.homm, bukh et al
I would still like to point out that linear differentiation techniques used in calculus is not enough to describe nature, despite the fact You consider math a mental construct. Math has internal structure which is not known, despite being a mental construct, and , in my opinion, this internal structure is objective as it is the reflection of the reality we live in as well, both real and imaginary.
So I tried to point out that in Time calculus, which adds a substructure to infinitesimals as a function of Time (subset of reals) , actually DESTROYS the view that discrete and continuous are two opposing things with nothing in between. In fact, there is possible continuous passage from discrete time to continuous , and in infinity of ways, each giving a different result in differentiation etc.
Interestingly, Time subsets ( which are ordered subsets of real numbers) do no include RATIONAL and IRRATIONAL numbers. What is left, than? Periodic NUMBERS only? This also is only logical that periodic numbers would represent time.
So my gut feeling is, that, both fractional ( rational) debroglie waves and irrational waves has a right to exist , but they are atemporal in a sense their forming does not involve passage of time in our scale.
Fractional (rational) de broglie waves are easy to imagine, since they will have to orbit more than once to form a standing wave- that is nothing new in dynamic systems. In my opinion, these form INTERNAL structure of particles.
Irrational de broglie waves even more interesting, since they can not form standing waves, therefore they must interact with/represent other dimensional structures, even infinitesimal.
One more thing is that Temporal de broglie waves (periodic numbers) HAS energy, but weak , non-thermal in normal understandign, so they are detectable, but becuase of weakness I know of only 2 experimental evidences, one of whihc is CBR, another neutrino absorbtion/emission.
Atemporal, or standing matter waves do not have temporal energy as such, they have mass energy, or , equavalently, mass.
Anyway, the attempt to define reality with imperfect math which is in our disposition is doomed. The connection lies in places our mind has not visited yet, but its obvious that it exists regardless of us visiting it.
Excuse me for philosophy instead of experiment, but, I think it is possible to progress also this way by trying to put together bits and pieces of mathematics as they come along.
QUOTE
If the world is discrete instead of continuous, then perhaps it only sometimes “includes all the positions at which the electron might be found.”
I would still like to point out that linear differentiation techniques used in calculus is not enough to describe nature, despite the fact You consider math a mental construct. Math has internal structure which is not known, despite being a mental construct, and , in my opinion, this internal structure is objective as it is the reflection of the reality we live in as well, both real and imaginary.
So I tried to point out that in Time calculus, which adds a substructure to infinitesimals as a function of Time (subset of reals) , actually DESTROYS the view that discrete and continuous are two opposing things with nothing in between. In fact, there is possible continuous passage from discrete time to continuous , and in infinity of ways, each giving a different result in differentiation etc.
Interestingly, Time subsets ( which are ordered subsets of real numbers) do no include RATIONAL and IRRATIONAL numbers. What is left, than? Periodic NUMBERS only? This also is only logical that periodic numbers would represent time.
So my gut feeling is, that, both fractional ( rational) debroglie waves and irrational waves has a right to exist , but they are atemporal in a sense their forming does not involve passage of time in our scale.
Fractional (rational) de broglie waves are easy to imagine, since they will have to orbit more than once to form a standing wave- that is nothing new in dynamic systems. In my opinion, these form INTERNAL structure of particles.
Irrational de broglie waves even more interesting, since they can not form standing waves, therefore they must interact with/represent other dimensional structures, even infinitesimal.
One more thing is that Temporal de broglie waves (periodic numbers) HAS energy, but weak , non-thermal in normal understandign, so they are detectable, but becuase of weakness I know of only 2 experimental evidences, one of whihc is CBR, another neutrino absorbtion/emission.
Atemporal, or standing matter waves do not have temporal energy as such, they have mass energy, or , equavalently, mass.
Anyway, the attempt to define reality with imperfect math which is in our disposition is doomed. The connection lies in places our mind has not visited yet, but its obvious that it exists regardless of us visiting it.
Excuse me for philosophy instead of experiment, but, I think it is possible to progress also this way by trying to put together bits and pieces of mathematics as they come along.
Hej Good Elf, Ivars mr homm et al-
QUOTE Good Elf: "On the Electrodynamics of Motionless Events
This is actually very "perceptual" and is very close to my view of how things actually operate. Not "exactly" but close enough to be able to create a view that pulls a few threads together."
In the above it is among others stated that: "it is a theory of pregeometric causes, from which measurable qualities arise, but definite physical consequences follow logically from them."
Yes - "pregeometric causes" - or dimensional configurations - that each number in our mathematics equals a dimension - a ratio - and for each "mathematical calculus / operation" there is a flash dimensional configuration placed exactly in 3D space.
So called physically existance is intimately related to the concept of repetition, without repetition there can be no "lasting" interference,
And on the bottom line Universe Exist Once Only - there exist - and I would like to think, literally there exist this flash-like configurations - each representing ONE exact calculated state of a progressively dividing and developing mathematical system based on ratios of Origen Dimensionality.
Kinetic versus Potential is solely being determined out from whether there is a repetition or not. In lowest scale everything is kinetic - until the moment that the first repetition occurs - and the scale takes a "physical" existance, the scale is born, and from then on and upwards it is a flux, oscillating with non-repeating and repeating configurations - and it takes repeating oscillations to build the foundation for the next coming repeating configuration. Repeating configuration - is equivalent to a standing wave - is equivalent to a Particle.
QUOTE Good Elf: "On the Electrodynamics of Motionless Events
This is actually very "perceptual" and is very close to my view of how things actually operate. Not "exactly" but close enough to be able to create a view that pulls a few threads together."
In the above it is among others stated that: "it is a theory of pregeometric causes, from which measurable qualities arise, but definite physical consequences follow logically from them."
Yes - "pregeometric causes" - or dimensional configurations - that each number in our mathematics equals a dimension - a ratio - and for each "mathematical calculus / operation" there is a flash dimensional configuration placed exactly in 3D space.
So called physically existance is intimately related to the concept of repetition, without repetition there can be no "lasting" interference,
And on the bottom line Universe Exist Once Only - there exist - and I would like to think, literally there exist this flash-like configurations - each representing ONE exact calculated state of a progressively dividing and developing mathematical system based on ratios of Origen Dimensionality.
Kinetic versus Potential is solely being determined out from whether there is a repetition or not. In lowest scale everything is kinetic - until the moment that the first repetition occurs - and the scale takes a "physical" existance, the scale is born, and from then on and upwards it is a flux, oscillating with non-repeating and repeating configurations - and it takes repeating oscillations to build the foundation for the next coming repeating configuration. Repeating configuration - is equivalent to a standing wave - is equivalent to a Particle.
mr_homm,
I believe after reading your post, the statement made seems to be a philosophical effort to solve the weirdness of QM:
To understand your direction in though as you walked could this relate also to Gelfand Triplet?
dawn
I believe after reading your post, the statement made seems to be a philosophical effort to solve the weirdness of QM:
QUOTE
Now tempered distributions raise an interesting point about the Born interpretation of QM. In this standard interpretation, Hermitian operators correspond to observables, eigenvalues to measurement outcomes, and component amplitudes to probabilities of outcomes. As long as the eigenvalue spectrum is discrete, there is no interpretation problem with this, and in fact you can use the Hilbert space l_2 of square summable sequences to represent the theory. However, when the spectrum is continuous, you need both stronger mathematics and a slightly different interpretation.
is this correct, Stuart?To understand your direction in though as you walked could this relate also to Gelfand Triplet?
dawn
Hi dawn, mr_homm, Ivars, bukh et al,
QUOTE (dawn+)
I believe after reading your post, the statement made seems to be a philosophical effort to solve the weirdness of QM:
QUOTE (mr_homm+)
Now tempered distributions raise an interesting point about the Born interpretation of QM. In this standard interpretation, Hermitian operators correspond to observables, eigenvalues to measurement outcomes, and component amplitudes to probabilities of outcomes. As long as the eigenvalue spectrum is discrete, there is no interpretation problem with this, and in fact you can use the Hilbert space l_2 of square summable sequences to represent the theory. However, when the spectrum is continuous, you need both stronger mathematics and a slightly different interpretation.
is this correct, Stuart?
To understand your direction in though as you walked could this relate also to Gelfand Triplet?
To understand your direction in though as you walked could this relate also to Gelfand Triplet?
I looked at your reference Dawn to Triplet and it is a way to see some of these things. I would be very interested in what Stuart has to say about this matter.
Hilbert Space or Gelfand Triplet - Time Symmetric or Time Asymmetric Quantum Mechanics
It is an interesting direction. Resonances "die down" after a certain period of time... or do they really? In a quantum system the energy can't be dissipated gradually. This is interesting. I guess this is a kind of temporal coherency. It is possible that time will be traversable but only for very short periods where coherency is possible... beyond a certain time length the quantum state may inevitably degenerate and might no longer be recoverable limiting the reversibility to some finite duration.
And then again it might not... perhaps this is where the "many worlds" come into the picture. It is pretty "heavy going" so perhaps others can assist all of us in a fuller understanding?
Cheer
Hilbert Space or Gelfand Triplet - Time Symmetric or Time Asymmetric Quantum Mechanics
It is an interesting direction. Resonances "die down" after a certain period of time... or do they really? In a quantum system the energy can't be dissipated gradually. This is interesting. I guess this is a kind of temporal coherency. It is possible that time will be traversable but only for very short periods where coherency is possible... beyond a certain time length the quantum state may inevitably degenerate and might no longer be recoverable limiting the reversibility to some finite duration.
And then again it might not... perhaps this is where the "many worlds" come into the picture. It is pretty "heavy going" so perhaps others can assist all of us in a fuller understanding?
Cheer
@dawn:
Hi Dawn, it's good to have you back again. Yes, you are correct about the philosophical nature of my thoughts. Although "attempt" is perhaps too serious a word for what I was doing. I have not put any effort into pursuing this idea; it is simply a thought which occured to me one day. It doesn't lead to any different predictions from the usual theory, so I'm not doing physics here, just philosophy. Of course, in my opinion philosophy is important, too, because it helps to clarify the interpretation of the mathematical predictions.
Also, yes the Gelfand triplet is another way of introducing additional structure into Hilbert space, allowing one to use rigorous mathematics and still have things like the delta distribution as part of its structure. I haven't investigated the mathematics past this point, but my hunch is that if you don't do something like the Gelfand triplet structure, you must lose at least some of the nice properties of Hilbert space, when you try to replace the wavefunctions with tempered distributions. For instance, H is its own dual space, but I suspect that the space of tempered distributions is not, so the tempered distributions are not directly a Hilbert space (I think; must investigate this further). The other two spaces in the Gelfand triplet are not their own duals either, but they are duals to each other, and so the triplet as a whole is self dual. In this way, self-duality is recovered at the level of the overall structure, while allowing one to have non-self-dual spaces as part of that structure. I think this is where the tempered distributions fit in. (BTW, ordinary distributions could probably be used just as well; I like tempered distributions because they are preserved under the action of Fourier transforms, which makes them convenient to compute with. The mathematics is sometimes a rather "loose fit" to the physics, in the sense that several similar mathematical structures might be used to do the same calculation, and still produce the same physical theory.)
That is all on the pure mathematics side of the discussion. As to the physics, what I think is interesting there is that the wave functions are now distributions acting on a space of test functions that represent experiments. Via the Gelfand triplet, (I think; must check) you can then set up a self-dual structure W*,H*=H,W, where W is the wavefunctions, and W* the set of linear operators on the wavefunctions. Since the wavefunctions themselves are linear operators on the space of test functions, it follows from standard mathematical theorems that the test functions are a subspace of W*. Therefore, since W* and W act on each other, you can have the physical interpretations that W* is a sort of enlarged class of experiments, while W is the wavefunctions. That means you have a space of experiments and a space of wavefunctions, which act linearly on each other with values in the complex numbers.
This is where I find the physical interpretation interesting: The geometric locations in space have dropped out of the formulation. They were originally the arguments of the test functions, but these have been abstracted to linear operators on the space of experiments, and are no longer point functions. Looking at things in this way is a big (philosophical) step toward BACKGROUND INDEPENDENCE. In fact, I think that the geometric space of our everyday experience can be extracted from W* by using the test functions as a sort of pseudo-topology. I don't think it satisfies the axioms of a topology, but will still generate a point space that is recognizable as our own. The points of physical space are then the LAST thing constructed, instead of the FIRST thing postulated, as in classical geometry. Points are merely limiting cases of very precise experiments, instead of fundamental entities. This is philosophically satisfying, because physics as an empirical science cannot verify statements about points, only statements about experiments.
@Good Elf, bukh, ivars:
Sorry I haven't answered your posts directly (yet). I've been busy for the last few days, and when I returned to the thread, the first post I saw was dawn's, and it started a whole new chain of ideas in my mind, which I wrote down in the paragraphs above. Unfortunately, that took enough time that now I have to go to work. Just some quick responses for now, but I promise fuller repsonses later:
bukh and ivars, please don't worry about hijacking the thread! I was away, and no one else had replied to the original post for the first three days anyway, so you probably kept the thread from dying.
Good Elf, as usual you provide very interesting links and discussion. Also as usual, once I start following your links, I end up all over the internet for several hours and eventually pull my head back out of the fog, full of new thoughts but with no time left to respond to your post! If your links weren't so interesting, I'd definitely answer sooner. But thats a GOOD thing.
More later.
--Stuart Anderson
Hi Dawn, it's good to have you back again. Yes, you are correct about the philosophical nature of my thoughts. Although "attempt" is perhaps too serious a word for what I was doing. I have not put any effort into pursuing this idea; it is simply a thought which occured to me one day. It doesn't lead to any different predictions from the usual theory, so I'm not doing physics here, just philosophy. Of course, in my opinion philosophy is important, too, because it helps to clarify the interpretation of the mathematical predictions.
Also, yes the Gelfand triplet is another way of introducing additional structure into Hilbert space, allowing one to use rigorous mathematics and still have things like the delta distribution as part of its structure. I haven't investigated the mathematics past this point, but my hunch is that if you don't do something like the Gelfand triplet structure, you must lose at least some of the nice properties of Hilbert space, when you try to replace the wavefunctions with tempered distributions. For instance, H is its own dual space, but I suspect that the space of tempered distributions is not, so the tempered distributions are not directly a Hilbert space (I think; must investigate this further). The other two spaces in the Gelfand triplet are not their own duals either, but they are duals to each other, and so the triplet as a whole is self dual. In this way, self-duality is recovered at the level of the overall structure, while allowing one to have non-self-dual spaces as part of that structure. I think this is where the tempered distributions fit in. (BTW, ordinary distributions could probably be used just as well; I like tempered distributions because they are preserved under the action of Fourier transforms, which makes them convenient to compute with. The mathematics is sometimes a rather "loose fit" to the physics, in the sense that several similar mathematical structures might be used to do the same calculation, and still produce the same physical theory.)
That is all on the pure mathematics side of the discussion. As to the physics, what I think is interesting there is that the wave functions are now distributions acting on a space of test functions that represent experiments. Via the Gelfand triplet, (I think; must check) you can then set up a self-dual structure W*,H*=H,W, where W is the wavefunctions, and W* the set of linear operators on the wavefunctions. Since the wavefunctions themselves are linear operators on the space of test functions, it follows from standard mathematical theorems that the test functions are a subspace of W*. Therefore, since W* and W act on each other, you can have the physical interpretations that W* is a sort of enlarged class of experiments, while W is the wavefunctions. That means you have a space of experiments and a space of wavefunctions, which act linearly on each other with values in the complex numbers.
This is where I find the physical interpretation interesting: The geometric locations in space have dropped out of the formulation. They were originally the arguments of the test functions, but these have been abstracted to linear operators on the space of experiments, and are no longer point functions. Looking at things in this way is a big (philosophical) step toward BACKGROUND INDEPENDENCE. In fact, I think that the geometric space of our everyday experience can be extracted from W* by using the test functions as a sort of pseudo-topology. I don't think it satisfies the axioms of a topology, but will still generate a point space that is recognizable as our own. The points of physical space are then the LAST thing constructed, instead of the FIRST thing postulated, as in classical geometry. Points are merely limiting cases of very precise experiments, instead of fundamental entities. This is philosophically satisfying, because physics as an empirical science cannot verify statements about points, only statements about experiments.
@Good Elf, bukh, ivars:
Sorry I haven't answered your posts directly (yet). I've been busy for the last few days, and when I returned to the thread, the first post I saw was dawn's, and it started a whole new chain of ideas in my mind, which I wrote down in the paragraphs above. Unfortunately, that took enough time that now I have to go to work. Just some quick responses for now, but I promise fuller repsonses later:
bukh and ivars, please don't worry about hijacking the thread! I was away, and no one else had replied to the original post for the first three days anyway, so you probably kept the thread from dying.
Good Elf, as usual you provide very interesting links and discussion. Also as usual, once I start following your links, I end up all over the internet for several hours and eventually pull my head back out of the fog, full of new thoughts but with no time left to respond to your post! If your links weren't so interesting, I'd definitely answer sooner. But thats a GOOD thing.
More later.
--Stuart Anderson
mr_homm, contributor's,
I understand Stuart, I know of no other theory of the physical world that has caused such consternation as QM, IMHO, no other theory has so completely overthrown the earlier cherished concepts of classical physics and our everyday apprehension of reality.
If you approach this with a philosophical mindset I feel you will keep your sanity much longer than the rest of us. It has been a romping ground of epistemological adventure, put mildly, my reluctance is resulting from the success with the mathematical approach to QM, it is very difficult for me to switch gears, to pursue alternatives seriously.
QM needs comprehensibility of clear expression this I feel we both agree yet, I hope we can be optimistic about physic's ability to expose ultimate truth as our goal also.
I must require myself now to confront with physical reality and a heady inhalation of new perspectives and attitudes. Like yourself, all scientist, mathematician's & technologists, it has been the key to advances in all fields of endeavor, from genetics to superconductivity, this could be the intellectual shadow that darkens our views & could very well be the culprit just to complete the task at hand without serious alternatives.
Please give me a couple of days after this reply to contemplate [only when I am given the luxury and time to empty myself of indoctrination of the mainline mindset], this will not be an easy task. My hope is that this post will thrive with many different perspective's, eagerly expecting later interactions on this subject.
dawn
GoodElf, Ivars, bukh, thank you for your replies, now I must give the comments made, some refection.
I understand Stuart, I know of no other theory of the physical world that has caused such consternation as QM, IMHO, no other theory has so completely overthrown the earlier cherished concepts of classical physics and our everyday apprehension of reality.
If you approach this with a philosophical mindset I feel you will keep your sanity much longer than the rest of us.
It has been a romping ground of epistemological adventure, put mildly, my reluctance is resulting from the success with the mathematical approach to QM, it is very difficult for me to switch gears, to pursue alternatives seriously.QM needs comprehensibility of clear expression this I feel we both agree yet, I hope we can be optimistic about physic's ability to expose ultimate truth as our goal also.
I must require myself now to confront with physical reality and a heady inhalation of new perspectives and attitudes. Like yourself, all scientist, mathematician's & technologists, it has been the key to advances in all fields of endeavor, from genetics to superconductivity, this could be the intellectual shadow that darkens our views & could very well be the culprit just to complete the task at hand without serious alternatives.
Please give me a couple of days after this reply to contemplate [only when I am given the luxury and time to empty myself of indoctrination of the mainline mindset], this will not be an easy task. My hope is that this post will thrive with many different perspective's, eagerly expecting later interactions on this subject.
dawn
GoodElf, Ivars, bukh, thank you for your replies, now I must give the comments made, some refection.
mr_homm, GoodElf, Ivars, burk, contributors,
Because of the landscape is so immense I would like to have some direction (theory/concept) you would like to investigate?
This would help to moderate time spent, this is new territory for me, in viewing some concepts from a philosophical perspective.
"Last thing I remember, I was
Running for the door
I had to find the passage back
To the place I was before
'Relax,' said the night man,
'We are programmed to receive.
You can check-out any time you like,
But you can never leave!''
- Hotel California -
This has become very thought provoking/overwhelming I must confess, I am grateful this is a relaxed forum.
dawn
Because of the landscape is so immense I would like to have some direction (theory/concept) you would like to investigate?
This would help to moderate time spent, this is new territory for me, in viewing some concepts from a philosophical perspective.
"Last thing I remember, I was
Running for the door
I had to find the passage back
To the place I was before
'Relax,' said the night man,
'We are programmed to receive.
You can check-out any time you like,
But you can never leave!''
- Hotel California -
This has become very thought provoking/overwhelming I must confess, I am grateful this is a relaxed forum.
dawn
Thank you. It does sort of segue into this, doesn't it? 
mr_homm is an artist. His palette and his paints are the minds of his many students.
The picture is very fine!
mr_homm is an artist. His palette and his paints are the minds of his many students.
The picture is very fine!
And now, back to catching up with older posts....
@Ivars
From my point of view, I don't have a problem with continuous probability per se. For instance, drop a pin on the ground and find the probability that the point of the pin will lie within a given area on the ground. This probability is certainly proportional to the area, so it is reasonable to call it a density. Note that the density is spread over area, but the EVENT is discrete. But when you have quantum uncertainty AND continuous probability, you run into interpretation problems, so we certainly agree there.
From my point of view, I don't have a problem with continuous probability per se. For instance, drop a pin on the ground and find the probability that the point of the pin will lie within a given area on the ground. This probability is certainly proportional to the area, so it is reasonable to call it a density. Note that the density is spread over area, but the EVENT is discrete. But when you have quantum uncertainty AND continuous probability, you run into interpretation problems, so we certainly agree there.
We are missing nuances in infinities in math by using only one infinity. We miss infinity of infinities , figuratively speaking, and we miss infinity of operations as well.
Actually, math uses many different infinities, as laid out in Georg Cantor's book "Contributions to the Foundation of a Theory of Transfinite Numbers." Hilbert spaces come with many different sizes of infinite dimension as well.
Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete- a physical analogy would be a looping of (imaginary) time.
Funny you should mention that -- in Fourier transform theory, when a function loops (i.e. is periodic, so that its graph can be wrapped around a circular axis instead of laid out along an infinite straight line), then its Fourier transform is discrete. When the function lies on an infinite non-looped axis, then its Fourier transform is continuous. It works for the inverse transform, too: if the function of time is discrete, its Fourier transform loops, and if it is continuous, its Fourier transform lies on an infinite non-looping axis. So looping and discreteness are deeply connected mathematically.
Funny you should mention that -- in Fourier transform theory, when a function loops (i.e. is periodic, so that its graph can be wrapped around a circular axis instead of laid out along an infinite straight line), then its Fourier transform is discrete. When the function lies on an infinite non-looped axis, then its Fourier transform is continuous. It works for the inverse transform, too: if the function of time is discrete, its Fourier transform loops, and if it is continuous, its Fourier transform lies on an infinite non-looping axis. So looping and discreteness are deeply connected mathematically.
If ht <E gives quantum uncertainty that means that h as such is linked to the probability distribution of these SQ things in electron time vortex, or Kolmogorov Vortex of Time (which equals electron black hole radius).
You've lost me here. What is a Kolmogorov Vortex? As far as I know, Professor Kolmogorov worked only with the foundations of probability theory.
@ bukh:
Posted: May 8 2008, 07:10 AM
...
Well - and if not - then it is just to acknowledge that continuous simply is not a viable concept - continuous is not part of "existance" in physical world -
It is true that events are discrete, so I agree with that. But in mathematics, there are various definitions of "continuous," some of which seem more physically reasonable than others.
It is true that events are discrete, so I agree with that. But in mathematics, there are various definitions of "continuous," some of which seem more physically reasonable than others.
And it calls for a definition - What IS physical world ?
I imagine that physical world - Our Universe - best can be envisaged as how information express itsself in a physical form.
This reminds me of John A. Wheeler's "It From Bit" idea.
And I further imagine that information best can be seen as a binary system - a binary math system - that mathematics in its very essence is binary. Universe is a binary system, characterized by dynamic dimensionalities in a 3D space.
All of mathematics can be built up from set theory, which has a binary decision at its basis. That decision is whether a particular item either IS or IS NOT a member of a set. All else flows from this.
All of mathematics can be built up from set theory, which has a binary decision at its basis. That decision is whether a particular item either IS or IS NOT a member of a set. All else flows from this.
Origin conditions are simplest possible - namely a dimension (3D)to which a binary principle is being applied.
Dimension is without any defined size - meaning infinite - no form - just space - and when the binary principle is being applied - "the unfolding of physical" - that is the very moment where space - dimension is being divided in two - two dimensions - no size - just a ratio of two.
When this principle is working on space - the result is, that space is being segregated in more and more ratios - presenting as dimensions in space - and the binary principle place the dimensions after a system in 3D, so each ratio of space is being defined by its exact position relative to neighboring ratios - it is not only a ratio - it is also a position.
Each and any ratio is the equivalent to a number in our math system, and each and any number in our math system represents a dimension with its corresponding position in 3D space.
Physical Universe is such dimensions arranged in configurations according to math system, in scales - more and more complex as the binary system grows - and the positioning becomes more and more complex in russian doll like configurations - inwards - fractal - everything we already know about in space - manifolds and and ---and possibly a lot more complexion that we have no insight into as yet. Universe is oscillating flash expressions of dimensional configurations in 3D space. Universe exists once only. The only difference between potential and kietic is the way that the kinetic is being played - when in repetitions - it is seen as potential, when not repeating it is seen as kinetic.
This reminds me very much of the development of J. H. Conway's number system, called the "surreal numbers." Starting from zero, more and more numbers are created by binary division among the numbers that existed before, eventually creating the entire real number system and much, much more. Every number is defined and located by its relation to the numbers that were created before it. Strangely, thys number system turns out to be infinite. Not only is it infinite, but it is a bigger infinity than the real number system. Yet every part of it is defined by relations to the "parent" numbers which it split off from.
@Ivars:
Posted: May 9 2008, 12:34 AM
An interesing link:
Time scales Hilger complex plane
Excerpt:
In Laplace transforms of continuous time signals, we have the s plane. In the ztransform of discrete time signals, there is the unit circle. In time scales, both are special cases of the Hilger circle shown here.
The Hilger circle hass a diameter equal to the reciprical of graininess and is tangent to the imaginary axis.
For discrete time, the graininess is one.
Thanks for the link. It looks like a useful hybrid of continuous and discrete, although it looks to me like it has a lot of limitations. For instance, the graniness would not normally be a constant, yet the formulas assume that it is. This somewhat limits the uses the theory can be put to. Still, it is a very interesting idea.
Next up: Good Elf.
More later.
--Stuart Anderson
Thanks for the link. It looks like a useful hybrid of continuous and discrete, although it looks to me like it has a lot of limitations. For instance, the graniness would not normally be a constant, yet the formulas assume that it is. This somewhat limits the uses the theory can be put to. Still, it is a very interesting idea.
Next up: Good Elf.
More later.
--Stuart Anderson
@Ivars
QUOTE
Posted: May 8 2008, 03:51 AM
hej Mr. homm
...
Probability in principle can be only attributed to discrete events, so fundamentally continuous probability density is not possible.
hej Mr. homm
...
Probability in principle can be only attributed to discrete events, so fundamentally continuous probability density is not possible.
From my point of view, I don't have a problem with continuous probability per se. For instance, drop a pin on the ground and find the probability that the point of the pin will lie within a given area on the ground. This probability is certainly proportional to the area, so it is reasonable to call it a density. Note that the density is spread over area, but the EVENT is discrete. But when you have quantum uncertainty AND continuous probability, you run into interpretation problems, so we certainly agree there.
QUOTE (->
| QUOTE |
| Posted: May 8 2008, 03:51 AM hej Mr. homm ... Probability in principle can be only attributed to discrete events, so fundamentally continuous probability density is not possible. |
From my point of view, I don't have a problem with continuous probability per se. For instance, drop a pin on the ground and find the probability that the point of the pin will lie within a given area on the ground. This probability is certainly proportional to the area, so it is reasonable to call it a density. Note that the density is spread over area, but the EVENT is discrete. But when you have quantum uncertainty AND continuous probability, you run into interpretation problems, so we certainly agree there.
We are missing nuances in infinities in math by using only one infinity. We miss infinity of infinities , figuratively speaking, and we miss infinity of operations as well.
Actually, math uses many different infinities, as laid out in Georg Cantor's book "Contributions to the Foundation of a Theory of Transfinite Numbers." Hilbert spaces come with many different sizes of infinite dimension as well.
QUOTE
Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete- a physical analogy would be a looping of (imaginary) time.
Funny you should mention that -- in Fourier transform theory, when a function loops (i.e. is periodic, so that its graph can be wrapped around a circular axis instead of laid out along an infinite straight line), then its Fourier transform is discrete. When the function lies on an infinite non-looped axis, then its Fourier transform is continuous. It works for the inverse transform, too: if the function of time is discrete, its Fourier transform loops, and if it is continuous, its Fourier transform lies on an infinite non-looping axis. So looping and discreteness are deeply connected mathematically.
QUOTE (->
| QUOTE |
Somewhere in the middle of all these infinities is a place where math goes from continuous to discrete- a physical analogy would be a looping of (imaginary) time. |
Funny you should mention that -- in Fourier transform theory, when a function loops (i.e. is periodic, so that its graph can be wrapped around a circular axis instead of laid out along an infinite straight line), then its Fourier transform is discrete. When the function lies on an infinite non-looped axis, then its Fourier transform is continuous. It works for the inverse transform, too: if the function of time is discrete, its Fourier transform loops, and if it is continuous, its Fourier transform lies on an infinite non-looping axis. So looping and discreteness are deeply connected mathematically.
If ht <E gives quantum uncertainty that means that h as such is linked to the probability distribution of these SQ things in electron time vortex, or Kolmogorov Vortex of Time (which equals electron black hole radius).
You've lost me here. What is a Kolmogorov Vortex? As far as I know, Professor Kolmogorov worked only with the foundations of probability theory.
@ bukh:
QUOTE
Posted: May 8 2008, 07:10 AM
...
Well - and if not - then it is just to acknowledge that continuous simply is not a viable concept - continuous is not part of "existance" in physical world -
It is true that events are discrete, so I agree with that. But in mathematics, there are various definitions of "continuous," some of which seem more physically reasonable than others.
QUOTE (->
| QUOTE |
Posted: May 8 2008, 07:10 AM ... Well - and if not - then it is just to acknowledge that continuous simply is not a viable concept - continuous is not part of "existance" in physical world - |
It is true that events are discrete, so I agree with that. But in mathematics, there are various definitions of "continuous," some of which seem more physically reasonable than others.
And it calls for a definition - What IS physical world ?
I imagine that physical world - Our Universe - best can be envisaged as how information express itsself in a physical form.
This reminds me of John A. Wheeler's "It From Bit" idea.
QUOTE
And I further imagine that information best can be seen as a binary system - a binary math system - that mathematics in its very essence is binary. Universe is a binary system, characterized by dynamic dimensionalities in a 3D space.
All of mathematics can be built up from set theory, which has a binary decision at its basis. That decision is whether a particular item either IS or IS NOT a member of a set. All else flows from this.
QUOTE (->
| QUOTE |
And I further imagine that information best can be seen as a binary system - a binary math system - that mathematics in its very essence is binary. Universe is a binary system, characterized by dynamic dimensionalities in a 3D space. |
All of mathematics can be built up from set theory, which has a binary decision at its basis. That decision is whether a particular item either IS or IS NOT a member of a set. All else flows from this.
Origin conditions are simplest possible - namely a dimension (3D)to which a binary principle is being applied.
Dimension is without any defined size - meaning infinite - no form - just space - and when the binary principle is being applied - "the unfolding of physical" - that is the very moment where space - dimension is being divided in two - two dimensions - no size - just a ratio of two.
When this principle is working on space - the result is, that space is being segregated in more and more ratios - presenting as dimensions in space - and the binary principle place the dimensions after a system in 3D, so each ratio of space is being defined by its exact position relative to neighboring ratios - it is not only a ratio - it is also a position.
Each and any ratio is the equivalent to a number in our math system, and each and any number in our math system represents a dimension with its corresponding position in 3D space.
Physical Universe is such dimensions arranged in configurations according to math system, in scales - more and more complex as the binary system grows - and the positioning becomes more and more complex in russian doll like configurations - inwards - fractal - everything we already know about in space - manifolds and and ---and possibly a lot more complexion that we have no insight into as yet. Universe is oscillating flash expressions of dimensional configurations in 3D space. Universe exists once only. The only difference between potential and kietic is the way that the kinetic is being played - when in repetitions - it is seen as potential, when not repeating it is seen as kinetic.
This reminds me very much of the development of J. H. Conway's number system, called the "surreal numbers." Starting from zero, more and more numbers are created by binary division among the numbers that existed before, eventually creating the entire real number system and much, much more. Every number is defined and located by its relation to the numbers that were created before it. Strangely, thys number system turns out to be infinite. Not only is it infinite, but it is a bigger infinity than the real number system. Yet every part of it is defined by relations to the "parent" numbers which it split off from.
@Ivars:
QUOTE
Posted: May 9 2008, 12:34 AM
An interesing link:
Time scales Hilger complex plane
Excerpt:
In Laplace transforms of continuous time signals, we have the s plane. In the ztransform of discrete time signals, there is the unit circle. In time scales, both are special cases of the Hilger circle shown here.
The Hilger circle hass a diameter equal to the reciprical of graininess and is tangent to the imaginary axis.
For discrete time, the graininess is one.
Thanks for the link. It looks like a useful hybrid of continuous and discrete, although it looks to me like it has a lot of limitations. For instance, the graniness would not normally be a constant, yet the formulas assume that it is. This somewhat limits the uses the theory can be put to. Still, it is a very interesting idea.
Next up: Good Elf.
More later.
--Stuart Anderson
QUOTE (->
| QUOTE |
Posted: May 9 2008, 12:34 AM An interesing link: Time scales Hilger complex plane Excerpt: In Laplace transforms of continuous time signals, we have the s plane. In the ztransform of discrete time signals, there is the unit circle. In time scales, both are special cases of the Hilger circle shown here. The Hilger circle hass a diameter equal to the reciprical of graininess and is tangent to the imaginary axis. For discrete time, the graininess is one. |
Thanks for the link. It looks like a useful hybrid of continuous and discrete, although it looks to me like it has a lot of limitations. For instance, the graniness would not normally be a constant, yet the formulas assume that it is. This somewhat limits the uses the theory can be put to. Still, it is a very interesting idea.
Next up: Good Elf.
More later.
--Stuart Anderson
hi mr.homm
Thanks for replies. Especially about Fourier transform.
As to Kolmogorov, his name is associated with the scale of smallest dissipating eddy in turbulence which is still and eddy of that phase (e.g water) eddies are forming into. Dissipation happens into another phase, mechanism ( e.g heat in water molecules).
Kolmogorov scales are still one of the few existing (only?) accurate descriptions of turbulence energy spectra despite not saying anything much about mechanics of turbulence.
Now, Kolmogorov based his theory on dimensional analysis and isotropic turbulence. However ( I have lost the links) there are works that show that also non isotropic turbulence of certain algebraic spiral vortex models also leads to the same spectra- which I think is more appropriate for space time as well.
What I am using Kolmogorov vortex for in my post is SPACETIME turbulence and vortexes. In this sense, Kolmogorov vortex of Spacetime( which has a speed c a Kolmogorov speed, electron black hole radius as Kolmgorov scale, and very fast frequency approx 10^65 Hz as Kolmogorov time) is a place where space time change phases from one that is ruled by c and interior different mechanism which is most likely linked to information origination of electron black holes and their entropy.
I dismiss ideas that such holes should evaporate - they will radiate high frequency informationally rich thermally weak radiation since it originates in different phase of space time, below Quantum. The spacetime inside such Kolmogorov vortex most likely has fractional SPATIAL dimensions, and correspondingly shortening time scales. These dimensions are related to rational numbers as such.
The infinities I brought in are just another dimensions of space time, not obtainable by infinite division as are fractional or rational. These dimensions are infinitesimal, and characterized most likely by irrational numbers , which also leads to the idea that the character of such space time has to be chaotic, or probabilistic.
Where i see connection to quantum uncertainty is that once You integrate over these probabilities, since they are infinitesimal, in most cases result will be deterministic, but the distribution of the speeds(Wonder what that means) will have its effect on the result. At quantum scales, this result leads to Heisenberg uncertainty, so h as such has to be linked with type and width of probability distribution of the speeds of these entities below quantum scale.
Here is link to Kolmogorov reference I use:
Kolmogorov scales in turbulence
Thanks for replies. Especially about Fourier transform.
As to Kolmogorov, his name is associated with the scale of smallest dissipating eddy in turbulence which is still and eddy of that phase (e.g water) eddies are forming into. Dissipation happens into another phase, mechanism ( e.g heat in water molecules).
Kolmogorov scales are still one of the few existing (only?) accurate descriptions of turbulence energy spectra despite not saying anything much about mechanics of turbulence.
Now, Kolmogorov based his theory on dimensional analysis and isotropic turbulence. However ( I have lost the links) there are works that show that also non isotropic turbulence of certain algebraic spiral vortex models also leads to the same spectra- which I think is more appropriate for space time as well.
What I am using Kolmogorov vortex for in my post is SPACETIME turbulence and vortexes. In this sense, Kolmogorov vortex of Spacetime( which has a speed c a Kolmogorov speed, electron black hole radius as Kolmgorov scale, and very fast frequency approx 10^65 Hz as Kolmogorov time) is a place where space time change phases from one that is ruled by c and interior different mechanism which is most likely linked to information origination of electron black holes and their entropy.
I dismiss ideas that such holes should evaporate - they will radiate high frequency informationally rich thermally weak radiation since it originates in different phase of space time, below Quantum. The spacetime inside such Kolmogorov vortex most likely has fractional SPATIAL dimensions, and correspondingly shortening time scales. These dimensions are related to rational numbers as such.
The infinities I brought in are just another dimensions of space time, not obtainable by infinite division as are fractional or rational. These dimensions are infinitesimal, and characterized most likely by irrational numbers , which also leads to the idea that the character of such space time has to be chaotic, or probabilistic.
Where i see connection to quantum uncertainty is that once You integrate over these probabilities, since they are infinitesimal, in most cases result will be deterministic, but the distribution of the speeds(Wonder what that means) will have its effect on the result. At quantum scales, this result leads to Heisenberg uncertainty, so h as such has to be linked with type and width of probability distribution of the speeds of these entities below quantum scale.
Here is link to Kolmogorov reference I use:
Kolmogorov scales in turbulence
mr homm
Thanks
Quote: "This reminds me very much of the development of J. H. Conway's number system, called the "surreal numbers." Starting from zero, more and more numbers are created by binary division among the numbers that existed before, eventually creating the entire real number system and much, much more. Every number is defined and located by its relation to the numbers that were created before it. Strangely, thys number system turns out to be infinite. Not only is it infinite, but it is a bigger infinity than the real number system. Yet every part of it is defined by relations to the "parent" numbers which it split off from."
How can we know that such a system IS infinite -
Thanks
Quote: "This reminds me very much of the development of J. H. Conway's number system, called the "surreal numbers." Starting from zero, more and more numbers are created by binary division among the numbers that existed before, eventually creating the entire real number system and much, much more. Every number is defined and located by its relation to the numbers that were created before it. Strangely, thys number system turns out to be infinite. Not only is it infinite, but it is a bigger infinity than the real number system. Yet every part of it is defined by relations to the "parent" numbers which it split off from."
How can we know that such a system IS infinite -
Hi dawn, mr_homm, Ivars, bukh et al,
QUOTE (Stuart Anderson+)
Next up: Good Elf.
More later. Sorry... I have left a pretty scattered trail behind me regarding this subject. When I said that some of those references are the "closest' to my point of view" that really does not help a lot since my point of view is relatively "unique" and somewhat isolated... unfortunately. This is not to say that the ideas I am putting forward are not "worthy", only that so much "might be wrong" with our general approach in the interpretation of the phenomena in Physics (due to 80 years of neglect) that it is like "sorting and classifying an entire can of worms into their respective lengths on a table". The worms keep objecting to the rigid formalism and want the right to "free association" to continue... he he he!
Recent theory and in particular experiment suggests that the transition between the quantum realm and the classical realm is not really a "real transition" from one environment to another it is actually more like a problem regarding out instruments than it is a problem of a philosophical nature. I like that article in New Scientist I have quoted from recently ...
Quantum randomness may not be random - 22 March 2008 Mark Buchanan Magazine issue 2648
It is a problem if people can't log in and read the full article. I have printed some of it here...
QUOTE (short exerpt from New Scientist "Quantum randomness may not be random "- 22 March 2008)
I really do not want to get into too much trouble regarding copyright but these issues are of great importance to be discussed in the Scientific Community at length. I would suggest that that section be read there where some issues are debated regarding the "Stalking Horse" of Bohmian Mechanics.
More later.
Sorry... I have left a pretty scattered trail behind me regarding this subject. When I said that some of those references are the "closest' to my point of view" that really does not help a lot since my point of view is relatively "unique" and somewhat isolated... unfortunately. This is not to say that the ideas I am putting forward are not "worthy", only that so much "might be wrong" with our general approach in the interpretation of the phenomena in Physics (due to 80 years of neglect) that it is like "sorting and classifying an entire can of worms into their respective lengths on a table". The worms keep objecting to the rigid formalism and want the right to "free association" to continue... he he he!Recent theory and in particular experiment suggests that the transition between the quantum realm and the classical realm is not really a "real transition" from one environment to another it is actually more like a problem regarding out instruments than it is a problem of a philosophical nature. I like that article in New Scientist I have quoted from recently ...
Quantum randomness may not be random - 22 March 2008 Mark Buchanan Magazine issue 2648
It is a problem if people can't log in and read the full article. I have printed some of it here...
QUOTE (short exerpt from New Scientist "Quantum randomness may not be random "- 22 March 2008)
I really do not want to get into too much trouble regarding copyright but these issues are of great importance to be discussed in the Scientific Community at length. I would suggest that that section be read there where some issues are debated regarding the "Stalking Horse" of Bohmian Mechanics.
QUOTE (Good Elf+)
For the full story you need to read the article. I do not subscribe to "Bohmian Mechanics" since this theory is not constructed to be a substitute for a "real theory" of everything. It is very clear that BM is a "Stalking Horse" for an underlying theory that is the real goal of present day Physics. The problem with BM is the "particle"... a source of charge as it were. That is not a necessary part of any real theory and it needs correction. I suggest everyone read the "whole article" to be found in the issue above which is quite extensive and interesting with appropriate references.
This is not the only article that is useful but recently there is an article in Nature called Quantum all the way:Nature :pp22-25 Published online 30 April 2008 | Nature | doi:10.1038/453022a
This pursues a similar subject in which a number of prominent experimentalists and some "doubting Thomas's" agree that this quantum boundary is not as clear cut as once thought and indeed this boundary is becoming "blurred" in a way that suggests that there really is no boundary at all. I will take some short sections from this article to quote here...
The next point I would like to emphasize is the way in which quantum states (in the vein of Wheeler-Feynman Absorber Theory) are event specific and each quantum event or transaction is singularly attributable to individual transference of qubits. We know this is the case in quantum communication "links" which are actually transmission lines. The transmission line is a special case of a cavity. And cavity solutions are solutions of Schrodinger's or Dirac's wave Equations in "cavities" (which are just bounded systems). I would like to call attention to the fruitful manipulation of stimulated color centers in diamonds that are showing even at room temperature a single reception of a quantum process such as spin can be finely controlled to the extent that the phase accumulation of the state in resonance from illumination by a coherent source.
This is not the only article that is useful but recently there is an article in Nature called Quantum all the way:Nature :pp22-25 Published online 30 April 2008 | Nature | doi:10.1038/453022a
This pursues a similar subject in which a number of prominent experimentalists and some "doubting Thomas's"
agree that this quantum boundary is not as clear cut as once thought and indeed this boundary is becoming "blurred" in a way that suggests that there really is no boundary at all. I will take some short sections from this article to quote here...QUOTE
Quantum all the way
Nature :pp22-25
Published online 30 April 2008 | Nature | doi:10.1038/453022a
How does our classical world emerge from the counterintuitive principles of quantum theory? Can we even be sure that the world doesn't 'go quantum' when no one is watching? Philip Ball talks to the theorists and experimentalists trying to find out.
[..]
Early quantum theorists treated the quantum-classical transition almost as a kind of sleight of hand, something that had to be imposed on quantum mechanics to recover the familiar world. Now, however, there are strong signs that the transition can be understood as something that emerges quite naturally and inevitably from quantum theory. If that's so, it implies that 'classicality' is at root simply another quantum phenomenon. "There's good reason to believe that we are just as much part of the quantum world as are the tiny atoms and electrons that sparked quantum theory in the first place,' says quantum theorist Maximilian Schlosshauer of the University of Melbourne in Australia.
Testing the new description of the quantum-classical transition involves experiments on systems ranging from photons to superconductors to microscopic vibrating beams. These efforts pose an extreme challenge to experimentalists, as they involve looking for very small effects on comparatively big things —rather like trying to detect the sag when a fly lands on San Francisco's Golden Gate Bridge. The effects very quickly get so small that many physicists believe it is absurd to try to see them. "One crowd says: 'Of course it will work —quantum mechanics says so'," says Schwab. "The other says: 'There's no way it will work —these guys are nuts'."
[..]
Thus one of the key questions in understanding the quantum-classical transition is what happens to the superpositions as you go up that atoms-to-apples scale? Exactly when and how does 'both/and' become 'either/or'?
Physicists have proposed many answers to that question over the decades. But the most failures one involves a phenomenon known as decoherence [3], which was identified and elucidated in the 1970s and 1980s. Crudely speaking, decoherence is a sort of leaking away of quantum behaviour when a particle interacts with its surroundings—for example, when an atom or molecule collides with those around or when light bounces off it. All we are left with is a partial picture of the system — a picture in which only a well-defined subset of macroscopic properties, such as position, are apparent.
[..]
In summary, decoherence offers a way "to understand classicality as emergent from within the quantum formalism', says Schlosshauer. Indeed, this picture means that the classical world no longer sits in opposition to quantum mechanics, but is demanded by it.
[...]
The decoherence description shows that there is no abrupt boundary, no critical size, at which quantum behaviour switches to classical. And that blurry boundary itself shifts depending on how it is measured. "It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical,"(Good Elf's emphasis) says Anton Zeilinger of the University of Vienna. His team provided an example of this nine years ago, when it demonstrated quantum interference between beams of C60 fullerene molecules [8] — hardly as classical as the footballs they resemble, but nonetheless big molecules that can be seen with an electron microscope. Interference — the addition or cancellation of overlapping waves — is in this case a purely quantum effect, and can't be understood if the molecules are viewed as discrete particles. It is possible only if the molecules are in a superposition of states — in several places at once. "If you scan with a scanning tunnelling microscope a surface to which fullerene molecules stick, you see the little soccer balls sitting there as classical objects," says Zeilinger. "But if you choose our interference experiment set-up, they are quantum mechanically delocalized." In other words, he says: "The same object can behave as a quantum system in one situation, and as a classical system in another."
[..]
Bouwmeester hopes that it will soon be possible to test an alternative theory of the quantum-classical transition devised by Roger Penrose of the University of Oxford, UK. Penrose suggests that the 'collapse' of a superposition, rather than being a gradual affair resulting from environment-induced decoherence, is a rather abrupt event that is mediated by gravity. That is, it involves the emission of a graviton, the hypothetical fundamental quantum of the gravitational force, in much the same way that the decay of an excited molecule may happen via emission of a photon. He thinks that the cost in gravitational potential energy of keeping objects in a superposition becomes too great as objects get bigger, so that the objects 'go classical' on a definite timescale, which he estimates to be about a second or so for dust particles. Bouwmeester's mirror experiment should, if he can scale it up without losing sensitivity, be able to spot such a switch. "I am sceptical about this idea, but think it is worth testing,” he says.
Understanding quantum states has become much more than an intellectual curiosity, because handling quantum data may hold the key to the future of information technology
[..]
The decoherence description of the quantum-classical transition is not necessarily the end of the matter— it leaves unresolved some more fundamental questions about the interpretation of quantum theory (see page 39). But at present, it seems a fair bet that what we think of as the classical world is really only the quantum world viewed through the lens of decohered states. "The conceptual leap would then be to conclude from this that quantum mechanics is truly universal,' says Schlosshauer, "in the sense that everything, including us, is described by entangled quantum states "
I am hopeful that this is not "overuse" of a four page article in Nature but it is a very important issue that needs to be seen by those who are now having second thoughts about the "entire phenomenon". Nature :pp22-25
Published online 30 April 2008 | Nature | doi:10.1038/453022a
How does our classical world emerge from the counterintuitive principles of quantum theory? Can we even be sure that the world doesn't 'go quantum' when no one is watching? Philip Ball talks to the theorists and experimentalists trying to find out.
[..]
Early quantum theorists treated the quantum-classical transition almost as a kind of sleight of hand, something that had to be imposed on quantum mechanics to recover the familiar world. Now, however, there are strong signs that the transition can be understood as something that emerges quite naturally and inevitably from quantum theory. If that's so, it implies that 'classicality' is at root simply another quantum phenomenon. "There's good reason to believe that we are just as much part of the quantum world as are the tiny atoms and electrons that sparked quantum theory in the first place,' says quantum theorist Maximilian Schlosshauer of the University of Melbourne in Australia.
Testing the new description of the quantum-classical transition involves experiments on systems ranging from photons to superconductors to microscopic vibrating beams. These efforts pose an extreme challenge to experimentalists, as they involve looking for very small effects on comparatively big things —rather like trying to detect the sag when a fly lands on San Francisco's Golden Gate Bridge. The effects very quickly get so small that many physicists believe it is absurd to try to see them. "One crowd says: 'Of course it will work —quantum mechanics says so'," says Schwab. "The other says: 'There's no way it will work —these guys are nuts'."
[..]
Thus one of the key questions in understanding the quantum-classical transition is what happens to the superpositions as you go up that atoms-to-apples scale? Exactly when and how does 'both/and' become 'either/or'?
Physicists have proposed many answers to that question over the decades. But the most failures one involves a phenomenon known as decoherence [3], which was identified and elucidated in the 1970s and 1980s. Crudely speaking, decoherence is a sort of leaking away of quantum behaviour when a particle interacts with its surroundings—for example, when an atom or molecule collides with those around or when light bounces off it. All we are left with is a partial picture of the system — a picture in which only a well-defined subset of macroscopic properties, such as position, are apparent.
[..]
In summary, decoherence offers a way "to understand classicality as emergent from within the quantum formalism', says Schlosshauer. Indeed, this picture means that the classical world no longer sits in opposition to quantum mechanics, but is demanded by it.
[...]
The decoherence description shows that there is no abrupt boundary, no critical size, at which quantum behaviour switches to classical. And that blurry boundary itself shifts depending on how it is measured. "It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical,"(Good Elf's emphasis) says Anton Zeilinger of the University of Vienna. His team provided an example of this nine years ago, when it demonstrated quantum interference between beams of C60 fullerene molecules [8] — hardly as classical as the footballs they resemble, but nonetheless big molecules that can be seen with an electron microscope. Interference — the addition or cancellation of overlapping waves — is in this case a purely quantum effect, and can't be understood if the molecules are viewed as discrete particles. It is possible only if the molecules are in a superposition of states — in several places at once. "If you scan with a scanning tunnelling microscope a surface to which fullerene molecules stick, you see the little soccer balls sitting there as classical objects," says Zeilinger. "But if you choose our interference experiment set-up, they are quantum mechanically delocalized." In other words, he says: "The same object can behave as a quantum system in one situation, and as a classical system in another."
[..]
Bouwmeester hopes that it will soon be possible to test an alternative theory of the quantum-classical transition devised by Roger Penrose of the University of Oxford, UK. Penrose suggests that the 'collapse' of a superposition, rather than being a gradual affair resulting from environment-induced decoherence, is a rather abrupt event that is mediated by gravity. That is, it involves the emission of a graviton, the hypothetical fundamental quantum of the gravitational force, in much the same way that the decay of an excited molecule may happen via emission of a photon. He thinks that the cost in gravitational potential energy of keeping objects in a superposition becomes too great as objects get bigger, so that the objects 'go classical' on a definite timescale, which he estimates to be about a second or so for dust particles. Bouwmeester's mirror experiment should, if he can scale it up without losing sensitivity, be able to spot such a switch. "I am sceptical about this idea, but think it is worth testing,” he says.
Understanding quantum states has become much more than an intellectual curiosity, because handling quantum data may hold the key to the future of information technology
[..]
The decoherence description of the quantum-classical transition is not necessarily the end of the matter— it leaves unresolved some more fundamental questions about the interpretation of quantum theory (see page 39). But at present, it seems a fair bet that what we think of as the classical world is really only the quantum world viewed through the lens of decohered states. "The conceptual leap would then be to conclude from this that quantum mechanics is truly universal,' says Schlosshauer, "in the sense that everything, including us, is described by entangled quantum states "
The next point I would like to emphasize is the way in which quantum states (in the vein of Wheeler-Feynman Absorber Theory) are event specific and each quantum event or transaction is singularly attributable to individual transference of qubits. We know this is the case in quantum communication "links" which are actually transmission lines. The transmission line is a special case of a cavity. And cavity solutions are solutions of Schrodinger's or Dirac's wave Equations in "cavities" (which are just bounded systems). I would like to call attention to the fruitful manipulation of stimulated color centers in diamonds that are showing even at room temperature a single reception of a quantum process such as spin can be finely controlled to the extent that the phase accumulation of the state in resonance from illumination by a coherent source.
QUOTE (->
| QUOTE |
| Quantum all the way Nature :pp22-25 Published online 30 April 2008 | Nature | doi:10.1038/453022a How does our classical world emerge from the counterintuitive principles of quantum theory? Can we even be sure that the world doesn't 'go quantum' when no one is watching? Philip Ball talks to the theorists and experimentalists trying to find out. [..] Early quantum theorists treated the quantum-classical transition almost as a kind of sleight of hand, something that had to be imposed on quantum mechanics to recover the familiar world. Now, however, there are strong signs that the transition can be understood as something that emerges quite naturally and inevitably from quantum theory. If that's so, it implies that 'classicality' is at root simply another quantum phenomenon. "There's good reason to believe that we are just as much part of the quantum world as are the tiny atoms and electrons that sparked quantum theory in the first place,' says quantum theorist Maximilian Schlosshauer of the University of Melbourne in Australia. Testing the new description of the quantum-classical transition involves experiments on systems ranging from photons to superconductors to microscopic vibrating beams. These efforts pose an extreme challenge to experimentalists, as they involve looking for very small effects on comparatively big things —rather like trying to detect the sag when a fly lands on San Francisco's Golden Gate Bridge. The effects very quickly get so small that many physicists believe it is absurd to try to see them. "One crowd says: 'Of course it will work —quantum mechanics says so'," says Schwab. "The other says: 'There's no way it will work —these guys are nuts'." [..] Thus one of the key questions in understanding the quantum-classical transition is what happens to the superpositions as you go up that atoms-to-apples scale? Exactly when and how does 'both/and' become 'either/or'? Physicists have proposed many answers to that question over the decades. But the most failures one involves a phenomenon known as decoherence [3], which was identified and elucidated in the 1970s and 1980s. Crudely speaking, decoherence is a sort of leaking away of quantum behaviour when a particle interacts with its surroundings—for example, when an atom or molecule collides with those around or when light bounces off it. All we are left with is a partial picture of the system — a picture in which only a well-defined subset of macroscopic properties, such as position, are apparent. [..] In summary, decoherence offers a way "to understand classicality as emergent from within the quantum formalism', says Schlosshauer. Indeed, this picture means that the classical world no longer sits in opposition to quantum mechanics, but is demanded by it. [...] The decoherence description shows that there is no abrupt boundary, no critical size, at which quantum behaviour switches to classical. And that blurry boundary itself shifts depending on how it is measured. "It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical,"(Good Elf's emphasis) says Anton Zeilinger of the University of Vienna. His team provided an example of this nine years ago, when it demonstrated quantum interference between beams of C60 fullerene molecules [8] — hardly as classical as the footballs they resemble, but nonetheless big molecules that can be seen with an electron microscope. Interference — the addition or cancellation of overlapping waves — is in this case a purely quantum effect, and can't be understood if the molecules are viewed as discrete particles. It is possible only if the molecules are in a superposition of states — in several places at once. "If you scan with a scanning tunnelling microscope a surface to which fullerene molecules stick, you see the little soccer balls sitting there as classical objects," says Zeilinger. "But if you choose our interference experiment set-up, they are quantum mechanically delocalized." In other words, he says: "The same object can behave as a quantum system in one situation, and as a classical system in another." [..] Bouwmeester hopes that it will soon be possible to test an alternative theory of the quantum-classical transition devised by Roger Penrose of the University of Oxford, UK. Penrose suggests that the 'collapse' of a superposition, rather than being a gradual affair resulting from environment-induced decoherence, is a rather abrupt event that is mediated by gravity. That is, it involves the emission of a graviton, the hypothetical fundamental quantum of the gravitational force, in much the same way that the decay of an excited molecule may happen via emission of a photon. He thinks that the cost in gravitational potential energy of keeping objects in a superposition becomes too great as objects get bigger, so that the objects 'go classical' on a definite timescale, which he estimates to be about a second or so for dust particles. Bouwmeester's mirror experiment should, if he can scale it up without losing sensitivity, be able to spot such a switch. "I am sceptical about this idea, but think it is worth testing,” he says. Understanding quantum states has become much more than an intellectual curiosity, because handling quantum data may hold the key to the future of information technology [..] The decoherence description of the quantum-classical transition is not necessarily the end of the matter— it leaves unresolved some more fundamental questions about the interpretation of quantum theory (see page 39). But at present, it seems a fair bet that what we think of as the classical world is really only the quantum world viewed through the lens of decohered states. "The conceptual leap would then be to conclude from this that quantum mechanics is truly universal,' says Schlosshauer, "in the sense that everything, including us, is described by entangled quantum states " |
I am hopeful that this is not "overuse" of a four page article in Nature but it is a very important issue that needs to be seen by those who are now having second thoughts about the "entire phenomenon".
The next point I would like to emphasize is the way in which quantum states (in the vein of Wheeler-Feynman Absorber Theory) are event specific and each quantum event or transaction is singularly attributable to individual transference of qubits. We know this is the case in quantum communication "links" which are actually transmission lines. The transmission line is a special case of a cavity. And cavity solutions are solutions of Schrodinger's or Dirac's wave Equations in "cavities" (which are just bounded systems). I would like to call attention to the fruitful manipulation of stimulated color centers in diamonds that are showing even at room temperature a single reception of a quantum process such as spin can be finely controlled to the extent that the phase accumulation of the state in resonance from illumination by a coherent source.
Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath
R. Hanson,1*† V. V. Dobrovitski,2 A. E. Feiguin,1 O. Gywat,1 D. D. Awschalom1
Phase coherence is a fundamental concept in quantum mechanics. Understanding loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.
[..]
From a softpedia source...
California NanoSystems Institute at the University of California and US Department of Energy Ames Laboratory researchers believe they can answer these questions, or at least a part of them. According to the researchers, the key lies into understanding how the classical world, as we know it, emerges from the quantum level of matter. Unraveling the quantum dynamics of a single particle spin coupled to a collection of particles with random spins may unlock the way to understanding why some materials around us behave the way they do, such as the quantum tunneling process or magnetic resonance.
"We were stunned by these unexpected experimental results, and extremely excited by the ability to control and monitor single quantum states, especially at room temperature," said author of the study David Awschalom from the University of California. Quantum mechanical properties loss is now more important than ever into the field of quantum information, due to the overwhelming advantages opposed to classical computation techniques.
Most of the work is focused on high fidelity coherent control of a single spin, such as that of the experiment conducted by physicists in Awschalom who investigated the electron spin in a diamond, studying spin-bath interactions and decoherence dynamics. The diamond has unique features which enable scientists to investigate coherent dynamics and precise optical control of a single spin that can only be viewed in diamonds. The team observed multiple extraordinary phenomenons, amongst which time-dependent disappearance and reappearance or quantum oscillations inside the diamond lattice.
"To our surprise, when looking at longer times, the oscillations disappeared and then re-appeared," said co-author Ronald Hanson. The first time the phenomenon appeared, the team believed it to be a random artifact, but upon reseting the experiment a couple of time, the measurements convinced them that the oscillation pattern was genuine.
The next point I would like to emphasize is the way in which quantum states (in the vein of Wheeler-Feynman Absorber Theory) are event specific and each quantum event or transaction is singularly attributable to individual transference of qubits. We know this is the case in quantum communication "links" which are actually transmission lines. The transmission line is a special case of a cavity. And cavity solutions are solutions of Schrodinger's or Dirac's wave Equations in "cavities" (which are just bounded systems). I would like to call attention to the fruitful manipulation of stimulated color centers in diamonds that are showing even at room temperature a single reception of a quantum process such as spin can be finely controlled to the extent that the phase accumulation of the state in resonance from illumination by a coherent source.
Coherent Dynamics of a Single Spin Interacting with an Adjustable Spin Bath
R. Hanson,1*† V. V. Dobrovitski,2 A. E. Feiguin,1 O. Gywat,1 D. D. Awschalom1
Phase coherence is a fundamental concept in quantum mechanics. Understanding loss of coherence is paramount for future quantum information processing. We studied the coherent dynamics of a single central spin (a nitrogen vacancy center) coupled to a bath of spins (nitrogen impurities) in diamond. Our experiments show that both the internal interactions of the bath and the coupling between the central spin and the bath can be tuned in situ, allowing access to regimes with surprisingly different behavior. The observed dynamics are well explained by analytics and numerical simulations, leading to valuable insight into loss of coherence in spin systems. These measurements demonstrate that spins in diamond provide an excellent test bed for models and protocols in quantum information.
[..]
From a softpedia source...
California NanoSystems Institute at the University of California and US Department of Energy Ames Laboratory researchers believe they can answer these questions, or at least a part of them. According to the researchers, the key lies into understanding how the classical world, as we know it, emerges from the quantum level of matter. Unraveling the quantum dynamics of a single particle spin coupled to a collection of particles with random spins may unlock the way to understanding why some materials around us behave the way they do, such as the quantum tunneling process or magnetic resonance.
"We were stunned by these unexpected experimental results, and extremely excited by the ability to control and monitor single quantum states, especially at room temperature," said author of the study David Awschalom from the University of California. Quantum mechanical properties loss is now more important than ever into the field of quantum information, due to the overwhelming advantages opposed to classical computation techniques.
Most of the work is focused on high fidelity coherent control of a single spin, such as that of the experiment conducted by physicists in Awschalom who investigated the electron spin in a diamond, studying spin-bath interactions and decoherence dynamics. The diamond has unique features which enable scientists to investigate coherent dynamics and precise optical control of a single spin that can only be viewed in diamonds. The team observed multiple extraordinary phenomenons, amongst which time-dependent disappearance and reappearance or quantum oscillations inside the diamond lattice.
"To our surprise, when looking at longer times, the oscillations disappeared and then re-appeared," said co-author Ronald Hanson. The first time the phenomenon appeared, the team believed it to be a random artifact, but upon reseting the experiment a couple of time, the measurements convinced them that the oscillation pattern was genuine.
The result was using the complex arrangement of magnetic fields the transfer of spin quanta at room temperature is not only technically "perfect"... These oscillations , even when they had died away into the apparently "irretrievable quantum background", are states that are capable of revival for very long periods of time compared with the Rabi Frequency damping period. This is a "staggering notion" to be not only "entertained" by an intellectual mind but to actually find that quantum states "in the wild" are "individually" controllable as to the individual site in which they are able to be absorbed, reflected or "revived" through the manipulation of some nearby states in the "spin bath" that the single state is to be found immersed. This is more like the tuning of a wireless receiver than random Heisenberg Uncertainty. In these cases (which are admittedly very well chosen) there is no apparent "uncertainty" since the source and the sinks are "highly tuned to each other and "manipulable". So it is becoming quite "obvious that the quantum phase is far more important than what was once thought to be the case. It was all fine when our experiments were not so refined to test these cases in these extreme situations and the argument was brow beaten down to some of the older pundits such as Schrodinger and Einstein by Bohr. Nowadays it is possible to test this "interpretation" and it is found "wanting". This is a good thing and not a bad thing since it is possible to to get so much more out of refined states through resonance which are examples of Quantum Zeno Processes. This "interpretation" has a knock on influence in the rest of quantum physics as I have illustrated here through some relatively learned opinions seem to suggest.
I still disagree with much of these implications because of matters I have discussed in other threads. The interpretation of "moving photons" in space and the concepts of coherence in holographic systems indicate to me that we are dealing with a far more complex situation than we may first imagine. It is the result of 80 years of neglect by the Physics community and a certain "ploughing on" regardless attempting to ignore the "finer points" in favor of the short term "applications". The idea that quanta of all kinds are like little billiard balls moving around and bouncing off each other on a very uneven pool table is most probably quite wrong. The quanta them selves are not "random" or subject to "quantum noise" but the sources we have access to in the past are "poor" as coherent sources and as far as our maths have been able to determine with the lack of truly "good data" indicated that these processes were the outcome of so many "rolls of the dice"... removing the causality and the history of individual events from serious discussion for a very long time. Now with better instruments and with real data we might begin to understand that "quantum weirdness" is due to interpreting the underlying wave phenomena as particle phenomena. The result has been "quantum magic shows" where the public have been subjected to "sleight of hand" and called "fools" for trying to understand this "interpretation".
I can now speak with a little confidence about these issues. I hope everyone can now see where we are being led not by our philosophies but by our experiments (which should have been the case all along). The "in joke" for the last 80 years has been "quantum indeterminacy" and the indistinguishably of ensembles of quantum events on a manifold which is a seething Dirac Sea. All along it would appear to me at least that the spacetime continuum is smoother than a "quantum baby's bottom" and the smaller you go at higher and higher energies the smoother this manifold actually gets. There are thermal processes but their influence has been "grossly exaggerated" through the adoption of an unrealistic "model" of our reality... the particle reality... particle which are entirely "local" in nature and "indistinguishable" as to source. Of course if you want to adopt that approach we have a very good system of statistics to deal with it. It is "correct" as far as it goes... And we have gone about as far as it is possible to go down along that "yellow brick 'particle' road". It is time to adopt a wave theory of "matter" in which the "particle" is totally non-local, and this is 'entirely explained" by the former particle behave as waves ... more so at low energy than at high energy according to the de Broglie-Einstein Relationship. At the same time "quanta" are simply the movements of "packets" of energy between resonant states at the speed of light. In that process the photons that connect everything of real interest in our Universe "connect" by a "propagation" along a null geodesic in which distant "targets" connect and "entangle" instantly while the "capacity to do work" is usually confined to the speed of light and the "many paths" it may travel to the sink as a series of stationary phase accumulated states. The process is mitigated by advanced and retarded waves instantly emitted by the sinks and the sources "simultaneously" and then "worked through" over time and the resonant connection established. We know that entanglement is instantaneous and non-local. We know what we are apparently measuring is "resonance" and the "collapse of the quantum state through "decoherence". Clearly there is far more than this going on and it is a very complex issue but something that even a radio tech could understand.
I am reminder to say that the phase information around us in space as interferences is quasi-stationary due to the location of spatial matter waves. If you think this is so unimportant and that the simple inner product is sufficient for our purpose I would call your attention to this highly graphic example of two images in which the phase information of one image is mixed with the inner product "amplitude" of another.
Fourier transform theory: figure 6: The phase data dominates our perception.
Clearly viewing this figure and the previous two images from which this composite information is taken we can immediately "grasp" that phase does matter... more that "size".
The next point to discuss is the way that the spatial Fourier domains of "collections of distributed sources" combine in ways that do not reflect a simple "ray theory of light".
Optical Fourier Processor - note that this is not a "ray" model
If not "rays" then photons are "something else and quite apart". The explanation is in a liberal wave interpretation of the phenomenon of gauge invariance of the propagating photon through stationary states... or at least "piecemeal" stationary states. We never really understand the nature of photons through the outcomes of the collapse of the state in "decoherence". No photon is observed without severely "restricting" this intermediate state. In the Wheeler-Feynman Absorber context the "events" are singular source to sink and the quanta is preserved in "ideal transmission" for single photons. Of course not every photon is transferred ideally but that is another matter regarding the ability in experiments to identify the "true source" and matching "true sink" of each and every single quantum event. Interference experiments strongly suggest that a single photon "explores" the entire "cavity" before choosing it's destination. This exploration is the "many paths" or "many histories" of the raylike photons in so many interpretative theories. The experiments above indicate that the quantum realm is not one in which we can chop and choose the paradigm in each and every case to "hide" the underlying principle. One principle must fit all. The single quantum state can in principle be prepared to receive a single event using conventional high technology.
There is a reciprocal connection in nature of time and frequency and space and reciprocal space that cohabit in our Universe (both spatially and temporally). This is not "grasped" by a particle interpretation of "trajectories"... it is more relevant through a spreading (or converging) wave interpretation of phenomena (especially in the phenomenon of "light" which so dominates our experience). We also know this "pictorial particle view" is going to have difficulties with those many paths and with the issue of "time symmetry". Five minutes of thinking about that one and I am sure we can all see the advantage of the wave approach.
I could say more about this problem but that is a little more "on course" than what I was saying just previously. It is also difficult for me to confine the discussion to "just one thing" because our Universe is such an "emergent phenomena". I sure hope this discussion has not made things "worse" than they already were.
Cheers
I still disagree with much of these implications because of matters I have discussed in other threads. The interpretation of "moving photons" in space and the concepts of coherence in holographic systems indicate to me that we are dealing with a far more complex situation than we may first imagine. It is the result of 80 years of neglect by the Physics community and a certain "ploughing on" regardless attempting to ignore the "finer points" in favor of the short term "applications". The idea that quanta of all kinds are like little billiard balls moving around and bouncing off each other on a very uneven pool table is most probably quite wrong. The quanta them selves are not "random" or subject to "quantum noise" but the sources we have access to in the past are "poor" as coherent sources and as far as our maths have been able to determine with the lack of truly "good data" indicated that these processes were the outcome of so many "rolls of the dice"... removing the causality and the history of individual events from serious discussion for a very long time. Now with better instruments and with real data we might begin to understand that "quantum weirdness" is due to interpreting the underlying wave phenomena as particle phenomena. The result has been "quantum magic shows" where the public have been subjected to "sleight of hand" and called "fools" for trying to understand this "interpretation".
I can now speak with a little confidence about these issues. I hope everyone can now see where we are being led not by our philosophies but by our experiments (which should have been the case all along). The "in joke" for the last 80 years has been "quantum indeterminacy" and the indistinguishably of ensembles of quantum events on a manifold which is a seething Dirac Sea. All along it would appear to me at least that the spacetime continuum is smoother than a "quantum baby's bottom" and the smaller you go at higher and higher energies the smoother this manifold actually gets. There are thermal processes but their influence has been "grossly exaggerated" through the adoption of an unrealistic "model" of our reality... the particle reality... particle which are entirely "local" in nature and "indistinguishable" as to source. Of course if you want to adopt that approach we have a very good system of statistics to deal with it. It is "correct" as far as it goes... And we have gone about as far as it is possible to go down along that "yellow brick 'particle' road". It is time to adopt a wave theory of "matter" in which the "particle" is totally non-local, and this is 'entirely explained" by the former particle behave as waves ... more so at low energy than at high energy according to the de Broglie-Einstein Relationship. At the same time "quanta" are simply the movements of "packets" of energy between resonant states at the speed of light. In that process the photons that connect everything of real interest in our Universe "connect" by a "propagation" along a null geodesic in which distant "targets" connect and "entangle" instantly while the "capacity to do work" is usually confined to the speed of light and the "many paths" it may travel to the sink as a series of stationary phase accumulated states. The process is mitigated by advanced and retarded waves instantly emitted by the sinks and the sources "simultaneously" and then "worked through" over time and the resonant connection established. We know that entanglement is instantaneous and non-local. We know what we are apparently measuring is "resonance" and the "collapse of the quantum state through "decoherence". Clearly there is far more than this going on and it is a very complex issue but something that even a radio tech could understand.
I am reminder to say that the phase information around us in space as interferences is quasi-stationary due to the location of spatial matter waves. If you think this is so unimportant and that the simple inner product is sufficient for our purpose I would call your attention to this highly graphic example of two images in which the phase information of one image is mixed with the inner product "amplitude" of another.
Fourier transform theory: figure 6: The phase data dominates our perception.
Clearly viewing this figure and the previous two images from which this composite information is taken we can immediately "grasp" that phase does matter... more that "size".
The next point to discuss is the way that the spatial Fourier domains of "collections of distributed sources" combine in ways that do not reflect a simple "ray theory of light". Optical Fourier Processor - note that this is not a "ray" model
If not "rays" then photons are "something else and quite apart". The explanation is in a liberal wave interpretation of the phenomenon of gauge invariance of the propagating photon through stationary states... or at least "piecemeal" stationary states. We never really understand the nature of photons through the outcomes of the collapse of the state in "decoherence". No photon is observed without severely "restricting" this intermediate state. In the Wheeler-Feynman Absorber context the "events" are singular source to sink and the quanta is preserved in "ideal transmission" for single photons. Of course not every photon is transferred ideally but that is another matter regarding the ability in experiments to identify the "true source" and matching "true sink" of each and every single quantum event. Interference experiments strongly suggest that a single photon "explores" the entire "cavity" before choosing it's destination. This exploration is the "many paths" or "many histories" of the raylike photons in so many interpretative theories. The experiments above indicate that the quantum realm is not one in which we can chop and choose the paradigm in each and every case to "hide" the underlying principle. One principle must fit all. The single quantum state can in principle be prepared to receive a single event using conventional high technology.
There is a reciprocal connection in nature of time and frequency and space and reciprocal space that cohabit in our Universe (both spatially and temporally). This is not "grasped" by a particle interpretation of "trajectories"... it is more relevant through a spreading (or converging) wave interpretation of phenomena (especially in the phenomenon of "light" which so dominates our experience). We also know this "pictorial particle view" is going to have difficulties with those many paths and with the issue of "time symmetry". Five minutes of thinking about that one and I am sure we can all see the advantage of the wave approach.
I could say more about this problem but that is a little more "on course" than what I was saying just previously. It is also difficult for me to confine the discussion to "just one thing" because our Universe is such an "emergent phenomena". I sure hope this discussion has not made things "worse" than they already were.
Cheers
Good Elf, contributers,
(Good Elf)
Good Elf, I just felt I needed to explain why I did not respond a few post back, I just (please blame it on me) did not understand what concept/idea you wanted to convey. It seems that you have clarified your position in which when time allows would like to respond after mr_homm because of respect for you both.
Thank you for the time you spent, I am sure it will be interesting.
dawn
(Good Elf)
QUOTE
Sorry... I have left a pretty scattered trail behind me regarding this subject.
Good Elf, I just felt I needed to explain why I did not respond a few post back, I just (please blame it on me) did not understand what concept/idea you wanted to convey. It seems that you have clarified your position in which when time allows would like to respond after mr_homm because of respect for you both.
Thank you for the time you spent, I am sure it will be interesting.
dawn
Hi dawn, mr_homm, Ivars, bukh et al,
No... not at all... entirely my fault. I am sure there are better ways to say all this. I hope you both forgive me for babbling on. As to actually clarifying the position it is actually scary to think of everything I would have liked to say...
I know I have promised you to do a few things and I never really get around to it.
Cheers
QUOTE
I just (please blame it on me) did not understand what concept/idea you wanted to convey.
No... not at all... entirely my fault. I am sure there are better ways to say all this. I hope you both forgive me for babbling on. As to actually clarifying the position it is actually scary to think of everything I would have liked to say...
I know I have promised you to do a few things and I never really get around to it.
Cheers
hi mr. homm, dawn
Thanks for bringing rigged Hilbert space to this thread.
I read about rigged Hilbert spaces and they nicely extrapolate in to the need of possibility of having a disconnected infinitedimensional ( with many levels of infinities) space which as such would not sustain Newtons first law since translation in such space is impossible, and correspondingly mass as inertia does not exist.
The connection to infinitesdimensional rigged Hilbert space which is, as far as i can understand, connected or multiply connected, is via ALL the space of the probability density function(s) which will characterize the distribution present in chaotic infinite dimensional spaces , so they will carry an deterministic influence on what goes on in Gelfand tripple spaces, while itself being 100% probabilistic.
I wonder it entropy of such infinitesimal chaotic space ( having infinitesimal CHAOTIC spacetime dimensions, most likely characterized by irrational numbers) would be negative. If so , the problem with complexity and 2nd law of TD will also disappear.
The only problem will remain with mathematics which does not explain today how phase transitions between different infinitesimal scales and spaces is possible due to lack of mathematics of operations, or rather , hyperoperations in today's language. But that is solvable if physical model will be clear enough to require certain properties of such math ( like speed fast enough to change types of numbers of some subsets of existing number types into others, or even , new types). Work is going on in this direction, but difficulties to compute such fast functions has also delayed analytical development- so far.
I do not see it as a big problem, though.
Thanks for bringing rigged Hilbert space to this thread.
I read about rigged Hilbert spaces and they nicely extrapolate in to the need of possibility of having a disconnected infinitedimensional ( with many levels of infinities) space which as such would not sustain Newtons first law since translation in such space is impossible, and correspondingly mass as inertia does not exist.
The connection to infinitesdimensional rigged Hilbert space which is, as far as i can understand, connected or multiply connected, is via ALL the space of the probability density function(s) which will characterize the distribution present in chaotic infinite dimensional spaces , so they will carry an deterministic influence on what goes on in Gelfand tripple spaces, while itself being 100% probabilistic.
I wonder it entropy of such infinitesimal chaotic space ( having infinitesimal CHAOTIC spacetime dimensions, most likely characterized by irrational numbers) would be negative. If so , the problem with complexity and 2nd law of TD will also disappear.
The only problem will remain with mathematics which does not explain today how phase transitions between different infinitesimal scales and spaces is possible due to lack of mathematics of operations, or rather , hyperoperations in today's language. But that is solvable if physical model will be clear enough to require certain properties of such math ( like speed fast enough to change types of numbers of some subsets of existing number types into others, or even , new types). Work is going on in this direction, but difficulties to compute such fast functions has also delayed analytical development- so far.
I do not see it as a big problem, though.
Good Elf
QUOTE: ""It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical"
Or put differently - am I right in supposing, that provided the measuring apparatus is choosen with a sufficiently "high" sensitivity - then ANY object IS quantic.
It is back to the good question - is continuous part of physical - or should continuous (and infinite) be reserved for pre-physical states - as potentials out from which physical can be "born"
And this also will have bearings to the very concept of a wave -
Can a wave be continuous - is it possible to have a dynamic - a change - without discreteness - and yes I know I have been asking that question (too) many times - anyhow
As long as there exist no definition of particle - it is meaningless - or at best difficult to discuss quantum vs. continuous.
Intuitively I would say that particle is intimately connected with repetition - without repetition it is not possible to interfere AND translate (transmit) a Physical "signal)
And intuitively I would say that physical involve a "Space" - physical cannot be based upon points
And intuitively I would say that mathematics and physics IS the same - just expressing themselves differently - physical can best be defined as everything which can be percepted by human physical senses - senses in the scale of human flesh and blood - and quantum behavior in this scale is measured or percepted as fairly big oscillations - no possibility to see the underlying oscillations, whereas mathematics is a mind perception - not bound to our physical senses - but in as much that mathematical and physical is the same - mathematics cannot be based upon points - because it is not possible to construct a space out from points. Perhaps it is a much too simplistic way of thinking - but mathematical points - any math number must therefore have a corresponding space aquainted.
So a wave - irrespective how we look at a wave and irrespective how small the wave may be - which scale it is looked at - then a wave is expressed out from discrete spacious "particles".
QUOTE: ""It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical"
Or put differently - am I right in supposing, that provided the measuring apparatus is choosen with a sufficiently "high" sensitivity - then ANY object IS quantic.
It is back to the good question - is continuous part of physical - or should continuous (and infinite) be reserved for pre-physical states - as potentials out from which physical can be "born"
And this also will have bearings to the very concept of a wave -
Can a wave be continuous - is it possible to have a dynamic - a change - without discreteness - and yes I know I have been asking that question (too) many times - anyhow
As long as there exist no definition of particle - it is meaningless - or at best difficult to discuss quantum vs. continuous.
Intuitively I would say that particle is intimately connected with repetition - without repetition it is not possible to interfere AND translate (transmit) a Physical "signal)
And intuitively I would say that physical involve a "Space" - physical cannot be based upon points
And intuitively I would say that mathematics and physics IS the same - just expressing themselves differently - physical can best be defined as everything which can be percepted by human physical senses - senses in the scale of human flesh and blood - and quantum behavior in this scale is measured or percepted as fairly big oscillations - no possibility to see the underlying oscillations, whereas mathematics is a mind perception - not bound to our physical senses - but in as much that mathematical and physical is the same - mathematics cannot be based upon points - because it is not possible to construct a space out from points. Perhaps it is a much too simplistic way of thinking - but mathematical points - any math number must therefore have a corresponding space aquainted.
So a wave - irrespective how we look at a wave and irrespective how small the wave may be - which scale it is looked at - then a wave is expressed out from discrete spacious "particles".
Hi bukh, dawn, mr_homm, Ivars et al,
QUOTE (bukh+)
QUOTE (Quantum all the way: Nature 30 April 2008+)
""It is the choice of the measuring apparatus that defines whether a specific object is quantum or classical"
Or put differently - am I right in supposing, that provided the measuring apparatus is choosen with a sufficiently "high" sensitivity - then ANY object IS quantic.
It is a "great sound byte" but it is to be understood with "extreme" caution. The instrument itself "should" not determine if a process is a quantum or is not yet an instrument is the way in which we can "sense" and interpret the measurements we are making in the Universe. "We" humans are not good recording instruments and we are not able to directly interpret these phenomena that we neither see or measure directly... they are beyond our sensory perception so they are open to question and interpret. This is where a mathematician can show how this new information fits with existing data. The mathematician can't make a result in an instrument prove his or her theory but a mathematician can show that the new data is able to be incorporated smoothly into existing theory (or not).
There is a difference between "measurements" and "observables". Two different scientific instruments will make measurements of a single observable (obviously not the one and same measurement or observable "simultaneously"... that's "impossible"). Everything being "equal"... and things are not equal in this World... These measurements will not necessarily measure the one and the same "value" (the numbers will be different). For instance the charge on an electron may be determined by two or more differently instruments (working on slightly different physical principles and interpretations of the "underlying quantities"... for instance the torsion coefficient of a quartz fiber or a quantity of mass in an oil droplet.. which are constructed to determine this quantity of "charge". There is usually no "individual dial or screen" on which this determination can be "explicitly" displayed, a number of separate determinations or readings will be required to determine this "one value" of electronic charge. There are several stages in this process and the values are sometimes inter-related through this process of the measurement itself. A careful calculation of errors must be a part of the process in order to convince the review process that the methodology is "right".
You can construct a one-off instrument but it will not necessarily "show" the parameter you wish to view because it is a complex inter-related technical piece of equipment. Systems are constructed that are not "absolute instruments" measuring quantities that are independent of laboratory and sample states and dependent only on the physical constants. The instrument must usually be individually calibrated to provide "scales" and "values" when compared with some "standard" that may not exist in a particular laboratory. A lot of "black art" is required in which the "right answer" is determined using quite reasonable assumptions about how that instrument behaves under that circumstance. The "right answer" quite often insists on it agreeing with some classically derived result and with the results derived from other laboratories. A "wrong answer" is one that might simply need instrument calibration or even redesign to improve the precision or accuracy (which are different). There may be undiscovered systematic errors as well.
There is also a desire to fulfill the parameters of the funding board. Experiments are not easy to describe when the funding board requires you to virtually know the answer to the problem you are trying to solve before you ask for the funding. Ontologically this is the wrong "question". There are going to be "right" and "wrong" answers. A "wrong" answer will not be allowed to be published since it is reviewed by a group of 'eminent persons" who are able to sanction the result or refuse the result based on their "expert opinion". Unpublished papers gain no kudos. That is all for "starters"... Here is an extract from a Philosophical Dictionary about "ontology"...
There is a difference between "measurements" and "observables". Two different scientific instruments will make measurements of a single observable (obviously not the one and same measurement or observable "simultaneously"... that's "impossible"). Everything being "equal"... and things are not equal in this World... These measurements will not necessarily measure the one and the same "value" (the numbers will be different). For instance the charge on an electron may be determined by two or more differently instruments (working on slightly different physical principles and interpretations of the "underlying quantities"... for instance the torsion coefficient of a quartz fiber or a quantity of mass in an oil droplet.. which are constructed to determine this quantity of "charge". There is usually no "individual dial or screen" on which this determination can be "explicitly" displayed, a number of separate determinations or readings will be required to determine this "one value" of electronic charge. There are several stages in this process and the values are sometimes inter-related through this process of the measurement itself. A careful calculation of errors must be a part of the process in order to convince the review process that the methodology is "right".
You can construct a one-off instrument but it will not necessarily "show" the parameter you wish to view because it is a complex inter-related technical piece of equipment. Systems are constructed that are not "absolute instruments" measuring quantities that are independent of laboratory and sample states and dependent only on the physical constants. The instrument must usually be individually calibrated to provide "scales" and "values" when compared with some "standard" that may not exist in a particular laboratory. A lot of "black art" is required in which the "right answer" is determined using quite reasonable assumptions about how that instrument behaves under that circumstance. The "right answer" quite often insists on it agreeing with some classically derived result and with the results derived from other laboratories. A "wrong answer" is one that might simply need instrument calibration or even redesign to improve the precision or accuracy (which are different). There may be undiscovered systematic errors as well.
There is also a desire to fulfill the parameters of the funding board. Experiments are not easy to describe when the funding board requires you to virtually know the answer to the problem you are trying to solve before you ask for the funding. Ontologically this is the wrong "question". There are going to be "right" and "wrong" answers. A "wrong" answer will not be allowed to be published since it is reviewed by a group of 'eminent persons" who are able to sanction the result or refuse the result based on their "expert opinion". Unpublished papers gain no kudos. That is all for "starters"... Here is an extract from a Philosophical Dictionary about "ontology"...
QUOTE (philosophical ontology+)
Derived from the Greek word for being, but a 17th-century coinage for the branch of metaphysics that concerns itself with what exists. Apart from the ontological argument itself there have existed many a priori arguments that the world must contain things of one kind or another: simple things, unextended things, eternal substances, necessary beings, and so on. Such arguments often depend upon some version of the principle of sufficient reason. Kant is the greatest opponent of the view that unaided reason can tell us in detail what kinds of thing must exist, and therefore do exist. In the 20th century, Heidegger is often thought of primarily as an ontologist. Quine's principle of ontological commitment is that to be is to be the value of a bound variable, a principle not telling us what things exist, but how to determine what things a theory claims to exist. These are the things the variables range over in a properly regimented formal presentation of the theory. Philosophers characteristically charge each other with reifying things improperly, and in the history of philosophy every kind of thing will at one time or another have been thought to be the fictitious result of an ontological mistake.
IMHO Science is not "immune" to ontological errors. Ontological errors can lead to the problems we are making right now in the assertions we are all making regarding the theory of "particles". This "unaided reason" is flawed as is all human activity. We must ground our ideas in reason that we can test. Metaphorically speaking.. I don't trust you to make a theory that I will accept on your assertion alone and you will not accept a theory that I simply put up here that I think is "philosophically sound". To do so is very "foolish"... You would be accepting ideas that are "unsound" and this would allow you to be manipulated by my ideas and visa versa. Many people are such individuals and you can get people in high rank and authority that are completely bound to baseless acceptance of "authorities".
That is why I must be "forced" to present independent experiment that is based not on the musings of philosophers but on the trials and questions placed directly before the Universe (herself) to answer. Like the Oracle of Delphi these question we place must be properly contrived to seek the underlying Truth and not the outcomes our ego's wish for... not an easy task. We are vain creatures and subject to vices of all kinds. Like the Oracle's Answers the "purity of your heart" is a deciding ingredient in the mix that will produce the seeker's individual prophecy, you will receive only what your heart truly seeks.
The final scene from "Indiana Jones and the Last Crusade" indicates the choices we all make in life in an allegorical way. Many choose a "poisoned chalice" rather than the Truth because we prefer the attractive resolution to our questions rather than some unpalatable fact that we do not want to fit into our "Cosmos". Which one do you want to be .... Indiana Jones or Walter Donovan who had sold out to the Nazis and accepted "poor" advice from Dr. Schneider :? ... he h
Metaphorically speaking.. I don't trust you to make a theory that I will accept on your assertion alone and you will not accept a theory that I simply put up here that I think is "philosophically sound". To do so is very "foolish"... You would be accepting ideas that are "unsound" and this would allow you to be manipulated by my ideas and visa versa. Many people are such individuals and you can get people in high rank and authority that are completely bound to baseless acceptance of "authorities".That is why I must be "forced" to present independent experiment that is based not on the musings of philosophers but on the trials and questions placed directly before the Universe (herself) to answer. Like the Oracle of Delphi these question we place must be properly contrived to seek the underlying Truth and not the outcomes our ego's wish for... not an easy task. We are vain creatures and subject to vices of all kinds. Like the Oracle's Answers the "purity of your heart" is a deciding ingredient in the mix that will produce the seeker's individual prophecy, you will receive only what your heart truly seeks.
The final scene from "Indiana Jones and the Last Crusade" indicates the choices we all make in life in an allegorical way. Many choose a "poisoned chalice" rather than the Truth because we prefer the attractive resolution to our questions rather than some unpalatable fact that we do not want to fit into our "Cosmos".
Which one do you want to be .... Indiana Jones or Walter Donovan who had sold out to the Nazis and accepted "poor" advice from Dr. Schneider :? ... he h