Challenge:
Develop a framework of mathematics which removes the "divide by zero" problem, both in the general and discreet case, or possibly just one or the other at a time, but still works accurately for real world calculations.
If this is impossible, "prove" it is impossible.
If new axioms or theories of Mathematics are needed, develop them and "prove" they work.
Philosophical Question:
If the above challenge is impossible, then what does that say about our framework of math and science, since our math involves equations which are undefined along their range or domain for some values, even when all component terms are defined or apparently defined individually?
Example:
Y = X / (X -1)
X and "X-1" are always defined, under present day math laws, yet Y is not.
if X = 1,
then Y = 1/0, which is Undefined.
Perhaps our concept of an "equalities, inequalities, and expressions," is flawed, since they necessarily give rise to "undefined" terms at times.
For example, if I simply write the term "5/0," the we can quickly argue "that's nonsense because division by zero is undefined."
But if I have the equality:
Y = X/(X-5)
If X = 5,
Then Y = 5/0, which is undefined.
The problem here is one math law requires that X is always defined, but the concept of an "equality" plus division forces the right hand side to produce a nonsense result.
I guess what I'm trying to say is this problem is bptj more complicated and more fundamental than it appears to be at first.
Perhaps the problem lies in the definition of Zero more so than the definition of division or equality?
This strikes me as THE biggest fundamental problem in both mathematics and physics today, and yet I've never seen a legitimate attempt to resolve it, or even an attempt to speculate on a line of reasoning that "might" resolve it.
Next Problem:
Negativity:
Four apples minus five apples equals negative one apple.
What the HELL is a "negative apple"?
I can owe a person an apple, but that is not a negative number.
On a number line, a negative one exists, and yet in the real world, a "negative apple" or an "owed apple" does not exist.
Therefore we should correct the above statement as follows:
"Four apples minus five apples is undefined."
After all, if you have only FOUR apples, then the very act of subtracting FIVE apples is in fact logically impossible. Nobody can possibly take away FIVE apples from you if you've only got FOUR to start with.
but that is not sufficient. In the real world we COUNT each apple, one at a time.
If they ATTEMPT to remove five apples, and find only four apples, they stop at four apples, leaving not "zero Apples," but rather just "nothing," since Zero apples does not exist either.
Zero Zeros
You may say "an empty basket has Zero Apples."
Possibly, but I find that problematic as well, as by that reasoning it also contains "zero oranges" as well as "zero pears" and "zero Orangutans" and it even contains "zero zeros".
How can an EMPTY basket contain "Zero Oranges" and "Zero Zeros" at the same time?
Yet by our present definition of mathematics and physics, it apparently does just that, even though such is self contradictory at a conceptual level....
If the basket is EMPTY then it must contain "nothing" which is actually most closely expressed as the "empty set" in mathematics, and yet in the real world no true "empty sets" appear to exist, because in reality an "empty basket" is not really "empty" it contains air and space-time, if nothing else...
Nevertheless an "empty" basket contains zero of everything and zero zeros simultaneously, once again, even though that is self-contradictory on at least TWO conceptual levels...
Perhaps "Zero times Zero," a.k.a. "0*0," is the problem....
The standard claim that "Zero equals nothing" does not seem to hold true, for if "Zero equals nothing" then "Zero times Zero" or "0*0" should undoubtedly produce a blank space, rather than a symbolic solution.
0*0 = 0
How?
For if I have zero zeros then I certainly cannot have one Zero at the same time.
Observe:
Zero Zeros equals one Zero...***?!?
"Zero Zeros" should be an empty set, so then why does it equal "One Zero"?
If I have no Zeros then how can I have one Zero?
Therefore the expressions "0*0 = 0" and "zero times zero equals zero" are illogical.
QUOTE
Develop a framework of mathematics which removes the "divide by zero" problem, both in the general and discreet case, or possibly just one or the other at a time, but still works accurately for real world calculations.
Why is it a problem? How many times can you reach into a bag of zero marbles and take out zero marbles? As many times as you want, aka, undefined.
QUOTE (->
| QUOTE |
| Develop a framework of mathematics which removes the "divide by zero" problem, both in the general and discreet case, or possibly just one or the other at a time, but still works accurately for real world calculations. |
Why is it a problem? How many times can you reach into a bag of zero marbles and take out zero marbles? As many times as you want, aka, undefined.
For if I have zero zeros then I certainly cannot have one Zero at the same time.
In case you haven't noticed, math works. That's pretty much the biggest and best argument for the many concepts that math introduces that do not exist in the real world. No apples plus no apples equals no apples. I don't think anything you've written here works on any level other than "I'm annoyed at math."
The perceptual "owing" of an apple is "real." Just not materially so at the time. It incorporates a four dimensional component, the future expectation of that apple being there because of the "act" of owing...
QUOTE (flyingbuttressman+Aug 1 2012, 11:18 PM)
Why is it a problem? How many times can you reach into a bag of zero marbles and take out zero marbles? As many times as you want, aka, undefined.
In case you haven't noticed, math works. That's pretty much the biggest and best argument for the many concepts that math introduces that do not exist in the real world. No apples plus no apples equals no apples. I don't think anything you've written here works on any level other than "I'm annoyed at math."
Multiplication and addition are not the same thing exactly.
Moreover, "zero zeros" isn't an addition at all.
This is One Zero: 0.
This is a better representation of Zero Zeros: {}.
Math doesn't work for forms involving "X/0"...
If I have zero zeros, then it would seem, paradoxically, that I must have at least one of everything, except zeros, of course!
Perhaps that's why existence exists, "If you have zero zeros you still have at least one of everything!"
But now you're defining a one-dimensional number line in terms of a fourth dimensional space, which is now a circular definition, or circular argument.
The numbers don't add up, because there is still an instant in time where you have zero apples, and by the number line anyway, should have negative apples.
Do we in fact have zero apples when we don't have any apples?
Is "Zero Apples" a thing we can possess?
How is it possible for a basket to contain "zero zeros" and "zero apples" at the same time?
It cannot contain zero zeros and zero apples at the same time, since if you have zero apples you have at least one zero, and one zero isn't zero zeros.
"One apple minus one apple equals zero apples."
The problem I find is "Zero Apples" do(es) not exist.
We subtracted a real object and obtained an abstract concept.
In case you haven't noticed, math works. That's pretty much the biggest and best argument for the many concepts that math introduces that do not exist in the real world. No apples plus no apples equals no apples. I don't think anything you've written here works on any level other than "I'm annoyed at math."
Multiplication and addition are not the same thing exactly.
Moreover, "zero zeros" isn't an addition at all.
This is One Zero: 0.
This is a better representation of Zero Zeros: {}.
Math doesn't work for forms involving "X/0"...
If I have zero zeros, then it would seem, paradoxically, that I must have at least one of everything, except zeros, of course!
Perhaps that's why existence exists, "If you have zero zeros you still have at least one of everything!"
QUOTE
The perceptual "owing" of an apple is "real." Just not materially so at the time. It incorporates a four dimensional component, the future expectation of that apple being there because of the "act" of owing...
But now you're defining a one-dimensional number line in terms of a fourth dimensional space, which is now a circular definition, or circular argument.
The numbers don't add up, because there is still an instant in time where you have zero apples, and by the number line anyway, should have negative apples.
Do we in fact have zero apples when we don't have any apples?
Is "Zero Apples" a thing we can possess?
How is it possible for a basket to contain "zero zeros" and "zero apples" at the same time?
It cannot contain zero zeros and zero apples at the same time, since if you have zero apples you have at least one zero, and one zero isn't zero zeros.
"One apple minus one apple equals zero apples."
The problem I find is "Zero Apples" do(es) not exist.
We subtracted a real object and obtained an abstract concept.
Ok, try this.
The following are links to pictures from pages of a book, I am sorry I don't know the book or the author, I encountered this on another forum during an discussion irrelevant to this forum, but it is an interesting piece of nonsense that also appears to be a metaphysical thought experiment.
The author invents several layers of potentially unnecessary abstraction, perhaps in a form of sarcasm against the notion of knowing what fundamental reality is, or perhaps just as humor.
https://sphotos.xx.fbcdn.net/hphotos-ash3/5...113641546_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-ash4/3...167746712_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...510098270_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-ash3/5...216686908_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...323506906_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...749356867_n.jpg
Now the funny thing is, by my reckoning, our universe contains alternate universes and possibly even alternate multiverses, if nothing else in the form of fiction. Yet fictional universes and multiverses are often defined or assumed to contain the real universe, so the real universe contains the fictional multiverse which contains the real universe.
This is another problem entirely, but related to math, abstraction, and language problems.
The following are links to pictures from pages of a book, I am sorry I don't know the book or the author, I encountered this on another forum during an discussion irrelevant to this forum, but it is an interesting piece of nonsense that also appears to be a metaphysical thought experiment.
The author invents several layers of potentially unnecessary abstraction, perhaps in a form of sarcasm against the notion of knowing what fundamental reality is, or perhaps just as humor.
https://sphotos.xx.fbcdn.net/hphotos-ash3/5...113641546_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-ash4/3...167746712_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...510098270_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-ash3/5...216686908_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...323506906_n.jpg
https://sphotos.xx.fbcdn.net/hphotos-prn1/5...749356867_n.jpg
Now the funny thing is, by my reckoning, our universe contains alternate universes and possibly even alternate multiverses, if nothing else in the form of fiction. Yet fictional universes and multiverses are often defined or assumed to contain the real universe, so the real universe contains the fictional multiverse which contains the real universe.
This is another problem entirely, but related to math, abstraction, and language problems.
If you think about how zero works in pure calculus you might get a different perspective.
If you differentiate y=x^2 with respect to x you get 2*x^1, differentiated again you get 2*x^0 and again you get zero (not x^-1 or 1/x).
In its simplest form differentiation is the application of n*x^(n-1) on all x in equations of the form a*x^2+b*x+c=0 (a, b and c being constants).
Integration is just applying (x^(n+1))/n in the opposite direction.
Calculus just doesn't work without a concept of zero as a base limit.
If you differentiate y=x^2 with respect to x you get 2*x^1, differentiated again you get 2*x^0 and again you get zero (not x^-1 or 1/x).
In its simplest form differentiation is the application of n*x^(n-1) on all x in equations of the form a*x^2+b*x+c=0 (a, b and c being constants).
Integration is just applying (x^(n+1))/n in the opposite direction.
Calculus just doesn't work without a concept of zero as a base limit.
The one place where division by 0 has always intuitively made sense to me is with respect to rotations around a circle (or raotations in general). Divide 360 by 6 and you get a 60 degree rotation. Divide it by 12, a 30 degree rotation. Dividing 360 by 0 corresponds with the "Do Nothing" State.
Of course, even in this sense, if one demands that the circle is defined by the rotation itself, rather than being pre-existing, then division by zero again becomes nonsense since the circle is never generated...
- RF
Of course, even in this sense, if one demands that the circle is defined by the rotation itself, rather than being pre-existing, then division by zero again becomes nonsense since the circle is never generated...
- RF
QUOTE (LaurieAG+Aug 4 2012, 10:19 PM)
If you think about how zero works in pure calculus you might get a different perspective.
If you differentiate y=x^2 with respect to x you get 2*x^1, differentiated again you get 2*x^0 and again you get zero (not x^-1 or 1/x).
In its simplest form differentiation is the application of n*x^(n-1) on all x in equations of the form a*x^2+b*x+c=0 (a, b and c being constants).
Integration is just applying (x^(n+1))/n in the opposite direction.
Calculus just doesn't work without a concept of zero as a base limit.
It doesn't work with zero either.
They just ignore all the forms for which it doesn't work....
====
I still think "Zero times Zero" should equal "Zero Zeros", not "Zero".
If you differentiate y=x^2 with respect to x you get 2*x^1, differentiated again you get 2*x^0 and again you get zero (not x^-1 or 1/x).
In its simplest form differentiation is the application of n*x^(n-1) on all x in equations of the form a*x^2+b*x+c=0 (a, b and c being constants).
Integration is just applying (x^(n+1))/n in the opposite direction.
Calculus just doesn't work without a concept of zero as a base limit.
It doesn't work with zero either.
They just ignore all the forms for which it doesn't work....
====
I still think "Zero times Zero" should equal "Zero Zeros", not "Zero".
Easier to ignore these problems, rather than seriously address them, I know, but I naively expected at least a few more attempts to offer a solution.
Admittedly, if you could ever "define" division by zero and prove it was true, somehow, or answer the "Does zero zeros equals one zero" question, you'd probably get a Nobel or two. That would be the biggest discovery in both mathematics and physics since probably at least a century.
Does anyone even have an idea as to how to proceed on these things?
They are so difficult that maybe nobody will ever even do serious research on solving these problems...
Who would spend their life trying to solve these for real, when they've been a dead end for centuries?
Admittedly, if you could ever "define" division by zero and prove it was true, somehow, or answer the "Does zero zeros equals one zero" question, you'd probably get a Nobel or two. That would be the biggest discovery in both mathematics and physics since probably at least a century.
Does anyone even have an idea as to how to proceed on these things?
They are so difficult that maybe nobody will ever even do serious research on solving these problems...
Who would spend their life trying to solve these for real, when they've been a dead end for centuries?
I don't get why this is so hard to understand. Division by zero is undefined because it can product any result.
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because you could guess any number, and it would be correct.
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because you could guess any number, and it would be correct.
QUOTE (flyingbuttressman+Aug 16 2012, 12:43 AM)
I don't get why this is so hard to understand. Division by zero is undefined because it can product any result.
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because it could guess any number, and it would be correct.
very well put.
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because it could guess any number, and it would be correct.
very well put.
QUOTE (flyingbuttressman+Aug 15 2012, 07:43 PM)
I don't get why this is so hard to understand. Division by zero is undefined because it can product any result.
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because you could guess any number, and it would be correct.
That is NOT the correct answer that is given in a college text or class room.
Division by zero is "undefined" because there is NO KNOWN REAL NUMBER that can be produced by dividing by zero.
Your claim that 0/0 = 1, is a special case, and is indeterminent.
http://en.wikipedia.org/wiki/Division_by_zero
But if the numerator is anything other than zero it is not just mere undetermined, there simply is no known value to solve the problem, and therefore it is called "undefined".
1/0 = ?
1 = ? * 0
"1/0," "n/0," and "0/0" are different cases which behave slightly differently.
1/0 and n/0 (where n is not zero,) or any form reducing to that result, are currently regarded as "meaningless expressions".
YET these same forms appear in both Newton's gravity equation and Einstein's relativity...for the special case where "r" equals zero, or "v" equals c...
Isn't it a little odd that formulas for laws considered "fundamental" to physics involve expressions that are "meaningless" for at least one term?!
Simple algebra:
1 * 0 = 0
2 * 0 = 0
3 * 0 = 0
Divide both sides by zero:
0/0 = 1
0/0 = 2
0/0 = 3
It's undefined because you could guess any number, and it would be correct.
That is NOT the correct answer that is given in a college text or class room.
Division by zero is "undefined" because there is NO KNOWN REAL NUMBER that can be produced by dividing by zero.
Your claim that 0/0 = 1, is a special case, and is indeterminent.
http://en.wikipedia.org/wiki/Division_by_zero
But if the numerator is anything other than zero it is not just mere undetermined, there simply is no known value to solve the problem, and therefore it is called "undefined".
1/0 = ?
1 = ? * 0
"1/0," "n/0," and "0/0" are different cases which behave slightly differently.
1/0 and n/0 (where n is not zero,) or any form reducing to that result, are currently regarded as "meaningless expressions".
YET these same forms appear in both Newton's gravity equation and Einstein's relativity...for the special case where "r" equals zero, or "v" equals c...
Isn't it a little odd that formulas for laws considered "fundamental" to physics involve expressions that are "meaningless" for at least one term?!
Multiplication by zero can be thought of as informational entropy. The product no longer give us any clue as to what the factors may have been. For example, 2*5=10. We know the factors of 10 are 1, 2, 5, & 10, so even if we cannot be entirely certain of the specific factors used to arrive at 10, the possibilities are extremely finite.
Now when we multiply by zero, 2*0=0, the resultant zero has an infinite number of factors. We have lost any bounds on the possible factors used to arrive at zero.
That's call calculus. You can divide by a value whose limit is approaching zero, and thereby approximate that value as some variable goes to zero.
Now when we multiply by zero, 2*0=0, the resultant zero has an infinite number of factors. We have lost any bounds on the possible factors used to arrive at zero.
QUOTE
YET these same forms appear in both Newton's gravity equation and Einstein's relativity...for the special case where "r" equals zero, or "v" equals c...
That's call calculus. You can divide by a value whose limit is approaching zero, and thereby approximate that value as some variable goes to zero.
QUOTE (synthsin75+Aug 16 2012, 06:16 PM)
Multiplication by zero can be thought of as informational entropy. The product no longer give us any clue as to what the factors may have been. For example, 2*5=10. We know the factors of 10 are 1, 2, 5, & 10, so even if we cannot be entirely certain of the specific factors used to arrive at 10, the possibilities are extremely finite.
Now when we multiply by zero, 2*0=0, the resultant zero has an infinite number of factors. We have lost any bounds on the possible factors used to arrive at zero.
That's call calculus. You can divide by a value whose limit is approaching zero, and thereby approximate that value as some variable goes to zero.
Problem is the Calculus solution does not work in Relativity, since in order for a full "limit" to be valid it must have both the same scalar value and the same sign.
For relativity, the limits are positive infinity when approaching "c" from the left, but the limit is an infinite imaginary number with no real component when approaching "c" from the right.
Therefore the limit for v=c does not exist, and the intuitive answer is invalidated, since the right handed limit and the left handed limit neither give the same sign, nor even the same numerical axis for their solutions.
Now when we multiply by zero, 2*0=0, the resultant zero has an infinite number of factors. We have lost any bounds on the possible factors used to arrive at zero.
That's call calculus. You can divide by a value whose limit is approaching zero, and thereby approximate that value as some variable goes to zero.
Problem is the Calculus solution does not work in Relativity, since in order for a full "limit" to be valid it must have both the same scalar value and the same sign.
For relativity, the limits are positive infinity when approaching "c" from the left, but the limit is an infinite imaginary number with no real component when approaching "c" from the right.
Therefore the limit for v=c does not exist, and the intuitive answer is invalidated, since the right handed limit and the left handed limit neither give the same sign, nor even the same numerical axis for their solutions.
QUOTE (synthsin75+Aug 16 2012, 11:16 PM)
You can divide by a value whose limit is approaching zero, and thereby approximate that value as some variable goes to zero.
Can you expand on that a little ?
Can you expand on that a little ?
QUOTE (Mekigal+Aug 16 2012, 10:54 PM)
Can you expand on that a little ?
It's wrong anyway.
In Calc 1 or Calc 2, I forget which, they prove cases where it doesn't work even when both the right and and left hand limits exists and are equal.
In cases where one side of the limit does not exist, or where both sides exist but are different, it simply does not necessarily work.
In normal applications in the real world, you might not be able to tell the difference, since real world structures rarely have decimal precision approaching that of theoretical calculus, i.e. there's no true macroscopic circles in the real world, and even elementary particles may not be true circles or spheres.
Real world structures have mathematical "patches" hiding infinite limits, so that a curve representing such a structure would be "piece-wise defined," to produce continuity, rather than a single continuous formula.
I would need to re-read my calculus text, or find my old notebook and look through 2 semesters of notes, but such is the case, I just don't remember the exact examples right off hand.
It's wrong anyway.
In Calc 1 or Calc 2, I forget which, they prove cases where it doesn't work even when both the right and and left hand limits exists and are equal.
In cases where one side of the limit does not exist, or where both sides exist but are different, it simply does not necessarily work.
In normal applications in the real world, you might not be able to tell the difference, since real world structures rarely have decimal precision approaching that of theoretical calculus, i.e. there's no true macroscopic circles in the real world, and even elementary particles may not be true circles or spheres.
Real world structures have mathematical "patches" hiding infinite limits, so that a curve representing such a structure would be "piece-wise defined," to produce continuity, rather than a single continuous formula.
I would need to re-read my calculus text, or find my old notebook and look through 2 semesters of notes, but such is the case, I just don't remember the exact examples right off hand.
Let's take "1/X"
Lim (1/X) as X->0- = - Infinity.
This reads, "The limit of "1/X" as X approaches Zero from the left equals negative infinity."
Lim (1/X) as X->0(plus) = Infinity
This reads, "The limit of "1/X" as X approaches Zero from the Right equals infinity."
The left hand limit and the right hand limit are not equal, therefore:
Lim (1/X) as X->0 = DNE.
This reads, "The limit of "1/X" as X approaches Zero does not exist."
The left-hand limit for Lorentz Factor in Relativity is reversed signed, and heavily right shifted version of the left hand limit, "lim (1/X) as X->0-".
The right-hand limit for the Lorentz Factor is the same as the right handed limit of 1/X, but heavily right-shifted, and of course rotated a full 90 degrees into the imaginary axis.
Left hand limit as v->c is (infinity, 0 * i).
Right hand limit as v->c is (0, Infinity * i).
The values are not equal, therefore:
Limit of the Lorentz Factor as v approaches c does not exist...
This fact is simply ignored in almost all physics discussions, because it's assumed that continuous acceleration could never meet or exceed c.
However, in Quantum Theory nothing is continuous, information and energy are transferred in discreet packets. Therefore it's conceivable that a massive particle could somehow "Jump" c, since in reality some particles "jump" some finite numbers anyway, and exist only at specific mass/energy values, and never between those values.
Because this is the case, the formula for Relativity appears to produce incredibly freaky results IF and when this phenomena ever occurs, because the particle would instantly jump from "almost infinite real time dilation with no imaginary time dilation" to "frozen in the real time axis, but almost infinite imaginary time dilation". Which appears to be an absurdity, and yet this same formula appears in the mathematical descriptions of Neutrinos...
Based on the formula, a "Tachyon" actually does not move backwards in time.
In fact, if it was only just barely moving greater than c, and if the ridiculous formula was correct, then the particle would be FROZEN in the real time axis at the instant it exceeded light speed, and would cease to exist in "normal real space" in the very next instant; further, it would be nearly infinitely time dilated in the imaginary axis.
However, tachyons could still have instantaneous intersection with "real number" space-time at a single point in space and time, but only exactly once, assuming they are moving in a straight line.
All of this assumes the right handed limit of the Lorentz Factor exists at all, and uses the same formula.
In any case, the LIMIT does not exist...
Lim (1/X) as X->0- = - Infinity.
This reads, "The limit of "1/X" as X approaches Zero from the left equals negative infinity."
Lim (1/X) as X->0(plus) = Infinity
This reads, "The limit of "1/X" as X approaches Zero from the Right equals infinity."
The left hand limit and the right hand limit are not equal, therefore:
Lim (1/X) as X->0 = DNE.
This reads, "The limit of "1/X" as X approaches Zero does not exist."
The left-hand limit for Lorentz Factor in Relativity is reversed signed, and heavily right shifted version of the left hand limit, "lim (1/X) as X->0-".
The right-hand limit for the Lorentz Factor is the same as the right handed limit of 1/X, but heavily right-shifted, and of course rotated a full 90 degrees into the imaginary axis.
Left hand limit as v->c is (infinity, 0 * i).
Right hand limit as v->c is (0, Infinity * i).
The values are not equal, therefore:
Limit of the Lorentz Factor as v approaches c does not exist...
This fact is simply ignored in almost all physics discussions, because it's assumed that continuous acceleration could never meet or exceed c.
However, in Quantum Theory nothing is continuous, information and energy are transferred in discreet packets. Therefore it's conceivable that a massive particle could somehow "Jump" c, since in reality some particles "jump" some finite numbers anyway, and exist only at specific mass/energy values, and never between those values.
Because this is the case, the formula for Relativity appears to produce incredibly freaky results IF and when this phenomena ever occurs, because the particle would instantly jump from "almost infinite real time dilation with no imaginary time dilation" to "frozen in the real time axis, but almost infinite imaginary time dilation". Which appears to be an absurdity, and yet this same formula appears in the mathematical descriptions of Neutrinos...
Based on the formula, a "Tachyon" actually does not move backwards in time.
In fact, if it was only just barely moving greater than c, and if the ridiculous formula was correct, then the particle would be FROZEN in the real time axis at the instant it exceeded light speed, and would cease to exist in "normal real space" in the very next instant; further, it would be nearly infinitely time dilated in the imaginary axis.
However, tachyons could still have instantaneous intersection with "real number" space-time at a single point in space and time, but only exactly once, assuming they are moving in a straight line.
All of this assumes the right handed limit of the Lorentz Factor exists at all, and uses the same formula.
In any case, the LIMIT does not exist...
Further mind screw...
If the right-handed formula for the Lorentz Factor is TRUE, then it is unprovable in the real world.
Here's why.
Let's say you have a particle detector, and you are trying to find the velocity of a particle which has collided with your detector.
If the tachyon has an imaginary time component and no real component, then it's velocity looks like this
v = d/t (standard average velocity formula)
v = d/(0, it)
i = sqrt(-1)
i^2 = -1
square both sides:
v^2 = d^2/(-t^2)
When this term appears in the kinetic energy equation, the only thing that will happen is the kinetic energy will appear as a negative value.
v^2 = (-d^2/t^2)
But in the real world, we can't actually tell the difference between positive and negative energy, except as a difference in direction of motion. (up vs down, left vs right, front vs backwards).
And so, the detector would not necessarily be able to tell whether the particle was a tachyon, as it's conceivable that even a "normal" particle could have exactly 1 point of contact and nothing more.
Further, it would not actually even be possible to measure the kinetic energy of a Tachyon UNLESS it was absorbed by a normal particle, since the tachyon will only be observed at a single point in space and time, but to measure kinetic energy you really need two points, OR a mass, temperature, or velocity change in a normal particle that has been fortunate enough to collide with it.
Since the tachyon will exist for exactly one instant in our time line, it is completely impossible to observe directly, regardless of it's mass or velocity, and even if it does collide with something, you won't be able to prove the energy change was caused by a tachyon, you can speculate, but you can't prove it.
Now, back to "divide by zero," since I've shown how screwed up the "real world" or at least "theoretical physics formulas" really are in the context of "divide by zero" situations.
If the right-handed formula for the Lorentz Factor is TRUE, then it is unprovable in the real world.
Here's why.
Let's say you have a particle detector, and you are trying to find the velocity of a particle which has collided with your detector.
If the tachyon has an imaginary time component and no real component, then it's velocity looks like this
v = d/t (standard average velocity formula)
v = d/(0, it)
i = sqrt(-1)
i^2 = -1
square both sides:
v^2 = d^2/(-t^2)
When this term appears in the kinetic energy equation, the only thing that will happen is the kinetic energy will appear as a negative value.
v^2 = (-d^2/t^2)
But in the real world, we can't actually tell the difference between positive and negative energy, except as a difference in direction of motion. (up vs down, left vs right, front vs backwards).
And so, the detector would not necessarily be able to tell whether the particle was a tachyon, as it's conceivable that even a "normal" particle could have exactly 1 point of contact and nothing more.
Further, it would not actually even be possible to measure the kinetic energy of a Tachyon UNLESS it was absorbed by a normal particle, since the tachyon will only be observed at a single point in space and time, but to measure kinetic energy you really need two points, OR a mass, temperature, or velocity change in a normal particle that has been fortunate enough to collide with it.
Since the tachyon will exist for exactly one instant in our time line, it is completely impossible to observe directly, regardless of it's mass or velocity, and even if it does collide with something, you won't be able to prove the energy change was caused by a tachyon, you can speculate, but you can't prove it.
Now, back to "divide by zero," since I've shown how screwed up the "real world" or at least "theoretical physics formulas" really are in the context of "divide by zero" situations.
QUOTE (Quantum_Conundrum+Aug 17 2012, 02:04 PM)
It's wrong anyway.
In Calc 1 or Calc 2, I forget which, they prove cases where it doesn't work even when both the right and and left hand limits exists and are equal.
In cases where one side of the limit does not exist, or where both sides exist but are different, it simply does not necessarily work.
In normal applications in the real world, you might not be able to tell the difference, since real world structures rarely have decimal precision approaching that of theoretical calculus, i.e. there's no true macroscopic circles in the real world, and even elementary particles may not be true circles or spheres.
Real world structures have mathematical "patches" hiding infinite limits, so that a curve representing such a structure would be "piece-wise defined," to produce continuity, rather than a single continuous formula.
I would need to re-read my calculus text, or find my old notebook and look through 2 semesters of notes, but such is the case, I just don't remember the exact examples right off hand.
well yeah . Just look at rock formations . The thing is the history is recorded in the information . That is the thing . The event order is recorded in the willy nilly of it all .
It is not willy nilly though as if you play the recording back you start to see correlations. Event streams correlate to there frame reference .
Don't go thinking like that one guy though that thinks time is just a string of events . That is like saying the wire is the information not the electrical charge that carries information . Its the wire not the signal !!! See how stupid that is . It is not right . Time is an animal it self any by the intricacies of events the animal breaths life by the movement that happens in time. Non of that negates the wire as being separate.
O.K. l;ets say no big bang . We got a "time " before any big bang/ multiple big bangs/ sputters and leaks in space time / what ever.
Now the question
Does time exist ?
I thought Tachyons were fictitious particles like poetry. Like little notes slipped under the door from the past . Time capsules and such . I think fiction writers came up with tachyons. Do you know ? Then the general populace made something out of it . Like a cult following . Do you know . Can you give me some history of its invention . The what do you call it " Etymology of the word ? What was the roots of the invention of the word Tachyon ? Can you tell Me ?
I think they can go back into the past . What is that experiment about Bob and Alice and the other guy . You know what experiment I am talking about ?
Anyway I like those little tachyon fairies . There fun to play with and they sing real pretty too . Beautiful creatures hands down . One of the objects of my affection
In Calc 1 or Calc 2, I forget which, they prove cases where it doesn't work even when both the right and and left hand limits exists and are equal.
In cases where one side of the limit does not exist, or where both sides exist but are different, it simply does not necessarily work.
In normal applications in the real world, you might not be able to tell the difference, since real world structures rarely have decimal precision approaching that of theoretical calculus, i.e. there's no true macroscopic circles in the real world, and even elementary particles may not be true circles or spheres.
Real world structures have mathematical "patches" hiding infinite limits, so that a curve representing such a structure would be "piece-wise defined," to produce continuity, rather than a single continuous formula.
I would need to re-read my calculus text, or find my old notebook and look through 2 semesters of notes, but such is the case, I just don't remember the exact examples right off hand.
well yeah . Just look at rock formations . The thing is the history is recorded in the information . That is the thing . The event order is recorded in the willy nilly of it all .
It is not willy nilly though as if you play the recording back you start to see correlations. Event streams correlate to there frame reference .
Don't go thinking like that one guy though that thinks time is just a string of events . That is like saying the wire is the information not the electrical charge that carries information . Its the wire not the signal !!! See how stupid that is . It is not right . Time is an animal it self any by the intricacies of events the animal breaths life by the movement that happens in time. Non of that negates the wire as being separate.
O.K. l;ets say no big bang . We got a "time " before any big bang/ multiple big bangs/ sputters and leaks in space time / what ever.
Now the question
Does time exist ?
I thought Tachyons were fictitious particles like poetry. Like little notes slipped under the door from the past . Time capsules and such . I think fiction writers came up with tachyons. Do you know ? Then the general populace made something out of it . Like a cult following . Do you know . Can you give me some history of its invention . The what do you call it " Etymology of the word ? What was the roots of the invention of the word Tachyon ? Can you tell Me ?
I think they can go back into the past . What is that experiment about Bob and Alice and the other guy . You know what experiment I am talking about ?
Anyway I like those little tachyon fairies . There fun to play with and they sing real pretty too . Beautiful creatures hands down . One of the objects of my affection
QUOTE (Quantum_Conundrum+Aug 16 2012, 07:00 PM)
Problem is the Calculus solution does not work in Relativity, since in order for a full "limit" to be valid it must have both the same scalar value and the same sign.
For relativity, the limits are positive infinity when approaching "c" from the left, but the limit is an infinite imaginary number with no real component when approaching "c" from the right.
Therefore the limit for v=c does not exist, and the intuitive answer is invalidated, since the right handed limit and the left handed limit neither give the same sign, nor even the same numerical axis for their solutions.
That doesn't mean calculus doesn't work. That means you can push something with mass up to the speed of light nor make something massless change speed from the speed of light.
For relativity, the limits are positive infinity when approaching "c" from the left, but the limit is an infinite imaginary number with no real component when approaching "c" from the right.
Therefore the limit for v=c does not exist, and the intuitive answer is invalidated, since the right handed limit and the left handed limit neither give the same sign, nor even the same numerical axis for their solutions.
That doesn't mean calculus doesn't work. That means you can push something with mass up to the speed of light nor make something massless change speed from the speed of light.
did you ever see that movie " The Letter " I think that was it . 2 people were leaving each other notes at different time zones. They were lovers . Now i think in the end they ended up together being a chick flick and all and having to have that climatic conclusion to get the woman off. That is beside the point .
What if the person in a past time zone believe the love of there life would manifest and if not in there time zone but in an eventual out come time zone and they had to tell them something so they would be aware of something important to them . Knowing life depended on it. Would the future lover understand the note ? Could the future lover take it to heart and follow the instructions knowing there mutual love in return .
That is how i see tachyons . Love notes of vital importance
What if the person in a past time zone believe the love of there life would manifest and if not in there time zone but in an eventual out come time zone and they had to tell them something so they would be aware of something important to them . Knowing life depended on it. Would the future lover understand the note ? Could the future lover take it to heart and follow the instructions knowing there mutual love in return .
That is how i see tachyons . Love notes of vital importance
Mekigal:
Not fictional at all.
http://en.wikipedia.org/wiki/Tachyon
though it appears standard practice to suggest imaginary mass, I see no good reason, or rather no PROVABLE reason to know exactly which variables are transformed to imaginary status.
In any case, the "Time dilation" problem still exists, and time is "dilated" in the imaginary axis when v>c...
Which is actually not discussed properly in this article.
Contrary to the article, the Lorentz Factor does NOT imply "negative time". It implies "Imaginary time," which I can prove rather easily from the time dilation formula.
Science fiction authors usually use a " real but negative time" tachyon.
Also, in Star Trek the "Warp Field" abuses the decrease in energy requirements past light speed, but the description ignores the imaginary component, and never actually explains how c is exceeded, only that the field somehow makes it possible...
Not fictional at all.
http://en.wikipedia.org/wiki/Tachyon
though it appears standard practice to suggest imaginary mass, I see no good reason, or rather no PROVABLE reason to know exactly which variables are transformed to imaginary status.
In any case, the "Time dilation" problem still exists, and time is "dilated" in the imaginary axis when v>c...
Which is actually not discussed properly in this article.
Contrary to the article, the Lorentz Factor does NOT imply "negative time". It implies "Imaginary time," which I can prove rather easily from the time dilation formula.
Science fiction authors usually use a " real but negative time" tachyon.
Also, in Star Trek the "Warp Field" abuses the decrease in energy requirements past light speed, but the description ignores the imaginary component, and never actually explains how c is exceeded, only that the field somehow makes it possible...
The negative time rate you are referring to regarding sci-fi isn't about the aging of the tachyon which is the imaginary time dilation factor you're confusing it with. Its about emission and reception events for tachyons transmitted in a particular way back to the original spatial location which effect I explain at the link
http://www.youtube.com/watch?v=8q019GXBLx0
http://www.youtube.com/watch?v=8q019GXBLx0
Here's a nice time travel lecture, not about tachyons though:
http://www.youtube.com/watch?v=mfS5l19fDwc
http://www.youtube.com/watch?v=mfS5l19fDwc
QUOTE (Quantum_Conundrum+Aug 17 2012, 06:36 PM)
Contrary to the article, the Lorentz Factor does NOT imply "negative time". It implies "Imaginary time," which I can prove rather easily from the time dilation formula.
Not sure what you mean by "imaginary time," but you might want to look at the two papers by Frank Wilcek (February 2012). If memory serves: "Classical Time Crystals" and "Quantum Time Crystals."
Wilczek proposes "Imaginary Time" which he terms "i-Time."
- RF
Not sure what you mean by "imaginary time," but you might want to look at the two papers by Frank Wilcek (February 2012). If memory serves: "Classical Time Crystals" and "Quantum Time Crystals."
Wilczek proposes "Imaginary Time" which he terms "i-Time."
- RF
QUOTE (Quantum_Conundrum+Aug 17 2012, 06:36 PM)
Mekigal:
Not fictional at all.
http://en.wikipedia.org/wiki/Tachyon
though it appears standard practice to suggest imaginary mass, I see no good reason, or rather no PROVABLE reason to know exactly which variables are transformed to imaginary status.
In any case, the "Time dilation" problem still exists, and time is "dilated" in the imaginary axis when v>c...
Which is actually not discussed properly in this article.
Contrary to the article, the Lorentz Factor does NOT imply "negative time". It implies "Imaginary time," which I can prove rather easily from the time dilation formula.
Science fiction authors usually use a " real but negative time" tachyon.
Also, in Star Trek the "Warp Field" abuses the decrease in energy requirements past light speed, but the description ignores the imaginary component, and never actually explains how c is exceeded, only that the field somehow makes it possible...
Did you check out the guy that coined the phrase in your wiki link?
Ah public cryonics , Telekinesis , Parakinesis,
Faster than the speed of light ? They can only go faster than the speed of light ?
Imaginary < Fictitious
the idea is romantic , but reality ? I don't know ? Maybe . It would tie in with my hidden language theorem .
O.K. I will settle for imaginary .
David , Dude . You ever thought about singing ? Your voice has a nice natural sound to it that could be developed into something magical . Tame the wild beast
Not fictional at all.
http://en.wikipedia.org/wiki/Tachyon
though it appears standard practice to suggest imaginary mass, I see no good reason, or rather no PROVABLE reason to know exactly which variables are transformed to imaginary status.
In any case, the "Time dilation" problem still exists, and time is "dilated" in the imaginary axis when v>c...
Which is actually not discussed properly in this article.
Contrary to the article, the Lorentz Factor does NOT imply "negative time". It implies "Imaginary time," which I can prove rather easily from the time dilation formula.
Science fiction authors usually use a " real but negative time" tachyon.
Also, in Star Trek the "Warp Field" abuses the decrease in energy requirements past light speed, but the description ignores the imaginary component, and never actually explains how c is exceeded, only that the field somehow makes it possible...
Did you check out the guy that coined the phrase in your wiki link?
Ah public cryonics , Telekinesis , Parakinesis,
Faster than the speed of light ? They can only go faster than the speed of light ?
Imaginary < Fictitious
the idea is romantic , but reality ? I don't know ? Maybe . It would tie in with my hidden language theorem .
O.K. I will settle for imaginary .
David , Dude . You ever thought about singing ? Your voice has a nice natural sound to it that could be developed into something magical . Tame the wild beast
QUOTE (Quantum_Conundrum+Aug 17 2012, 02:36 PM)
Let's take "1/X"
Lim (1/X) as X->0- = - Infinity.
This reads, "The limit of "1/X" as X approaches Zero from the left equals negative infinity."
Lim (1/X) as X->0(plus) = Infinity
This reads, "The limit of "1/X" as X approaches Zero from the Right equals infinity."
The left hand limit and the right hand limit are not equal, therefore:
Lim (1/X) as X->0 = DNE.
This reads, "The limit of "1/X" as X approaches Zero does not exist."
The left-hand limit for Lorentz Factor in Relativity is reversed signed, and heavily right shifted version of the left hand limit, "lim (1/X) as X->0-".
The right-hand limit for the Lorentz Factor is the same as the right handed limit of 1/X, but heavily right-shifted, and of course rotated a full 90 degrees into the imaginary axis.
Left hand limit as v->c is (infinity, 0 * i).
Right hand limit as v->c is (0, Infinity * i).
The values are not equal, therefore:
Limit of the Lorentz Factor as v approaches c does not exist...
This fact is simply ignored in almost all physics discussions, because it's assumed that continuous acceleration could never meet or exceed c.
However, in Quantum Theory nothing is continuous, information and energy are transferred in discreet packets. Therefore it's conceivable that a massive particle could somehow "Jump" c, since in reality some particles "jump" some finite numbers anyway, and exist only at specific mass/energy values, and never between those values.
Because this is the case, the formula for Relativity appears to produce incredibly freaky results IF and when this phenomena ever occurs, because the particle would instantly jump from "almost infinite real time dilation with no imaginary time dilation" to "frozen in the real time axis, but almost infinite imaginary time dilation". Which appears to be an absurdity, and yet this same formula appears in the mathematical descriptions of Neutrinos...
Based on the formula, a "Tachyon" actually does not move backwards in time.
In fact, if it was only just barely moving greater than c, and if the ridiculous formula was correct, then the particle would be FROZEN in the real time axis at the instant it exceeded light speed, and would cease to exist in "normal real space" in the very next instant; further, it would be nearly infinitely time dilated in the imaginary axis.
However, tachyons could still have instantaneous intersection with "real number" space-time at a single point in space and time, but only exactly once, assuming they are moving in a straight line.
All of this assumes the right handed limit of the Lorentz Factor exists at all, and uses the same formula.
In any case, the LIMIT does not exist...
Quantum Conundrum,
I find what you are pointing out extremely interesting. I have in the past noticed certain odd aspects about objects which exist in this (what up until now I thought was a mathematically legitimate) limit, and it may be pertinent to mention these here:
1) Objects for which v=c "observe" their own duration of existence in spacetime to be exactly zero, because a zero proper time implies that the moment they are "observed" by spacetime observers to come into existence and the moment they are "observed" to go out of existence are in their frame one and the same.
Some people I have discussed this with have dismissed the significance of this argument because it assumes that it makes sense to speak of the frames of such objects. They interpret the fact that no spacetime observer can transform to those frames as meaning that it makes no sense to speak of such frames. In my view, this is backwards: It does make sense to speak of such frames, and in particular, one can precisely say about such frames that no spacetime observer can transform to them. Moreover, one can take the above observation as a possible explanation for why this is not possible: In order to transform to such a frame you would, in effect, have to transform to a frame in which you observe your own duration of existence in spacetime to be zero. There exists no spacetime observer frame for which this could possibly be true, and hence, you can't transform to this kind of a frame.
2) The four vectors associated with objects for which v=c are not true four vectors, because, being null vectors, one of their components can *always* be expressed in terms of the other three. If this doesn't seem clear, consider this analogy: suppose that you wanted to represent in ordinary Euclidean space in Cartesian coordinates the "three vector" (x,y,r) where r was defined as sqr(x^2+y^2). In one sense, the vector doesn't really exist anywhere in that three space, because you also need to specify a z-coordinate to put it at a definite location, but once you supply one, say z_0, this vector only really exists in the plane z_0 i.e. a 2-dimensional subspace of the original Euclidean 3-space. The point is, because you can express one of the components in terms of the others, it is redundant, this three vector is really just the two-vector (x,y). I see no reason why the analogous argument should not also hold for null-four vectors in Minkowski spacetime.
These and some other arguments have convinced me that objects for which v=c don't exist in Minkoswki spacetime at all, but rather in a 2+1 dimensional "subspace", which I have taken the liberty to call areatime.
Before this is dismissed as just another crackpot idea, let me mention that there is a way to "understand" quantum mechanics completely independently from the above arguments by considering it as the theoretical description of observations of spacetime observers of objects which exist in a 2+1 subspace before they emerge in spacetime (a process we currently call a "measurement"). For further details, you are invited to follow the thread I started, I don't want to further distract from your arguments.
Getting back to your observations, I have long asked myself how one could show mathematically that the limit v=c describes objects which don't exist in Minkowski spacetime. Thanks to you I realize that I have been making at least one incorrect assumption all along, namely that v=c constitutes a legitimate mathematical limit. Allow me to express my gratitude for having learned something significant from you.
What is especially interesting is how simple your argument it is, I wonder why I didn't notice this before. But then perhaps someone reading what I wrote above might ask themselves the same question.
Anyway, thank you again and keep up thinking independently.
Lim (1/X) as X->0- = - Infinity.
This reads, "The limit of "1/X" as X approaches Zero from the left equals negative infinity."
Lim (1/X) as X->0(plus) = Infinity
This reads, "The limit of "1/X" as X approaches Zero from the Right equals infinity."
The left hand limit and the right hand limit are not equal, therefore:
Lim (1/X) as X->0 = DNE.
This reads, "The limit of "1/X" as X approaches Zero does not exist."
The left-hand limit for Lorentz Factor in Relativity is reversed signed, and heavily right shifted version of the left hand limit, "lim (1/X) as X->0-".
The right-hand limit for the Lorentz Factor is the same as the right handed limit of 1/X, but heavily right-shifted, and of course rotated a full 90 degrees into the imaginary axis.
Left hand limit as v->c is (infinity, 0 * i).
Right hand limit as v->c is (0, Infinity * i).
The values are not equal, therefore:
Limit of the Lorentz Factor as v approaches c does not exist...
This fact is simply ignored in almost all physics discussions, because it's assumed that continuous acceleration could never meet or exceed c.
However, in Quantum Theory nothing is continuous, information and energy are transferred in discreet packets. Therefore it's conceivable that a massive particle could somehow "Jump" c, since in reality some particles "jump" some finite numbers anyway, and exist only at specific mass/energy values, and never between those values.
Because this is the case, the formula for Relativity appears to produce incredibly freaky results IF and when this phenomena ever occurs, because the particle would instantly jump from "almost infinite real time dilation with no imaginary time dilation" to "frozen in the real time axis, but almost infinite imaginary time dilation". Which appears to be an absurdity, and yet this same formula appears in the mathematical descriptions of Neutrinos...
Based on the formula, a "Tachyon" actually does not move backwards in time.
In fact, if it was only just barely moving greater than c, and if the ridiculous formula was correct, then the particle would be FROZEN in the real time axis at the instant it exceeded light speed, and would cease to exist in "normal real space" in the very next instant; further, it would be nearly infinitely time dilated in the imaginary axis.
However, tachyons could still have instantaneous intersection with "real number" space-time at a single point in space and time, but only exactly once, assuming they are moving in a straight line.
All of this assumes the right handed limit of the Lorentz Factor exists at all, and uses the same formula.
In any case, the LIMIT does not exist...
Quantum Conundrum,
I find what you are pointing out extremely interesting. I have in the past noticed certain odd aspects about objects which exist in this (what up until now I thought was a mathematically legitimate) limit, and it may be pertinent to mention these here:
1) Objects for which v=c "observe" their own duration of existence in spacetime to be exactly zero, because a zero proper time implies that the moment they are "observed" by spacetime observers to come into existence and the moment they are "observed" to go out of existence are in their frame one and the same.
Some people I have discussed this with have dismissed the significance of this argument because it assumes that it makes sense to speak of the frames of such objects. They interpret the fact that no spacetime observer can transform to those frames as meaning that it makes no sense to speak of such frames. In my view, this is backwards: It does make sense to speak of such frames, and in particular, one can precisely say about such frames that no spacetime observer can transform to them. Moreover, one can take the above observation as a possible explanation for why this is not possible: In order to transform to such a frame you would, in effect, have to transform to a frame in which you observe your own duration of existence in spacetime to be zero. There exists no spacetime observer frame for which this could possibly be true, and hence, you can't transform to this kind of a frame.
2) The four vectors associated with objects for which v=c are not true four vectors, because, being null vectors, one of their components can *always* be expressed in terms of the other three. If this doesn't seem clear, consider this analogy: suppose that you wanted to represent in ordinary Euclidean space in Cartesian coordinates the "three vector" (x,y,r) where r was defined as sqr(x^2+y^2). In one sense, the vector doesn't really exist anywhere in that three space, because you also need to specify a z-coordinate to put it at a definite location, but once you supply one, say z_0, this vector only really exists in the plane z_0 i.e. a 2-dimensional subspace of the original Euclidean 3-space. The point is, because you can express one of the components in terms of the others, it is redundant, this three vector is really just the two-vector (x,y). I see no reason why the analogous argument should not also hold for null-four vectors in Minkowski spacetime.
These and some other arguments have convinced me that objects for which v=c don't exist in Minkoswki spacetime at all, but rather in a 2+1 dimensional "subspace", which I have taken the liberty to call areatime.
Before this is dismissed as just another crackpot idea, let me mention that there is a way to "understand" quantum mechanics completely independently from the above arguments by considering it as the theoretical description of observations of spacetime observers of objects which exist in a 2+1 subspace before they emerge in spacetime (a process we currently call a "measurement"). For further details, you are invited to follow the thread I started, I don't want to further distract from your arguments.
Getting back to your observations, I have long asked myself how one could show mathematically that the limit v=c describes objects which don't exist in Minkowski spacetime. Thanks to you I realize that I have been making at least one incorrect assumption all along, namely that v=c constitutes a legitimate mathematical limit. Allow me to express my gratitude for having learned something significant from you.
What is especially interesting is how simple your argument it is, I wonder why I didn't notice this before. But then perhaps someone reading what I wrote above might ask themselves the same question.
Anyway, thank you again and keep up thinking independently.
QUOTE (Mekigal+Aug 17 2012, 03:50 PM)
I thought Tachyons were fictitious particles like poetry. Like little notes slipped under the door from the past . Time capsules and such . I think fiction writers came up with tachyons. Do you know ?
My educated layman understanding is that tachyons arise from the mathematics of 26 dimensional bosonic string theory. In fact, it is the theoretical existence of these particles that is considered the biggest flaw in that particular flavor of string theory. (Although without 26-D string theory we would no more have the later versions of string theory than we would have the valence model of the atom without the flawed Bohr model.)
- RF
My educated layman understanding is that tachyons arise from the mathematics of 26 dimensional bosonic string theory. In fact, it is the theoretical existence of these particles that is considered the biggest flaw in that particular flavor of string theory. (Although without 26-D string theory we would no more have the later versions of string theory than we would have the valence model of the atom without the flawed Bohr model.)
- RF
As we approach the speed of light time slows and distances contract. At the speed of light, time stops and distance becomes a point. If we theoretically continue to increase the velocity beyond C, time reverses from zero and begins to speed up, but in a negative time direction Distance starts to expand but in a negative direction.
Mathematically, positive space-time (<C) and negative space-time (>C) will add. The result of tachyons within our space-time would be less contraction of space-time than expected from purely mass and velocity calculations.
If we had a star with a given space-time well, due to mass M, and added Tachyons its well would appear to reverse and get shallower than expected of the mass.It would almost appear like anti-gravity. Time will start to get faster due to the negative time.
Say we were moving faster than C. We will not be isolated from inertial space-time but rather would see the impact of inertial reference moving less than C. This will add positive to the negative time reference. Things would appear less negative due to the addition. In that alternate place, faster than C, some things appear more contracted then they should be in >C space-time; place-holders of inertial reality.
Mathematically, positive space-time (<C) and negative space-time (>C) will add. The result of tachyons within our space-time would be less contraction of space-time than expected from purely mass and velocity calculations.
If we had a star with a given space-time well, due to mass M, and added Tachyons its well would appear to reverse and get shallower than expected of the mass.It would almost appear like anti-gravity. Time will start to get faster due to the negative time.
Say we were moving faster than C. We will not be isolated from inertial space-time but rather would see the impact of inertial reference moving less than C. This will add positive to the negative time reference. Things would appear less negative due to the addition. In that alternate place, faster than C, some things appear more contracted then they should be in >C space-time; place-holders of inertial reality.
QUOTE (Raphie Frank+Aug 19 2012, 02:14 PM)
My educated layman understanding is that tachyons arise from the mathematics of 26 dimensional bosonic string theory. In fact, it is the theoretical existence of these particles that is considered the biggest flaw in that particular flavor of string theory. (Although without 26-D string theory we would no more have the later versions of string theory than we would have the valence model of the atom without the flawed Bohr model.)
- RF
interesting Frankie, Dude you are the man . That Bohr he was right there doing L.S.D. with Timothy Leary right ? Was he . Did I interpret that right ? I was very young and impressionable . I get the feeling the whole Berkley movement was revolving around the development of theses ideas .
So something said : Transform your frame so you could observe your own duration .
You ever do L.S.D.
I did a couple times when I was 14. I still remember what it felt like . Just saying???
That is the same place my language lives too. I call it Advanced communication . It is direct and to the point and it happens before any normal types of communication . Instant. So instant that a single thought answered before you can blink your eye and if you do you miss it . It is an altered state than normal comprehension and I am saying right now it is real ! It is not fictitious. I think it drives people to insanity or people that realize it flip out and appear to be crazy . Totally related to people that hear voices in there head and find them selves doing the dastardly based on theses voices .
It is an alternate reality. I know it is . I continually test the language. It is not quite something you can quite put in a test tube setting for awareness of the observation by the ones being observed interpret the natural candid flow of information going back and forth . Like under scrutiny of a test the creature does just like any creature . It hides . Just like if you and someone were talking about some one and they sneaked up on you and who you you were talking to . You would naturally pause right and go Ah. Interrupted by the observation of the center of the conversation .
Anyway If I seem a little more coherent as of late it is because I have been living in the mundane world of drag time. Regular human perception time of conscious task orientation . Not near as dreamy but good for painting doors and talking to every day people . Yeah .
Disclaimer :
- RF
interesting Frankie, Dude you are the man . That Bohr he was right there doing L.S.D. with Timothy Leary right ? Was he . Did I interpret that right ? I was very young and impressionable . I get the feeling the whole Berkley movement was revolving around the development of theses ideas .
So something said : Transform your frame so you could observe your own duration .
You ever do L.S.D.
I did a couple times when I was 14. I still remember what it felt like . Just saying???
That is the same place my language lives too. I call it Advanced communication . It is direct and to the point and it happens before any normal types of communication . Instant. So instant that a single thought answered before you can blink your eye and if you do you miss it . It is an altered state than normal comprehension and I am saying right now it is real ! It is not fictitious. I think it drives people to insanity or people that realize it flip out and appear to be crazy . Totally related to people that hear voices in there head and find them selves doing the dastardly based on theses voices .
It is an alternate reality. I know it is . I continually test the language. It is not quite something you can quite put in a test tube setting for awareness of the observation by the ones being observed interpret the natural candid flow of information going back and forth . Like under scrutiny of a test the creature does just like any creature . It hides . Just like if you and someone were talking about some one and they sneaked up on you and who you you were talking to . You would naturally pause right and go Ah. Interrupted by the observation of the center of the conversation .
Anyway If I seem a little more coherent as of late it is because I have been living in the mundane world of drag time. Regular human perception time of conscious task orientation . Not near as dreamy but good for painting doors and talking to every day people . Yeah .
Disclaimer :
QUOTE (waitedavid137+Aug 17 2012, 04:07 PM)
That doesn't mean calculus doesn't work. That means you can push something with mass up to the speed of light nor make something massless change speed from the speed of light.
can water change the speed of light / light passes threw water at what % of the speed of light . Maybe I didn't understand your statement ? Clarify please .
Also translucent materials ?
That makes me wonder about atmosphere. Is there difference in the speed of light in atmosphere verses deep cold space . Time frame difference maybe ? Does light travel at c once it penetrates atmosphere. How about thicker atmospheres than earth like Venus or even gas planets like Jupiter.
Could the slow down be attributed to time dilation due to the medium penetrated .
Take black and its absorption and the heated results of the object that is black. Could that be considered a time dilation it self . Where as the excessive slow down actually creates the heat. The friction caused by abrupt dilation of time from one frame to the next. So the heat on the other side of a plain of glass is a by product of the reduced time frame of the light caused directly by the reduction of the speed of light yet it is not a reduction of speed at all but a time dilation and the excesses of time lost is what causes the heat . Friction from time slowing down to its new reference frame ?
What do think Dave137 . Kawackery at its finest. Get your pistols out and shoot the dung out of that one .
Dave maybe you can do a mock up with math . It seems it should be able to be checked. The heat build up against the reduction of the speed of light to see if they off set each other . Conservation of energy test . I think we know the speed of light threw different mediums so all you have to do is measure the heat of the object before and after a beam of light went threw it . Depends on what type of light I imagine . I am thinking full spectrum light right now , but the testing could be expanded to individual frequencies of light considering different materials absorb different spectrum.
It could be another proof for time dilation if they match up to relativity?
Speculations of a crank
can water change the speed of light / light passes threw water at what % of the speed of light . Maybe I didn't understand your statement ? Clarify please .
Also translucent materials ?
That makes me wonder about atmosphere. Is there difference in the speed of light in atmosphere verses deep cold space . Time frame difference maybe ? Does light travel at c once it penetrates atmosphere. How about thicker atmospheres than earth like Venus or even gas planets like Jupiter.
Could the slow down be attributed to time dilation due to the medium penetrated .
Take black and its absorption and the heated results of the object that is black. Could that be considered a time dilation it self . Where as the excessive slow down actually creates the heat. The friction caused by abrupt dilation of time from one frame to the next. So the heat on the other side of a plain of glass is a by product of the reduced time frame of the light caused directly by the reduction of the speed of light yet it is not a reduction of speed at all but a time dilation and the excesses of time lost is what causes the heat . Friction from time slowing down to its new reference frame ?
What do think Dave137 . Kawackery at its finest. Get your pistols out and shoot the dung out of that one .
Dave maybe you can do a mock up with math . It seems it should be able to be checked. The heat build up against the reduction of the speed of light to see if they off set each other . Conservation of energy test . I think we know the speed of light threw different mediums so all you have to do is measure the heat of the object before and after a beam of light went threw it . Depends on what type of light I imagine . I am thinking full spectrum light right now , but the testing could be expanded to individual frequencies of light considering different materials absorb different spectrum.
It could be another proof for time dilation if they match up to relativity?
Speculations of a crank
That almost makes sense. Think about it . The rate of decay on an object from southern exposure of sun light or the decay of an object in general . Were as the condensed energy is a condensation of time it self by matter being in a different time dilation than light .
So instead of it being a reduction of speed and matter being in a stable state , but rather matter is in a different time dilation then pure energy or light . because of the reduction of speed except it is not speed but still matter is moving at the speed of light but the time reference is what is really changing . Time slows down depending on the decay rate of the object and the decay rate is at the constant of c except it is in a different frame reference of time lapsing due to the over all speed of frequency with in the object it self
So energy is gained or lost by the change in reference frames going up or down .
Just imagine if your were going the speed of light and time of an hour was years in earth frame and then you came to an instant stop to the earth frame . The friction would be off the charts i would think and if so could it be the dilation of time it self causing ? Would it be considered kinetic energy ? I got to look up kinetic energy . See what exactly what that is . Maybe it is the excessive time lost ? Not that it is lost but rather the rate of decay has changed but all still moving at the speed of light and as time slows down to its new reference it gives off energy and that energy is the time loss
So instead of it being a reduction of speed and matter being in a stable state , but rather matter is in a different time dilation then pure energy or light . because of the reduction of speed except it is not speed but still matter is moving at the speed of light but the time reference is what is really changing . Time slows down depending on the decay rate of the object and the decay rate is at the constant of c except it is in a different frame reference of time lapsing due to the over all speed of frequency with in the object it self
So energy is gained or lost by the change in reference frames going up or down .
Just imagine if your were going the speed of light and time of an hour was years in earth frame and then you came to an instant stop to the earth frame . The friction would be off the charts i would think and if so could it be the dilation of time it self causing ? Would it be considered kinetic energy ? I got to look up kinetic energy . See what exactly what that is . Maybe it is the excessive time lost ? Not that it is lost but rather the rate of decay has changed but all still moving at the speed of light and as time slows down to its new reference it gives off energy and that energy is the time loss
I don't know to say it . I want to say or ask ? Is there energy gain in some other form from time dialing down to slower references of time ?
QUOTE (Mekigal+Aug 20 2012, 02:04 PM)
can water change the speed of light / light passes threw water at what % of the speed of light . Maybe I didn't understand your statement ? Clarify please .
Also translucent materials ?
That makes me wonder about atmosphere. Is there difference in the speed of light in atmosphere verses deep cold space . Time frame difference maybe ? Does light travel at c once it penetrates atmosphere. How about thicker atmospheres than earth like Venus or even gas planets like Jupiter.
Could the slow down be attributed to time dilation due to the medium penetrated .
Take black and its absorption and the heated results of the object that is black. Could that be considered a time dilation it self . Where as the excessive slow down actually creates the heat. The friction caused by abrupt dilation of time from one frame to the next. So the heat on the other side of a plain of glass is a by product of the reduced time frame of the light caused directly by the reduction of the speed of light yet it is not a reduction of speed at all but a time dilation and the excesses of time lost is what causes the heat . Friction from time slowing down to its new reference frame ?
What do think Dave137 . Kawackery at its finest. Get your pistols out and shoot the dung out of that one .
Dave maybe you can do a mock up with math . It seems it should be able to be checked. The heat build up against the reduction of the speed of light to see if they off set each other . Conservation of energy test . I think we know the speed of light threw different mediums so all you have to do is measure the heat of the object before and after a beam of light went threw it . Depends on what type of light I imagine . I am thinking full spectrum light right now , but the testing could be expanded to individual frequencies of light considering different materials absorb different spectrum.
It could be another proof for time dilation if they match up to relativity?
Speculations of a crank
Materials don't actually change the speed of the light. What happens is the photons travel at c between the material's atoms and loose a small time between their destruction and creation upon absorption and emission events. The overall effect is to have a slowed transit time through the material. But while they are actually in transit between the atoms they do still travel at c. You can't change this.
Also translucent materials ?
That makes me wonder about atmosphere. Is there difference in the speed of light in atmosphere verses deep cold space . Time frame difference maybe ? Does light travel at c once it penetrates atmosphere. How about thicker atmospheres than earth like Venus or even gas planets like Jupiter.
Could the slow down be attributed to time dilation due to the medium penetrated .
Take black and its absorption and the heated results of the object that is black. Could that be considered a time dilation it self . Where as the excessive slow down actually creates the heat. The friction caused by abrupt dilation of time from one frame to the next. So the heat on the other side of a plain of glass is a by product of the reduced time frame of the light caused directly by the reduction of the speed of light yet it is not a reduction of speed at all but a time dilation and the excesses of time lost is what causes the heat . Friction from time slowing down to its new reference frame ?
What do think Dave137 . Kawackery at its finest. Get your pistols out and shoot the dung out of that one .
Dave maybe you can do a mock up with math . It seems it should be able to be checked. The heat build up against the reduction of the speed of light to see if they off set each other . Conservation of energy test . I think we know the speed of light threw different mediums so all you have to do is measure the heat of the object before and after a beam of light went threw it . Depends on what type of light I imagine . I am thinking full spectrum light right now , but the testing could be expanded to individual frequencies of light considering different materials absorb different spectrum.
It could be another proof for time dilation if they match up to relativity?
Speculations of a crank
Materials don't actually change the speed of the light. What happens is the photons travel at c between the material's atoms and loose a small time between their destruction and creation upon absorption and emission events. The overall effect is to have a slowed transit time through the material. But while they are actually in transit between the atoms they do still travel at c. You can't change this.
zigzagging then ? Traveling a longer distance? When you say transit ?
QUOTE (Mekigal+)
Also translucent materials ?
zigzagging then ? Traveling a longer distance? When you say transit?
When we speak of "refraction," we say that "the speed of light is slower in glass," but in fact, the speed of light does not change in the material.
Transparency allows light to pass through the material without appreciable scattering so that images are seen clearly. Translucency allows light to pass through but diffusing it so that images are not clearly visible.
When moving through a clear transparent medium, such as glass, the absorption and reemission explanation for slowing light just doesn’t cut it.
Normally, in glass, absorption in the visible spectrum is extremely small. That’s what makes it transparent. To interpret refraction (Snell's law; index of refraction) and the (apparent) slower speed of light in glass in terms of quantum mechanics you have to think of the medium as a field.
The electrons behave like little oscillators. When the energy from the incoming light exhorts a force on the electrons, they move (oscillate) and this creates a modified field, and as it turns out it’s modified in such a way that the field in the glass appears to be moving at a slower speed.
"As the wave passes through, the fields busily polarize and magnetize all the molecules, and the resulting (oscillating) dipoles create their own electric and magnetic fields. These combine with the original fields in such a way as to create a single wave with the same frequency, but a different speed." ~ David J. Griffiths
http://cua.mit.edu/8.421_S08/Reading/Feyman_refr_index.pdf
QUOTE (Wikipedia+)
When light propagates through a material, it travels slower than the vacuum speed. This is a change in the phase velocity of the light and is manifested in physical effects such as refraction. This reduction in speed is quantified by the ratio between c and the phase velocity.
At the microscale, an electromagnetic wave's phase speed is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.
Group speed is equal to phase speed only when the refractive index is a constant when the phase velocity varies with frequency, velocities differ and the medium is called dispersive.
At the microscale, an electromagnetic wave's phase speed is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) proportional to the electric susceptibility of the medium. (Similarly, the magnetic field creates a disturbance proportional to the magnetic susceptibility.) As the electromagnetic fields oscillate in the wave, the charges in the material will be "shaken" back and forth at the same frequency.
Group speed is equal to phase speed only when the refractive index is a constant when the phase velocity varies with frequency, velocities differ and the medium is called dispersive.
QUOTE (Mekigal+Aug 20 2012, 10:04 PM)
zigzagging then ? Traveling a longer distance? When you say transit ?
No, its due to a lag in absorption emission. In material like air water or other mostly there is just empty space. In this empty space inside the material the speed of light is c. When the photons of the light pass through the electrons there is a probabilistic scattering event where for something clear like air or water the light that it is clear to has the best chance of the absorption emission scattering event ending in a photon continuing along its way on the other side of the electron. The probabilistic time between absorption emission events accumulates a lag in how long it takes the light to get through the material. In between the electrons of the material the vast majority of what the photon sees is empty space so its real speed inside is still c, but overall its speed is lowers by some factor c/n where n is called the index of refraction for the material. This n is characteristic of the material as the energy levels and configurations of the electrons inside are unique to a given material, but the index of refraction n will also have some wavelength dependence. Really everything I've said is way oversimplified as I'm giving you whats mostly a classical particle picture of whats really a quantum wave-particle scattering problem but its the best I think you'll be able to get anything from since the wave picture looking very different requires understanding of superposition among other things.
No, its due to a lag in absorption emission. In material like air water or other mostly there is just empty space. In this empty space inside the material the speed of light is c. When the photons of the light pass through the electrons there is a probabilistic scattering event where for something clear like air or water the light that it is clear to has the best chance of the absorption emission scattering event ending in a photon continuing along its way on the other side of the electron. The probabilistic time between absorption emission events accumulates a lag in how long it takes the light to get through the material. In between the electrons of the material the vast majority of what the photon sees is empty space so its real speed inside is still c, but overall its speed is lowers by some factor c/n where n is called the index of refraction for the material. This n is characteristic of the material as the energy levels and configurations of the electrons inside are unique to a given material, but the index of refraction n will also have some wavelength dependence. Really everything I've said is way oversimplified as I'm giving you whats mostly a classical particle picture of whats really a quantum wave-particle scattering problem but its the best I think you'll be able to get anything from since the wave picture looking very different requires understanding of superposition among other things.
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