AlphaNumeric
I would hold you in very high regards if you can accept you were wrong... Thus i present the following >
''The idea of GUT is highly misunderstood, as they are neither Grand nor Unified... anything can change this system at any time...''
And Hawkings says
''Even though we know the relevant laws that govern the universe, we do not know how they will operate in the long-run... into the future. This is the law of Chaos.''
So, how is that i have misunderstood what he says... What the prof. says here is quite reasonable...
For those wondering, this is NeoNo.1's continuation of this thread. He's been demonstrated to be wrong there so he does as many cranks do, starts the discussion elsewhere to avoid acknowledging it.
NeoNo.1, you are interpreting Hawking's comments to say "Since GUTs contain chaotic systems, we cannot formulate a GUT". This is wrong. Newtonian gravity, as I've explained several times in the other thread, contains chaotic systems but Newton still formulated it over 300 years ago.
Hawking says "Even though we know the relevant laws that govern the universe, we do not know how they will operate in the long-run... into the future. This is the law of Chaos.''
I do not argue with this. He is saying that while you can write down the governing equations for a dynamical system, solving the equations to get an explicit expression for one or more of the objects within the system is not possible and in some cases (ie chaotic ones) the system is extremely sensitive to initial conditions.
I don't deny any of that, I understand that part of chaotic systems (the same can't be said for many people on here who buzzword drop 'chaos' into their posts). However, that doesn't have any corrollary when it comes to trying to find a GUT for fundamental particles. Finding such a GUT would involve finding the unifying governing equations for the 3 quantized forces. Notice that 'chaos' doesn't preclude that. Chaos would preclude solving the governing equations analytically (though not all analytically unsolvable systems are chaotic!).
See the difference? BM1957 and I have explained it to you a few times now but you seem totally unable to grasp the simple difference, even when given an explicit example. Instead, you decide to post a new thread about it and draw even more attention to the fact you don't understand.
It's no skin off my nose, it's not my job to stop you making an idiot of yourself. Infact, I consider it to be quite the opposite
Job done then.
NeoNo.1, you are interpreting Hawking's comments to say "Since GUTs contain chaotic systems, we cannot formulate a GUT". This is wrong. Newtonian gravity, as I've explained several times in the other thread, contains chaotic systems but Newton still formulated it over 300 years ago.
Hawking says "Even though we know the relevant laws that govern the universe, we do not know how they will operate in the long-run... into the future. This is the law of Chaos.''
I do not argue with this. He is saying that while you can write down the governing equations for a dynamical system, solving the equations to get an explicit expression for one or more of the objects within the system is not possible and in some cases (ie chaotic ones) the system is extremely sensitive to initial conditions.
I don't deny any of that, I understand that part of chaotic systems (the same can't be said for many people on here who buzzword drop 'chaos' into their posts). However, that doesn't have any corrollary when it comes to trying to find a GUT for fundamental particles. Finding such a GUT would involve finding the unifying governing equations for the 3 quantized forces. Notice that 'chaos' doesn't preclude that. Chaos would preclude solving the governing equations analytically (though not all analytically unsolvable systems are chaotic!).
See the difference? BM1957 and I have explained it to you a few times now but you seem totally unable to grasp the simple difference, even when given an explicit example. Instead, you decide to post a new thread about it and draw even more attention to the fact you don't understand.
It's no skin off my nose, it's not my job to stop you making an idiot of yourself. Infact, I consider it to be quite the opposite
Job done then.
OH MY GOD. You are so incorrect. I said that (I) personally don't think that a GUT will ever evolve from our calculations, simply because Hawkings highlighted a very real cause not to trust everything in our attempts. Where does that leave the evidence you so amptly required, because, even though i proved your initial arguement wron, you also attempted to increase your pathalogical lie even further by involving subjects which i wasn't talking about. I was simply qouting Mr. Hawkings and then translating, in the most likely friggin translation. I can't see anything else emerging out of what he is saying, and neither have you provided any other translation, all you have said is that my translation is wrong. Prove it. Qoute the lines i metioned, and then give me your translation.... I am dieing for this one! Come on!
Neo
Neo
I side with AN's opinion; I think you are suffering from "confirmation bias" when you read Hawking's and other's remarks that appear on the surface to support your partially thoughtout position.
QUOTE (NeoNo.1+Sep 12 2007, 05:03 PM)
I said that (I) personally don't think that a GUT will ever evolve from our calculations, simply because Hawkings highlighted a very real cause not to trust everything in our attempts.
We've already got a unification for the weak force and the electromagnetic force, which is experimentally verified.
We've already got a unification for the weak force and the electromagnetic force, which is experimentally verified.
QUOTE (NeoNo.1+Sep 12 2007, 05:03 PM)
. Where does that leave the evidence you so amptly required, because, even though i proved your initial arguement wron, you also attempted to increase your pathalogical lie even further by involving subjects which i wasn't talking about
I mentioned Newton as an example of being able to derive a model which is chaotic. An example of how your initial claim was incorrect.
QUOTE (NeoNo.1+Sep 12 2007, 05:03 PM)
I was simply qouting Mr. Hawkings and then translating, in the most likely friggin translation.
And you know it's the 'most likely friggin translation' because? Your extensive knowledge of physics, particularly GUTs and chaos?
QUOTE (NeoNo.1+Sep 12 2007, 05:03 PM)
I can't see anything else emerging out of what he is saying, and neither have you provided any other translation, all you have said is that my translation is wrong.
I have provided an alternative 'translation' to what he said. It's in the thread this thread sprouted from, other people in that thread managed to understand, why can't you? Actually think when you read my posts, if you are reading my posts at all.
QUOTE (NeoNo.1+Sep 12 2007, 05:03 PM)
Prove it. Qoute the lines i metioned, and then give me your translation.... I am dieing for this one! Come on!
I see you're employing Zephir's logic. You ignore things people say to you, then demand they present you with information they've already told you. I guess it's a standard crank method.
NoCleverName
Yeh... I kinda gathered you would. It wasn't much of a surprise really. Just another sheep AlphaNumeric... He must indeed be feeling smug of himself right now.
But, as i said, none of this will deter me from my fight against this total waste of space... I stick my ground yet, call me the rebelion.
Neo
Yeh... I kinda gathered you would. It wasn't much of a surprise really. Just another sheep AlphaNumeric... He must indeed be feeling smug of himself right now.
But, as i said, none of this will deter me from my fight against this total waste of space... I stick my ground yet, call me the rebelion.
Neo
QUOTE (NeoNo.1+Sep 12 2007, 05:53 PM)
Just another sheep AlphaNumeric
Ah, the usual crank/nut logic of "Anyone who disagrees with me is a sheep! They're in some kind of cahoots together!". Couldn't possibly be that more than one person has a viable reason to disagree with you, could it
Ah, the usual crank/nut logic of "Anyone who disagrees with me is a sheep! They're in some kind of cahoots together!". Couldn't possibly be that more than one person has a viable reason to disagree with you, could it
QUOTE (NeoNo.1+Sep 12 2007, 05:53 PM)
He must indeed be feeling smug of himself right now.
Not really, since I don't feed my ego from showing online nuts to be idiots. It's so easy it's not a challenge and so not ego bolstering.
QUOTE (NeoNo.1+Sep 12 2007, 05:53 PM)
But, as i said, none of this will deter me from my fight against this total waste of space
As my feedback demonstrates, people consider my posts on the whole a positive thing. If anyone wishes to discuss any particular part of physics or maths I'm always up for that as discussions on geometry/topology or Lie groups have demonstrated in the past. It's just too few people here are interested in that, too many are cranks who prefer starting threads about their personal theory of everything which never amounts to anything.
Of course I could start a thread about the specifics of some part of mainstream science and post a lot about it, to avoid being called a 'waste of space', but no doubt I'd be accussed of showing off or being a walking advert for mainstream physics. Catch 22.
Of course I could start a thread about the specifics of some part of mainstream science and post a lot about it, to avoid being called a 'waste of space', but no doubt I'd be accussed of showing off or being a walking advert for mainstream physics. Catch 22.
QUOTE (AlphaNumeric+Sep 12 2007, 04:29 PM)
And you know it's the 'most likely friggin translation' because? Your extensive knowledge of physics, particularly GUTs and chaos?
Perhaps he studied the friggin Bayesian theory and sleeps with a copy of Treasure Island so he knows that Hawkings fellow will soon lead him to treasure, Yarrr!
(Apologies to residents of Cornwall.)
Perhaps he studied the friggin Bayesian theory and sleeps with a copy of Treasure Island so he knows that Hawkings fellow will soon lead him to treasure, Yarrr!
(Apologies to residents of Cornwall.)
Then resite your explanations please... And i repeat for a second time, will you please qoute what i said, and tell me an alternative anwer.
If you are a scientist at all, then please respond to previous knowledge. This is what professionals do. They evaluate all other perspectives.
If anyone else is willing to be decieved by this crank, please speak up. I've already had two missionary's working for him, so please, the more the merrier... But please, consider my arguement before dismissing it with contempt. Do not be biast.
I Will admit, AlphaN has a wider veiw of mathematics than i ever can... I envy him for this view of a mathematical world... But at any time, i would be willing to see reason, but because he shows me with the same dogmatism, similar to the way he has treated several people, perhaps even more, and yet, we know he is intelligent... Nothing defies this truth... It is just that with his intelligence, he is rather clouded from the fact there are equally intelligent folks out there that can see errors inhis own work.
He has had a great deal to say and point out errors in others work... I can point out his, and whenever i do remark, i do it in a kind manor, and he get all rived-up.
And if he says that it was me who started it... listen to this AlphaN... being a mathematician, you will have heard of ''The Square Root''... Well, that equation talks in variables and evaluates a single answer yes? Well, you can get to the square root of an arguement, and the root will always lead to you, because before we ever first argued, you said that i was a crank-pot based on my thread made on Bible Mathematics... And when we did start argueing, you made that clear whenever i attempted to defend my faith in a [possible] subject.
So... again, and i'll ask one last time. Would you like a knowledge test wth me... I know you want to!
Neo
If you are a scientist at all, then please respond to previous knowledge. This is what professionals do. They evaluate all other perspectives.
If anyone else is willing to be decieved by this crank, please speak up. I've already had two missionary's working for him, so please, the more the merrier... But please, consider my arguement before dismissing it with contempt. Do not be biast.
I Will admit, AlphaN has a wider veiw of mathematics than i ever can... I envy him for this view of a mathematical world... But at any time, i would be willing to see reason, but because he shows me with the same dogmatism, similar to the way he has treated several people, perhaps even more, and yet, we know he is intelligent... Nothing defies this truth... It is just that with his intelligence, he is rather clouded from the fact there are equally intelligent folks out there that can see errors inhis own work.
He has had a great deal to say and point out errors in others work... I can point out his, and whenever i do remark, i do it in a kind manor, and he get all rived-up.
And if he says that it was me who started it... listen to this AlphaN... being a mathematician, you will have heard of ''The Square Root''... Well, that equation talks in variables and evaluates a single answer yes? Well, you can get to the square root of an arguement, and the root will always lead to you, because before we ever first argued, you said that i was a crank-pot based on my thread made on Bible Mathematics... And when we did start argueing, you made that clear whenever i attempted to defend my faith in a [possible] subject.
So... again, and i'll ask one last time. Would you like a knowledge test wth me... I know you want to!
Neo
I volunteer to be the judge.
Good. Thankyou rpenner.
Then here are the coordinates.
1. You must choose a set of twelve questions.
2. You must not be biast towards either of us.
That's it... Just wait and we shall see whether AlphaN shows up.
This will be interesting indeed.
Neo
Then here are the coordinates.
1. You must choose a set of twelve questions.
2. You must not be biast towards either of us.
That's it... Just wait and we shall see whether AlphaN shows up.
This will be interesting indeed.
Neo
QUOTE (NeoNo.1+Sep 12 2007, 10:20 PM)
This will be interesting indeed.
Argghhhh - choices, choices. The sporting schedules have left me to choose between:
Rubgy: Italy vs Romania
Football: England vs Russia
Physics: AlphaNumeric vs NeoNo.1
I wonder what odds I'd get on that last bout.
Rubgy: Italy vs Romania
Football: England vs Russia
Physics: AlphaNumeric vs NeoNo.1
I wonder what odds I'd get on that last bout.
Quote 1 :
Quote 2 :
Quote 2 :
Let us imagine, a few years down the line, Hawkings and Penrose announces that they have completed the unification of physics, and it described the universe as a field of force from Big Bang to Big Crunch, we would all say, ''Yahh! Brilliant! Fantastic!''
But then, how would we know that the equations would unfold the way we have been told they would?
Quote 3 :
In Quote 1 NeoNo.1 implies that he's unsure that a GUT can be formulated because dynamical systems can sometimes exhibit chaos, a mathematical property which leads to extreme sensitivity to initial conditions and an inability to solve analytically governing equations. He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down. NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.
In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.
In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery? He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.
Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.
Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?
In Quote 1 NeoNo.1 implies that he's unsure that a GUT can be formulated because dynamical systems can sometimes exhibit chaos, a mathematical property which leads to extreme sensitivity to initial conditions and an inability to solve analytically governing equations. He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down. NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.
In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.
In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery? He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.
Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.
Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?
1. You must choose a set of twelve questions.
Me too!
(I'm in the mood for a good train wreck today)
QUOTE
There are many reasons why i am unsure about a grand unification. One reason lyes in the unpredictability of events.... the so-called Chaos Theory.
Quote 2 :
QUOTE (->
| QUOTE |
| There are many reasons why i am unsure about a grand unification. One reason lyes in the unpredictability of events.... the so-called Chaos Theory. |
Quote 2 :
Let us imagine, a few years down the line, Hawkings and Penrose announces that they have completed the unification of physics, and it described the universe as a field of force from Big Bang to Big Crunch, we would all say, ''Yahh! Brilliant! Fantastic!''
But then, how would we know that the equations would unfold the way we have been told they would?
Quote 3 :
QUOTE
A tiny fluction in the universe could change the course of our future, and this worries me from a unified theoretical veiwpoint.
We also have numerous other problems. We need to find a GUT that is universally accepted... Could you imagine what the world would act like if the string theorists came along and said, ''Well, our theory can mathematically answer for a GUT.''
We also have numerous other problems. We need to find a GUT that is universally accepted... Could you imagine what the world would act like if the string theorists came along and said, ''Well, our theory can mathematically answer for a GUT.''
In Quote 1 NeoNo.1 implies that he's unsure that a GUT can be formulated because dynamical systems can sometimes exhibit chaos, a mathematical property which leads to extreme sensitivity to initial conditions and an inability to solve analytically governing equations. He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down. NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.
In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.
In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery? He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.
Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.
Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?
QUOTE (->
| QUOTE |
| A tiny fluction in the universe could change the course of our future, and this worries me from a unified theoretical veiwpoint. We also have numerous other problems. We need to find a GUT that is universally accepted... Could you imagine what the world would act like if the string theorists came along and said, ''Well, our theory can mathematically answer for a GUT.'' |
In Quote 1 NeoNo.1 implies that he's unsure that a GUT can be formulated because dynamical systems can sometimes exhibit chaos, a mathematical property which leads to extreme sensitivity to initial conditions and an inability to solve analytically governing equations. He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down. NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.
In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.
In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery? He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.
Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.
Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?
1. You must choose a set of twelve questions.
The issue being they must be questions you cannot answer with a simple google. I regularly ask cranks to answer questions from question sheets found here, which are the question sheets I used to have to do as an undergrad (not all of them, depends which topics I took). I've never had anyone answer any question from that list, be it a first year question on solving an ODE or a 3rd year question involving connections on Riemannian manifolds.
QUOTE (Euler+Sep 12 2007, 10:27 AM)
Me too!
(I'm in the mood for a good train wreck today)
I guess the IQ measuring questions are least biased?. Public IQ fight?
I am wondering somewhat what the point of this is. Is NeoNo.1 so insecure that he has to challenge people if it looks like they are correcting him on something. Kinda like Brian in 'Family Guy' when he says "You wanna arm wrestle!?" upon there being a question about his emotional well being.
A list of questions like "Who said..." or "State the formula for..." are pointless, anyone with Google can answer those. Long algebraic manipulation is difficult to do online unless you upload Latex'd pdfs or scanned in pictures and knowing how to do certain things depends heavily on what areas of physics you do (I know very little fluid mechanics formalism but I know a lot of QFT formalism). Conceptual questions are harder to evaluate and still suffer from being heavily skewed by use of Wikipedia and Google.
I'm happy to let my posts speak for themselves, such as my last one. I was asked for a longer explaination of my comments in relation to specific things NeoNo.1 said and I've given it. I can elaborate on any area he (or anyone else) wishes me to, though I worry any reply from NeoNo.1 will not be as coherent as my response, thus negating the possiblity of a constructive discussion/debate.
I'm happy to do some more mathematical things, I've done so in the past but it would be more constructive in terms of others learning things if they have a context or were part of a discussion. Deriving the uniqueness of the Schwarzchild solution is tedious but if in context of a discussion can be useful (better that than the Positive Energy Theorem).
I suspect that NeoNo.1 doesn't like being corrected on things, particularly if that correction is coherent, and is being a bit insecure about himself. If he were confident about his knowledge and physics understanding he'd be happy to lay back and let his posts do the talking for him over time. He'd give coherent, on topic, useful explainations/answers to people's questions, not hissy fits when someone says "Are you sure that's right?".
Instead he's done as a somewhat immature child (well, boy) will do when challenged, he's done the physics forum equivalent of "Do you want to take this outside?". This also gives him a way of avoiding addressing any issues I raise, be the issues correct or incorrect. Such as my request he provides a source for his supposed Einstein quote about "mathematics ws not a necessity to a good quantum theory.". I've asked a few times for him to back that up, nothing yet.
A list of questions like "Who said..." or "State the formula for..." are pointless, anyone with Google can answer those. Long algebraic manipulation is difficult to do online unless you upload Latex'd pdfs or scanned in pictures and knowing how to do certain things depends heavily on what areas of physics you do (I know very little fluid mechanics formalism but I know a lot of QFT formalism). Conceptual questions are harder to evaluate and still suffer from being heavily skewed by use of Wikipedia and Google.
I'm happy to let my posts speak for themselves, such as my last one. I was asked for a longer explaination of my comments in relation to specific things NeoNo.1 said and I've given it. I can elaborate on any area he (or anyone else) wishes me to, though I worry any reply from NeoNo.1 will not be as coherent as my response, thus negating the possiblity of a constructive discussion/debate.
I'm happy to do some more mathematical things, I've done so in the past but it would be more constructive in terms of others learning things if they have a context or were part of a discussion. Deriving the uniqueness of the Schwarzchild solution is tedious but if in context of a discussion can be useful (better that than the Positive Energy Theorem).
I suspect that NeoNo.1 doesn't like being corrected on things, particularly if that correction is coherent, and is being a bit insecure about himself. If he were confident about his knowledge and physics understanding he'd be happy to lay back and let his posts do the talking for him over time. He'd give coherent, on topic, useful explainations/answers to people's questions, not hissy fits when someone says "Are you sure that's right?".
Instead he's done as a somewhat immature child (well, boy) will do when challenged, he's done the physics forum equivalent of "Do you want to take this outside?". This also gives him a way of avoiding addressing any issues I raise, be the issues correct or incorrect. Such as my request he provides a source for his supposed Einstein quote about "mathematics ws not a necessity to a good quantum theory.". I've asked a few times for him to back that up, nothing yet.
In Quote 1 NeoNo.1 implies that he's unsure that a GUT can be formulated because dynamical systems can sometimes exhibit chaos, a mathematical property which leads to extreme sensitivity to initial conditions and an inability to solve analytically governing equations....'' [ME > good, until now] >
''He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues...'' [ME > I do not mistake any difficulty. If anything, the dificulty is equivalant to ever finding the differential to be able to write it down initially.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
[ME> Yes... and don't forget that garvity is intrinsic right now, including discovering dark matter and dark energy's initial plans for the universe. Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton.]
''Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down.'' Good until now >
''NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.''
[ME >Equations of motions are statistical analysis. They are applied at an earlier time t>1. I never presumed to imply that the difficulty of the equation was a variable, but rather our incapability. This is what prevents such a theory transpiring.]
''In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.''
[ME > yes that is true, and an invaluable thing to consider here.]
''In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery?
[Me> Yes... close... anyone of them... Perhaps not you winning the lottery though, the universe doesn't revolve around you]
cont.
''He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.''
[ME > I give an explanation why, but it still isn't enough. Its not enough that it is possible? Your professor also works in probability. His is also probable. He is also yet to present empiracle proof. Not just myself... But the longer a unification cannot be brougth forth, the more i am proven correct]
''Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.''
[ME > Eh... hense the Heirarchy Problem? Right now, no theory can answer this, not even Chaos, unless of course, there was a Chaotic fluctuation in the past, the we could answer the results as a discrepency in the present, unaware it was of natural cause, like the Einsteins cosmological constant, which is 120 times smaller than what it should be...]
''Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?''
[ME > You patronizing prick. Why don't you keep going. So far, ive seen many oversights you have missed, including a few mistakes.]
Neo
''He is mistaking the difficulty in solving a differential with the difficulty in writing the differential equation down. These are two different issues...'' [ME > I do not mistake any difficulty. If anything, the dificulty is equivalant to ever finding the differential to be able to write it down initially.
To 'find a GUT' is to find a single gauge group which accounts for all the symmetries seen in the Standard Model (and perhaps gravity too, but GUT typically doesn't refer to that). The SM gauge group is SU(3)xSU(2)xU(1), relating to colour, weak charge and electromagnetic charge respectively. A GUT would have a single gauge group (such as SU(5) or SO(10) or even E6 or E8) which has these groups as subgroups and which explains the interactions of the fields at high energies (typically of the order 10^16 GeV, see renormalisation group couplings).
[ME> Yes... and don't forget that garvity is intrinsic right now, including discovering dark matter and dark energy's initial plans for the universe. Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton.]
''Writing down such a group and a Lagrangian (ie list of quantum fields, interactions, masses) with such a symmetry would not be affected by the complexity of the solutions to the Lagrangian's equations of motions (ie the dynamics of the system). We have plenty of such Lagrangians already in quantum field theory (see QED and QCD), where the equations of motion are analytically unsolvable but the Lagrangian is a doddle to write down.'' Good until now >
''NeoNo.1 is claiming that the difficulty of the equations of motion's solutions precludes us knowing the equations of motion. As demonstrated by QED, QCD, String theory, General relativity and even a great many classical (some chaotic!) systems, this is not true.''
[ME >Equations of motions are statistical analysis. They are applied at an earlier time t>1. I never presumed to imply that the difficulty of the equation was a variable, but rather our incapability. This is what prevents such a theory transpiring.]
''In Quote 2 NeoNo.1 worries that as people work through the equations of a GUT (so he agrees governing equations can be found, which amounts to 'Finding a GUT') people will find chaotic or analytically unsolvable systems. This would be nothing new nor would it be unexpected. We have approximation techniques or a variety of tools to map certain problems into easier situations, physicists have been doing such things for centuries now. Again, having difficult systems to solve doesn't prevent you from having the equations which govern the system.''
[ME > yes that is true, and an invaluable thing to consider here.]
''In Quote 3, NeoNo.1 expresses his worry that a 'fluctuation in the universe' would alter our understanding of a GUT. He doesn't quantify what such a fluctuation would be, the sun explodes? Light speed halves? Electromagnetism doubles in strength? I win the lottery?
[Me> Yes... close... anyone of them... Perhaps not you winning the lottery though, the universe doesn't revolve around you]
cont.
''He does however claim it would have a knock on effect in our ability to solve complex dynamical systems. He doesn't say how. He does however mention string theorist's and GUTs. The gauge groups used within Heterotic String Theory (SO(32) and E8xE8) do contain the aforementioned SM gauge groups within them as subgroups. Infact, one of the most viable groups for GUT research (one of the professors in my department does extensive research on it!) is the E6 subgroup of E8. E6 breaks down to the SM groups in a very nice way. So infact, string theory is giving us hints that it might have GUT formalism built right into it, along with gravity. Great.''
[ME > I give an explanation why, but it still isn't enough. Its not enough that it is possible? Your professor also works in probability. His is also probable. He is also yet to present empiracle proof. Not just myself... But the longer a unification cannot be brougth forth, the more i am proven correct]
''Examples of systems where we know the governing equations exactly but are unable to solve analytically are QCD strong force interactions. Not chaotic, but analytically unsolvable, even perturbatively in many cases. An even simpler example of the (already mentioned many times) 3 body gravitational system. And an even simpler system is a pendulum swinging when you don't make the approximation sin(x) ~ x. If you keep it as x'' = -ksin(x), you cannot solve it exactly, yet you know the governing equation.''
[ME > Eh... hense the Heirarchy Problem? Right now, no theory can answer this, not even Chaos, unless of course, there was a Chaotic fluctuation in the past, the we could answer the results as a discrepency in the present, unaware it was of natural cause, like the Einsteins cosmological constant, which is 120 times smaller than what it should be...]
''Is that enough of an elaboration on what you've said and what I was trying to say NeoNo.1 or should I type a bit slower so you can keep up?''
[ME > You patronizing prick. Why don't you keep going. So far, ive seen many oversights you have missed, including a few mistakes.]
Neo
Last time I checked the whole point of Chaos theory was the modelling of non-linear systems from linear equations (driven into non-linear behaviour).
There are plenty of examples of this working.
Not only that, but non-linear systems are capable of behaving in linear ways (the classic bifurcation diagram demonstrates that). The equations also let us calculate the range of possible behaviours of the system (even though we might not be able to exactly extrapolate backwards or forwards to/from any particular state, unless we know the values of the variables exactly.
Chaotic systems are not completely unpredictable. The Lorentz attractor, the taffy pulling machine, and the weather are examples of that, as are your heart-beat, the crystalization of snow flakes, the propogation of some chemical reactions...
I could go on naming systems, but I don't have time.
The point is that Alphanumeric is very much correct on this matter and NeoNo.1 is very much wrong.
There are plenty of examples of this working.
Not only that, but non-linear systems are capable of behaving in linear ways (the classic bifurcation diagram demonstrates that). The equations also let us calculate the range of possible behaviours of the system (even though we might not be able to exactly extrapolate backwards or forwards to/from any particular state, unless we know the values of the variables exactly.
Chaotic systems are not completely unpredictable. The Lorentz attractor, the taffy pulling machine, and the weather are examples of that, as are your heart-beat, the crystalization of snow flakes, the propogation of some chemical reactions...
I could go on naming systems, but I don't have time.
The point is that Alphanumeric is very much correct on this matter and NeoNo.1 is very much wrong.
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME > I do not mistake any difficulty. If anything, the dificulty is equivalant to ever finding the differential to be able to write it down initially.
They might be 'as difficult' but they are seperate problems. When researching, trying to find the governing equations, you aren't being governed by chaos because you aren't trying to solve a chaotic system.
They might be 'as difficult' but they are seperate problems. When researching, trying to find the governing equations, you aren't being governed by chaos because you aren't trying to solve a chaotic system.
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME> Yes... and don't forget that garvity is intrinsic right now, including discovering dark matter and dark energy's initial plans for the universe. Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton.]
Gauge groups are not useless, they are applied to excellent effect within the Standard Model right now. They explain the properties of all observed bosons. The gauge groups/fields we see now are the remnants of a 'broken symmetry' from the GUT scale (10^16 GeV). At huge energies, the 3 forces act as a single coherent force obeying a large gauge group symmetry. At low energies we see three seperate forces obeying three seperate symmetries, but we still see them!
We already know (and have verified!) one unification. At energies above 90GeV, the weak and electromagnetic forces unify to obey a different kind of gauge symmetry from that which they have below those energies.
Inclusion of gravity (wether you consider space-time diffeomorphisms the same as a gauge field symmetry is an open question) doesn't alter this.
We already know (and have verified!) one unification. At energies above 90GeV, the weak and electromagnetic forces unify to obey a different kind of gauge symmetry from that which they have below those energies.
Inclusion of gravity (wether you consider space-time diffeomorphisms the same as a gauge field symmetry is an open question) doesn't alter this.
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME >Equations of motions are statistical analysis. They are applied at an earlier time t>1. I never presumed to imply that the difficulty of the equation was a variable, but rather our incapability. This is what prevents such a theory transpiring.]
Equations of motion are not a statistical analysis. They apply in classical, Newtonian, systems too which have no statistical behaviour at all. Even in the quantum world, they are not statistical, they are always obeyed. How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion. For instance, each Feynman diagram for a given process is an example of the system evolving in terms of it's equations of motion but in different ways.
Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical.
The book "An Introduction to Quantum Field Theory" by Peskin and Schroder is an excellent book for this kind of stuff. Covers QFT from the beginning all the way through the gauge group unification in electroweak theory.
Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical.
The book "An Introduction to Quantum Field Theory" by Peskin and Schroder is an excellent book for this kind of stuff. Covers QFT from the beginning all the way through the gauge group unification in electroweak theory.
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME > yes that is true, and an invaluable thing to consider here.]
So you see the difference between 'Finding a GUT' and 'Solving it's dynamics'?
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME > I give an explanation why, but it still isn't enough. Its not enough that it is possible? Your professor also works in probability. His is also probable. He is also yet to present empiracle proof. Not just myself... But the longer a unification cannot be brougth forth, the more i am proven correct]
My professor is a 'she'. Also, as I've said several times, unified gauge theory in the form of electroweak theory has been done and experimentally verified. Considerable progress is being made in full SM unification. And while my supervisor doesn't do GUTs (she does string theory), I know someone who does and his work isn't statistical. It involves seeing how large gauge groups break (since that affects predicted particle content) and then seeing how the new gauge particles interact with other particles from the groups. Take this paper for example. Gauge groups, gauge couplings, particle familes are all considered. It's not very much to do with statistics is it?
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME > Eh... hense the Heirarchy Problem? Right now, no theory can answer this, not even Chaos, unless of course, there was a Chaotic fluctuation in the past, the we could answer the results as a discrepency in the present, unaware it was of natural cause, like the Einsteins cosmological constant, which is 120 times smaller than what it should be...]
Do you actually know what the Heirarchy problem is? And it's not solved by GUTs, it's solved either by fine tuning or by supersymmetry which is a different kind of symmetry from a GUT symmetry.
Also, not all fluctuations are chaotic fluctuations. Quantum fluctuations for instance are not chaotic because they are not deterministic systems, which a chaotic system is in principle. There's a difference between 'random' and 'chaotic'.
And for the cosmological constant, there's no value it 'should be', it's about relative scales. Besides, it's not 120 times smaller, it's 10^120 smaller. A bit of a blind spot in your knowledge there. One of many.
Also, not all fluctuations are chaotic fluctuations. Quantum fluctuations for instance are not chaotic because they are not deterministic systems, which a chaotic system is in principle. There's a difference between 'random' and 'chaotic'.
And for the cosmological constant, there's no value it 'should be', it's about relative scales. Besides, it's not 120 times smaller, it's 10^120 smaller. A bit of a blind spot in your knowledge there. One of many.
QUOTE (NeoNo.1+Sep 12 2007, 07:49 PM)
[ME > You patronizing prick. Why don't you keep going. So far, ive seen many oversights you have missed, including a few mistakes.]]
As with most cranks, they see errors in their own knowledge as flaws in mainstream work and work by the mentality "I'm not wrong, everyone else is". You, Sylwester, Zephir, Precursor, StevenA, Bloy, you're all doing precisely that. If you don't know it, it's mainstream physics' fault!
Though I'm sure it'll suprise you, I regularly find myself thinking "I have no clue how that can be true..." but rather than going "... but I'm perfect so it's the book which is wrong!" I sit and think about it or ask someone for help or read some more books/papers till I do understand it. Happened earlier today. I ask there because I know I won't get an answer here.
But feel free to give an answer if you know it. Show us all your knowledge of differential geometry.
/edit
Oh, and you continue to ignore my request you back up your supposed quote of Einstein with a valid source.
Though I'm sure it'll suprise you, I regularly find myself thinking "I have no clue how that can be true..." but rather than going "... but I'm perfect so it's the book which is wrong!" I sit and think about it or ask someone for help or read some more books/papers till I do understand it. Happened earlier today. I ask there because I know I won't get an answer here.
But feel free to give an answer if you know it. Show us all your knowledge of differential geometry.
/edit
Oh, and you continue to ignore my request you back up your supposed quote of Einstein with a valid source.
QUOTE (AlphaNumeric+Sep 12 2007, 08:19 PM)
Happened earlier today.
It's a consequence of the fact Spin(6) ≡ SU(4) - it's up to you in which way you choose to represent your spinors.
Caveat: I have no clue whatsoever what this has to do with constructions via susy - which will come as no surprise to you! So this might be totally unhelpful.
It's a consequence of the fact Spin(6) ≡ SU(4) - it's up to you in which way you choose to represent your spinors.
Caveat: I have no clue whatsoever what this has to do with constructions via susy - which will come as no surprise to you! So this might be totally unhelpful.
I had a feeling it was something like that, you aren't dealing with specific space-time indices so much as degrees of freedom and operators which behave in a representation-invariant way. I prefer thinking of that particular issue in terms of representations of SO(6) instead. Seems to make more sense to me.
Been a while since I wrote out a vector/spinor in column format and not just in index notation.
Ricci flat Kahler manifolds with SU(N) holonomy are known as Calabi-Yau manifolds (since Yau proved Calabi's conject that R=0 and H=SU(N) => R_ab = 0).
And that's why Calabi Yau spaces are in string theory, if anyone was interested
Been a while since I wrote out a vector/spinor in column format and not just in index notation.
QUOTE
I have no clue whatsoever what this has to do with constructions via susy - which will come as no surprise to you! So this might be totally unhelpful
SUSY transformations lead to you need a unique covariantly constant spinor on the compact 6D space. That then leads to the holonomy subgroup of SO(6). SO(6) has the 4 = 3+1 and to N=1 SUSY you have the singlet as the holonomy invariant so the 3 can be suffled around if you want so your holonomy is precisely SU(3). That then leads you to the metric being Ricci flat via a similar argument (but in reverse) as in chapter 8 of Nakahara.Ricci flat Kahler manifolds with SU(N) holonomy are known as Calabi-Yau manifolds (since Yau proved Calabi's conject that R=0 and H=SU(N) => R_ab = 0).
And that's why Calabi Yau spaces are in string theory, if anyone was interested
Alphanumeric thought that the potential energy of a brick in gravity would apply to light. It is just the reverse.
Mitch Raemsch
Mitch Raemsch
QUOTE (AlphaNumeric+Sep 12 2007, 08:43 PM)
SUSY transformations lead to you need a unique covariantly constant spinor on the compact 6D space. That then leads to the holonomy subgroup of SO(6). SO(6) has the 4 = 3+1 and to N=1 SUSY you have the singlet as the holonomy invariant so the 3 can be suffled around if you want so your holonomy is precisely SU(3). That then leads you to the metric being Ricci flat via a similar argument (but in reverse) as in chapter 8 of Nakahara.
Ricci flat Kahler manifolds with SU(N) holonomy are known as Calabi-Yau manifolds (since Yau proved Calabi's conject that R=0 and H=SU(N) => R_ab = 0).
And that's why Calabi Yau spaces are in string theory, if anyone was interested
I guess this is an excuse for me to go back through Nakahara. Something worth pointing out:
Look what just happened - a topic intimately related to physics, a question was posed, a discussion happened and (hopefully!) it was helpful all round. This is a good example of what actually happens in academia/physics communities. Rational discussion, reference to works, specific examples and links to further work. It's not a conspiracy, we don't just recite other peoples' work - we actually think, work through problems and help each other out! Shock horror!
Ricci flat Kahler manifolds with SU(N) holonomy are known as Calabi-Yau manifolds (since Yau proved Calabi's conject that R=0 and H=SU(N) => R_ab = 0).
And that's why Calabi Yau spaces are in string theory, if anyone was interested
I guess this is an excuse for me to go back through Nakahara. Something worth pointing out:
Look what just happened - a topic intimately related to physics, a question was posed, a discussion happened and (hopefully!) it was helpful all round. This is a good example of what actually happens in academia/physics communities. Rational discussion, reference to works, specific examples and links to further work. It's not a conspiracy, we don't just recite other peoples' work - we actually think, work through problems and help each other out! Shock horror!
''They might be 'as difficult' but they are seperate problems. When researching, trying to find the governing equations, you aren't being governed by chaos because you aren't trying to solve a chaotic system''
> They seperate problems? Yes... your right, but that is just as much problems it creates.
''Gauge groups are not useless, they are applied to excellent effect within the Standard Model right now. They explain the properties of all observed bosons. The gauge groups/fields we see now are the remnants of a 'broken symmetry' from the GUT scale (10^16 GeV). At huge energies, the 3 forces act as a single coherent force obeying a large gauge group symmetry. At low energies we see three seperate forces obeying three seperate symmetries, but we still see them!
We already know (and have verified!) one unification. At energies above 90GeV, the weak and electromagnetic forces unify to obey a different kind of gauge symmetry from that which they have below those energies.
Inclusion of gravity (wether you consider space-time diffeomorphisms the same as a gauge field symmetry is an open question) doesn't alter this.''
> I never said they where useless. I said they where, in so many words, insufficiant. The queen-theory they represent is string theory, and even that is now faiding into the past as nothing but a curiosity. There are several pioneers now in high regards among the scientific hall suggesting that string theory isn;t even a science anymore.
''Equations of motion are not a statistical analysis. They apply in classical, Newtonian, systems too which have no statistical behaviour at all. Even in the quantum world, they are not statistical, they are always obeyed. How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion. For instance, each Feynman diagram for a given process is an example of the system evolving in terms of it's equations of motion but in different ways.
Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical.
The book "An Introduction to Quantum Field Theory" by Peskin and Schroder is an excellent book for this kind of stuff. Covers QFT from the beginning all the way through the gauge group unification in electroweak theory''
> Yeh... whatever you say. Actually, if you had ever studied this area yet, you will find that the equations of motion not only locate, but have non-locality equations, suggesting that some equations must be statistical being bound by the uncertainty principle of quantum theory. You also said >
''How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion.''
> Well, yes, at last we agree on something.
And again > you said, Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical...''
>Well no. You are right and wrong again. If the Lagrangian equation represent future predictions, which all theories strive to reach, then there exists an invariant equalling a possible risk of a chaotic system.
''My professor is a 'she'. Also, as I've said several times, unified gauge theory in the form of electroweak theory has been done and experimentally verified. Considerable progress is being made in full SM unification. And while my supervisor doesn't do GUTs (she does string theory), I know someone who does and his work isn't statistical. It involves seeing how large gauge groups break (since that affects predicted particle content) and then seeing how the new gauge particles interact with other particles from the groups. Take this paper for example. Gauge groups, gauge couplings, particle familes are all considered. It's not very much to do with statistics is it?''
> And i've said, until your string theorist buds get gravity and quantum cosmology into a bundle with th other three forces, i'll admit i was wrong. But i will make a prediction. Give it three more years and scientists will have found a whole new theory for matter. I mean, for goodness sake, String Theories are unfalsfiable. So how can the theory ever be right?
''Do you actually know what the Heirarchy problem is? And it's not solved by GUTs, it's solved either by fine tuning or by supersymmetry which is a different kind of symmetry from a GUT symmetry.''
> As i said, do not patronize me. I know you are doing this intentionally, so please stop. I improvised you to consider that the Heirarchy Problem was a considerable mechanism in your proposal. I never proposed it solved guts... Gee Whiz... Also, supersymmetry holds many of the keys needed, but you are again missing out intrinsic properties needed. Do you know yet from your training that the Higgs Boson is unified of origin. It describes the Standard Model, which is equaly intrinsic to the study of Strings. We first need to find the Higgs. If that doesn't exist, you can kiss your dream goodbye, for it will set the scientists back decades. And, if that wasn't enough, we also need to understand dark matter... And to do so, we either needto find a neutrino or a axion... We are not sure about the rest... And also, dark energy is also a mystery... we still don't know what it is, other than it has a negative pressure and that it permeates the entire outer-regions of the hypersphere.
''As with most cranks, they see errors in their own knowledge as flaws in mainstream work and work by the mentality "I'm not wrong, everyone else is". You, Sylwester, Zephir, Precursor, StevenA, Bloy, you're all doing precisely that. If you don't know it, it's mainstream physics' fault!''
>anyone else you want to slag off there while you're at it?
''But feel free to give an answer if you know it. Show us all your knowledge of differential geometry.''
> What do you mean? This is not a term i recognize.
/edit
''Oh, and you continue to ignore my request you back up your supposed quote of Einstein with a valid source''
> Well, sorry to disappoint you, but he was so much better than both of us put together...
Neo
> They seperate problems? Yes... your right, but that is just as much problems it creates.
''Gauge groups are not useless, they are applied to excellent effect within the Standard Model right now. They explain the properties of all observed bosons. The gauge groups/fields we see now are the remnants of a 'broken symmetry' from the GUT scale (10^16 GeV). At huge energies, the 3 forces act as a single coherent force obeying a large gauge group symmetry. At low energies we see three seperate forces obeying three seperate symmetries, but we still see them!
We already know (and have verified!) one unification. At energies above 90GeV, the weak and electromagnetic forces unify to obey a different kind of gauge symmetry from that which they have below those energies.
Inclusion of gravity (wether you consider space-time diffeomorphisms the same as a gauge field symmetry is an open question) doesn't alter this.''
> I never said they where useless. I said they where, in so many words, insufficiant. The queen-theory they represent is string theory, and even that is now faiding into the past as nothing but a curiosity. There are several pioneers now in high regards among the scientific hall suggesting that string theory isn;t even a science anymore.
''Equations of motion are not a statistical analysis. They apply in classical, Newtonian, systems too which have no statistical behaviour at all. Even in the quantum world, they are not statistical, they are always obeyed. How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion. For instance, each Feynman diagram for a given process is an example of the system evolving in terms of it's equations of motion but in different ways.
Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical.
The book "An Introduction to Quantum Field Theory" by Peskin and Schroder is an excellent book for this kind of stuff. Covers QFT from the beginning all the way through the gauge group unification in electroweak theory''
> Yeh... whatever you say. Actually, if you had ever studied this area yet, you will find that the equations of motion not only locate, but have non-locality equations, suggesting that some equations must be statistical being bound by the uncertainty principle of quantum theory. You also said >
''How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion.''
> Well, yes, at last we agree on something.
And again > you said, Computing the total of all those different ways is difficult (or analytically impossible) but the governing equations (and Lagrangian) are not statistical...''
>Well no. You are right and wrong again. If the Lagrangian equation represent future predictions, which all theories strive to reach, then there exists an invariant equalling a possible risk of a chaotic system.
''My professor is a 'she'. Also, as I've said several times, unified gauge theory in the form of electroweak theory has been done and experimentally verified. Considerable progress is being made in full SM unification. And while my supervisor doesn't do GUTs (she does string theory), I know someone who does and his work isn't statistical. It involves seeing how large gauge groups break (since that affects predicted particle content) and then seeing how the new gauge particles interact with other particles from the groups. Take this paper for example. Gauge groups, gauge couplings, particle familes are all considered. It's not very much to do with statistics is it?''
> And i've said, until your string theorist buds get gravity and quantum cosmology into a bundle with th other three forces, i'll admit i was wrong. But i will make a prediction. Give it three more years and scientists will have found a whole new theory for matter. I mean, for goodness sake, String Theories are unfalsfiable. So how can the theory ever be right?
''Do you actually know what the Heirarchy problem is? And it's not solved by GUTs, it's solved either by fine tuning or by supersymmetry which is a different kind of symmetry from a GUT symmetry.''
> As i said, do not patronize me. I know you are doing this intentionally, so please stop. I improvised you to consider that the Heirarchy Problem was a considerable mechanism in your proposal. I never proposed it solved guts... Gee Whiz... Also, supersymmetry holds many of the keys needed, but you are again missing out intrinsic properties needed. Do you know yet from your training that the Higgs Boson is unified of origin. It describes the Standard Model, which is equaly intrinsic to the study of Strings. We first need to find the Higgs. If that doesn't exist, you can kiss your dream goodbye, for it will set the scientists back decades. And, if that wasn't enough, we also need to understand dark matter... And to do so, we either needto find a neutrino or a axion... We are not sure about the rest... And also, dark energy is also a mystery... we still don't know what it is, other than it has a negative pressure and that it permeates the entire outer-regions of the hypersphere.
''As with most cranks, they see errors in their own knowledge as flaws in mainstream work and work by the mentality "I'm not wrong, everyone else is". You, Sylwester, Zephir, Precursor, StevenA, Bloy, you're all doing precisely that. If you don't know it, it's mainstream physics' fault!''
>anyone else you want to slag off there while you're at it?
''But feel free to give an answer if you know it. Show us all your knowledge of differential geometry.''
> What do you mean? This is not a term i recognize.
/edit
''Oh, and you continue to ignore my request you back up your supposed quote of Einstein with a valid source''
> Well, sorry to disappoint you, but he was so much better than both of us put together...
Neo
QUOTE (Nick+Sep 12 2007, 08:53 PM)
Alphanumeric thought that the potential energy of a brick in gravity would apply to light. It is just the reverse.
So you do vaguely retain knowledge of things I've said to you. Too bad about the understanding.
I explained to you, long ago, that just as a brick loses energy when you throw it up, so does light. A brick loses velocity while light, which is unable to lose velocity, loses frequency since it's energy is directly related to it's frequency. Similarly, when a photon moves down through a potential, it will gain energy in terms of it's oscillations.
A photon also is affected less by redshift as it reduces it's frequency, as if it's (in some equivalent sense) getting lighter. A brick will stop (unless you throw it really fast) while a photon will never redshift to zero frequency.
No doubt you'll now whine about 'energy-less light" and claim Einstein predicted it when I've explained to you many times (in the thread you read me use the brick analogy!) that relativity never predicts any photon having zero energy. A photon can be redshifted by as large a finite quantity as you wish but that's not the same thing.
I'd watch out if I were you NeoNo.1, with Nick here you've now got some serious competition for "Most incoherent non-sequitur poster in the thread".
So you do vaguely retain knowledge of things I've said to you. Too bad about the understanding.
I explained to you, long ago, that just as a brick loses energy when you throw it up, so does light. A brick loses velocity while light, which is unable to lose velocity, loses frequency since it's energy is directly related to it's frequency. Similarly, when a photon moves down through a potential, it will gain energy in terms of it's oscillations.
A photon also is affected less by redshift as it reduces it's frequency, as if it's (in some equivalent sense) getting lighter. A brick will stop (unless you throw it really fast) while a photon will never redshift to zero frequency.
No doubt you'll now whine about 'energy-less light" and claim Einstein predicted it when I've explained to you many times (in the thread you read me use the brick analogy!) that relativity never predicts any photon having zero energy. A photon can be redshifted by as large a finite quantity as you wish but that's not the same thing.
I'd watch out if I were you NeoNo.1, with Nick here you've now got some serious competition for "Most incoherent non-sequitur poster in the thread".
There is bigger fish in the sea.
To be fair, I would like to cover a large area of physics. To ensure that, eight of my questions will be chosen to address various basic theories as outlined by Okun. As this is a "knowledge test", but we are using pseudonyms on the Internet, this will be "open book." Likewise it is also open-calculator and open-computer. (It would be hard for you to respond otherwise.) Use any resource you want, but be sure to explain the answer in a way of demonstrating your knowledge of how to solve the problem, not just the answer.
You may answer these questions across several posts, but each post must be complete with respect to the numbered questions. You have 48 hours from the posting of these questions to reply. Your last post on a numbered question will be taken as final, stand-alone and complete. Scoring will be relative, with the burden on later answers to actually best the prior answers response. But you are allowed to repost. Being the first one to post a correct answer for a question may thus give a strong competitive advantage to the early poster. Giving a complete and well-explained answer will trump a sketchy early answer. Scoring will be simple, with points equally distributed between the parts of a question.
Please post a short acknowledgment or objection to the terms.
Question 1. [10 points] In Newtonian Mechanics, assuming no gravity, a point particle of mass M and velocity v in the +x direction collides at (0,0,0) inelastically with an initially static infinite half-space of masses connected by springs in a cubic lattice. If the lattice spacing is a=1, the spring constant k, and each mass is m then
1A. What is the expected time for the disturbance to reach (1732,0,0)
1B. What is the expected time for the disturbance to reach (1000,1000,1000)
Question 2. [20 points] In Newtonian Gravity, two small bodies, A and B, orbit one much more massive larger body, C, with the minimum distance between C and the outer body, B, more than two times as large as the maximum distance of the inner body, A.
2A. Write down the Lagrangians for the complete system and the A - C system.
2B. What is the solution for the A - C system in terms of velocity at the furthest distance and in terms of orbital parameters?
2C. What are the conserved quantities of the A-C system?
2D. In the complete system, what is the approximate solution for the change of A's orbital parameters?
Question 3. [20 points] In Quantum Mechanics, what are the eigenfunctions and eigenvalues of energy for a particle in
3A. ... a regular tetrahedral box?
3B. ... a general ellipsoidal box?
Question 4. [20 points] In Special Relativity, assume a "parton" moves at velocity |v| about a "core" but with a uniformly random direction.
4A. What is the distribution of v_x in the core frame?
4B. If the parton-core system has velocity (+V,0,0) in the lab frame, what is the distribution of u_x, the parton's velocity in the x direction in the lab frame?
4C. Assume two "cores" each moving at velocity |V| but in opposite directions come close in the lab frame and their respective "partons" collide completely inelastically. What is the the distribution of the parton-parton velocity in the lab frame.
4D. If gamma for v is 100 and gamma for V is 10000, then roughly what percentage of parton-partons are below c/50000 ?
Question 5. [30 points] In Newtonian Quantum Gravity,
5A. What can be said about the approximate quantum numbers of an otherwise free electron at Earth's surface?
5B. What is the characteristic energy of emitted radiation for a delta-N = -1 transition?
5C. Compare this to the Maxwellian prediction of radiation from an accelerated electron.
Question 6. [30 points] In Quantum Field Theory,
6A. Demonstrate asymptotic freedom in SU(3).
Question 7. [30 points] In General Relativity, lets talk about in-plane circular orbits about a rotating black hole of mass M.
7A. What is the expression for the proper time to complete an orbit in the direction of rotation?
7B. And if you are orbiting "the wrong way" ?
7C. What do the extremal solutions correspond to?
Question 8. [40 points] In GUTs,
8A. Prove SU(4) will never cut it.
8B. Explain why SU(5) is experimentally rejected.
8C. Why is Bosonic string theory rejected?
8D. Why is unification of U(1)xSU(2)xSU(3) simply not enough.
Question 9. [20 points] In Chaos theory,
9A. There is a universality to the scaling of the periodic modes of the quadratic unimodal map as chaos is approached. What is the corresponding rule for the tent map?
9B. What is the corresponding behavior of the quartic unimodal map?
Question 10. [30 points] Let f() be a function of x over R, such that f(f(x)) = e^x. Then f(x) is something like the square root of the exponential function with regard to composition.
10A. Find a possible Taylor expansion of f().
10B. Can f() be defined over the Complex plane?
10C. Can there be a h() != f() such that h(h(x)) = e^x ? If so, is there a preferred form of the square root of the exponential?
10D. What types of finite matrices have square roots?
10E. What are the quantum theoretical application of this?
Question 11. [10 points] What is the sum of the 7th powers of the numbers 1 .. n ? Give a short proof.
Question 12. [10 points] Experimentally, what are the kinematics of neutron decay and what is the strength of the negative mass-squared results for the electron neutrino?
// Edit -- changed half-plane to half-space in Question 1.
You may answer these questions across several posts, but each post must be complete with respect to the numbered questions. You have 48 hours from the posting of these questions to reply. Your last post on a numbered question will be taken as final, stand-alone and complete. Scoring will be relative, with the burden on later answers to actually best the prior answers response. But you are allowed to repost. Being the first one to post a correct answer for a question may thus give a strong competitive advantage to the early poster. Giving a complete and well-explained answer will trump a sketchy early answer. Scoring will be simple, with points equally distributed between the parts of a question.
Please post a short acknowledgment or objection to the terms.
Question 1. [10 points] In Newtonian Mechanics, assuming no gravity, a point particle of mass M and velocity v in the +x direction collides at (0,0,0) inelastically with an initially static infinite half-space of masses connected by springs in a cubic lattice. If the lattice spacing is a=1, the spring constant k, and each mass is m then
1A. What is the expected time for the disturbance to reach (1732,0,0)
1B. What is the expected time for the disturbance to reach (1000,1000,1000)
Question 2. [20 points] In Newtonian Gravity, two small bodies, A and B, orbit one much more massive larger body, C, with the minimum distance between C and the outer body, B, more than two times as large as the maximum distance of the inner body, A.
2A. Write down the Lagrangians for the complete system and the A - C system.
2B. What is the solution for the A - C system in terms of velocity at the furthest distance and in terms of orbital parameters?
2C. What are the conserved quantities of the A-C system?
2D. In the complete system, what is the approximate solution for the change of A's orbital parameters?
Question 3. [20 points] In Quantum Mechanics, what are the eigenfunctions and eigenvalues of energy for a particle in
3A. ... a regular tetrahedral box?
3B. ... a general ellipsoidal box?
Question 4. [20 points] In Special Relativity, assume a "parton" moves at velocity |v| about a "core" but with a uniformly random direction.
4A. What is the distribution of v_x in the core frame?
4B. If the parton-core system has velocity (+V,0,0) in the lab frame, what is the distribution of u_x, the parton's velocity in the x direction in the lab frame?
4C. Assume two "cores" each moving at velocity |V| but in opposite directions come close in the lab frame and their respective "partons" collide completely inelastically. What is the the distribution of the parton-parton velocity in the lab frame.
4D. If gamma for v is 100 and gamma for V is 10000, then roughly what percentage of parton-partons are below c/50000 ?
Question 5. [30 points] In Newtonian Quantum Gravity,
5A. What can be said about the approximate quantum numbers of an otherwise free electron at Earth's surface?
5B. What is the characteristic energy of emitted radiation for a delta-N = -1 transition?
5C. Compare this to the Maxwellian prediction of radiation from an accelerated electron.
Question 6. [30 points] In Quantum Field Theory,
6A. Demonstrate asymptotic freedom in SU(3).
Question 7. [30 points] In General Relativity, lets talk about in-plane circular orbits about a rotating black hole of mass M.
7A. What is the expression for the proper time to complete an orbit in the direction of rotation?
7B. And if you are orbiting "the wrong way" ?
7C. What do the extremal solutions correspond to?
Question 8. [40 points] In GUTs,
8A. Prove SU(4) will never cut it.
8B. Explain why SU(5) is experimentally rejected.
8C. Why is Bosonic string theory rejected?
8D. Why is unification of U(1)xSU(2)xSU(3) simply not enough.
Question 9. [20 points] In Chaos theory,
9A. There is a universality to the scaling of the periodic modes of the quadratic unimodal map as chaos is approached. What is the corresponding rule for the tent map?
9B. What is the corresponding behavior of the quartic unimodal map?
Question 10. [30 points] Let f() be a function of x over R, such that f(f(x)) = e^x. Then f(x) is something like the square root of the exponential function with regard to composition.
10A. Find a possible Taylor expansion of f().
10B. Can f() be defined over the Complex plane?
10C. Can there be a h() != f() such that h(h(x)) = e^x ? If so, is there a preferred form of the square root of the exponential?
10D. What types of finite matrices have square roots?
10E. What are the quantum theoretical application of this?
Question 11. [10 points] What is the sum of the 7th powers of the numbers 1 .. n ? Give a short proof.
Question 12. [10 points] Experimentally, what are the kinematics of neutron decay and what is the strength of the negative mass-squared results for the electron neutrino?
// Edit -- changed half-plane to half-space in Question 1.
QUOTE (NeoNo.1+Sep 12 2007, 11:48 AM)
AlphaNumeric
I would hold you in very high regards if you can accept you were wrong... Thus i present the following >
''The idea of GUT is highly misunderstood, as they are neither Grand nor Unified... anything can change this system at any time...''
And Hawkings says
''Even though we know the relevant laws that govern the universe, we do not know how they will operate in the long-run... into the future. This is the law of Chaos.''
So, how is that i have misunderstood what he says... What the prof. says here is quite reasonable...
Yes, linear operations are easily reversible. We can do linear transformations all day long and then reverse the entire chain in a single step, but non-linear interactions generate the equivalent of new dimensions of interactions that aren't linearly dependent upon the "parents" of the operation and if you have this in a recursive structure that continually multiplies these non-linearities, then you get exponentially expanding chaotic results that aren't easily reversible.
Encryption technologies typically use this effect to construct a preferred direction in computation. It's easy to multiply but potentially much harder to divide and this makes it so that you can have a message publicly displayed in the multiplied form, but the divisors are kept hidden so that the process can't be easily reversed.
Likely this is also why we see time heading in a specific direction 3 dimensionally. You need at least 3 points to construct a nonlinearity (if you only have 2, then you can only draw a straight line and every new point will always inherit the exact properties of that line), but if you have a point lying outside this line, then you can construct an infinite number of curves between them and each curve has its own unique mathematical properties that are generally incompatible with the other curves.
I would hold you in very high regards if you can accept you were wrong... Thus i present the following >
''The idea of GUT is highly misunderstood, as they are neither Grand nor Unified... anything can change this system at any time...''
And Hawkings says
''Even though we know the relevant laws that govern the universe, we do not know how they will operate in the long-run... into the future. This is the law of Chaos.''
So, how is that i have misunderstood what he says... What the prof. says here is quite reasonable...
Yes, linear operations are easily reversible. We can do linear transformations all day long and then reverse the entire chain in a single step, but non-linear interactions generate the equivalent of new dimensions of interactions that aren't linearly dependent upon the "parents" of the operation and if you have this in a recursive structure that continually multiplies these non-linearities, then you get exponentially expanding chaotic results that aren't easily reversible.
Encryption technologies typically use this effect to construct a preferred direction in computation. It's easy to multiply but potentially much harder to divide and this makes it so that you can have a message publicly displayed in the multiplied form, but the divisors are kept hidden so that the process can't be easily reversed.
Likely this is also why we see time heading in a specific direction 3 dimensionally. You need at least 3 points to construct a nonlinearity (if you only have 2, then you can only draw a straight line and every new point will always inherit the exact properties of that line), but if you have a point lying outside this line, then you can construct an infinite number of curves between them and each curve has its own unique mathematical properties that are generally incompatible with the other curves.
QUOTE (rpenner+Sep 13 2007, 01:12 AM)
<snip>
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> They seperate problems? Yes... your right, but that is just as much problems it creates.
Which means what exactly?
Which means what exactly?
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> I never said they where useless. I said they where, in so many words, insufficiant.
You said (and I quote) " Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton. Demonstrably false since we've done non-gravitational gauge theories for centuries. Even Maxwell's classical electromagnetism was a gauge theory, just not a quantum one.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
The queen-theory they represent is string theory, and even that is now faiding into the past as nothing but a curiosity. There are several pioneers now in high regards among the scientific hall suggesting that string theory isn;t even a science anymore.
String theory is still very much at the fore front of theoretical physics. It's still the most published topic area of 'next generation physics', it still has a large proportion of PhD students going into it. While theres now people who are vocal about their dislike of it, that's always been true. They are now just more vocal and with the spread of the internet science is a lot more accessible than it once was. How much did you know about string theory in 1990? Not a lot, despite it being over a decade old.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> Yeh... whatever you say. Actually, if you had ever studied this area yet, you will find that the equations of motion not only locate, but have non-locality equations, suggesting that some equations must be statistical being bound by the uncertainty principle of quantum theory.
The HUP comes from non-commuting operators. You construct local functions and operators using non-commuting operators in QFT all the time. Plenty of non-statistical things are built upon the non-commuting properties of x and p. Non-local operators generally have all sorts of inconsistency problems with them due to violating the special relativity constraints. Non-relativistic operators suffer from this the most, since the theory isn't formulated with special relativity.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
'How they are obeyed is another question, which is statistical, since there's often numerous ways a system can evolve in accordance with it's equations of motion.''
> Well, yes, at last we agree on something.
> Well, yes, at last we agree on something.
I didn't agree that finding the equations of motion is a statistical or probabilitistic procedure. I said there's a variety of ways for a system to go from one state to another and the particular way it does it in any given experiment is probabilistic. Again, it's the difference between "Finding the governing equations" and "Solving the governing equations". Haven't quite wrapped your noggin around that have you?
Have you read that book I mentioned? I covers causality in the second chapter.
Have you read that book I mentioned? I covers causality in the second chapter.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
>Well no. You are right and wrong again. If the Lagrangian equation represent future predictions, which all theories strive to reach, then there exists an invariant equalling a possible risk of a chaotic system.
The Lagrangian isn't an equation, it's an expression. I guess variational principles, the foundation of QFT, are not known to you. "an invariant equalling a possible risk of a chaotic system."? Care to elaborate (ie make that coherent and meaningful)?
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> And i've said, until your string theorist buds get gravity and quantum cosmology into a bundle with th other three forces, i'll admit i was wrong. But i will make a prediction. Give it three more years and scientists will have found a whole new theory for matter. I mean, for goodness sake, String Theories are unfalsfiable. So how can the theory ever be right?
I like how you're moving the usual meaning of "GUT" up to include gravity. String theory makes plenty of predictions, some of which we know to be right (gravity in general relativity), others we're close to testing (supersymmetry) and a huge amount which are outside our abilities to measure. As time progresses and people develop the theory one of three things will happen
1. Someone comes up with a concrete falsification experiment for string theory which we can do. Then it'll be make or break for the theory.
2. Someone shows a huge internal inconsistency which can't be resolved. String theory dies.
3. The current status continues.
It would seem we're moving slowly from case 3 to case 1. Phenomenological string theory is becoming more and more prominent.
1. Someone comes up with a concrete falsification experiment for string theory which we can do. Then it'll be make or break for the theory.
2. Someone shows a huge internal inconsistency which can't be resolved. String theory dies.
3. The current status continues.
It would seem we're moving slowly from case 3 to case 1. Phenomenological string theory is becoming more and more prominent.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
I improvised you to consider that the Heirarchy Problem was a considerable mechanism in your proposal. I never proposed it solved guts
You implied the Heirarchy problem was something of the same ilke as a system whose governing equations were known but which couldn't be solved. It's not. It's nothing to do with chaos either. It's about mass corrections to the Higgs and why they are so small. If you were familiar with quantum field theory you'd know about such processes.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
Do you know yet from your training that the Higgs Boson is unified of origin. It describes the Standard Model, which is equaly intrinsic to the study of Strings.
The Higgs describes the origin of rest mass within the SM, not the entire thing. There are Higgs-less Standard Model formulations but they aren't as elegant. And if the Higgs doesn't exist it wouldn't be a problem for string theory since it's not at the stage of formulating the SM particle families with gauge groups (it is compatible with the MSSM but only in terms of particles, no couplings yet). You can study strings while being oblivious to the state of the Higgs.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
If that doesn't exist, you can kiss your dream goodbye, for it will set the scientists back decades.
There are Higgs-less models and with such a huge issue, it would be the number one research topic on the planet. It wouldn't be decades before a new explaination would be arrived at, particularly given the information the LHC will provide.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
And, if that wasn't enough, we also need to understand dark matter... And to do so, we either needto find a neutrino or a axion
You mean 'neutralino'. Neutrinos, axions nor microblack holes can account for dark matter.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
And also, dark energy is also a mystery... we still don't know what it is, other than it has a negative pressure and that it permeates the entire outer-regions of the hypersphere.
Any evidence the universe is a hypersphere or are you just trying to use fancy words? (or worse, parrot Nick).
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> What do you mean? This is not a term i recognize.
I just wanted to see if you could do a bit of differential geometry, the kind I do a bit of.
QUOTE (NeoNo.1+Sep 12 2007, 08:57 PM)
> Well, sorry to disappoint you, but he was so much better than both of us put together...
Did you even read what I said? I was asking you to prove the thing you attributed to Einstein was something he actually said and not just your own claim with "Einstein said..." before it. Einstein knew the power of mathematics, he worked closely with Hilbert. I doubt he'd say what you attribute to him.
QUOTE (Euler+Sep 12 2007, 08:57 PM)
Look what just happened - a topic intimately related to physics, a question was posed, a discussion happened and (hopefully!) it was helpful all round. This is a good example of what actually happens in academia/physics communities. Rational discussion, reference to works, specific examples and links to further work. It's not a conspiracy, we don't just recite other peoples' work - we actually think, work through problems and help each other out! Shock horror!
Yes, a discussion on differential geometry, SUSY and groups is a refreshing change for this thread, even if it was brief and went over NeoNo.1's head
QUOTE (StevenA+Sep 12 2007, 08:57 PM)
Yes, linear operations are easily reversible.
No they don't have to be Steven. How many times have we been over this? You continue to post BS even when you know you'll be called on it.
You really are pathetic if you're so desperate to be thought well read.
You really are pathetic if you're so desperate to be thought well read.
Which means what exactly?
> That the amount of ''things'' it answers for, is in equal proportion to the problems it causes.
You said (and I quote) " Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton. Demonstrably false since we've done non-gravitational gauge theories for centuries. Even Maxwell's classical electromagnetism was a gauge theory, just not a quantum one
> That the amount of ''things'' it answers for, is in equal proportion to the problems it causes.
You said (and I quote) " Gauge groups are also useless without string theory presence of Gravitno's, which by the way, have yet to be found, along with the graviton. Demonstrably false since we've done non-gravitational gauge theories for centuries. Even Maxwell's classical electromagnetism was a gauge theory, just not a quantum one
What a load of baloney! And what? Your saying that axions and neutrinos are not types of dark matter... Well, i propose you are utterly incorrect. Gee, do you know anything about particle groups?
Damn it, I typed up several answers to Rpenner questions and then closed the wrong Opera window.
****!!
Rpenner, for Q6, do you want loop diagram computations (which I can provide) or something else?
****!!
Rpenner, for Q6, do you want loop diagram computations (which I can provide) or something else?
QUOTE (NeoNo.1+Sep 12 2007, 09:59 PM)
What a load of baloney! And what? Your saying that axions and neutrinos are not types of dark matter... Well, i propose you are utterly incorrect. Gee, do you know anything about particle groups?
The neutrino is not a candidate for dark matter, it's too light. Axions are either also ruled out or pushed into very convoluted formulations of the SM.
The neutrino is not a candidate for dark matter, it's too light. Axions are either also ruled out or pushed into very convoluted formulations of the SM.
I said, ''until your string theorist buds get gravity and quantum cosmology into a bundle with th other three forces, i'll admit i was wrong. But i will make a prediction. Give it three more years and scientists will have found a whole new theory for matter. I mean, for goodness sake, String Theories are unfalsfiable. So how can the theory ever be right?''
You said...
''I like how you're moving the usual meaning of "GUT" up to include gravity. String theory makes plenty of predictions, some of which we know to be right (gravity in general relativity), others we're close to testing (supersymmetry) and a huge amount which are outside our abilities to measure. As time progresses and people develop the theory one of three things will happen.''
So I will say...
If this is true, then i'll make a pact with you. We only have a few weeks left until the LHC activates its searches for proof of supersymmetry and the Higgs Boson (intrinsic to a unified theory of everything, i'll say once more without you ignoring what i said,) let us both wait and see if either two of these functions/mechanisms are discovered. If they are found, i will write you an entire eport how you where right, and i was wrong. Deal?
You said...
''I like how you're moving the usual meaning of "GUT" up to include gravity. String theory makes plenty of predictions, some of which we know to be right (gravity in general relativity), others we're close to testing (supersymmetry) and a huge amount which are outside our abilities to measure. As time progresses and people develop the theory one of three things will happen.''
So I will say...
If this is true, then i'll make a pact with you. We only have a few weeks left until the LHC activates its searches for proof of supersymmetry and the Higgs Boson (intrinsic to a unified theory of everything, i'll say once more without you ignoring what i said,) let us both wait and see if either two of these functions/mechanisms are discovered. If they are found, i will write you an entire eport how you where right, and i was wrong. Deal?
Oh... and... Neutrino's do count as being a candidate. No one has ever detected one, and no one knows how such a light particle (nearly massless), might interact with our matter. Some results have been hypothesized that it contains intrinsic properties to that of a Dark Matter... NASA also confirmed similar thoughts, with their evidence suggesting that Neutrino's create a gravity percentage of 7% of all mass in the universe. This is a large amount, no matter how you look at it. Because a billion Neutrino's pass through our bodies in one second, and yet we have never detected it, also, from my opinion, holds qualities of that of the Axion particle, which is actually classified in the Standard Model, (if you bothered to look it up), in the catagory of Dark Matter. It has properties that can travel through solid objects, and might be closely related to the electromagnetic forces. In fact, several scientists have formed a group to study the Dark Matter byusing a transverse magnetic field, and they hope to tease the the Axions out, and pass through a wall, only to be absorbed by a second magnetic transverse field, and obtain the photons again. The photons disregarded will be seen on the screen. The is a big step in quantum theory.
Neo
Neo
QUOTE (AlphaNumeric+)
No they don't have to be Steven. How many times have we been over this? You continue to post BS even when you know you'll be called on it.
You really are pathetic if you're so desperate to be thought well read.
Well likely the reason you find it difficult to invert a linear transformation is because you're not working with a linear transform (you just call them linear but don't recognize the non-linearities embedded within them).
You really are pathetic if you're so desperate to be thought well read.
Well likely the reason you find it difficult to invert a linear transformation is because you're not working with a linear transform (you just call them linear but don't recognize the non-linearities embedded within them).
QUOTE (NeoNo.1+Sep 12 2007, 10:25 PM)
Oh... and... Neutrino's do count as being a candidate. No one has ever detected one, and no one knows how such a light particle (nearly massless), might interact with our matter.
They've been detected for many years now. They interact via Weak bosons. Their mass splitting has been measured enough to know they are too light to account for all the dark matter.
Is that an example of how up to speed you are with particle physics?
They've been detected for many years now. They interact via Weak bosons. Their mass splitting has been measured enough to know they are too light to account for all the dark matter.
Is that an example of how up to speed you are with particle physics?
QUOTE (NeoNo.1+Sep 12 2007, 10:25 PM)
If this is true, then i'll make a pact with you. We only have a few weeks left until the LHC activates its searches for proof of supersymmetry and the Higgs Boson (intrinsic to a unified theory of everything, i'll say once more without you ignoring what i said,) let us both wait and see if either two of these functions/mechanisms are discovered. If they are found, i will write you an entire eport how you where right, and i was wrong. Deal?
It'll take years before the LHC is up to speed, output data and the data analyised. Do you think they flick a switch and the computer outputs "Higgs Found". 
And I'll repeat myself again, there are Higgsless models. http://en.wikipedia.org/wiki/Higgsless_model
And I'll repeat myself again, there are Higgsless models. http://en.wikipedia.org/wiki/Higgsless_model
QUOTE (StevenA+Sep 12 2007, 10:25 PM)
Well likely the reason you find it difficult to invert a linear transformation is because you're not working with a linear transform (you just call them linear but don't recognize the non-linearities embedded within them).
Still redefining words you don't understand and claiming you know more than maths professors I see StevenA.
Have you recently stopped taking vital medication or are you just plain stupid?
Have you recently stopped taking vital medication or are you just plain stupid?
I am not even going to properly reply to that. It is not even worth it.
Sorry for the break, but I needed lunch. (and breakfast.)
QUOTE (AlphaNumeric+Sep 12 2007, 09:11 PM)
Damn it, I typed up several answers to Rpenner questions and then closed the wrong Opera window.
This happens often enough to me, that I allowed separate answers to each of the numbered questions.
This happens often enough to me, that I allowed separate answers to each of the numbered questions.
QUOTE (AlphaNumeric+Sep 12 2007, 09:11 PM)
Rpenner, for Q6, do you want loop diagram computations (which I can provide) or something else?
Feel free to answer this question as you need to. In addition to perturbative methods, I though there are some non-perturbative work on this limited topic, but I think it would be easier to do the analytical work rather than explain Wilson loops.
QUOTE (NeoNo.1+Sep 12 2007, 10:56 PM)
I am not even going to properly reply to that. It is not even worth it.
You're right, it's not. The fact I have provided evidence against your claims like the Higgs being "intrinsic to a unified theory of everything" makes your claims clearly nonsense.
How about some more, like http://en.wikipedia.org/wiki/Neutrino#Neutrino_detection . Got any other shiners you want to pull out of the bag? You and Steven really are peas in a pod. You ignore evidence against you and ignore direct questions (still waiting on evidence for that quote you claimed was Einsteins!).
Do we even need to go through the pointless effort of answering (or in your case BS'ing) the questions? I suppose Rpenner did put a lot of effort in so we should do a few at least.
You're right, it's not. The fact I have provided evidence against your claims like the Higgs being "intrinsic to a unified theory of everything" makes your claims clearly nonsense.
How about some more, like http://en.wikipedia.org/wiki/Neutrino#Neutrino_detection . Got any other shiners you want to pull out of the bag?
You and Steven really are peas in a pod. You ignore evidence against you and ignore direct questions (still waiting on evidence for that quote you claimed was Einsteins!).Do we even need to go through the pointless effort of answering (or in your case BS'ing) the questions? I suppose Rpenner did put a lot of effort in so we should do a few at least.
QUOTE (NeoNo.1+Sep 12 2007, 04:56 PM)
I am not even going to properly reply to that. It is not even worth it.
QUOTE (NeoNo.1+Sep 12 2007, 09:56 PM)
I am not even going to properly reply to that. It is not even worth it.
Well, I guess thats it then
Well, I guess thats it then
QUOTE (rpenner+Sep 12 2007, 09:12 PM)
Question 6. [30 points] In Quantum Field Theory,
6A. Demonstrate asymptotic freedom in SU(3).
http://www.savefile.com/files/1050968
Full derivation of asymptotic freedom in one loop scalar QCD with general SU(N) gauge group. The Feynman diagrams aren't labelled, I never could get FeynMF to stop screwing around with label placement.
6A. Demonstrate asymptotic freedom in SU(3).
http://www.savefile.com/files/1050968
Full derivation of asymptotic freedom in one loop scalar QCD with general SU(N) gauge group. The Feynman diagrams aren't labelled, I never could get FeynMF to stop screwing around with label placement.
QUOTE (rpenner+Sep 12 2007, 09:12 PM)
Question 8. [40 points] In GUTs,
8A. Prove SU(4) will never cut it.
8B. Explain why SU(5) is experimentally rejected.
8C. Why is Bosonic string theory rejected?
8D. Why is unification of U(1)xSU(2)xSU(3) simply not enough.
8A. Prove SU(4) will never cut it.
8B. Explain why SU(5) is experimentally rejected.
8C. Why is Bosonic string theory rejected?
8D. Why is unification of U(1)xSU(2)xSU(3) simply not enough.
A. The reason SU(3) is a viable flavour symmetry is that the masses (and their mass splittings) between the u, d and s quarks are small compared to the QCD mass scale, Lambda, which is approximately 300MeV. The flavour SU(3) symmetry is pretty much an effective theory of QCD, with 1/Lambda being the expansion parameter.
The charm quark has a mass more than an order of magnitude above the s quark and several times bigger than Lambda (source). Thus, so while you can rearrange the quark mass terms for the u, d and s into a nice multiplet of SU(3), you cannot do this for any of the more massive quarks. (Details on Page 219 of Georgi - Lie Algebras in Particle Physis)
B. SU(5) breaks into SU(3)xSU(2)xU(1) in such a way as to predict extra gauge bosons on a GUT mass scale. While not observable at current energies as physical particles, they would play mediation roles within virtual processes. Within SU(5) all the SM particles live in the same multiplet, not seperate ones. Thus the gauge symmetries normally protecting things like baryon number no longer exist, since SU(5) doesn't distinguish between leptons or baryons when unbroken. As such, baryon violating decays would be possible with an SU(5) GUT model. The proton is a prime candidate for testing such predictions. Unfortunately an SU(5) GUT would allow the heavy boson mediated decay of the proton with such 'ease' that it would have a half life below the experimentally verified level.
Specific details are found in Chapter 18 of the aforementions Georgi book and Chapter 6 of Balin & Love's 'Supersymmetry Gauge Field Theory and String Theory'.
C. Aside from the obvious fact it doesn't contain fermions, a phenomenologically required field type, it has a tachyonic ground state in that when you use the generators of the Virassora Algebra to compute the mass-squared of a Fock space vacuum in the theory, it comes out to be mē = -1/2α', where α' is the usual string parameter. This leads to an unstable and unviable vacuum state. It is only resolved consistently using a superstring formulation and the GSO projection.
D. I don't follow the question. Do you mean we need to include some kind of formalism for gravity or that string theory (since part C mentions it) and/or supersymmetry has a concept of a hidden sector which doesn't couple to any of the SM fields but does to gravity and this might have a different gauge group setup and needs to be taken into account, for instance by considering the E8xE8 gauge group of Heterotic string theory to represent the hidden and the visible sectors?
It's hard to be precise on the last part.
I've done the black hole one too but on paper. I'll scan it in tomorrow in the department.
The charm quark has a mass more than an order of magnitude above the s quark and several times bigger than Lambda (source). Thus, so while you can rearrange the quark mass terms for the u, d and s into a nice multiplet of SU(3), you cannot do this for any of the more massive quarks. (Details on Page 219 of Georgi - Lie Algebras in Particle Physis)
B. SU(5) breaks into SU(3)xSU(2)xU(1) in such a way as to predict extra gauge bosons on a GUT mass scale. While not observable at current energies as physical particles, they would play mediation roles within virtual processes. Within SU(5) all the SM particles live in the same multiplet, not seperate ones. Thus the gauge symmetries normally protecting things like baryon number no longer exist, since SU(5) doesn't distinguish between leptons or baryons when unbroken. As such, baryon violating decays would be possible with an SU(5) GUT model. The proton is a prime candidate for testing such predictions. Unfortunately an SU(5) GUT would allow the heavy boson mediated decay of the proton with such 'ease' that it would have a half life below the experimentally verified level.
Specific details are found in Chapter 18 of the aforementions Georgi book and Chapter 6 of Balin & Love's 'Supersymmetry Gauge Field Theory and String Theory'.
C. Aside from the obvious fact it doesn't contain fermions, a phenomenologically required field type, it has a tachyonic ground state in that when you use the generators of the Virassora Algebra to compute the mass-squared of a Fock space vacuum in the theory, it comes out to be mē = -1/2α', where α' is the usual string parameter. This leads to an unstable and unviable vacuum state. It is only resolved consistently using a superstring formulation and the GSO projection.
D. I don't follow the question. Do you mean we need to include some kind of formalism for gravity or that string theory (since part C mentions it) and/or supersymmetry has a concept of a hidden sector which doesn't couple to any of the SM fields but does to gravity and this might have a different gauge group setup and needs to be taken into account, for instance by considering the E8xE8 gauge group of Heterotic string theory to represent the hidden and the visible sectors?
It's hard to be precise on the last part.
I've done the black hole one too but on paper. I'll scan it in tomorrow in the department.
S(N) = Sum from 1 to N of n^7 = (3/24)N^8 + (12/24)N^7 + (14/24)N^6 - (7/24)N^4 + (2/24)N^2
Proof by induction :
S(1) = 1^7 = 1
True for N=1
Assume true for N=k
S(k) = (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2
By definition, S(k+1) = S(k) + (k+1)^8 . Thus proven if I demonstrate S(k+1)-S(k) = (k+1)^8
S(k+1) - S(k) = (3/24)(k+1)^8 + (12/24)(k+1)^7 + (14/24)(k+1)^6 - (7/24)(k+1)^4 + (2/24)(k+1)^2 - [ (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2]
A lot of expanding, cancelling and collecting later and you have your answer.
Do you want me to actually do it or is that sufficent?
Proof by induction :
S(1) = 1^7 = 1
True for N=1
Assume true for N=k
S(k) = (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2
By definition, S(k+1) = S(k) + (k+1)^8 . Thus proven if I demonstrate S(k+1)-S(k) = (k+1)^8
S(k+1) - S(k) = (3/24)(k+1)^8 + (12/24)(k+1)^7 + (14/24)(k+1)^6 - (7/24)(k+1)^4 + (2/24)(k+1)^2 - [ (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2]
A lot of expanding, cancelling and collecting later and you have your answer.
Do you want me to actually do it or is that sufficent?
QUOTE (AlphaNumeric+Sep 13 2007, 08:01 AM)
A photon also is affected less by redshift as it reduces it's frequency, as if it's (in some equivalent sense) getting lighter.
That is an interesting point. Lower energy photons traveling at the same speed as higher energy photons - that seems to indicate that the speed limit has nothing to do with the light at all, but only that it is most obvious when observing light. The speed limit is due to "how long is a piece of string" maybe? My only knowledge of string theory is from reading A Brief History of Time, but it seems plausible to me that there could be a link between the speed limit and string length (as observed in the standard 4 dimensions).
Is there an upper limit to how much energy a photon can have? Is it theoretically possibly to overload a photon so that it travels at a speed < c? When I say theoretically possible, I mean that if we ignore any upper limit to photon energy, do any calculations indicate that the photon would travel at speeds < c?
That is an interesting point. Lower energy photons traveling at the same speed as higher energy photons - that seems to indicate that the speed limit has nothing to do with the light at all, but only that it is most obvious when observing light. The speed limit is due to "how long is a piece of string" maybe? My only knowledge of string theory is from reading A Brief History of Time, but it seems plausible to me that there could be a link between the speed limit and string length (as observed in the standard 4 dimensions).
Is there an upper limit to how much energy a photon can have? Is it theoretically possibly to overload a photon so that it travels at a speed < c? When I say theoretically possible, I mean that if we ignore any upper limit to photon energy, do any calculations indicate that the photon would travel at speeds < c?
Well I dunno lemme check.....
BTW, if you are having problems with closing the wrong browser window, you can type your posts up in a text document (which allows you to save via Ctrl+s as often as you please) and then just copy and paste when you feel it is complete. Nice and simple, and doesn't take much additional time.
QUOTE (AlphaNumeric+Sep 12 2007, 11:00 PM)
S(N) = Sum from 1 to N of n^7 = (3/24)N^8 + (12/24)N^7 + (14/24)N^6 - (7/24)N^4 + (2/24)N^2
Proof by induction :
S(1) = 1^7 = 1
True for N=1
Assume true for N=k
S(k) = (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2
By definition, S(k+1) = S(k) + (k+1)^8 . Thus proven if I demonstrate S(k+1)-S(k) = (k+1)^8
S(k+1) - S(k) = (3/24)(k+1)^8 + (12/24)(k+1)^7 + (14/24)(k+1)^6 - (7/24)(k+1)^4 + (2/24)(k+1)^2 - [ (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2]
A lot of expanding, cancelling and collecting later and you have your answer.
Do you want me to actually do it or is that sufficent?
Dear Alphanumeric,
Proof by induction
S(1)
S(K)
S(K+1)
Proof.
This is good enough to pass but not with honours......
You would look stupid if it did not work for S(2)
S(1),S(2),S(3)..........S(K), S(K+1)......proof by induction.......S(N-1), S(N)=...............
You can never prove a theory correct, but it only takes once to prove it wrong.
Experiment, experiment, experiment and calculate.
Alphanumeric is living proof, that Quasars exist.
Alphanumeric is living proof, that black holes exist.
Alphanumeric is living proof, that anti-matter exist.
Alphanumeric is living proof, that Hawking Radiation exist.
Alphanumeric is living proof, that Quantum Electrons exist.
Why do I know this, by experiment.....
Alphanumeric is one in 6 billion.
How do I know this?
He disagrees with.......
Kind Regards
Terry Giblin
HAL 9000 & 42
Proof by induction :
S(1) = 1^7 = 1
True for N=1
Assume true for N=k
S(k) = (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2
By definition, S(k+1) = S(k) + (k+1)^8 . Thus proven if I demonstrate S(k+1)-S(k) = (k+1)^8
S(k+1) - S(k) = (3/24)(k+1)^8 + (12/24)(k+1)^7 + (14/24)(k+1)^6 - (7/24)(k+1)^4 + (2/24)(k+1)^2 - [ (3/24)k^8 + (12/24)k^7 + (14/24)k^6 - (7/24)k^4 + (2/24)k^2]
A lot of expanding, cancelling and collecting later and you have your answer.
Do you want me to actually do it or is that sufficent?
Dear Alphanumeric,
Proof by induction
S(1)
S(K)
S(K+1)
Proof.
This is good enough to pass but not with honours......
You would look stupid if it did not work for S(2)
S(1),S(2),S(3)..........S(K), S(K+1)......proof by induction.......S(N-1), S(N)=...............
You can never prove a theory correct, but it only takes once to prove it wrong.
Experiment, experiment, experiment and calculate.
Alphanumeric is living proof, that Quasars exist.
Alphanumeric is living proof, that black holes exist.
Alphanumeric is living proof, that anti-matter exist.
Alphanumeric is living proof, that Hawking Radiation exist.
Alphanumeric is living proof, that Quantum Electrons exist.
Why do I know this, by experiment.....
Alphanumeric is one in 6 billion.
How do I know this?
He disagrees with.......
Kind Regards
Terry Giblin
HAL 9000 & 42
QUOTE (Terry Giblin+Sep 13 2007, 12:49 AM)
You would look stupid if it did not work for S(2)
You don't actually know what proof by induction is do you? Another thing taught to A Level students you don't know.
You don't actually know what proof by induction is do you?
Another thing taught to A Level students you don't know.QUOTE (Terry Giblin+Sep 13 2007, 12:49 AM)
You can never prove a theory correct, but it only takes once to prove it wrong.
I was proving a mathematical result, not a physical hypothesis. But good job on parroting a quote you so obviously don't understand.
QUOTE (Terry Giblin+Sep 13 2007, 12:49 AM)
HAL 9000 & 42
At least Hal knew how to do mathematics and physics.
QUOTE (AlphaNumeric+Sep 13 2007, 12:04 AM)
You don't actually know what proof by induction is do you? Another thing taught to A Level students you don't know.
I was proving a mathematical result, not a physical hypothesis. But good job on parroting a quote you so obviously don't understand.
At least Hal knew how to do mathematics and physics.
Dr Reed, Springfield Grammer School, Jarrow, 1982 taught me Proof By Induction, he was the best Pure Mathematics Teacher I have ever met.
He would have given your answer a pass rate, but he had to give my answer a distinction.
If you don't believe me ask any good Pure mathematics teacher, who's maths answer is the correct one, yours or mine?
Have you checked to make sure it works for S(2) or are you assuming, as usual.
Assumption is the mother of all Alpha ups.
Never assume.
Nature does not always play by your rules.
Alphamuneric anti induction, anti matter........anti Terry Giblin
1 in 6,000,0000,0000
Kind Regards
Terry Giblin
HAL-9000 & 42
Another thing taught to A Level students you don't know.I was proving a mathematical result, not a physical hypothesis. But good job on parroting a quote you so obviously don't understand.
At least Hal knew how to do mathematics and physics.
Dr Reed, Springfield Grammer School, Jarrow, 1982 taught me Proof By Induction, he was the best Pure Mathematics Teacher I have ever met.
He would have given your answer a pass rate, but he had to give my answer a distinction.
If you don't believe me ask any good Pure mathematics teacher, who's maths answer is the correct one, yours or mine?
Have you checked to make sure it works for S(2) or are you assuming, as usual.
Assumption is the mother of all Alpha ups.
Never assume.
Nature does not always play by your rules.
Alphamuneric anti induction, anti matter........anti Terry Giblin
1 in 6,000,0000,0000
Kind Regards
Terry Giblin
HAL-9000 & 42
QUOTE (Terry Giblin+Sep 12 2007, 07:22 PM)
Dr Reed, Springfield Grammer School, Jarrow, 1982 taught me Proof By Induction, he was the best Pure Mathematics Teacher I have ever met.
He would have given your answer a pass rate, but he had to give my answer a distinction.
If you don't believe me ask any good Pure mathematics teacher, who's maths answer is the correct one, yours or mine?
He would have given your answer a pass rate, but he had to give my answer a distinction.
If you don't believe me ask any good Pure mathematics teacher, who's maths answer is the correct one, yours or mine?
QUOTE (Terry Giblin+Sep 13 2007, 01:22 AM)
If you don't believe me ask any good Pure mathematics teacher, who's maths answer is the correct one, yours or mine?
Nope, it's explained here : http://en.wikipedia.org/wiki/Mathematical_induction
You'll find that Professor Gowers of Cambridge talks about the same method in his book, as well as the lecture course of his I attended where he goes about constructing the Reals via such logic.
My method was correct. You fail to grasp the point of induction.
You'll find that Professor Gowers of Cambridge talks about the same method in his book, as well as the lecture course of his I attended where he goes about constructing the Reals via such logic.
My method was correct. You fail to grasp the point of induction.
QUOTE (Terry Giblin+Sep 13 2007, 01:22 AM)
Have you checked to make sure it works for S(2) or are you assuming, as usual.
Still not getting it are you. You don't need to prove it works for S(2) if you prove S(1) is true and that if S(k) is true then S(k+1) is true.
A. S(1) is true
B. S(k) => S(k+1)
If A. then B => S(2).
If A. then (B=>S(2)) => S(3)
If A. then ((B=>S(2)) => S(3)) => S(4)
etc etc
No need to prove S(2) by hand, the power of induction does it for you.
Still not getting it are you. You don't need to prove it works for S(2) if you prove S(1) is true and that if S(k) is true then S(k+1) is true.
A. S(1) is true
B. S(k) => S(k+1)
If A. then B => S(2).
If A. then (B=>S(2)) => S(3)
If A. then ((B=>S(2)) => S(3)) => S(4)
etc etc
No need to prove S(2) by hand, the power of induction does it for you.
QUOTE (Terry Giblin+Sep 13 2007, 01:22 AM)
He would have given your answer a pass rate, but he had to give my answer a distinction.
No, you'd get a fail because you have obviously failed to understand how the method works.
Notice how, in this thread, when someone's challenged me to explain myself or to demonstrate I can do some of the things I claim, I do. Notice how whenever someone's asked you to do that Terry, you fail miserably. Not once have you got a passing grade in justifying any of your claims.
0 out of 10. Do not pass go. Go directly to psychotic ward.
Notice how, in this thread, when someone's challenged me to explain myself or to demonstrate I can do some of the things I claim, I do. Notice how whenever someone's asked you to do that Terry, you fail miserably. Not once have you got a passing grade in justifying any of your claims.
0 out of 10. Do not pass go. Go directly to psychotic ward.
QUOTE (Terry Giblin+Sep 13 2007, 01:22 AM)
Assumption is the mother of all Alpha ups.
My methodology was fine, no problems with it. Ignorance is the root of all your problems. Well, ignorance and wacked out delusion.
(bonk)
well, after an entire day, i'm still struggling with f(f(x))=exp
my attempt so far:
Df(f(x))=Df(f(x))*Df(x)=exp.
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
so,
f(x)=x
f'(x)=exp^x/2
f''(x)=1/2*exp^x/2
etc...
f(y)=x+(exp^x/2)(y-x)+1/4(exp^x/2)(y-x)^2+...
///
for sum(x^7,x=1..n), i'd get maple to find it, then prove by induction.
well, after an entire day, i'm still struggling with f(f(x))=exp
my attempt so far:
Df(f(x))=Df(f(x))*Df(x)=exp.
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
so,
f(x)=x
f'(x)=exp^x/2
f''(x)=1/2*exp^x/2
etc...
f(y)=x+(exp^x/2)(y-x)+1/4(exp^x/2)(y-x)^2+...
///
for sum(x^7,x=1..n), i'd get maple to find it, then prove by induction.
[post removed]
Terry, answer honestly, are you bi-polar or some other condition related to neurological imbalances? It's just nothing in that post even came close to addressing your claims or what I'd said. Nothing was particularly relevent and in some cases, completely random.
I guess you realise you're incorrect so try to get out of it by appearing to be a completely insane *****.
Anyway....
I guess you realise you're incorrect so try to get out of it by appearing to be a completely insane *****.
Anyway....
QUOTE (xaos+)
well, after an entire day, i'm still struggling with f(f(x))=exp
my attempt so far:
Df(f(x))=Df(f(x))*Df(x)=exp.
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
my attempt so far:
Df(f(x))=Df(f(x))*Df(x)=exp.
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
On the surface, this appears a valid method (I thought a similar thing when I got up this morning) but it relies on the assumption that there's a Real solution to x = e^x, which there isn't. Since f:R->R, if the solution(s) to x = e^x are complex then you're not able to expand about such solutions. If you can (ie taking it into the complex plane), the solution is readily forthcoming.
I'll admit, I have gone around in circles with the first part of the question but I can do the rest of it.
I'll admit, I have gone around in circles with the first part of the question but I can do the rest of it.
Dear Xaos,
QUOTE (Xaos+)
Df(f(x))=Df(f(x))*Df(x)=exp.
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
so,
f(x)=x
f'(x)=exp^x/2
f''(x)=1/2*exp^x/2
etc...
Well done, you're almost their, but you have made one to many assumptions,
Everyone appears to have forgotten one very important thing
Which applies to everything in the universe, from a black holes down to the quantum electrons.
Which raises the immediate questions.
What is imaginary?
What is time?
Now it works.
Answers on a post card........
Sincere Regards
Terry Giblin
HAL-9000 & 42
choose f(x)=x as the center, so Df(x)^2=exp or Df(x)=sqrt(exp)=exp^x/2
so,
f(x)=x
f'(x)=exp^x/2
f''(x)=1/2*exp^x/2
etc...
Well done, you're almost their, but you have made one to many assumptions,
Everyone appears to have forgotten one very important thing
Which applies to everything in the universe, from a black holes down to the quantum electrons.
Which raises the immediate questions.
What is imaginary?
What is time?
Now it works.
Answers on a post card........
Sincere Regards
Terry Giblin
HAL-9000 & 42
QUOTE (Terry Giblin+Sep 13 2007, 05:12 PM)
Everyone appears to have forgotten one very important thing
....[pictures of two forms of the UP]
And you're forgetting that the question he's trying to do is a mathematical equation, solving a series of equations. There's nothing in it to do with quantum mechanics when it comes to solving the question itself.
By your logic 1+1 isn't equal to 2 because of quantum mechanics. Nonsense, we're dealing with maths here, not physics.
Another example of you failing to grasp anything about maths or physics. Why don't you just go back to spamming your BS in your thread over in "Off Topic". At least there you kept out of the way.
....[pictures of two forms of the UP]
And you're forgetting that the question he's trying to do is a mathematical equation, solving a series of equations. There's nothing in it to do with quantum mechanics when it comes to solving the question itself.
By your logic 1+1 isn't equal to 2 because of quantum mechanics. Nonsense, we're dealing with maths here, not physics.
Another example of you failing to grasp anything about maths or physics. Why don't you just go back to spamming your BS in your thread over in "Off Topic". At least there you kept out of the way.
QUOTE (Terry Giblin+Sep 13 2007, 03:34 PM)
Dear anti-numeric,
You're 1 in 6,000,000,000
Proof by induction;
What is the probability Terry Giblin is always dealt a Royal Flush.
Hand S(1) =
Hand S(k) =
The probability that Giblets was dealt this hand:
1:1
You're 1 in 6,000,000,000
Proof by induction;
What is the probability Terry Giblin is always dealt a Royal Flush.
Hand S(1) =
Hand S(k) =
The probability that Giblets was dealt this hand:
1:1
Giblin's a wild card a full house couldn't beat.
More like 55 cards short of a deck!
QUOTE (rpenner+Sep 12 2007, 09:12 PM)
Question 7. [30 points] In General Relativity, lets talk about in-plane circular orbits about a rotating black hole of mass M.
7A. What is the expression for the proper time to complete an orbit in the direction of rotation?
7B. And if you are orbiting "the wrong way" ?
7C. What do the extremal solutions correspond to?
In this, are you after photon, particle or both kinds of orbits? Also, do you want the expression for the possible circular orbit radius (or radii as the case may be) or the proper time just in terms of r=R, rather than r = [long expression from solving certain equations]?
I've got to admit, Q10 has been bugging the crap out of me. I can do all but the first part. I can do the first part if working over the complex numbers but not if f:R->R. I can prove various properties of f and it's domain/range but just getting the Taylor expansion over R is a roadblock.
Xaos, you thought in a good direction but the issue is that you've assumed that there's an x such that f(x) = x. That implies that e^x = f(f(x)) = f(x) = x. There's no Real solution for x = e^x unfortunately!
I've seen similar questions before like "Find f(x) such that f(x+y) = f(x)+f(y) and f(f(x)) = -x". That's got a rather unpleasant solution (it's a linear map on the Reals as a vector space over Q, the rationals!) and not differentiable itself (though it's self composite is).
I wonder if NeoNo.1 is doing any of them? I'll admit I've not put pen to paper for the earlier questions (somewhat uninteresting) so he could answer those. Even if I answered no more, still ahead of him. Maybe he's asked the questions on other forums and is waiting for an answer or ten?
Unfortunately tonight and tomorrow are friends birthdays and tomorrow I'm sorting out work with my supervisor for our visit to Spain so I'll look at some of the others when I have time. Sketch answers on methodology would be enough for some of them anyway.
7A. What is the expression for the proper time to complete an orbit in the direction of rotation?
7B. And if you are orbiting "the wrong way" ?
7C. What do the extremal solutions correspond to?
In this, are you after photon, particle or both kinds of orbits? Also, do you want the expression for the possible circular orbit radius (or radii as the case may be) or the proper time just in terms of r=R, rather than r = [long expression from solving certain equations]?
I've got to admit, Q10 has been bugging the crap out of me. I can do all but the first part. I can do the first part if working over the complex numbers but not if f:R->R. I can prove various properties of f and it's domain/range but just getting the Taylor expansion over R is a roadblock.
Xaos, you thought in a good direction but the issue is that you've assumed that there's an x such that f(x) = x. That implies that e^x = f(f(x)) = f(x) = x. There's no Real solution for x = e^x unfortunately!
I've seen similar questions before like "Find f(x) such that f(x+y) = f(x)+f(y) and f(f(x)) = -x". That's got a rather unpleasant solution (it's a linear map on the Reals as a vector space over Q, the rationals!) and not differentiable itself (though it's self composite is).
I wonder if NeoNo.1 is doing any of them? I'll admit I've not put pen to paper for the earlier questions (somewhat uninteresting) so he could answer those. Even if I answered no more, still ahead of him. Maybe he's asked the questions on other forums and is waiting for an answer or ten?
Unfortunately tonight and tomorrow are friends birthdays and tomorrow I'm sorting out work with my supervisor for our visit to Spain so I'll look at some of the others when I have time. Sketch answers on methodology would be enough for some of them anyway.
I keep wanting to ask if using the taylor series for ln(x) and then examining
ln(x) - x = 0
Is useful.
ln(x) - x = 0
Is useful.
QUOTE (Trippy+Sep 13 2007, 07:06 PM)
I keep wanting to ask if using the taylor series for ln(x) and then examining
ln(x) - x = 0
Is useful.
Say Trippy,
You can take the series for ln((x+1)/(x-1)), then work out what x is, however a better series is called the PADE series which accumulates one poly series divided by another poly series. Oviously, the more terms you have the more accurate your series but the PADE series is more accurate and compact than Taylors.
Hope this helps
Darren
ln(x) - x = 0
Is useful.
Say Trippy,
You can take the series for ln((x+1)/(x-1)), then work out what x is, however a better series is called the PADE series which accumulates one poly series divided by another poly series. Oviously, the more terms you have the more accurate your series but the PADE series is more accurate and compact than Taylors.
Hope this helps
Darren