# Symmetry the new Ptolemaic Theory?

## Main Question or Discussion Point

Having watched with interest the "progress" in theory since my retirement, I have come to the conclusion that it well may be in the state that Ptolemaic astromical theory was in its heyday. That is to say since the circle was the most 'perfect' figure everything else could be understood using only circles. Substitute 'symmetry groups' and one comes up to date. Few predictions, and when facts get awkward just add another group.
Of course if the Higgs particle is discovered and leads to lots of confirmed predictions, I shall have to change my mind, won't I?
Ernie

## Answers and Replies

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ahrkron
Staff Emeritus
Gold Member
But what about all the predictions already confirmed?

To some extent, the last 10 or so years in particle physics have been composed basically of experimental confirmations of standard model predictions (with some exceptions, like neutrino physics and probably the size of CP violation). I'm not saying that new physics will not be found around the corner, but so far symmetry groups seem to have done a great job.

samalkhaiat
ahrkron said:
I'm not saying that new physics will not be found around the corner, but so far symmetry groups seem to have done a great job.
And, they (symmetry groups) will play an important part in any "new physics".

sam

samalkhaiat
Ernies said:
Having watched with interest the "progress" in theory since my retirement, I have come to the conclusion that it well may be in the state that Ptolemaic astromical theory was in its heyday.
Physicists try to find as symmetric a model of the world as can be fitted to their experience of reality. The whole history of science has been the gradual realization that our world must be symmetric. The symmetry of the world can be taken as an axiom; deviations from this symmetry are what have to be explained.
According to Plato, the world is ultimately reducible to nothing but geometrical objects.The five so-called "perfect" platonic solids (the cube,tetrahedron,octahedron,dodecahedron and the icosahedron). This is beauty & simplicity.
This is exactly what Einstein meant by: "nature is the realization of the simplest conceivable mathematical ideas".
Yes, we now believe that the world is ultimately reducible to nothing but the fundamental & irreducible representations of some symmetry group. This is exactly what the quarks, leptons and the gauge bosons are.
I do not think this is going to change in the future, because symmetry plays an essential role in our reasoning. It seems as if the brain, not just prefers, but also looks for symmetric solutions to problems.

In retirement or not, you must know that almost all scientific knowledge can be formulated in terms of symmetry principles.

regards

sam

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Staff Emeritus
Gold Member
Dearly Missed
And what about Noether's Theorem? Any symmetry of the action corresponds to a conserved quantity in the equations of motion. This alone would guarantee that physicists would pay close attention to symmetries.

samalkhaiat said:
Ernies said:
... The symmetry of the world can be taken as an axiom; deviations from this symmetry are what have to be explained....
I do not think this is going to change in the future, because symmetry plays an essential role in our reasoning. It seems as if the brain, not just prefers, but also looks for symmetric solutions to problems.
In retirement or not, you must know that almost all scientific knowledge can be formulated in terms of symmetry principles.
regards
sam
Sure! Because we built them that way---including the logic system. I would remind you of what several eminent pre-WW2 theoreticians said.
In its simplest form "the trouble is not that the universe is queerer than we think, but that it well may be queerer than we can think".
I do not suggest giving up, merely to avoid rounding the corners of square pegs to make them fit round holes.
Cheers
Ernie

CarlB
Homework Helper
I do think that symmetries have worn out their welcome a bit.

The problem is not so much the use of symmetries to solve problems but in defining the problem in terms of symmetries.

The physics cat chases its tail a bit on the subject of mass and it shows up in the symmetries. Elementary particles are defined in terms of their energies and angular momenta. Where do energy and angular momentum come from? They're defined classically. Of the units involved, the one that is suspicious is mass.

Sure mass is defined classically, but it is redefined in quantum mechanics according to the Higgs mechanism. So there is an inherent self referential quality built into the symmetry strucuture of quantum mechanics that prevents it from carefully examining its foundations.

What we need, I think, is to define the particles according to their position and velocity eigenstates instead of their energy and momentum eigenstates. Then one can define mass as an interaction between the left and right handed chiral particles.

Carl

samalkhaiat
Ernies said:
Sure! Because we built them that way---including the logic system.
No, we do not make symmetries, we discover them. The real symmetries of the world are objective (not subjective) features.
Logic is an arbitrary set of rules, you could make your owns.
"the trouble is not that the universe is queerer than we think, but that it well may be queerer than we can think".
It is, isn't it.

Cheers

sam

samalkhaiat
CarlB said:
I do think that symmetries have worn out their welcome a bit.
Well carl, you thought wrong.
The problem is not so much the use of symmetries to solve problems but in defining the problem in terms of symmetries.
Yes, we define physical problems in terms of symmetries. And, there will be no escape of this fact because our brain seems to function this way. When you talk about art an science, your brain forces you to talk in terms of symmetries.
All body of theoretical physics can be derived from action principle.
The action integral is defined to be invariant under certain symmetry groups.
Physics progresses by discovering more and more accurate symmetries of the world.The ultimate goal in physics is; Finding that single symmetry group of our world.This is,of course, equivalent to "The Theory of Everything".
The physics cat chases its tail a bit on the subject of mass and it shows up in the symmetries.
What is this

Elementary particles are defined in terms of their energies and angular momenta.
No, they are defined as the fundamental representation of certain symmetry (Poincare & Gauge) groups.These groups assign mass, spin angulare momentum & charges to all representations (eigenvales of Casimir operators).
Where do energy and angular momentum come from?
The energy-momentum 4-vector(P) and the angular momentum tensor(M)are the generators of Poincare's group.We use them to find Casimir operators ( p^2, P.M )
The form of p and M can be derived from the invariance of the action integral under Poincare group which also shows their conservation laws(Noether Theorem).The form of (P,M ) can be used to show that particles transform in the right way (consistency check).
Sure mass is defined classically, but it is redefined in quantum mechanics according to the Higgs mechanism.
The Higgs phenomena does not redefine the mass. It provides the gauge bosons with the usual,classically defined, mass.It does that by hiding the internal symmetry.
What we need, I think, is to define the particles according to their position and velocity eigenstates
Can you show us, How is this possible? What about uncertainty principle And how can you account for the differences between Quarks and Cucumber?
Then one can define mass as an interaction between the left and right handed chiral particles.
Before I ask you to show me how this leads to mass, I need to know;What kind of interaction is this?
All interactions in nature arise naturally from gauging certain global Lie symmetries of the action
Chiral Particles?
So your interaction (whatever it is) is invariant under the chiral symmetry group SU(n)_L X SU(n)_R ?
What happened to "..symmetries have worn out their welcome.."
Carl, if you don't have a clear and definite formulation (from defining particles to defining their mass and charge), then all of your statements are nothing but "Garbage Theory".

cheers

sam

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Kea
Ernies said:
Substitute 'symmetry groups' and one comes up to date.
Well, Ernie, I'm with you all the way!

On the thread https://www.physicsforums.com/showthread.php?t=102840 there is a link to a short article by 't Hooft expressing similar sentiments. Of course, when I express similar sentiments I usually get tied up to my chain.

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CarlB
Homework Helper
samalkhaiat said:
All body of theoretical physics can be derived from action principle.
This is true for modern physics, but it is not a necessary part of it. It's just a convenient way of enforcing symmetries. The other day I read an interesting book by a physicist that described, for a popular audience, his "variable speed of light" theory. (I think the title was "Faster than Light".) You can read his paper and the many papers extending his theory (which was to explain inflation in cosmology) by searching for "VSL" on arxiv.org. Anyway, when he first submitted his paper to a journal, one of the complaints about it was that it did not include an action principle. I don't recall if he added one in or if he managed to argue past the referees, but he did get his paper published in Phys Rev.

samalkhaiat said:
The action integral is defined to be invariant under certain symmetry groups.
This is true, but the effect reminds me of how students work problems by peeking at the answer. In this case, the answer, provided by experiment, is the symmetry group. When one writes an action integral according to the limitations of that symmetry, one is, in effect, using the answer to define the model.

A big problem with using symmetries in this way is that man being a finite creature, none of our experiments can distinguish between a perfect symmetry and a near perfect symmetry. This has been a problem throughout physics. For example, before the late 19th century, there was no experimental evidence against Gallilean relativity and so it was accepted as a perfect symmetry. The current situation may be worse in that symmetry violations at Plank scale may be beyond the reach of any experiment.

samalkhaiat said:
Physics progresses by discovering more and more accurate symmetries of the world.The ultimate goal in physics is; Finding that single symmetry group of our world.
This is just rot. The biggest early success of quantum mechanics was in the explanation of the periodic table of the elements. Previously, the table had been organized according to symmetry considerations. But those symmetries were a bit, well, broken. With the discovery of Schroedinger's equation, the periodic table was completely explained in detail.

Before Schroedinger, the prevalent quantum mechanics was "matrix mechanics" which bears a certain resemblance to the crippled theory of the present.

samalkhaiat said:
Can you show us, How is this [use velocity eigenstates instead of momentum eigenstates] possible?
Yes. It's rather elegant, but it's beyond the scope of this short comment. The hint on how to do it was included by Feynman in a footnote on the electron propagator in his book for the popular reader "QED: The Strange Theory of Matter and Light". The footnote is on how one may obtain a massive propagator from a massless one by resummation. (Warning, Feynman uses non standard notation in the above so you'll have to read the book to translate it into physics.)

Of course the massless propagators (in the momentum representation) that Feynman refers to are eigenstates of energy, but you can do another stage of resummation before that. That is, propagators for eigenstates of velocity (that will be of form 1/k using the usual Dirac or Clifford algebra) can be converted into propagators of form 1/p by resummation. And then, the massless propagators can be resummed to produce the massive ones. Feynman's footnote, along with the hint that for fermions you're going to have to assume separate left and right handed "bare" velocity eigenstates, should be enough to get you through the derivation.

samalkhaiat said:
What about uncertainty principle. And how can you account for the differences between Quarks and Cucumber?
Huh?

samalkhaiat said:
Carl, if you don't have a clear and definite formulation (from defining particles to defining their mass and charge), then all of your statements are nothing but "Garbage Theory".
Hey, I'm just throwing up a trial balloon. The mathematics is very easy, but the physical interpretation is, well, a bit cranky.

Carl

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samalkhaiat
CarlB said:
This is true for modern physics, but it is not a necessary part of it.
What is your necessary part of modern physics?
The biggest early success of quantum mechanics was in the explanation of the periodic table of the elements. Previously, the table had been organized according to symmetry considerations. But those symmetries were a bit, well, broken. With the discovery of Schroedinger's equation, the periodic table was completely explained in detail.
What a garbage.
Mendeleev table has nothing to do with the groups of transformations which define symmetries in physics which is the point of this thread.
Look at the following correspondence, between symmetries and theories, which explains what I meant by: "physics progresses..."
Galilean symmetry<===>Classical Mechanics,QM
Poincare symmetry<===>CFT,QFT
Poicare+U(1)-gauge symmetry<==>Maxwell's CED,QED
General covariance,or Local Poicare Symmetry<==>Einstein's GR
Poicare+non-abelian gauge symmetry<==>Yang-Mill's theories(QCD)
Supersymmetries<==>Super gravity, superstrings and super M-theories.
This is a real progress. if you can not see it, then you have a problem!
It's rather elegant, but it's beyond the scope of this short comment. The hint on how to do it was included by Feynman in a footnote on the electron propagator in his book for the popular reader "QED: The Strange Theory of Matter and Light". The footnote is on how one may obtain a massive propagator from a massless one by resummation.
Of course the massless propagators (in the momentum representation) that Feynman refers to are eigenstates of energy, but you can do another stage of resummation before that. That is, propagators for eigenstates of velocity (that will be of form 1/k using the usual Dirac or Clifford algebra) can be converted into propagators of form 1/p by resummation. And then, the massless propagators can be resummed to produce the massive ones.
You have just opened more cans of garbage.
I have been playing with propagators for 15 years,teaching them for 8 years, and I have read almost all Feynman technical papers and books, Yet I understood one, and only onething about your statements, That is:
"THEY MAKE NO SENSE AT ALL"
Certainly, you misunderstood Feynman's words.
Feynman's footnote, along with the hint that for fermions you're going to have to assume separate left and right handed "bare" velocity eigenstates, should be enough to get you through the derivation.
The mathematics is very easy, but the physical interpretation is, well, a bit cranky.
I am asking you again to show me how do you define particles in terms of their position and velocity eigenstates? And how can you arrive at their masses?
Forget the "cranky" physical interpretation, just do the Math.
Hard or Easy, math will be fine OK, I'm waiting:tongue2:

regards

sam

CarlB
Homework Helper
samalkhaiat said:
I have been playing with propagators for 15 years,teaching them for 8 years, and I have read almost all Feynman technical papers and books, Yet I understood one, and only onething about your statements, That is: "THEY MAKE NO SENSE AT ALL". Certainly, you misunderstood Feynman's words.
Hey, while I was mostly educated in mathematics, I did have enough time as a grad student in physics, educated in propagators by guys who'd been teaching them for years, and they didn't know what I have learned since then either. If you know what one physicist thinks about something you pretty much know what the whole lot thinks. Alain Connes put it this way in his advice to young mathematicians:

Advice to the Beginner
"I was asked to write some advice for young mathematicians. The first observation is that each mathematician is a special case, and in general mathematicians tend to behave like "fermions" i.e. avoid working in areas which are too trendy whereas physicists behave a lot more like "bosons" which coalesce in large packs and are often "overselling" their doings, an attitude which mathematicians despise."
ftp://ftp.alainconnes.org/Companion.pdf[/URL]

[QUOTE=samalkhaiat]I am asking you again to show me how do you define particles in terms of their position and velocity eigenstates? And how can you arrive at their masses?[/QUOTE]

There are two stages of resummation between the velocity eigenstates and standard physics. Feynman's comments cover one of those two stages, and I'll restrict my comments to that one. Let me quote directly from his popular book:

[QUOTE=Feynman, QED: The Strange Theory of Light and Matter, pp90-91]The second action fundamental to quantum electrodynamics is: An electron goes from point A to point B in space-time. (For the moment we will imagine this electron as a simplified, fake electron, with no polarization -- what the physicists call a "spin-zero" electron. In reality, electrons have a type of polarization, which doesn't add anything to the main ideas; it only complicates the formulas a little bit.) The formula for the amplitude for this action, which I will call E(A to B) also depends on $$(X_2-x_1)$$ and $$(T_2-T_1)$$ (in the same combination as described in note 2) as well as on a number I will call "$$n$$," a number that, once determined, enables all our calculations to agree with experiment. (We will see later how we determine $$n$$'s value.) It is a rather complicated formula, and I'm sorry that I don't know how to explain it in simple terms. However, you might be interested to know that the formula for P(A to B) -- a photon going from place to place in space-time -- is the same as that for E(A to B) -- an electron going from place to place -- if n is set to zer.[3]

Footnote [3]: The formula for E(A to B) is complicated, but there is an interesting way to explain what it amounts to. E(A to B) can be represented as a giant sum of a lot of different ways an electron could go from point A to point B in space-time (see Fig. 57): the electron could take a "one-hop flight", going directly from A to B; it could take a "two-hop flight," stopping at an intermediate point C; it could take a "three-hop flight," stopping at points D and E, and so on. In such an analysis, the amplitude for each "hop" -- from one point F to another point G -- is P(F to G), the same as the amplitude for a photon to go from a point F to a point G. The amplitude for each "stop" is represented by $$n^2$$, $$n$$ being the same number I mentioned before which we used to make our calculations come out right.

The formula for E(A to B) is thus a series of terms: P(A to B) [the "one-hop" flight] + P(A to C) * $$n^2$$ * P(C to B) ["two-hop" flights, stopping at C] + P(A to D) * $$n^2$$ * P(D to E) * $$n^2$$ P(E to B) ["three-hop" flights, stopping at D and E] + ... for [I]all possible intermediate points[/I] C, D, E and so on.
Note that when $$n$$ increases, the nondirect paths make a greater contribution to the final arrow. When $$n$$ is zero (as for the photon), all terms with an $$n$$ drop out (because they are also equal to zero), leaving only the first term, which is P(A to B). Thus E(A to B) and P(A to B) are closely related.[/QUOTE]

Most of the above should be obvious from context, except perhaps the "arrow", which is Feynman's term, in this popular book, for a complex number.

The above quote from Feynman should make it obvious to the physics educated readers how to do the same thing for spin-1/2 particles. Clearly Feynman wouldn't have given a method that only worked for scalars, but if you want hints on how to do it with left and right handed (massless) chiral electron states to form them into a single massive electron propagator, just ask and I'll point you in the right direction.

What Feynman didn't mention in the above is that there is another resummation, one that gets you from the propagator for a velocity eigenstate to the photon propagator. If I recall correctly, the method is to use propagators of 1/v (in Dirac algebra notation), and vertices of E. The resummation turns this set of Feynman diagrams into a propagator of 1/p.

It's a fairly amusing theory. For example, one of the problems with a prefered reference frame (as is so often discussed in recent articles on Arxiv) is that a global reference frame allows one to distinguish between otherwise identical particles that have different energies. The resummation, from velocity eigenstates to energy eigenstates, allows one to obtain all energies of electrons as combinations of the velocity eigenstate electron.

Carl

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Sam seems to be talking past rather than to CarlB, and seems to display the same kind of devotion as was accorded to the original theory in the 1930s. Having lived through three physics 'revolutions' with like supporters I'm sceptical about all of them as even pointing to completion. Do you remember 'forbidden transitions' various 'parity conservations' and the like. A symmetry is an imposed mental construct, and to have a symmetry group for the whole universe points to megalomania.
Ernie

CarlB
Homework Helper
samalkhaiat said:
All body of theoretical physics can be derived from action principle.
There are reasons for exploring a basis for physics other than an action principle. Like you said, the human eye appreciates beauty and symmetry, but this is not a good thing. Humans can see patterns where no patterns exist and the psychology papers are replete with examples.

In exploring alternative approaches to physics I can at least claim to be in the company of physicists such as Feynman. For example, see

"On Feynman's Approach to the Foundations of Gauge Theory"
M. C. Land, N. Shnerb, L. P. Horwitz
abstract: "In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations coordinates and velocities. ..."
http://arxiv.org/abs/hep-th/9308003

Clifford algebra, as used by David Hestenes in his Geometric Algebra, provides a method of obtaining not just commutation relations but a full algebra amongst the coordinates. And as I showed in the previous post, it is possible to resum massless velocity eigenstate propagators to get the massive ones.

Carl

samalkhaiat
CarlB said:
and in general mathematicians tend to behave like "fermions" i.e. avoid working in areas which are too trendy whereas physicists behave a lot more like "bosons" which coalesce in large packs and are often "overselling" their doings, an attitude which mathematicians despise."
I have to disagree with Connes on this.His statement does not do justice to at least one physicist. Hartland Snyder (Phys.Rev.1947) introduced the idea of non-commutative geometry 50 years before A. Connes. Even before Connes was born, Weyl,,Hiesengerg and Paule spoke about non-commutative spacetime.
By the way, human beings (mathematicians included) behave like bosons with respect to any "profitable" activities. Nothing wrong with this.
As a physicist, I would say to Connes:
Human beings are bosons. They are a classical system.Therefore, they can not behave like fermions.Fermions have no classical limit:rofl:
Any way, let us move on,this is hardly an issue in this thread.
There are two stages of resummation between the velocity eigenstates and standard physics. Feynman's comments cover one of those two stages, and I'll restrict my comments to that one. Let me quote directly from his popular book:
Carl, Feynman was explaining,to school kids, the first three terms of the perturbation series for the 2-point Green's function.
So, tell me and show me the math:surprised
What is the connection between Feynman's statements(perturbation theory) and your statements about defining particles and their mass?
If you,as you say, educated in mathematics, then show us:
1) How do you define particles in terms of their position and velocity eigenstates?
2) How can you get mass from your undefined interaction?

I want to see your math.
if you want hints on how to do it with left and right handed (massless) chiral electron states to form them into a single massive electron propagator, just ask and I'll point you in the right direction.
No, I don't want "hints", Prove your claims.
Let me tell you something about propagators.Have you herd about the integral representation of Huygen's principle? Well, it is:
w(c) = Integ.[K(c,a).w(a)] da.
In QM, we write this as:
<c|w> = Integ.[<c|a><a|w>] da.
The Huygen's kernel K(.,.), the transition amplitude from a to c (<c|a>), The Green's function G(x,y), and the matrix element of the time evolution operator(<x|U(t,T)|y>) are names for propagator:
Propagator<x,t|y,T>=G(x,t;y,T)=<x|G(t,T)|y>=<x|exp[iH(T-t)]|y>.
In field theory, the propagator in p-space can be obtained by inverting the Fourier-transformed differential operator contained in the action integral:
S~ w(x).D(x).w(x).
Propagator=1/D(k),
or, equivalently, the Fourier-transformed vacuum expectation value of the time-ordered product of fields(2-point Green's function):
<0|:{w(x)w(x)}:|0> = G(x,y).
In Feynman diagrams,we assign a propagator to internal lines=virtual particles.
For photons(in Feynman gauge), It is ~1/k^2
For (massless) electrons: ~p/p^2.
***
If you remember, this thread was about the importance of symmetries in physics,your example of symmetry(the Mendeleev table!) made me laugh, then,you made a very strange claim about particles and mass.I had to ask you to prove your claim.You said it is easy! Yet you proved nothing.You didn't write a single equation to support your claim
To make matter worst, you brought about Feynman and his propagator "hint" story:grumpy:,
If I recall correctly, the method is to use propagators of 1/v (in Dirac algebra notation), and vertices of E. The resummation turns this set of Feynman diagrams into a propagator of 1/p.
and,now you say this
Is this meant to be a statement about physics?
Do you,seriously believe, that you could sell such a mumbo-jumbo garbage to me?
Carl, your "physics" painted,for me,the following pictures about you:
1) You didn't understand Feynman.:rofl:
2) You don't understand propagators.

So, I suggest you leave physics for the professionals.

cheers

sam

Symmetry

CarlB said:
samalkhaiat said:
There are reasons for exploring a basis for physics other than an action principle. Like you said, the human eye appreciates beauty and symmetry, but this is not a good thing. Humans can see patterns where no patterns exist and the psychology papers are replete with examples.
In exploring alternative approaches to physics I can at least claim to be in the company of physicists such as Feynman. [End of quote]
How true! At least four times in my own research I have been beguiled by 'beauty', and wasted months if not longer. The only way of testing a theory is to make predictions and later check them out. (Of course this can only disprove a theory). If the one that fits the new facts is not so pretty, hard luck! And of course there is the indisputable fact that for any set of facts there is at least a non-denumerable infinity of theories which will account for them (which I suppose is why people go for the prettiest, but that doesn't make it true).
Ernie

samalkhaiat
Ernies said:
Do you remember 'forbidden transitions' various 'parity conservations' and the like
Yes, and do you remember what I said regarding "...discovering more and more accurate symmetries" In this case, the more accurate symmetry is the so-called PCT-invariance which seems to be respected by all laws.
A symmetry is an imposed mental construct,
If this is the case,then the laws of nature are mental construct too!
This is nonsense.
The universe does not evolve according to our,mentally constructed, rules. On the contrary, our brain uses the definite, symmetrical,laws of nature to construct mental pictures.:grumpy:
and to have a symmetry group for the whole universe points to megalomania.
99% of physicists believe that the ultimate goal in physics is The Theory of Everything.:surprised
Ernies, you and, may be,Carl are very lonly on this matter.

regards

sam

samalkhaiat
CarlB said:
In 1948, Feynman showed Dyson how the Lorentz force and Maxwell equations could be derived from commutation relations
Yes, I never forget this!
When I first saw Feynman's derivation (16 years ago), I liked it very much and did some work on it.Here is the story:
To derive something "looks like" Maxwell's equations,Feynman used the following axioms:
1) Commutators (which we normaly associate with QM),
2) Newton's 2nd law (which is classical equation of motion).
So, I asked myself:
Why do we need to mix quantum mechanical objects (commutators) with classical object (Newton law) to arrive at the "classical" Maxwell's equations?
So, I changed axiom #1 to the corresponding classical brackets (Poisson brackets), and managed to arrive at Feynman results!
I was very happy with my work which seemed more consistent than Feynman's work
So, I went to show it to the late Daivd Bohm. This is what he had to say to me:
"commutators or no commutators, These are not Maxwell equations. I said this to Feynman more than 40 years ago"
Then, he explained to me the trubles with Feynman's derivations, which turned out to be (guess what) the violation of Lorentz symmetry! He also pointed out that restoring Lorentz invariance would lead to another problem regarding reparametrization invariance.

Let us assume,just for a moment, that all the diseases in Feynman derivation can be cured!!. Does this make Feynman's result independent of the action principle?. No, it does not, because Feynman axioms 1) & 2) can be derived from the so-called Schwinger's action principle.
Do you now see the reason for saying: all body of theoretical physics can be derived from action principle.:tongue2:

David Hestenes in his Geometric Algebra
Hestenes methods wont buy us anything.

regards

sam

CarlB
Homework Helper
samalkhaiat said:
CarlB said:
I was very happy with my work which seemed more consistent than Feynman's work So, I went to show it to the late Daivd Bohm. This is what he had to say to me:
"commutators or no commutators, These are not Maxwell equations. I said this to Feynman more than 40 years ago"

Then, he explained to me the trubles with Feynman's derivations, which turned out to be (guess what) the violation of Lorentz symmetry
You should have ignored Bohm, and broken Lorentz symmetry.

On a related topic, before you say that Hestenes' methods won't make any progress, you should read:

A. Lasenby, C. Doran, & S. Gull, "Gravity, gauge theories and geometric
algebra," Phil. Trans. R. Lond. A 356: 487-582 (1998).

The above is discussed by Hestenes in several papers here:
http://modelingnts.la.asu.edu/html/GCgravity.html [Broken]

But you have to go to the original to get the beauty of the calculations. In short, they've got Einstein's GR on flat coordinates and can make simple calculations for things like the electric field of a point charge near (and inside the horizon of) a black hole. Hestenes says it makes GR obsolete and I agree with him.

The fact that it is on flat coordinates (which Hestenes gives a beautiful mathematical justification for that has to do with the definition of tangent vectors) suggests that one should assume an underlying prefered reference frame. That makes Lorentz symmetry an accidental and probably not exact symmetry. The Coleman-Mandula theorem is a great argument for the assumption that Lorentz symmetry is not exact.

I am reminded of the situation when physicists naturally assumed that parity was an exact symmetry. That turned out to be not only violated but violated maximally. Feynman's derivation of the massive propagator from the massless one violates Lorentz symmetry, also maximally, and that suggests to me that it should be considered as the next breakthrough.

It has been the eternal hubris of mankind to assume that the relationships that he sees at one level can be extrapolated through an infinite number of orders of magnitude to arbitrary situations. No, only God can do that. To assume that a Lorentz symmetric world can only arise from Lorentz symmetric interactions is the result of a combination of ignorance and arrogance. A parity symmetric world arises from parity asymmetric interactions so go figure.

Carl

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samalkhaiat
CarlB said:
samalkhaiat said:
You should have ignored Bohm
,
I am glad I didn't ignore the great man.This is why my name now start with Dr. and have a great job.

The Coleman-Mandula theorem is a great argument for the assumption that Lorentz symmetry is not exact.
THIS JUST TELLS ME THAT YOU DO NOT KNOW ANY THING ABOUT THIS (NO-GO) THEOREM.
I am reminded of the situation when physicists naturally assumed that parity was an exact symmetry. That turned out to be not only violated but violated maximally
WRONG.Apart from the weak processes, P-invariance is 100% intact. In physics, we say: P commutes with the Hamiltonian.

Feynman's derivation of the massive propagator from the massless one
I told you in post #16, There is no such thing. Feynman never said or did such a thing, simply because this gibberish is a product of your imagination.
I can not understand why the moderators of this forums let you continue with your continuous nonsense!
violates Lorentz symmetry, also maximally
Lorentz-invariance is 100% intact in EM, weak and strong processes. It is also 100% intact on the tangent space of GR ( read the work of YOUR Hestenes).

It has been the eternal hubris of mankind to assume that the relationships that he sees at one level can be extrapolated through an infinite number of orders of magnitude to arbitrary situations. No, only God can do that
Garbage + Garbage = Garbage.
To assume that a Lorentz symmetric world can only arise from Lorentz symmetric interactions is the result of a combination of ignorance and arrogance. A parity symmetric world arises from parity asymmetric interactions so go figure.
ALL YOUR STATEMENTS HAVE BEEN NOTHING BUT GIBBERISH, MUMBO-JUMBO GARBAGE, NONSENSE AND UNINTELLIGIBLE TALK.
Carl, I ask you, as I did in post #16, to find something other than science to talk about. You may find a talent outside the domain of physics.

sam

CarlB
Homework Helper
samalkhaiat said:
I am glad I didn't ignore the great man.This is why my name now start with Dr. and have a great job.
Perhaps his advice was that violating Lorentz symmetry would not be the best way of obtaining either a PhD or tenure, but which is more important, truth or money?

Repeatedly over the years, following the advice of senior physicists has been about the worst way of discovering anything new. If the old bulls knew where the grass was greener they'd be over there themselves instead of letting you enjoy it.

I suppose you would have listened to the advice of Lord Kelvin and avoided physics altogether back just before the quantum and relativity revolutions. Certainly plenty of people jumped on the string theory bandwagon and went nowhere at all. But they did get PhDs and tenure, I suppose.

THIS JUST TELLS ME THAT YOU DO NOT KNOW ANY THING ABOUT THIS (NO-GO) THEOREM.
Theorems are very simple things. They have a list of assumptions and they have a list of conclusions. It's a simple fact that Coleman Mandula relies on Poincare invariance as an assumption and cannot apply to theories that assume otherwise.

For the interested reader, here's an example of an extension of the Coleman Mandula theorem extended to extra dimensions with the wording that makes it clear that it applies only to "relativistic" theories:

"Generalization of the Coleman-Mandula Theorem to Higher Dimension"
I.1 The Coleman Mandula theorem
Symmetry plays a key role in modern physics, and in the investigation of the foundations of physics in particular. Symmetry considerations were found extremely useful in the understanding of physical phenomena (e.g. particle classification, selection rules) and in the formulation of theories describing a given physical system. The choice of a symmetry group of the system determines to a great extent its properties. a relativistic theory, this group must contain (as a subgroup) the Poincare group: translations, rotations and Lorentz transformations. In 1967, Coleman and Mandula [1] proved a theorem which puts a severe restriction on the groups that can serve as physical symmetry groups.
http://www.arxiv.org/abs/hep-th/9605147

Note the wording. The Coleman Mandula theorem applies to "relativistic theory". If a theory is not Lorentz symmetric, the Coleman Mandula theorem places no restrictions on it because the assumptions of the proof are not obtained.

Consequently, any theory that is not Lorentz symmetric, (but which establishes the standard model as an "effective" field theory that is therefore approximately Lorentz symmetric), need not satisfy the Coleman Mandula Theorem. And the method of converting massless propagators to massive ones that Feynman gave most certainly does not satisfy Lorentz symmetry.

I told you in post #16, There is no such thing. Feynman never said or did such a thing, simply because this gibberish is a product of your imagination.
I gave you the quote from Feynman in my post #13 and you ignored it. Go back to post #13 and answer it.

I can not understand why the moderators of this forums let you continue with your continuous nonsense!
Try correcting my errors with logic instead of just shouting at me.

Lorentz-invariance is 100% intact in EM, weak and strong processes.
The same could be said of parity symmetry a few decades ago, or Classical mechanics circa 1900.

It is also 100% intact on the tangent space of GR ( read the work of YOUR Hestenes).
I agree with you here, and I don't think that Hestenes will come around on this. But do read the latest from Hestenes, he's converting to a flat coordinate space where the tangent space is interpreted as actual coordinates. That's a bit of a start. Hey, revolutions don't happen overnight.

I am not looking for your advice, wisdom or opinions, nor am I particularly interested in your degrees and income. Hey, I've got good strong calloused hands that don't need tenure to earn a living. What I am interested in is physics and these things (money and tenure) are not physics. What I want is to see your logic.

If you can generalize the Coleman Mandula theorem to no longer require Poincare invariance in the field theory that it applies to, please tell me how you will do this. And if you have found a problem with Feynman's derivation of the massive propagators from the massless ones (other than the obvious that it is in violation of Poincare invariance), that I gave in post #13, please comment.

Carl

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samalkhaiat said:
Ernies said:
Yes, and do you remember what I said regarding "...discovering more and more accurate symmetries" In this case, the more accurate symmetry is the so-called PCT-invariance which seems to be respected by all laws.
If this is the case,then the laws of nature are mental construct too!
This is nonsense.
The universe does not evolve according to our,mentally constructed, rules. On the contrary, our brain uses the definite, symmetrical,laws of nature to construct mental pictures.:grumpy:
99% of physicists believe that the ultimate goal in physics is The Theory of Everything.:surprised
Ernies, you and, may be,Carl are very lonly on this matter.
regards
sam
Yes, Sam, people tend to use the Procrustes Principle of manipulating the patient to fit the bed. I deny that 99% of physicists really believe thst the goal of physics is a theory of everything -- at least if that means nore than the unification of gravity theory with the rest. The reason is very simple -- Godel's Theorem-- which certainly applies since no-one can handle in detail a non-denumerable infinty of axioms. Only fanatics, religious and otherwise, think that a human mind can arrive at the explanation of everything. Since we are part of the universe it is like lifting ourselves by our own bootstraps ____ I hope you don't believe you can.
And stop telling CarlB he is stupid: he isn't. Like at least a couple of dozen
world-ranking scientists that I know of he just doesn't agree with you
Ernie

CarlB
Homework Helper
samalkhaiat said:
So, I changed axiom #1 to the corresponding classical brackets (Poisson brackets), and managed to arrive at Feynman results! I was very happy with my work which seemed more consistent than Feynman's work So, I went to show it to the late Daivd Bohm. This is what he had to say to me:
"commutators or no commutators, These are not Maxwell equations. I said this to Feynman more than 40 years ago"
Then, he explained to me the trubles with Feynman's derivations, which turned out to be (guess what) the violation of Lorentz symmetry! He also pointed out that restoring Lorentz invariance would lead to another problem regarding reparametrization invariance.
It's interesting that Bohm would reject a theory based on it being a violation of Lorentz symmetry. Here's what he says about the subject in his classic introduction to what is called Bohmian mechanics:

The Undivided Universe
D. Bohm & B. J. Hiley, Routlege, 1993
<<<
Chapter 12: On the relativistic invariance of our ontological interpretation p 271]

In this chapter we shall examine the question of how far Lorentz invariance of our ontological interpretation can be maintained.

We shall see that it is indeed possible to provide a Lorentz invariant interpretation of the one-body Dirac equation. For the many-body system we find that it is still possible to obtain a Lorentz invariant description of the manifest world of ordinary large scale experience which we introduced in chapter 7. In addition we show that all statistical predictions of the quantum theory are Lorentz invariant in our interpretation. This means that our approach is consistent with Lorentz invariance in all experiments that are thus far possible.

When this question is pursued further however, it is found that twe cannot maintain a Lorentz invariant interpretation of the quantum nonlocal connection of distant systems. This is, of course, not surprising. Indeed we show that there has to be a unique frame in which these nonlocal connections are instantaneous. A similar result is also shown to hold for field theories. These likewise give Lorentz invariant results in the manifest world of ordinary experience and for the statistical predictions of the quantum theory. But where individual quantum processes are concerned, our ontological interpretation requires a unique frame of the kind we have described both for field theories and particle theories.

We discuss the meaning of this preferred frame and show that the idea is not only perfectly consistent, but also fits in with an important tradition regarding the way in which new levels of reality (e.g. atoms) are introduced in physics to explain older levels (e.g. continuous matter) on a qualitatively new basis.
>>>

As it turns out, Hestenes is a supporter of Bohmian mechanics, or at least so he told me a few years ago. He said that the reason he hadn't written any papers applying Geometric Algebra to QFT was that he did not believe in QFT, and that he was doubtful of the usual interpretations of quantum mechanics, preferring the Bohmian interpretation.

The problem with extending Bohmian mechanics to QFT is not so much in the nature of QFT itself, but instead appears in the requirement that particles be created and destroyed. The version of QFT that I'm using, the Schwinger measurement algebra, is interesting in that it does not, at least in Schwinger's version, allow the creation or destruction of particles.

By the way, I've just quickly reread the thread and I realize I probably didn't broad enough hints for the method of getting from position eigenstates to a massive propagator. I'll go ahead and type something up and release it, but give me until the 1st of the year before complaining that it is late.

In fact, it's sufficiently outrageous, (but entertaining) that I'll submit it to the "alternative theories" or "independent research" or whatever it is they call the crank theories thread around here and won't comment further on it here.

Carl

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samalkhaiat
CarlB but which is more important said:
Let us be clear on this.My PhD does not earn me a lot of money, thanks to the taxman. However,I earn a modest living by doing something interesting, something I love and enjoy doing, and that is theoretical physics.Is this not a "great job"?

I.1 The Coleman Mandula theorem
Symmetry plays a key role in modern physics, and in the investigation of the foundations of physics in particular. Symmetry considerations were found extremely useful in the understanding of physical phenomena (e.g. particle classification, selection rules) and in the formulation of theories describing a given physical system. The choice of a symmetry group of the system determines to a great extent its properties.

Carl, you entered this thead by saying that symmetries are no longer important in physics.Now you insert this quote which points to the fundamental importance of symmetries that I have been talking about!
I gave you the quote from Feynman in my post #13 and you ignored it. Go back to post #13 and answer it.
Read post #16,I did not ignore any of your points, even though they're worth ignoring.I even gave you a brief lesson on propagators.
As for the quote from Feynman, I told you that he was explaining to the "layman", the perturbative expansion of the 2-point Green's function and how higher order terms (graphs) would modify the form of propagator in QED processes:
G-->G(a,d)+G(a,b)V(b)G(b,d)+G(a,b)V(b)G(b,c)V(c)G(c,d)+...
Or,
x---x --> x---x + x---x---x + x---x---x---x + ...
There is no "derivation of massive propagator from massless one" in here. And certainly, there is no violation of Lorentz invariance. Indeed, every term in the expansion respects lorentz invariance.
Carl, we know of no QED-process that violates the principles of relativity (Lorentz invariance). Feynman was talking about these QED, Lorentz invariance, processes.So, saying that "any" of these processes violate Lorentz invariance, is both theoretically and experimentally wrong.
Try correcting my errors with logic instead of just shouting at me.
Logically, a theory (QED) can not violate it's own axiom (Lorentz invariance).
X ==> ~X,
You also made the same contradiction when you said that Coleman-Mandula theorem is an argument against Lorentz symmetry.
To violate Lorentz invariance, your Lagrangian needs to depend on a "fixed" object (vector,matrix) as well as on the ordinary set of fields.
Examples:
1) Schwinger/Zwanziger QEMD (quantum field theory of electric and magnetic charge). relativistic invariance of this theory was shown to be a consequence of the Schwinger's charge quantization condition:
e.g = 4(pi)N.
2) A.Connes non-commutative field theories.
"I" "think" Lorentz invariant non-commutative field theory can be formulated, if the fixed matrix (theta) viewed as operator (I am not sure though).
Regarding mass: we know 2 methods for generating mass;
1) is the successful Higgs phenomena.
2) not so successfull.it is done by going to a higher dimensional spacetime. For example, massless vector field in 5D is equivalent to massive,degenerate, vector and scalar fields in 4D.

sam