Symmetry the new Ptolemaic Theory?

1. Dec 3, 2005

Ernies

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

2. Dec 3, 2005

ahrkron

Staff Emeritus

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.

3. Dec 3, 2005

samalkhaiat

And, they (symmetry groups) will play an important part in any "new physics".

sam

4. Dec 3, 2005

samalkhaiat

Last edited: Dec 3, 2005
5. Dec 3, 2005

Staff Emeritus
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.

6. Dec 4, 2005

7. Dec 4, 2005

CarlB

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

8. Dec 6, 2005

9. Dec 6, 2005

samalkhaiat

Last edited: Dec 6, 2005
10. Dec 6, 2005

Kea

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.

Last edited: Dec 6, 2005
11. Dec 6, 2005

CarlB

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.

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.

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.

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.

Huh?

Hey, I'm just throwing up a trial balloon. The mathematics is very easy, but the physical interpretation is, well, a bit cranky.

Carl

Last edited: Dec 6, 2005
12. Dec 9, 2005

samalkhaiat

13. Dec 9, 2005

CarlB

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:

"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

Last edited by a moderator: Apr 21, 2017
14. Dec 10, 2005

Ernies

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

15. Dec 13, 2005

CarlB

16. Dec 13, 2005

samalkhaiat

17. Dec 14, 2005

Ernies

Symmetry

18. Dec 14, 2005

samalkhaiat

19. Dec 14, 2005

samalkhaiat

20. Dec 14, 2005

CarlB

Last edited by a moderator: May 2, 2017