Who Was Right - Poincare, Einstein or Neither

[martinbn]

Maybe because Poincare thought that math should be consistent with the common sense. That would be perfectly consistent with the Poincare's oppositions to the Cantor's theory of infinite sets.

I wasn't aware of this. Quite interesting, i'll have to look up the details.

 

[Demystifier]

I wasn't aware of this. Quite interesting, i'll have to look up the details.

What you were not aware of? That Poincare didn't like Cantor's theory, or that Poincare thought that math should be consistent with common sense? The former is a historical fact, the latter is my interpretation of that fact.

Another personal interpretation. Poincare studied dynamical systems. The very concept of a dynamical system implicitly assumes that the concept of time has a special role which, among other things, makes it different from the concept of space. From that point of view, Minkowski space-time looks like a rather foreign concept.

 

[martinbn]

What you were not aware of? That Poincare didn't like Cantor's theory, or that Poincare thought that math should be consistent with common sense? The former is a historical fact, the latter is my interpretation of that fact.

The first.

Another personal interpretation. Poincare studied dynamical systems. The very concept of a dynamical system implicitly assumes that the concept of time has a special role which, among other things, makes it different from the concept of space. From that point of view, Minkowski space-time looks like a rather foreign concept.

He also studied many other things, where there is no notion of time whatsoever. For example he was interested in geometry/analysis on the upper half plane. Minkowski space-time should have been very appealing to him.

Here is my personal speculation. Poincare was too burdened by philosophy and in questions like this one was not thinking like a mathematician.

 

[PAllen]

I also think the credit issues were important to Poincare. His letters with Felix Kein were quite biting at times when Poincare felt Klein was implying priority.

 

[Paul Colby]

That's certainly true in high-energy physics, but not in condensed-matter physics. In the latter, one starts with non-relativistic QM (without any particularly interesting symmetries) and arrives at emergent symmetries as collective macroscopic effects in specific phases of matter.

Good point on emergent symmetries. It's not clear to me crystal symmetries emerge if the underlying space isn't translationally and rotationally symmetric, though. I think Einstein' s answer today would have been the same and for the same reasons.

 

[Demystifier]

Good point on emergent symmetries. It's not clear to me crystal symmetries emerge if the underlying space isn't translationally and rotationally symmetric, though. I think Einstein' s answer today would have been the same and for the same reasons.

Yes, but in condensed matter physics you can start with "fundamental" Galilean symmetry and arrive at emergent macroscopic Lorentz symmetry for propagation of phonons (with the speed of sound instead of the speed of light). Essentially, this is the standard aether theory of sound waves. In principle, a similar aether theory of light is also possible. The Michelson-Morley experiment does not prove that such a theory is impossible, this experiment only excludes the simplest versions of such a theory. Einstein just applied the Ockam's razor and concluded that the simplest theory - the one without aether for light - is the most reasonable one. If future experiments will show violations of Lorentz invariance at very small distances, then some aether theory of light may start look simpler than theories without the aether.

 

[atyy]

Bell thought this whole geometry space-time thing pure philosophy and seemed to prefer a presentation of SR along the lines of LET. In light of modern physics with things like Noether etc can such a position be maintained I think symmetry is the foundation of modern physics so is more than mere philosophy - it a very real unifying concept.

This is because Bell was interested in a realistic solution of the measurement problem. His theorem rules out local realism, hence if realism is kept, one would favour LET.

 

[zonde]

Bell thought this whole geometry space-time thing pure philosophy and seemed to prefer a presentation of SR along the lines of LET. In light of modern physics with things like Noether etc can such a position be maintained I think symmetry is the foundation of modern physics so is more than mere philosophy - it a very real unifying concept.

IMHO It is the basis of mechanics, SR, QM, QFT - pretty much all of physics up to now. But is this right - or is Bell on the right track?

I think the difference is if you want to look at common abstract (mathematical) things in physics laws (and maybe discover new ones) or rather you want to combine them for application to particular occurrence of some complex physical process.

Say you look at similar bodies that are at different states of inertial motion and you see the symmetry. But then you look at physical process of acceleration/deceleration of particular physical body. You will say that from perspective of any inertial reference frame some physical transformation is taking place and that's about it concerning symmetry. But to describe all the physical interactions and processes that are going on you will pick some reference frame.

[Moderator's note: deleted off topic speculation.]

 

[PeterDonis]

@zonde, I have deleted the last paragraph of your post #38. Please review the PF rules on personal speculation.

 

[vanhees71]

From a physics point of view, I think Einstein was right. This is no surprise given that Poincare was a mathematician. He could never overcome his "ether prejudices" and a typically 19th-century attitude that all physics has to be somehow explained by mechanical models. That's by the way also the way Maxwell was thinking and how he got his famous equations. Only later he gave up on the mechanical models and came to the conclusion that it is much simpler to take the modern field-point of view, which by the way was introduced by Faraday on a more intuitive basis lead by experiments.

Indeed, nowadays relativity (both special and general) is rather thought of as the mathematical description of spacetime, which is the basis for all of physics from mechanics (point particles as well as continuum mechanics) to field theories and also quantum (field) theory. It's also pretty clear that classical point mechanics is nuissance for relativity and there's no fully satisfactory formulation of it although FAP at least for electromagnetism a good approximation seems to be the Landau-Lifshitz equation of charged point particles including radiation reaction (at least that's what comes out of numerical studies comparing hydro-like descriptions with point-particle descriptions using various flavors of Abraham-Lorentz-Dirac equations; at the moment, I can't find the reference for this interesting study, which was made by some French accelerator physicists dealing with this problem from a quite practical point of view).

In any case that's why nowadays the field-point of view is the more fundamental one, and indeed also in the quantum realm the most successful formulation is relativistic local quantum field theory, which however is not yet a mathematically rigorous theory either. In the sense of perturbative renormalized QFT it's only plagued by less severe problems than classical point mechanics ;-)).

 

[martinbn]

From a physics point of view, I think Einstein was right. This is no surprise given that Poincare was a mathematician. He could never overcome his "ether prejudices" and a typically 19th-century attitude that all physics has to be somehow explained by mechanical models.

That is very puzzling to me. It seems backwards. Why should a mathematician cling to ether and mechanical description instead of embracing a new and interesting mathematical way! In this instant Poincare is the physicist and Einstein the mathematician.

 

[vanhees71]

Well, I don't know. Mathematicians tend to have developed a different kind of intuition than physicists. Although often great theoretical physicists (as Poincare, Minkowski, Weyl, von Neumann, and Hilbert) get wrong ideas put into beautiful math. The most famous example is Weyl, who developed in 1918 an idea to unify electromagnetism and gravity by gauging the scale invariance of vacuum GR. We call this procedure of making a global symmetry local "gauge theory" today, because of this wrong idea. That it is wrong was pointed out to Weyl by Einstein in a very polite way and also by Pauli in a much less polite way ("It's not even wrong"). It's very simple to disprove: If Weyl had been right, the geometric properties of a body would depend in its "electromagnetic history", which is not observed in the sense of the theory.

 

[bhobba]

That is very puzzling to me. It seems backwards. Why should a mathematician cling to ether and mechanical description instead of embracing a new and interesting mathematical way! In this instant Poincare is the physicist and Einstein the mathematician.

Nowadays its obvious. It was a mathematician Minkowski that developed the correct mathematics so that Einstein's physical ideas could proceed. At first he thought it useless formalism, but later realized its critical importance.

We all are slaves to you pre-conceived prejudices and it takes time and other viewpoints to break through them. Sometimes its a mathematician, sometimes a physicist. Each enriches the other doing so. As I said Poincare, along with Landau, Von-Neumann, and Feynman are my heroes - but each for different reasons. Poincare was a polymath of the highest order - but perhaps too old by then to absorb readily new ideas. Maybe that's why they don't give Fields Medals to people over 40. Von-Neumann deserved one but was 40 in 1943 and it only started in 1936 and you had the secret stuff he did during the war so likely wasn't producing that much publishable. He really invented the A-Bomb - they were stuck how to detonate it and called him in - he figured out using the shock-waves from a conventional bomb. In other words it was just bad timing.

Thanks
Bill