FWIW, catching up on old threads.

Penny, if Einstein was a mathematician so am I. I meant the ability to research math including theorems. Presumably this was his reasons to work with Grossman. For the rest, see my previous comment.

Einstein, as a teen, also was wondering what the world might look like if he could ride a light bean–a thought experiment,
NOT an experiment.

The most brilliant minds are conceptual–they have deep
IDEAS. Often, long before any experiment shows the necessity
of those ideas.

If you read his paper on SR ” On the electrodynamics of moving bodies”, you will see that his math proofs are very elegant–and similarly in his work on Brownian motion. He claimed he had NEVER heard of Brownian motion until he had submitted the paper. Similarly, for the Michaelson-Morley experiment.

His main ideas “SR and GR” were based on group theory–
the Lorentz group, and the diffeomorphism group–with a lot
of differential geometry in GR.

The motivation for SR originally (aka before the paper, according to Einstein) was that Maxwell’s equations were not
invariant under Galilean transformation–if one looked at
a moving conductor in a magnetic field in two reference frames the MATH predicted incompatible answers.
NO EXPERIMENT NEEDED.

His principle in GR was that fundamental physics was basically….
Geometry.

And, indeed, Hilbert showed that if one extremized the simplest possible geometric energy invariant –the integral of the scalar curvature–one gets the Vacuum Einstein Equations.
Thus, this would have happened anyway as mathematicians were exploring such things. In fact, there is an eight day difference ( and a priority conflict–which I hold in favor of Einstein) in publication.

Adding the stress energy tensor to get a divergence free
right hand side if you are not in a vacuum was a standard thing–even then–already familar from Maxwell, and
in solid and fluid dynamics.

When asked if he would wait up for the results of the Eddington eclipse experiment he replied, ” If they UNDERSTOOD my theory, they wouldn’t need to do an
experiment”.

The concept of Space-time ( sometimes called Lorentz geometry) was actually due to Einstein’s math prof
Herman Mink. No experiment was needed to motivate this.

The theory of causality in Lorentz geometry–largely due to Penrose ( who is a phd in math, a student of the same thesis advisor–Hodge–as Michael Atiyah) is another triumph of the math approach to physics.

Similarly for Penrose’s theory of Twistors ( Which predated him in pure algebraic geometry–a Robinson congruence is simple the Hopf Fibration), was not motivated by experiments.

And, thus we see again that :

Some physicists have done as you say, but some have not.
When, Feynman was working on a version of the four vertex
theory, it didn’t match the experimental data—like Newton he
said: ” The experimental data must be wrong, because my theory is too mathematically elegant to be wrong.” Feynman was incidentally a math Putnam scholarship winner!

Consider the Penrose singularity theorem, the Hawking Penrose singularity theorem, the work on Black hole area
thermodynamics–no experiments motivated this work.

The string theorists were motivated purely by math–in the spirit of Einstein–and it all started with an addition formula
for Beta functions.

We didn’t get Black holes, neutron stars, Einstein rings,
from experiments. The MATH came first–the experiments came later–often decades later.

In the same way, Maxwell’s equations ( yes, Faraday’s experiments had input–but the main idea was Maxwell’s pure thought idea of the displacement current–missed by Gauss etc.) PREDICTED Radio waves decades before they were observed. Maxwell, the ….mathematician.

In Quantum theory consider for example ” The Casimir effect”, which was predicted mathematically by the physicist
( who did enough rigorous pure group theory, like Eugene Wigner, to have an independent stellar career in math–geniuses!) Casimir decades before any experimental
confirmation.

One might say the same for the currently popular theory of
“wormholes”.

In the end, if several experiments disagree with predictions of math, the theory is discarded–as well it should be.

But, many of the absolutely top level theorists, are far more motivated by mathematical ideas than our education process
in physics makes clear. In fact, history is rewritten to make it look like the opposite is true in textbooks.

For example–Faraday is portrayed as a mathematical incompetent who didn’t know calculus and was primarly a tinkerer–meanwhile, Faraday invented a theory of flux tubes that contained many of the ideas of topology and led him to
conjecture the radio wave ( proved more standardly by Maxwell’s partial differential equations method). The radio wave was math before it was experiment.

p.s. Einstein himself always was falsely modest–saying he wasn’t much of a mathematician. His letter from his
Realgymnasium teacher said he was a “mathematical
genius”, his work in the statistical mechanics of Brownian
motion etc., say he was a very talented mathematician–real proofs.

He was also a large believer in the use of ” thought experiments”–another name for ” elegant mathematical
proofs”. In this, he was inspired by Galileo–who faked his
experimental data–but, as a mathematican–trusted his proofs.

In the “false” history of textbooks, Galileo dropped a heavy and a light object from the leaning tower to show that they fall at the same rate in a vacuum. In fact, Galileo gave a mathematical proof–a thought experiment–involving an imaginary line dividing an object into heavy and light objects.
He never dropped things from the leaning tower.

The impossibility of a pepetual motion engine was proved by
Simon Stevin–a medieval mathematician–by a geometric proof involving a weighted chain and an inclined plane.
Stevin was also led by this to the concept of momentum.

I have given plenty of examples to support my point. You have simply pontificated and reiterated yours.

Enough. It’s been fun.

This was however a minor nitpick, which won’t lead to an agreement in any case. But I accept your (or mine argument against string theory.

As I said: I gave examples: The work of Newton, Einstein, Dirac, Hawking,
etc.

I agree, this has been fun, but I have said enough.

Penny

String theory is not the only natural road to supersymmetry. Again, if string theory does work–aka, some prediction will made and tested–that it
would be YET another example of the mathematical approach to physics–for it has sustained its creation, and thirty to forty years of work,
by thousands of “Physicists” who have been willing to work on mathematical theories without having ANY experimental justification to do so. They follow Einstein’s philosophical lead in this.

And, since I have some small piece in it. It would please me, if string theory were correct.

As I said, my argument against it is basically your “physicist” argument–that it makes no solid experimental predictions.

Supersymmetry is independent of string theory–though picked up later by string theorists.

Yes, but AFAIU it gets a more thorough and natural physical motivation there.

The black hole entropy is a retrodiction

My point was that it will be a prediction if confirmed by observation. I see that is your criteria as well.

The method of physics lets physicists cut corners when they can do experiments–but, they can’t always–consider string theory.

There will be no difference there, when they get observations.

Lots of mathematicians have played around in labs.

Yet they want to use math instead of physics methods in physics. (Gauss made it work, which is why I give him kudos.) Which remains my point.

I’m sorry, but I don’t see that we can come to an agreement here.

It is obvious to me that one should use physics methods in physics, since in science math is a tool but not the essence of the observational method or of all of theory. Others may not agree, which is fine with me but when they need to demonstrate that alternate methods works. That is all I have to say.

Einstein:
The theory of Brownian Motion by kinetic molecular methods
The theory of the photoelectric effect
Special Rel
General Rel
Bose-Einstein Stats
A correct unification of Electric fields and Gravity ( different from the one
done by O.Klein) using torsion connections and teleparallel geometry
The first paper on “amplification by stimulated emission of radiation”

GOOD GOD!!!!

Thinking of Fermi–I am also very impressed. By Einstein just blows my mind.