Monday, May 20, 2024

Einstein's Futile Search for Unified Field Theory

Sabine Hossenfelder posted her latest video:
Einstein’s Other Theory of Everything

Einstein completed his theory of general relativity in 1915 when he was 37 years old. What did he do for the remaining 40 years of his life? He continued developing his masterwork of course! Feeling that his theory was incomplete, Einstein pursued a unified field theory. Though he ultimately failed, the ideas he came up with were quite interesting. I have read a lot of old Einstein papers in the past weeks and here is my summary of what I believe he tried to do.

She insists on pronouncing his name INE-shtine. Maybe Germans pronounce it that way, but not Americans.

She summarizes Einstein's foolish and misguided unified field theories. If he did not already have a fancy reputation, this would be considered crackpot work.

She also mentions the more successful Kaluza–Klein theory:

In physics, Kaluza–Klein theory (KK theory) is a classical unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the common 4D of space and time and considered an important precursor to string theory. In their setup, the vacuum has the usual 3 dimensions of space and one dimension of time but with another microscopic extra spatial dimension in the shape of a tiny circle. Gunnar Nordström had an earlier, similar idea.
This is also described as a failure. She says you need supersymmetry to make it work, but that has been rejected.

That theory is a minor variant of a 1918 H. Weyl proposal to unify gravity (general relativity) and electromagnetism. That was promptly attacked by Einstein, and mostly forgotten.

There the story ends. But not really. Einstein's ideas were, in fact, worthless, and led several generations of physicists astray. I wrote a whole book about it.

But Weyl's idea was essentially correct. In the modern Standard Model, that everyone accepts, there is an extra tiny circle at every spacetime point (event) to account for electromagnetism. In modern lingo, it is a circle bundle over a spacetime manifold. Gravity is a connection on the tangent bundle, and electromagnetism is a connection on the circle bundle. In both cases, the field is the curvature. It is the simplest and most natural relativistic theory.

Physicists studied Weyl and Kaluza-Klein for decades, without ever figuring out that they were just adding extra terms that ruined the theory. I guess they wanted to unify the gravity with the electromagnetism by hypothesizing some interactions, but that was just foolishness.

If Weyl were really smart, he would have conjectured using other Lie groups form the strong and weak interactions, alongside the circle for electromagnetism. Then we could have had the Standard Model, before quantization, about 50 years before we did.

One of the Lessons of the Standard Model is that all four forces (gravity, electromagnetism, weak, and strong) all have the same math structure (field strength is curvature of a bundle connection), but the force are essentially orthogonal. They do not have much to do with each other. There is some twisting between the weak and electromagnetism, but that's all. Many people thought that they would be unified like electricity and magnetism, where you cannot study one without the other.

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