0
$\begingroup$

In his later life, Albert Einstein was trying to extend his general theory of relativity to incorporate electromagnetism and other fundamental forces with it, something he himself called "The theory of everything" or "Unified field theory". My question is, has Einstein published anything about this work, and if so, are they proved wrong?

$\endgroup$
1
$\begingroup$

Einstein started us all on the path towards looking for a "unified" theory. In his day none were found. Al least no a serious contender.

Before we understood the nature of the weak force it seemed that Gravity and EM were the only two and some serious attempts emerged. One is Kaluza-Klein theory. Here one starts with a 5-dim space-time, one extra space like dimension. As it turns out the geometry field associated with the 5th dimension creates the EM force in the other 3+1 dim. But there was not really a eureka moment here as there were a lot of unjustified assumptions and some extra fields had to be made = 0 with no real cause. It was a "model" in the strictest sense and a theory in the loosest sense. K-K theory saw a renaissance in the 1980'2 with work by Duff. He was able to find a more rigorous approach that provided similar models without the problems. But then string theory and gauge theory were firmly in place.

Another attempt by Einstein was to introduce an antisymmetric part to the metric tensor, the source of gravity. The new set of fields has no effect of GR but couple to spinors, it gives rise to something called the torsion field. He wrote about it in his last edition of the Meaning of Relativity before his death. It is an interesting topic but has not led to a real UT of any sort.

One thing to keep in mind as a significant difference between K-K theory and modern gauge theories is that in modern gauge theory the "extra dimensions" are not in any way part of space-time. They are internal parameters of the quantum fields that make up matter. Whereas in K-K theory the extra degrees of freedom are geometric in nature and in theory we could move through them. In most models they are curled up. Torsion is also geometric by nature.

Einstein did write some about this as did many of his contemporaries and these ideas are still actively studied. For a nice historical account you can read The Dawning of Gauge Theory by Lochlainn O'Raifeartaigh

https://press.princeton.edu/titles/5989.html

$\endgroup$
  • $\begingroup$ Are the KK theory and Einstein's attempt to introduce an antisymmetric part to the metric tensor unable to explain nuclear forces? If so, they cannot be true. $\endgroup$ – Ali Lavasani Jan 10 at 22:02
  • $\begingroup$ "Can" is a relative term. You cannot get SU(2) or SU(3) but in a high enough dimension you can get a covering group that contains them, which is the nature of a GUT, something like SO(10) but you need 10 extra dimensions of space. The torsion field does in fact generate a gauge field in the space with internal indices for the extra dimensions (I did my thesis on this). But there are other couplings that may rule them out or may be show to match unexplained data. One needs a quadratic curvature action. $\endgroup$ – ggcg Jan 10 at 22:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.