A Were there any valid classical unified field theories ?

[Rohan]

TL;DR Summary

Amongst what seems like a plethora of classical Unified Field Theories; that seemed to exist in the first half of the 20th century;
were they all abandoned because of failure to account for quantised phenomena, as matter consisting of discrete particles and fields;
as opposed to observational failure in the classical realm ?

1/ Amongst what seems like the plethora of classical Unified Field Theories; that seemed to exist in the first half of the 20th century; see for example https://link.springer.com/article/10.12942/lrr-2014-5
[caution 50MB download]
were they all abandoned just because of failure to account for quantised phenomena, as matter consisting of discrete particles and fields; as opposed to observational failure in the classical realm ?

2/ Is it possible that any of them, whilst incomplete in this way never-the-less are valid as purely classical theories ? here I have in mind that Maxwell's Electro-Magnetism, fails utterly in the quantum realm, yet retains great utility in the classical !

Contextually many of these theories , (eg Einstein seemed to have considered several ) ; seemed to have been not just attempting to unify General Relativity and Maxwell's Electro-Magnetism but also attempting to offer an alternative to Quantum Mechanics. Thus it seems the possibility of an "incomplete" Classical Unified Field Theory
may have been overlooked ! I suppose the hope which such a theory seems to represent to me is the possibility of (in Wheeler's terminology) :
-electro-geometrodynamic phenomena ...strange electrical 'forcefield' effects; at everyday energies !
General Relativity and Maxwell's Electro-Magnetism don't seem to predict such interactions;
until the mass/ energies approximate the mass of stars and then only as an electromagnetic contribution to the gravitational field !

 

[Vanadium 50]

There's Maxwell, that unified electricity and magnetism. Then there's Kaluza, which immediately ran into the problem that we don't live ina 5-D world.

 

[cosmik debris]

There's Maxwell, that unified electricity and magnetism. Then there's Kaluza, which immediately ran into the problem that we don't live ina 5-D world.

We don't live in a 10, 11, or 26D world either but that doesn't stop some people.

Cheers

 

[haushofer]

There's Maxwell, that unified electricity and magnetism. Then there's Kaluza, which immediately ran into the problem that we don't live ina 5-D world.

That's not the real problem. The problem was to stabilize this extra "small dimension". GR dictates that if you start out small spatially, it doesn't need to stay that way.

String theory exhibits the same problem. It's solution is called "moduli stabilization" (where the "modulus" is roughly the radius of the small circle in this case).

 

[Rohan]

As an addendum to my query above; I wonder whether the peculiar mathematical properties of 4 dimensional manifolds; (apparently they unlike higher dimensional manifolds " don't have a unique differentiation structure"..Simon Donaldson 1982 Oxford Uni.); places any constraints on these theories, some of which required more than 4 dimensions ?