Unifying Quantum Mechanics and General Relativity: Why Hasn't It Been Done Yet?

[T.O.E Dream]

I'm thirteen years old and for the past two years i'v been learning quantum mechanics and relativity. I'm aware that one of the most important tasks of physics today is to unify the four fundamental forces. that is to put quantum mechanics and general relativity together. I'm always a huge thinker and i have some ideas but before i can put everything together (which might take years, i know) i need to actually know why can't these two theories put together in a mathematical way. Just so you know we don't know much about mathematics like calculus or whatever at this age so be very descriptive. I hope you can help!

Also, i know there's super string theory or m-theory but the whole ideas of parallel universe and 11 dimensions kind of seem to fictional. I know Einstein wouldn't have liked it if he was alive. plus there's no proof (or at least important and considerable proof)of anything that string theory states.

I know the theoretical framework of quantum mechanics and general relativity but not the mathematical. So again i hope you can help!

 

[confinement]

There are two big problems:

(1) In the standard model, fundamental forces are descrbed by Yang-Mills fields. Classically, these fields are the curvature of a principal G-bundle over spacetime i.e. G = SU(3)xSU(2)xU(1) is the symmetry group of the standard model, and the principal bundle is formed by putting a copy of G (which is an intricate 12-dimensional manifold) at every point in space time. Anyway, classical Yang-Mills equations always have well behaved solutions e.g. no black holes. General relativity is not a Yang-Mills theory, although it can be seen as a generalization of these, and as we know it has more poorly behaved classical solutions.

2) The basics mathematics of general relativity and quantum spin necessitate a massless graviton with spin 3/2. The Weinberg–Witten theorem states that in all renormalizable* Lorentz-invariant** quantum field theories, massless (composite or elementary) particles with spin j greater than one cannot exist.

* A theory is renormlizable if we can extract finite answers from it in a consistent manner; this s a requirement for any complete modern theory.

**Mathematically, Lorentz-invariance is equivalent to special relativity, and tests are the latter strongly constrain the exactness of the former. Therefore this is considered to be a requirement for any modern theory.

The bottom line is that acceptable modern theories do not allow massless particles with spin greater than 1, but we know gravitons are massless and have spin 3/2. This is why everyone knows* that gravitons are strings.

*Not everybody knows, and it can be a sensitive issue. LQG is strongly represented on these forums, but as far as I can tell even their approach must get around the Weinberg–Witten theorem by using loops (instead of strings).

Also, i know there's super string theory or m-theory but the whole ideas of parallel universe and 11 dimensions kind of seem to fictional. I know Einstein wouldn't have liked it if he was alive. plus there's no proof (or at least important and considerable proof)of anything that string theory states.

Without mathematics, the prediction of 11 dimensional spacetime would be absurd. But string theory allows you to calculate the dimension of spacetime, it is not a parameter chosen by hand, that means D > 4 for our spacetime is one of the most fascinating predictions of modern physics. It is possible that the compact extra dimensions are on the scale of micrometers, and experimental research teams are trying to detect them.

 

[Fredrik]

(1) In the standard model, fundamental forces are descrbed by Yang-Mills fields. Classically, these fields are the curvature of a principal G-bundle over spacetime i.e. G = SU(3)xSU(2)xU(1) is the symmetry group of the standard model, and the principal bundle is formed by putting a copy of G (which is an intricate 12-dimensional manifold) at every point in space time.
...

Good answer. There's just one small problem...

I'm thirteen years old

 

[DaveC426913]

Good answer. There's just one small problem...

No fair. The OP asked a valid question and framed his knowledge-level in detail. Frankly, he's already demonstrated himself to be more eloquent than a large fraction of the transients on this board. He (or she) deserves the answer he asked for.


Here is a discussion on that very topic: https://www.physicsforums.com/showthread.php?t=51851

 

[Fredrik]

No fair. The OP asked a valid question and framed his knowledge-level in detail.

Which is precisely why we know that he's not going to have much use for an answer that mentions principal G-bundles. Your makes me .