[martincmartin]

Quantum entanglement falls out of the quantum mechanics, so in some sense, the prevailing theory to explain quantum entanglement is quantum mechanics.

Of course, it's unintuitive and unsettling, so you could generate other theories about other dimensions if you like. But as far as predicting the results of any experiments we can do, QM is all you need.

Also, there are two very different theories of relativity, the special and the general. Special relativity is taught in 1st year undergraduate physics, you really only need high school math & physics, plus an open mind, to understand it. This has E = mc^2, twin paradox, length contraction, time dilation, speed of light as a limit. It's actually a pretty small topic, it usually doesn't have a separate course because it wouldn't fill a one semester course. QM is fully consistent with Special Relativity.

The other is general relativity, which revises gravity in light of special relativity. This is a much bigger topic and typically taught in grad school, although there are some undergrad texts now that don't require math as advanced as the grad school ones. QM and GR are incompatible, and the search for a "quantum theory of gravity" is a key plank in any "theory of everything."

[martincmartin]

It's easy to explore QM and SR, because it's easy to accelerate fundamental particles to near the speed of light. Here's a video from 1962 where electrons were accelerated, they measure the time between passing two points (to get speed), and heat energy deposited on a target (to get kinetic energy) to show how SR works. Nothing QM specific, but shows how easy it is to get quantum particles moving that fast, so you can do experiments on them: https://www.youtube.com/watch?v=B0BOpiMQXQA

Combining gravity, which needs great mass, with QM, which needs small space scales, is "hard" to do in a lab.