What is the prevailing theory to explain quantum entanglement? Must there be another dimension we cannot access or measure that is not subject to the laws of relativity? (I understand the laws of relativity break down at the quantum level but please ELI5)
I think people get confused when they think that each object has a wave function. This is not correct. The universe has one wave function. The wave function consists of a bunch of possible states along with the coefficient for each state. You can think of each state as being a distinct snapshot of what the universe might look like - including for example the position and spin of each particle. In the example of two electrons shown here, the wave function has non-zero coefficients only for states where the two electron spins are in opposite directions.
When we make a measurement, the state of the universe appears to collapse, meaning any state that is not consistent with that measurement disappears. This means the other electron is left in the opposite spin state. (Important aside here, some people believe the wave function collapses, "Copenhagen interpretation" and some people believe the wave function doesn't change but the the brain of the observer correlates/entangles with the electron, "Many Worlds Interpretation". Either way there is an operational collapse of the wave function.)
A special case for a wave function is when the coefficients are arranged so that state of one particle, say particle 1 spin, is symmetric no matter what the state of another particle, particle 2, is. This special case is when particles are NOT entangled.
I think what I get hung up on with explanations like this is, what changes once the wave function has collapsed? Are there observable characteristics before wave function collapse that become different after the wave function collapses?
Maybe this question just reduces to “how can we tell the difference between two entangled particles having always been in some state (but we didn’t know it) vs. being simultaneously in both states until we make a measurement?”
Based on other comments in this post, it seems like the answer may be: Bell’s theorem proves that classical explanations have an upper bound on correlations between the particles, but quantum mechanics predicts a correlation the violates the classical upper bound. And we can experimentally test the correlations in practice.
I want to add to my above comment. Non-entanglement is a special mathematical case, but it happens quite often. If the two particles never interact in any way, then the special condition will be true and they will not be entangled. There is another case where the particles _appear_ not to be entangled. This is when the wave function is so jumbled that even though the particles are entangled you can't detect it. This is called a decoherence. This also happens quite often and is why macroscopic quantities don't exhibit entanglement and hence quantum behavior.
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."
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.
There isn't really an "explanation" for quantum entanglement. It is a fundamental property of the universe, arguably the fundamental property of the universe. But the Right Way to think about it IMHO is this: the quantum wave function is not defined over physical space, it is defined over configuration space. A wave function defined over physical space is a special case that pertains when you are dealing with a system consisting of a single particle, in which case physical space and configuration space are the same. But as soon as you add a second particle, this physical intuition breaks down.
The prevailing theory that explains quantum entanglement is precisely the theory of quantum mechanics, OP. If you're genuinely curious, I strongly encourage you to obtain an undergraduate degree in physics, which will equip you with the mathematical and theoretical background to see how the one explains the other.
The next time I make the case for accounting to be a required course in high school I'm going to reference to this thread as Exhibit A: Assets & Liabilities Illiteracy.
I think the difference is this: If you owe me money, I can cancel your debt. But if I won't cancel it, you could also end the debt by forcing dragonwriter to pay me. That's different because there's a third party involved.
