There's no need to "model" entanglement as if it were some unexplained phenomena.
It's explained and predicted by Quantum Theory and confirmed by experiment.
I think these kind of expectations of entanglement being some mysterious phenomena to be explained come from popular books that explain it as "spooky action at a distance". In reality there is no "action at a distance" because in entanglement the particles aren't remotely affecting each other faster than light. They're simply correlated with each other.
Now the strange thing is it's a correlation incompatible with the notion of there being an objective value for physical quantities that pre-exists measurement. When you drop the requirement of physical quantities having values outside of measurement you're allowed a broader class of correlations and the new correlations that become possible are called "entanglement".
Just to say for general interest, the quantum wavefunction is not a physical wave. It's a compact summary of an observer's beliefs/credence. Today we often say the "statistical operator" instead. It no more needs an etheric model than gambling odds in general.
I do not accept wave theories grounded in quantum theory as evidence against the ether, either
nwr mentioned Maxwell's equations, which are classical not quantum. There are quantum versions of them, though their meaning there is quite different, but still still Maxwell's equations are classical.
my ether model would have it that quantum waveforms are primarily generated by etheric processes
Related to my post above, quantum "waveforms" aren't physical things that need to be generated by physical processes. They're just bets/credences/beliefs expressed in a compact mathematical form.
It's like saying you have a model for how thermal processes can generate bets on the next election.
Since convincing Michael would be like poor Cnut commanding the tide, I thought a little summary of quantum theory would be nice.
The basic set up of quantum theory involves three components:
A microscopic system
A macroscopic system selected by the observer. Often called "The Device" or "The measuring apparatus. It doesn't literally have to be our lab equipment though.
Quantum Theory's central concern is predicting the chance of how the microscopic system will affect the macroscopic system. To this it requires two pieces of information:
A summary of the observer's current knowledge of the microscopic system. This is summarised mathematically in an object called the statistical operator*. This knowledge is usually obtained from previous experiments on the system or how it was prepared. It's not objective of course, because it depends to some degree on the observer's pre-existent beliefs about how the preparation procedure works or how the previous experiments worked.
How the macroscopic system works, i.e. in what way it couples to/can be affected by the microscopic system, i.e. does it develop a mark at some point, does it pick up energy or momentum or angular momentum. Most ways of the macroscopic systems react can't be analysed in terms of older classical quantities like Energy etc, it will just be things like "its detection needle moves 5cm".
The theory will then spit out the chances of various effects occurring given (i) and (ii) as inputs. If you plan to look at the system again after the current experiment it also calculates how the observer should update their beliefs based on the outcomes of the most recent experiment. This updating was called "collapse" in older literature, but it is not a physical process.
The typical issues people have with the theory are that:
It doesn't actually describe microsystems beyond how they affect some macrosystems. So if there are no detection devices around it has little to say about microsystems. In short it doesn't actually describe microsystems.
The presence of an observer and their knowledge
The theory supplies no mechanism describing how the observer selects the macrosystem. This is just required as an input
The overwhelming majority opinion among those who study the foundations of quantum theory is that these features are simply here to stay and you have to get used to them.
Yeah as mentioned above Entanglement doesn't need an explanation, since we already have one.
Most people here will be familiar with correlations. Bell, CHSH* and others have set up a variety of scenarios where you test two or more systems, by measuring two or more properties of each and then checking the correlations between them. If you assume the quantities have values prior to your measurement then you can show the correlations must be less than some number (2 in the case of the CHSH scenario).
When you perform the tests in real life the values are greater than this number. Hence the unusually strong correlations in QM are explained by measured quantities not having values outside of measurement, sometimes called the violation of "realism" although I don't like that name much.
For anybody curious the actual origin of quantum theory is the emission spectrum of helium, i.e. the frequencies of light helium emits. People had tried to handle this problem by adding stochasticity (non-determinism) and discreteness into the Bohr-like Solar System models of the atom to no avail.
Heisenberg went to Helgoland in 1925 and took as his basis two empirical facts: the emission spectra of hydrogen first predicted by Bohr and the emission rates worked out by Einstein. Emission rates roughly being how rapidly hydrogen will give off a frequency of light when supplied with the energy to do so. His idea was that if he could find a framework where he could derive the emission rates from the spectrum then this framework would also be able to handle helium. He also imposed the requirement that the equations relating spectra and emission rates from classical electromagnetism continued to be true in the atomic regime.
So he had three ingrediants: 1. Bohr's Emission spectra 2. Einstein's Emission rates 3. The classical equations relating spectra and rates
He found the only way to feed 1 into 3 was by dropping the idea that electrons had positions or momenta, once he did that he could instantly compute 2 using 1 and 3.
Shortly after with Born and Jordan he expanded his new framework out from just spectra to an entirely new rewrite of mechanics.
Schrodinger came up with what initially seemed like a new theory, but was later shown by Born and Dirac to actually be identical to Heisenberg's formalism, just written in a different notation.
Bohr then tighten the framework by showing that the central point from which everything flowed was dropping the notion of observation independent properties, a central concept of everyday human thought. Physics was now a symbolism of atomic scale measurements, not a direct description of the atomic world.
Pauli and others then showed that Helium could be correctly handled by this new theory and thus by 1931 the new quantum mechanics was fully formulated.
Re: To summarize the most basic partsRe: Actual origin of QM
In an attempt to recover something useful out of this I'll say one thing.
Entanglement actually is pretty simple, or at least simpler than most things in quantum theory. It's when the measurements on one quantum system (be it a single particle, a supercool gas, etc) are correlated with the measurements on another quantum system.
That's it. It's not about systems influencing each other faster than light or anything like that*. Just correlation.
*The faster than light stuff is just a common misunderstanding
Re: To summarize the most basic partsRe: Actual origin of QM
It took me a while to get a copy of the article since most universities here don't stock the magazine. I just had to check it was what I thought it was.
So this 4/3 problem is fairly common in classical treatments of systems involving electromagnetism. It's generic in that you commonly get 4/3 times the correct experimental answer when classical electrodynamics is applied to many relativistic situations. It doesn't just apply to E = mc^2 but to a few other cases as well. Sometimes it's 8/3 or more rarely other constants.
It's completely fixed when you model the matter correctly, either by including quantum mechanical or thermodynamical effects. Rothman and some others say this isn't a proper answer since it involves components outside of classical electrodynamics and thus doesn't solve it in the manner that respects Hasenöhrl's original set up. And so classical electrodynamics seems to say E = mc^2 in general but it's also giving you E = 4/3mc^2 in some situations and thus contradicting itself.
Yeah to be honest most of us don't really care/ignore the issue of seeking total internal consistency in a theory we know to be wrong in that regime anyway. If it was still showing up in quantum electrodynamics then we would care, but the issue of how to make classical electrodynamics internally consistent isn't pressing. Classical Mechanics has tons of self-contradictions and paradoxes that only QM resolves anyway.