DrChinese said:
Sorry, in the exchange I lost the sense of what you are asserting. I don't dispute that there are a variety of ways of express entanglement and/or conversation laws besides PDC photon pairs. But they produce Bell states that have 2 important properties: they display the "perfect" correlations when measured at identical settings, and they violate Bell inequalities at specificied other settings.
On the other had, the individual streams of Type I PDC crystals show neither of these qualities. yet when 2 output streams are combined, each photon pair emerging individually gains the Bell state attributes. Now, how can a mechanical explanation provide an answer in this case? I say that the QM formalism does precisely because it is *silent* on the mechanics and does not insist on "realism". On the other hand, any realistic explanation - even non-local ones - are going to have a severe problem here. I would propose that any non-local mechanical hypothesis be required to explain this Type I PDC paradox satisfactorily without resorting to the familiar "My theory always gives the same answers as QM" mantra.
Once again, the paradox is: A single particle pair emerges in a Bell state ONLY when the output of 2 PDC crystals are combined, even though that same particle pair must emerge from the source PDC crystal *without* being a Bell state. The presence of the 2nd crystal, from which the pair could not have emerged, does nonetheless figure into the emergence of the Bell state. In a deterministic theory (as BM/dBB claims to be, for example), it must have gone through one or the other and not a superposition of both. So I say that BM/dBB cannot truly claim to be a deterministic theory and still provide an adequate explanation of this paradox.
I will argue that a “mechanistic” or classical explanation is possible for the experiment you propose and also for all of the famous quantum experiments (double slit, EPR, quantum erasers, etc.).
I will point out why the belief that QM is inherently non-classical is founded on a hidden assumption that has no justification except for our intuition that it must be true. I will also explain why this assumption is so generally accepted and why it is probably false.
I also want to stress the fact that I do not claim to have this classical interpretation of QM. What I claim is only that it is possible under some scientifically acceptable assumptions. So I wouldn’t invoke gods, aliens, conspiracies, etc.
1. What the evidence says
We know that QM is a contextual theory. The result of a measurement cannot be associated with a property of a system that exists independently of the act of measurement itself. Any non-contextual theory fails to predict correctly the EPR results. In other words, if we want a realistic theory of particles moving in a 3D space ( a classical theory, if you want) we have to accept the idea that a particle is somehow aware of what is going around it (how many detectors, pdc’s, mirrors, beam splitters, slits, etc. we have, what their state is, and so on). Of course, a particle doesn’t “know” about our understanding of how all those objects behave, it only “sees” them as big groups of other particles.
2. The classical explanation of the evidence
So, here it comes the million dollar question: is there any classical concept that can explain us how a particle “knows” the configuration of other particles? Well, I think there is such a concept and it is named
FIELD. The existence of a field that is associated to each particle is enough to explain all static quantum experiments. In the single/double slit experiment, for example, the particle “knows” how many slits are there because of the field produced by the particles in the wall. One slit requires a different matter configuration than two slits, different matter configurations produce different fields and different fields correspond to different particle trajectories. The same explanation works for the experiment you propose, replace only “slit” with “pdc crystal”. There is no contradiction to classical realism whatsoever.
For the experiments testing non-locality (Aspect, delayed choice) the assumption of determinism is also required. The field remains local, but, because it evolves deterministically, the future matter configuration is encoded in it. So, our particle “knows” how it is going to be measured because the local field uniquely determines it.
So, if the particles are accompanied by a long-range local field that evolves deterministically there is no reason to reject classical realism.
3. Where the deniers of realism went wrong
If you take a look at the proposed classical explanations for various quantum experiments you will see that all of them are variations of a billiard ball model. The particles are supposed to travel in straight lines and change direction (or other properties) only at direct collisions. In your experiment you assume that a photon can be affected by the second crystal only if it passes through it. Well, such an assumption fails if the particles interact through a long-ranged field. Often I see the requirement that a particle cannot be influenced by a distant object presented as a locality condition. This is again wrong. Classical electromagnetism is local but it does not comply with such a requirement. Two charged objects interact without a direct collision.
In conclusion, the realism deniers are beating a dead horse, the billiard ball model of reality. Of course, such a model cannot explain pure classical physics like gravity or electromagnetism. It shouldn’t be a surprise that it also fail to explain QM.
4. Why the deniers of realism went wrong
One may wonder why great minds as Feynman made the same mistake of identifying classical realism with billiard balls. My guess is that we don’t directly experience a world dominated by fields (Earth gravity is an exception). Gravity is too weak to notice, electromagnetism is hidden by the fact that macroscopic object are electrically neutral. There is also the fact that these two fields decrease with the square of the distance so there exists a certain independence between the evolution of macroscopic objects.
I thing that importing the observed behavior of the macroscopic objects to the quantum world is wrong. Quantum particles may interact through a field that does not decrease with the distance. It might be periodic for example. Adding the fields produced by many particles you could still regain the inverse square law and by averaging the trajectories of many particles you could get billiard ball like trajectories. But when you deal with single particles (or entangles pairs) the things might change.