Bell inequalities in astronomical scale?

[Duda Jarek]

Quantum mechanics ‘works’ in proton + electron scale. Let’s enlarge it – imagine proton rotating around chloride anion … up to two charged oppositely macroscopic bodies rotating in vacuum.

We can easily idealize the last picture to make it deterministic (charged, not colliding points).

However, many people believe that Bell’s inequalities says that the first picture just cannot be deterministic.

 

So I have a question – how this qualitative difference emerge while changing scale?

In what scale an analog of EPR experiment would start giving Bell’s inequalities?

 

I know – the problem is: it’s difficult to get such analog.

Let’s try to construct a thought experiment on such macroscopic rotating charged bodies, which are so far, that we can measure only some of its parameters and so we can only work on some probabilistic

theory describing their behavior.

For simplicity we can even idealize that they are just point objects and that they don’t collide, so we can easily describe deterministically their behavior using some parameters, which are ‘hidden’ from the observer (far away).

 

The question is: would such probabilistic theory have quantum-mechanical ‘squares’, which make it contradicting Bell inequalities?

If not – how would it change while changing scale?

Personally I believe that the answer is yes – for example thermodynamics among trajectories also gives these ‘squares’ (http://arxiv.org/abs/0910.2724), but I couldn’t think of any concrete examples…

 

How to construct an analog to EPR experiment for macroscopic scale objects?

Would it fulfill Bell inequalities?

[swansont]

How is the system entangled?

[Duda Jarek]

One of the reasons to to introduce the concept of entanglement was the EPR experiment.

Standard quantum measurement is projection into eigenstate basis of some hermitian operator (Heisenberg uncertainty principle applies to these measurements).

EPR uses some additional, qualitatively different type of information - we know that because of angular momentum conservation, produced photons have opposite spin.

 

In deterministic picture - there was no entanglement - there was just created some one specific pair of photons - 'hidden variables'.

In this picture quantum mechanics is only a tool to estimate probabilities and the concept of entanglement is essential to work on such uncertain situations, but it isn't directly physical.

But Bell's inequalities made many people believe that we cannot use such picture.

 

However, such moving 'macroscopic charged points' can be well described deterministically - when we doesn't have full information, we could construct probabilistic theory with 'hidden variables'.

And when we know that there was created two pairs of rotating bodies, such that we couldn't measure it's parameters, we still would know that e.g. because of angular momentum conservation, they would have to rotate in opposite direction - so to work on such probabilities we would have to introduce some concept of entanglement ...

So the question stays - would that theory have 'squares' like quantum mechanics, which make it contradict Bell inequalities?

 

If no - how this qualitative difference emerges while rescaling?

Why we can describe rotating macroscopic points with 'hidden variables', but we cannot do it with microsocpic ones?