The entanglement of two macroscopic bodies, M1 and M2, consisting, each one, from many parts, is not a relation directly between the parts, but, first of all between the movements of the two bodies taken, each one, as a whole.
For instance, if M1 and M2 are two gaseous masses, the entanglement between them is not an entanglement between the molecules in the two gases, but between the global movement (center-of-mass movement) of the two gaseous masses.
Here begins the question. Is such an entanglement possible? The simplest entanglement is
Ψ = ψa φc + ψb φd ,
where the wave-packets ψ belong to M1 and φ to M2 . From the preparation region the wave-packets of M1 exit with velocities Va and Vb, whereas the wave-packets of M2 exit with velocities Vc and Vd.
Do macroscopic bodies have wave-packets? We know from Feynman's path integral that macroscopic objects have trajectories, not wave-functions, because for such objects the action function is huge in comparison with Planck's constant.
For illustrating simply the situation, assume that the two masses are equal, M = 1Kg, and |Va| = |Vb| = |Vc| = |Vd| = V. Let's require that the wavelength of the movement of each such wave-packet be at least as big as the nuclear radius, 10-12cm, and let's see how big is V. The well-known relation
λ = 2πh/MV => V = 2πh/Mλ
yields V = 6.28×10-27/(103×10-12) ≈ 6.28×10-18cm/s.
In short, the four wave-packets never leave the preparation region.
Dear Sofia,
In my theory of Information Relativity, entanglement is not an action at a distance, but rather a local realistic phenomena, that occurs between any two bodies in relative motion. I am aware of the fact that you are loyal to the quantum theoretic regime, but it will not hurt you to inspect other explanations (see link below).
Moreover, the fascinating experiments on walking droplets, pioneered by a Yves Couder and his colleagues are stark examples of entanglement between macroscopic bodies.
see: dualwalkers.com
Link: https://www.researchgate.net/publication/303989854_If_God_plays_dice_must_we_do_the_same_Quantum_phase_transition_and_quantum_entanglement_as_deterministic_phenomena?
Best regards,
Ramzi
Conference Paper If God plays dice, must we do the same? Quantum phase transi...
Dear Ramzi,
I had a look, but I have a problem with the divergence between you and the standard theory of relativity. Whatever local theory for entanglements you build, it's desirable to build it on the standard relativity. Otherwise you raise from the beginning the reluctance of the reader.
Personally, I "smell" that if one claims that he can create entanglements without non-locality, these would be classical entanglements. But I didn't reach that point. I fell immediately on the problem with the standard relativity.
With kind regards
@Suleiman:
"Moreover, the fascinating experiments on walking droplets, pioneered by a Yves Couder and his colleagues are stark examples of entanglement between macroscopic bodies."
These are indeed fascinating experiments. But they are not examples of entanglement between macroscopic bodies. The explanation of the experiments is completely classical. They are not thought to represent macroscopic quantum states. Rather, they constiute macroscopic analogues of Bohmian mechanics, i.e. particles (macroscopic droplets here) guided by a wave (capillary waves of an ordinary liquid here).
Dear @Klaus,
You keep silent about my arguments in the question. Do you agree with them? Do you disagree? What is your position?
With kind regards!
You ask such interesting question Sophia, although I have no idea.
Dear Dina,
You are a very lovely person. If I send a message to you for reading a question of mine, I think that, at least, you would enjoy it. I also know that if you would be aware of some relevant and serious material, you would tell me. I noticed that you are good at browsing in Internet for interesting material.
With kind regards,
Sofia
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