Andrei Khrennikov wrote:
Michel:
Philosophical:
Could we say that the entanglement of two particles reduces to the fact
that a measure done on the first particle indicates something on the
second particle just because they are interacting ?
Andrei: Einstein and I would say: yes! But the conventional viewpoin:
no! -- because the Bell inequality.
Bell's formulation implies that the hidden variable is independent of
the configuration of the detectors. On the other hand, if we allow for
the fact that the hidden variable is dependent on the mutual
configuration, then there is no need to abandon the classical framework.
To some extent this does imply some sort of non-locality. But it is the
same type of non-locality as in a perfectly classical context. Let me
describe an experiment.
Imagine a bathtub. Imagine primitive measurement technology that
involves putting person A in the water so that his nose is aligned with
the water. He is measuring the incoming waves, and outputs 1 when a wave
splashes into his eyes, and 0 otherwise. There is another person B
measuring in the same way on the other side of the bathtub. You can
change the orientation of both people, and this will clearly affect the
frequency of water splashing into their eyes. Now throw a stone in the
bathtub, creating an entangled pair of wavefronts propagating in both
directions. Measure the correlation of splashes into person A's eyes and
person B's eyes.
There are three interpretations of the resulting correlations of splashes:
* (QM) The waves are in a superposition of splashing and not-splashing,
until person A experiences a splash or not-splash, and collapses the
wave function. The collapse telepathically "informs-at-a-distance" the
other entangled wavefront whether person B will experience a splash or not.
* (New Age) The two detectors are not independent - they are an
entangled pair in the aether of global consciousness, with the
incredible ability of transmitting thoughts at a distance.
* (classical) The fact that two people are in a bathtub with their big
measuring apparatuses (bodies, noses and eyes) will affect the joint
distribution of splashes. The position of one person will affect the
measurements experienced by the other person, because it affects the
shape of the body of water in which the wavefronts propagate.
I am not saying that Bell's inequality is trivial. It is extremely
important. While it does not refute the hidden variable theory, it
informs the classicists among us that the way of measuring on one side
of the bathtub is not independent of measuring on the other side of the
bathtub.
We may only be able to measure splashes, but maybe there is more to
reality than the mere splash in the eyes. While there is indeed some
quantization around, this doesn't mean that all there is are quanta.
Disclaimer: I am not a physicist.
Best regards,
Aleks Jakulin
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