Entanglement is a mysterious quantum phenomenon that is widely, but mistakenly, described as capable of transmitting information over vast distances faster than the speed of light. It has proved very popular with science writers, philosophers of science, and many scientists who hope to use the mystery to deny some of the basic concepts underlying quantum physics. Beyond this claim, which violates Einstein's principle of special relativity, is the claim that entanglement "connects" every particle in the universe with every other particle, implying a "holistic" or "implicate" order in the universe, which is popular with "new age" thinkers and other mystics who see in it pan-psychism, or "cosmic consciousness," or at a minimum "telepathic powers" between entangled minds.
The classic example of quantum entanglement studied by John Bell is a pair of particles that have been entangled with opposite spins. The particles separate and one is measured (by Alice) who finds spin up, say. Then immediately the other particle will be found to be spin down by Bob.
Here is a crude two-dimensional animation of this picture,
If you move the timeline playhead slowly you can see the two spins are oscillating back and forth, always keeping the total spin zero. Richard Feynman described them as arrows spinning randomly in all directions, but neither visualization does justice to the underlying fact that there is no preferred direction for the rotationally symmetric total spin zero state of the entangled Ψ12 wave function.
In the famous Einstein-Podolsky-Rosen (EPR) Paradox of 1935, Einstein said the particles had clearly separated, so measurement A must have instantly caused the outcome of measurement at B by means of a "spooky action at a distance." Erwin Schrödinger immediately wrote to Einstein and explained that his Ψ12 wave function could not be separated until a measurement or interaction collapses the wave function.
We regard this three-part "causal chain" of events as a "common cause" in the sense of Hans Reichenbach's Common Cause Principle
If an improbable coincidence has occurred, then there must have been a common cause.3
Reichenbach, H. (1991). The Direction of Time. U. California Press. p.157
In our case, if events at A and B are perfectly correlated, then either A causes B, B causes A, or there is a common cause C coming to A and B. Since A and B occur simultaneously, neither can cause the other. Any cause from A to B or vice versa would need to travel faster than light.
We propose that simultaneous measurement outcomes at two entangled particles widely separated in space are caused to be perfectly correlated as the result of 1) local causes at initial entanglement, 2) a conservation principle as the particles travel to the measurement devices which limits the measurement outcomes, and 3) measurements at A and B that are made in a (previously agreed upon arbitrary) single plane that replaces the spherical symmetry of the two-particle wave function with planar symmetry that conserves the perfectly correlated measurement outcomes. There is no superluminal action from A to B or vice versa.
ΨAB = 1/√2 (ΨA ↑ΨB ↓) - 1/√2 (ΨA ↓ΨB ↑)
Conservation of total spin zero maintains the spherical symmetry of this wave function ΨAB as the particles travel to A and B (provided no environmental interaction disturbs the symmetry). While this constant of the motion is not "causally local," it puts a "condition" or constraint on the final measurements. It's not the "hidden variable" that many have looked for, but we can consider it a "hidden constant". The condition or constraint is simply that total spin must be conserved as zero. This condition or constraint travels (with the particles) subluminally for fermions (electrons) and at the speed of light for bosons (photons).
It does what David Mermin's "instruction sets" were thought to do.
This condition or "hidden constant" does not mean that the spin directions were determined (fixed) at the initial entanglement. They remain undetermined until they are statistically found 50% up-down (ΨA ↑ΨB ↓) or 50% down up (ΨA ↓ΨB ↑) as long as they are measured in an agreed-upon direction.
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