In 1964, John Bell put limits on David Bohm's "hidden variables." Bell found they would be "nonlocal."

Although we find no need for "hidden variables," whether local or non-local, we might say that the conservation laws give us a "hidden constant." Conservation of a particular property is often described as a "constant of the motion." These constants might be viewed as "local," in that they travel along with particles at all times, or as "global," in that they are a property of the two-particle probability amplitude wave function Ψ₁₂ as it spreads out in space.

This agrees with Bohm, and especially with Bell, who says that the spin of particle 2 is "predetermined" to be found up if (and only if) particle 1 is measured to be down (when measured in the same direction). They are implicitly using conservation of angular momentum.

But recall that the Copenhagen Interpretation says we cannot know a spin property until it is measured. So some claim that both spins are in an unknown combination of spin down and spin up until the measurements. It is this that suggests the possibility that both spins might be found in the same direction, violating the conservation laws.

Since electron spins in this situation are never found experimentally in the same direction, this gave rise to the idea of a hidden variable as some sort of signal that could travel to particle 2 after the measurement of particle 1, causing it to change its spin to be opposite that of particle 1. What sort of signal might this be? And what mechanism exists in a bare electron that could cause it to change a property like its spin without an external force of some kind?

Eugene Wigner's explicit view that a conservation law is operating, and the implicit claims of Bohm and Bell that the electron spins are created in opposite states, give us the simplest and clearest explanation of the entanglement paradox.

Despite accepting that a particular value of some "observables" can only be "known" by a measurement (knowledge is an epistemological problem) Einstein asked whether the particle actually (really, ontologically) has a path and position, even other properties, before we measure it? His answer was yes.

Einstein might have thought that the two particles have had their spins predetermined from the time of their entangling interaction. But as we have shown, the perfectly correlated properties were not created at the initial entanglement preparation but at the later measurements by Alice and/or Bob. What must pre-exist is the joint property of conserved total momentum in all directions, a symmetry property of the initial entanglement of the two particles.

Here is a crude animation illustrating the assumption that the two electrons are prepared, one in a spin-up, the other in a spin-down state. They remain in opposite states no matter how far they separate, provided neither interacts with anything else until the measurements at A and B.

"Hidden constants" of the motion, requiring one spin up, one down, at all times, so total spin is always zero and the two-particle wave function is rotationally symmetric, completely explain the fact of perfect correlations of opposing spins. "Nature's" random choice of up-down versus down-up explains why the two perfectly correlated bit strings can be used in quantum cryptography. That the two strings appear at widely separated places without the possibility of an eavesdropper between them makes this the preferred method for quantum key distribution (QKD).