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Quantum entanglement

Quantum mechanics make two seemingly incompatible assumptions. It assumes conservation laws7.11are absolute and it assumes probabilities are irreducible. In classical physics there are mechanisms that explains how the conservation laws are `enforced'. By claiming probabilistic laws are absolute one precludes the possibility of an enforcing mechanism.

This leads to a serious issue. When a pair of particles are created and travel off in opposite directions they must have exactly equal momentum in opposite directions. Yet observing the momentum of either of these particles is statistical. The result can vary over a range of values. But once an observation is made, we know with similar accuracy the momentum of the other particle which may be far away even on the other side of the universe.

Einstein explained this difficulty in the previously cited paper known by the initials of its authors EPR[21]. Einstein and his colleagues concluded that quantum mechanics must be incomplete. For momentum must have an objective reality independent of each observation if momentum is conserved absolutely. Nature is doing a sort of cosmic bookkeeping to make sure momentum is never created or destroyed and their needs to be a mechanism not part of any existing theory that implements this accounting procedure. The principle on which Einstein's argument is based is uniformly true in classical physics. It was argued that this principle does not apply to quantum mechanics. The debate is closed for most physicists and decided against Einstein. I suspect Einstein will ultimately be proved correct.

Probabilistic observations and absolute conservation laws leads to quantum entanglement. In classical physics state evolution is local. If particles are far apart they cannot affect each other except by transferring some signal at a speed that cannot exceed that of light. Because of quantum entanglement this is not true of quantum mechanics. Observations of one particle can instantaneously put constraints on observations of a second particle with which the first has become entangled even if the two particles are a billion light years apart. Every corner of the universe can be instantaneously influenced by every other corner of the universe. The physicist David Bohm embraced this nonlocal model as support for a philosophy that saw the universe as whole[9]. But is it true? And how can it be true and relativity also be true?

An absolute contradiction with special relativity is avoided through quantum randomness. The effects transmitted instantaneously are in effect encrypted with quantum uncertainty. Such effects always involve two events at distant locations $A$ and $B$. Violations of classical locality that are consistent with the predictions of relativity always happen in a way that it is impossible to know if the effect goes from location $A$ to $B$ or vice versa. In some inertial frames of reference it will be seen to go in one direction and in other frames of reference it will be seen to go in the opposite direction. Neither relativistic view of the situation contradicts the predictions of quantum mechanics because quantum randomness is claimed to be absolute and not reducible to some causal model that would show how the effect operates.

This factor also makes it impossible to send a faster than light signal using quantum entanglement. One can only tell that information has been transferred instantaneously by comparing the results at $A$ and $B$ and that comparison requires that information be transferred no faster than the speed of light.

This is a very strange situation. The inability to separate space into local regions that are causally independent is fundamental to the idea of special relativity yet it is egregiously violated in quantum mechanics. Yet there is no contradiction in the predictions of the two theories. The next chapter explores these and other issues in integrating these two theories that have an uneasy coexistence at the core of contemporary physics.


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