Mermin's Challenge
In his first article on entanglement, N David Mermin issued a challenge to other physical scientists...
It is left as a challenging exercise to the physicist reader
to translate the elementary quantum-mechanical reconciliation
of cases (a) and (b) into terms meaningful to a
general reader struggling with the dilemma raised by the
device.
American Journal of Physics 49(10) (1981): p.943
One group of scientists recently suggested a response to Mermin's challenge in terms of a "preferred frame" like that in special relativity.
Herein, we show how “conservation per no preferred reference frame (NPRF)” answers that challenge.
In short, the explicit conservation that obtains for Alice and Bob’s Stern-Gerlach spin measurement outcomes in the same
reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3)
invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert
space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of
time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special
relativity via their “mysteries” is the restricted Lorentz group.
Answering Mermin’s Challenge with Conservation per No Preferred Reference Frame arXiv:1809.08231v6 [quant-ph]x 28 Jul 2020
We agree that a conservation principle is the simplest explanation of entanglement. And conservation (of total spin angular momentum) is only possible if Alice and Bob agree in advance to make their measurements
at the same angle in a
preferred frame. But this has nothing to do with special relativity. The two particles' spin angular momentum is conserved from the moment of initial entanglement in an apparatus located centrally between Alice and Bob to the moment of the first measurement (by either Alice or Bob) Either measurement
collapses the two-particle wave function Ψ
12 into a product of single-particle wave functions Ψ
1 and Ψ
2.
This is standard two-particle quantum theory since 1926 when
Erwin Schrödinger developed his formulation of wave mechanics. We regard the conservation as a
common cause of the entanglement coming from the central apparatus in the past light cone of the measurements. We also view the conserved total spin as a
constant of the motion. No "hidden variables" are needed.
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