Quantum Action-at-a-Distance: The Mystery of Einstein-Podolsky-Rosen Correlations

Lorentz-Invariant, Retrocausal, and Deterministic Hidden Variables

“…6 we can deduce [9,12] different joint and conditional probabilities for detecting particles + and -in separated regions of space-time. First, we have at time t ′′ out > t ′′ the joint probability P (D + , D − ) = 1 12 (7) meaning that the probability of a joint outcome in wavepackets D + and D − is not vanishing (this formula doesn't require the simultaneity of D + and D − measurements). We have also the conditional probabilities…”

“…However, as stated by Hardy [12], Bohm [3,6,27], and Bell [1,3] there is no experiment that can be performed to determine what this preferred frame is (even if the absolute reference frame associated with the 2.7 K microwave cosmological background is often recalled [3,8] as a good candidate in this context). Vigier and coworkers [7] also proposed to use the center of mass of the full particle ensemble to define a preferred frame in BM. Similarly, Durr, Struyve et all.…”

“…Interestingly, whereas in BM the dynamics of particles guided by the quantum state is not fully Lorentz invariant the theory is still Lorentz invariant at the statistical level meaning that the Aether is thus essentially hidden. Nevertheless, while this preferred foliation proposal mixing Newtonian and Einsteinian concepts motivates alternative theories going far beyond present-day quantum mechanics and general relativity [7,8,3,27] it is difficult, or even impossible, not to see here a failure of the full deterministic hidden-variable program. In other words, assuming an Occam razor principle most researchers would better agree that deterministic hidden variables can not be made to agree with Minkowsky space-time and should thus preferably be abandoned as an explanation of QN.…”

“…where we omit the subscript n and the probability element dP (F 0 ) acts on the configuration space S of all the foliations. Here we used Born's rule for defining P (α, Ψ ) and the right hand part of the equation is obtained from the definition of a deterministic hidden variable 7 .…”

“…Bohm and also Valentini and Bell [3,5,1,6] already favored the view admitting a preferred space-time foliation or reference frame acting as a kind of new Aether (sometimes called the 'sub-quantum' Aether [3,7,8]). For many this perspective would seriously represent a tentative of regression to the pre-Einsteinian era when Lorenz and others proposed a mechanical explanation of electromagnetic phenomena in a preferred reference frame.…”