31 August 2007 Nonlocality as a function of PDE type
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Abstract
Here we postulate a geometrical 2D closed path invariant ds=dst+dsΦ (geometrical interpretation) with the observer's own 2D ds=dst+dsΦ then giving a total direct sum 2⊕2=4 degrees of freedom for the resulting (observer translation) Dirac equation pde and its ψ. There are several, more or less technical, ways of stating the consequences of that new "observer interpretation" Dirac equation pde. Two such ways are "wave function collapse," and in a more common sense vein "Bertlmann's socks." Note that wavefunction collapse to ψ then (and experimental nonlocality implications) is the "observables translation" of that fundamental postulate and so not itself postulated. Also that geometrical postulate does not allow a Bohmian hidden variable interpretation because of its fundamental nature (i.e., we cannot go any deeper). For example that postulate states no x or p that we would be certain of in some hidden variable context. Thus we can ignore here the straw man arguments of J.S. Bell that are in response to Bohmian hidden variable theories only. Thus there cannot result Bell's kink at θ=0 in the correlation function between the polarization measurements on the two ends of an EPR experimental apparatus (Bell, 1987). Recall this kink required correlating in a hidden variable, classical statistical mechanical context, with resulting superluminal implications. Also note here the "observer interpretation" boundary condition conservation of angular momentum of the initial singlet state for our 4D Dirac pde results in this being a time independent solution to this pde. Thus wave function collapse to the measured value in no way implies superluminal communication. In laymen terms it is just the Bertlmann's socks common sense fact that we knew before hand about the original singlet state of the central emitter, no superluminal communication between the left and right ends of the Aspect apparatus was required to know about this. Thus our new observer representation Dirac equation pde (the below equation 3.7), and the geometrical postulate it originated from, solves the nonlocality problem which has been an enigma to physics ever since that original EPR paper of many decades ago. This is relevant to the origin of the photon since this wave function collapse is also a basic behavior of light and photons.
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David Maker, "Nonlocality as a function of PDE type", Proc. SPIE 6664, The Nature of Light: What Are Photons?, 66640U (31 August 2007); doi: 10.1117/12.729237; https://doi.org/10.1117/12.729237
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