Abstract
A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.
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Notes
- 1.
This also raises the question of quantum statistics. It has been noted in a previous paper (13) that Fermi-Dirac statistics is a consequence of indistinguishable particles forming spin-singlet states, while Bose-Einstein statistics follows as a consequence of breaking the rotational invariance associated with the singlet states. Moreover, the easiest way for this breaking to occur is for the spin states of the particles to be statistically independent. It follows as a trivial consequence of the above theory that bosons cannot be second quantized as fermions and fermions cannot be second quantized as bosons, in that particles which are forming spin-singlet states with probability one cannot be considered statistically independent. It also follows that spin 0 particles must obey Bose-Einstein statistics. For example, if S and T represent the spin observables of two particles such that \(P(S = 0) = P(T = 0) = 1\) then \(P(S = 0,T = 0) = P(S = 0)P(T = 0) = 1.1 = 1\), and hence the spin observables S and T are statistically independent.
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O’Hara, P. (2010). Minkowski Space and Quantum Mechanics. In: Petkov, V. (eds) Space, Time, and Spacetime. Fundamental Theories of Physics, vol 167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13538-5_4
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DOI: https://doi.org/10.1007/978-3-642-13538-5_4
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