Special relativity, causality and quantum mechanics — 1

Guruprasad Kar, Samir Kunkri, Sujit K. Choudhary

Francis R. Halpern

Alan Francis McCulloch

Probability amplitude waves described by quantum mechanics are globally coherent relativistically space-like space-time structures, having no internal causal links. In this sense these non-classical structures are anticipated by the classical ontology of special relativity, which also delineates (in a completely different way) space-like non-causal intervals in space-time. I discuss and distinguish two broad classes of globally coherent relativistically space-like space-time structure, and suggest a parsimonious extension of the core ontology of physics to include both (rather than only one as at present), as a way of resolving some puzzles in the interpretation of quantum mechanics, and motivating its formalism. This ontological extension yields well known formal features usually postulated ad-hoc, such as separability of the wave function, and explains the puzzling absolute nature of time in quantum mechanics. The curious fact that the ontologies of both special relativity and quantum mechanics delineate (in strikingly different ways) strictly non-causal intervals in space-time suggests the existence of an explanatory “last common ancestor” ontology, at a higher level of abstraction than the ontologies of either. I briefly sketch such an ontology, consisting of world self-mappings, in terms of which there are two distinct concepts of time, intrinsic and extrinsic, which together play an abstract identity role in the world, and which suggests part of the meaning of both special relativity and quantum mechanics, and of the non-causal coherence of non-classical space-time structures, concerns extrinsic abstract structure, in particular extrinsic time.

Andreas Schlatter

T. M. Helliwell, D. A. Konkowski

A potential causality paradox in quantum mechanics involving the measurement of a correlated system of two atoms that have moved far apart is constructed along the lines of a classical causality paradox involving the exchange of superluminal signals between distant observers. It is shown that the quantum measurement example does not lead to a paradox, but that the results have implications for the interpretation of quantum mechanics. The thought experiments presented have been used in undergraduate courses in special relativity and quantum mechanics.

Goran Amidzic

The emergence of P = 4 and d0 = 3 from causal axioms P1P4 [1] suggests thata metric structure may underlie this discrete geometry. This paper proceeds phe-nomenologically: we investigate the consequences of the hypothesis that the relationbetween emergent proper time τ , spatial displacement |Δpos|, and causal step dLtakes the form τ 2 + |Δpos|2 = dL2. All results are conditional on this hypothesisand a complementarity assumption stated explicitly in Section 2. This work does notreproduce the quantitative predictions of quantum mechanics or special relativity.It provides a structural perspective only.Under these two assumptions, of the eight possible combinations of sharp and un-sharp quantities, three are naturally consistent with known physics: the macrocosm(Special Relativity), the microcosm (Heisenberg uncertainty), and quantum entan-glement. This paper further suggests that wave-particle duality, the measurementproblem, and the special status of time in quantum mechanics may nd a naturalinterpretation within this framework.