An Observer's View on Relativity: Space-Time Splitting and Newtonian Limit

Reddiger, Maik

doi:10.48550/arxiv.1802.04861

Cited by 1 publication

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“…2 (see Chap. 4 in [32]). ii) In practice, Σ 0 should be chosen to be 'maximal' in the sense that one is able to capture all possible particle positions.…”

Section: Remarkmentioning

confidence: 99%

“…§2 in [38]). For details we refer to the original articles on the Fermi-Walker derivative [17,38], the article by Mast and Strathdee [24], as well as the first author's thesis [32] ( §3.2 and §3.4.2 in particular).…”

Section: Introductionmentioning

confidence: 99%

“…A time-orientable Lorentzian manifold is space-orientable if and only if it is orientable (cf. p. 30 in[32]). Of course, a manifold admits a volume form if and only if it is orientable.…”

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confidence: 99%

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The One-Body Born Rule on Curved Spacetime

Reddiger¹,

Poirier²

2020

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A recent article has treated the question of how to generalize the Born rule from non-relativistic quantum theory to curved spacetimes (Lienert and Tumulka, Lett. Math. Phys. 110, 753 (2019)). The supposed generalization originated in prior works on 'hypersurface Bohm-Dirac models' as well as approaches to relativistic quantum theory developed by Bohm and Hiley. In this comment, we raise three objections to the rule and the broader theory in which it is embedded. In particular, to address the underlying assertion that the Born rule is naturally formulated on a spacelike hypersurface, we provide an analytic example showing that a spacelike hypersurface need not remain spacelike under proper time evolution-even in the absence of curvature. We finish by proposing an alternative 'curved Born rule' for the one-body case, which overcomes these objections, and in this instance indeed generalizes the

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“…2 (see Chap. 4 in [32]). ii) In practice, Σ 0 should be chosen to be 'maximal' in the sense that one is able to capture all possible particle positions.…”

Section: Remarkmentioning

confidence: 99%