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arXiv:quant-ph/0003149 · Foundations of Physics

Local Measurements of Nonlocal Observables and the Relativistic Reduction Process

G. C. Ghirardi

Published Sep 1, 2000• 32 citations
arXivHTMLPDF
DOI
10.1023/a:1026497632474

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We study the instantaneity of the state-reduction process in relativistic quantum mechanics. The conclusion of various authors that this instantaneity will restrict the set of relativistic observables to purely local ones (i.e., that the measurement of any nonlocal property of a system at a well-defined time would give rise to violations of relativistic causality) is found to be erroneous, and experiments (of a kind not encountered before in measurement theory) are described whereby certain nonlocal properties of some simple physical systems can be measured at a well-defined time without violating causality. The attempts of certain authors to reconcile the reduction process with the covariance of the relativistic quantum state are considered and found wanting, and it is argued that the covariance of relativistic quantum theories resides exclusively in the experimental probabilities, and not in the underlying quantum states. The problem of nonlocal measurement is considered in general: distinctions (which are not to be met with in the nonrelativistic case) arise in relativistic quantum mechanics between what can be measured for fermions and what can be measured for bosons, between what can be measured for individual systems and what can be measured for ensembles, and between what kinds of states can be verified by measurement and what kinds of states can be prepared by measurement; and these pose difficult questions about the nature of measurement itself.
This work presents a conceptual and semi-formal analysis of quantum entanglement, locality, and determinism, motivated by a thought experiment involving double-slit measurements performed on entangled particles at spacelike separation. While quantum correlations appear instantaneous, the paper demonstrates that no superluminal information transfer or causal influence is required to explain observed outcomes.Building upon the Einstein–Podolsky–Rosen framework and Bell’s theorem, the study distinguishes between local dynamical processes and nonlocal informational correlations encoded in the global quantum state. It argues that measurement outcomes are locally realized yet globally constrained, leading to an effectively deterministic universal description while preserving epistemic uncertainty for observers.The paper reframes quantum nonlocality as a manifestation of global consistency rather than physical influence, offering insights into the relationship between realism, free will, and relativistic causality. The discussion is interpretational in nature and does not introduce new experimental claims, aiming instead to clarify foundational assumptions underlying quantum theory.This work is intended for researchers and students interested in quantum foundations, the philosophy of physics, and the conceptual structure of modern physical theories.
Evolution of a Physical State Vector (PSV) is described as governed by two distinct physical laws: Continuous, unitary time evolution and a relativistically covariant reduction process. Non-local measurements, proposed by Aharanov and Albert, are excluded when the reduction is attributed to measurement devices which are included in the PSV. The existence of a PSV allows to formulate phenomenological laws of reduction. A proposal ismade for which the collapse time is found tobe τ c = bh /Δ E , where Δ E is a difference in energy distribution between alternative world branches. Experiments yield the bounds 1.35·10 11 < b <4.5·10 18 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.