A thought experiment is presented that provides a hint as to how quantum wave functions can collapse in a relativistically consistent way. The thought experiment consists of a central source of photon pulses midway between two detectors, which is examined relativistically from both the lab frame and a frame moving with respect to the source and detectors. The total number of pulses between the two detectors is the only invariant and this leads to the idea that collapse might occur along special spacetime intervals, which we call symmetric spacetime intervals. In the current formalism of quantum mechanics, collapse is envisioned to occur “instantaneously”, in clear violation of relativity. It is shown that what the current formalism actually specifies is that collapse is merely spacelike. However, if quantum collapse occurs along symmetric spacetime intervals, then collapse of the wave function can be made consistent with relativity and all observers can agree upon which of two spacelike-separated causally connected events is the cause and which the effect. Nomenclature x = normalized distance in light seconds (ls) t = normalized time in seconds (s) γ = Lorentz factor s = spacetime interval u = normalized velocity (ls/s) c = speed of light (1.0 ls/s) y = a quantum object z = a quantum object d = separation between pulses (ls) L = separation between detectors (ls) ν = frequency (s-1) n = number of pulses β = slope of the symmetric interval (s/ls) I.
A thought experiment is presented that provides a hint as to how quantum wave functions can collapse in a relativistically consistent way. The thought experiment consists of a central source of photon pulses midway between two detectors, which is examined relativistically from both the lab frame and a frame moving with respect to the source and detectors. The total number of pulses between the two detectors is the only invariant and this leads to the idea that collapse might occur along special spacetime intervals, which we call symmetric spacetime intervals. In the current formalism of quantum mechanics, collapse is envisioned to occur “instantaneously”, in clear violation of relativity. It is shown that what the current formalism actually specifies is that collapse is merely spacelike. However, if quantum collapse occurs along symmetric spacetime intervals, then collapse of the wave function can be made consistent with relativity and all observers can agree upon which of two spacelike-separated causally connected events is the cause and which the effect. Nomenclature x = normalized distance in light seconds (ls) t = normalized time in seconds (s) γ = Lorentz factor s = spacetime interval u = normalized velocity (ls/s) c = speed of light (1.0 ls/s) y = a quantum object z = a quantum object d = separation between pulses (ls) L = separation between detectors (ls) ν = frequency (s-1) n = number of pulses β = slope of the symmetric interval (s/ls) I.
It has previously been shown that collapse of the quantum wave function can be made consistent with relativity by specifying collapse to occur along special spacelike spacetime intervals. The special case of two entangled particles has been considered in some detail. When the entangled particles have the same mass, the world line of their center of mass bisects the spacetime interval along which collapse occurs, so we have taken to calling them symmetric spacetime intervals. In previous work, symmetric spacetime intervals were taken as a hypothesis. In this paper, they are derived and the concept is shown to apply equally well to entangled photons at light speed and to matter particles at sublight speeds. The derivation shows that the slope of the symmetric spacetime interval is numerically equal to the velocity of the center of mass of the entangled pair as previously hypothesized. Nomenclature x = normalized distance in light seconds (ls) t = normalized time in seconds (s) γ = Lorentz factor s = spacetime interval u = normalized velocity (ls/s) c = speed of light (1.0 ls/s) d = separation between pulses L = separation between detectors ν = frequency n = number of pulses β = slope of the symmetric interval (s/ls) I.
In the current formalism of quantum mechanics, collapse of the wave function is envisioned as occurring “instantaneously”. Since this is in conflict with the fact that “simultaneity” is not a relativistic invariant, quantum mechanics and relativity are in conflict with each another. This conflict is benign as long as faster-than-light (FTL) phenomena are disallowed. This paper explores this conflict and considers the implications if collapse can be specified to occur in a way that is consistent with relativity. In particular, relativistically consistent wave function collapse forces us to reconsider our preconceptions of causality. We are led to consider two cases; timelike and spacelike. For two events that are causally connected by a timelike interval, the earlier-in-time event is the cause in all reference frames, but the spatial ordering is not preserved. For two events that are causally connected by a spacelike interval, the temporal ordering is not preserved but the spatial ordering is, just the reverse. This is philosophically disturbing since for spacelike causes half the reference frames see the cause as proceeding backwards in time. However, in and of itself this is not logically inconsistent. Backwards-in-Time Causality (BTC) seems at first glance to permit temporal paradox, since two spacelike causal connections can be used to create a closed causal loop in spacetime. While temporal paradox is logically inconsistent, BTC can still be allowed if there is also a censor mechanism that prevents temporal paradox. In relativity, FTL and BTC are two sides of the same coin, so the major implication of relativistically consistent wave function collapse is that quantum systems should be able to support both FTL and BTC phenomena despite Eberhard’s “proof.”
Collapse as Category Error: Why Wave Function Collapse Cannot Be a Spacetime Event (v2.0) This paper argues that the demand for wave function collapse to be a spacetime-localised physical event constitutes a category error in relativistic quantum mechanics. In scenarios involving spacelike-separated measurements on entangled systems, different inertial frames assign different temporal orderings to measurement events. Treating collapse as a physical event with a definite time and place therefore requires a preferred foliation of spacetime, in violation of Lorentz covariance. The paper shows that all empirically accessible quantities—local measurement outcomes and their joint probability distributions—are Lorentz-invariant and can be derived without invoking any spacetime collapse event. “Collapse” is instead most coherently understood as a relational, non-dynamical re-description of correlation structure conditioned on local measurement context. The contribution is strictly one of conceptual clarification and structural constraint analysis. The paper does not propose a new interpretation of quantum mechanics, introduce dynamical collapse models, or claim to resolve the measurement problem. Version 2.0 extends the analysis with: (i) a structured evaluation matrix (HATI-QM) for comparing interpretational frameworks against Lorentz covariance and epistemic transparency; (ii) an explicit falsifiability architecture (“semantic kill-switch”); and (iii) a formal mapping to the Ecological Homeostasis framework for distributed adaptive systems, identifying collapse localisation as an instance of a broader “pathological localisation” error. The paper is intended for researchers in quantum foundations, philosophy of physics, and information-theoretic approaches to quantum theory.
The collapse of a spatial probability distribution is triggered by a measurement at a given spacetime point. It is customarily assumed that this collapse occurs along an equal-time hypersurface, say, t = 0. However, such a naïve instantaneous collapse process is inconsistent with relativity, because the equal-time hypersurfaces of different inertial reference frames are different. The attempts at implementation of instantaneous collapse in several different reference frames then lead to violations of probability conservation and violations of the scalar character of the probability contained in given volume elements. This problem affects not only the Copenhagen interpretation of quantum mechanics, but also other interpretations in which it is still necessary to specify what changes in probabilities occur when and where in a manner consistent with relativistic spacetime geometry. In the 1980s Schlieder and Hellwig and Kraus proposed that collapse of the probability distribution along the past light cone of the measurement point avoids these difficulties and leads to a Lorentz-invariant collapse scenario. Their proposal received little attention and some negative criticisms. In this paper I argue that the proposed past-light cone collapse is not only reasonable, but is compelled by Lorentz invariance of probability conservation, and is equally valid for the spatial probability distributions in quantum mechanics and for those in a game of chance, for instance, the probability distribution for a game with playing cards scattered over some spatial region. I examine the objections that have been made to the past-light-cone collapse scenario and show that these objections are not valid. Finally, I propose two possible interferometer experiments that can serve as direct tests of past-light-cone collapse, one with an atom interferometer, and the other with a light interferometer.
A relativistic version of the (consistent or decoherent) histories approach to quantum theory is developed on the basis of earlier work by Hartle, and used to discuss relativistic forms of the paradoxes of spherical wave packet collapse, Bohm's formulation of the Einstein-Podolsky-Rosen paradox, and Hardy's paradox. It is argued that wave function collapse is not needed for introducing probabilities into relativistic quantum mechanics, and in any case should never be thought of as a physical process. Alternative approaches to stochastic time dependence can be used to construct a physical picture of the measurement process that is less misleading than collapse models. In particular, one can employ a coarse-grained but fully quantum-mechanical description in which particles move along trajectories, with behavior under Lorentz transformations the same as in classical relativistic physics, and detectors are triggered by particles reaching them along such trajectories. States entangled between spacelike separate regions are also legitimate quantum descriptions, and can be consistently handled by the formalism presented here. The paradoxes in question arise because of using modes of reasoning which, while correct for classical physics, are inconsistent with the mathematical structure of quantum theory, and are resolved (or tamed) by using a proper quantum analysis. In particular, there is no need to invoke, nor any evidence for, mysterious long-range superluminal influences, and thus no incompatibility, at least from this source, between relativity theory and quantum mechanics.
The relativity of simultaneity together with the definition of a quantum state collapse results in experimental situations where multiple measurements can be taken on an uncollapsed quantum state. The quantum state's collapse is defined to be instantaneous in a rest inertial frame of a detector performing measurements on the quantum system. The definition is consistent with the Copenhagen interpretation and in agreement with all measurements performed with detectors at rest in an arbitrary Lorentz (laboratory) frame. From the introduced collapse model follows that under certain conditions multiple measurements are allowed on the same uncollapsed quantum state. An application of the developed approach is shown on measurement of photon-pair state entangled in polarization and energy. Conditions under which two measurements can be taken on the uncollapsed photon-pair state are derived. Serious consequences follow from the allowance of multiple measurements on the same uncollapsed state. For example, the measurements taken by both detectors in this situation are uncorrelated. Moreover, all the conservation laws could be violated in individual measurements, but not in mean values. This statement is proved on the two-photon state entangled in energy. This is in contradiction with experimental results observed by the detectors in rest relative to each other. It is shown that the property of measuring uncorrelated results with detectors in relative movement is related solely to the proposed collapse model. The remaining collapse models---the preferred Lorentz frame, Aharonov-Albert, and Hellwig-Kraus---are examined and discussed with respect to the designed experiment, which involves spacelike separated measurements.