Abstract A thought experiment is considered on the observation of the instantaneous collapse of an extended wave packet. According to the relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. The probabilistic nature of quantum-mechanical phenomena eliminates any contradictions between these two apparently conflicting statements. It is shown that the consistency of quantum collapse with relativity follows directly from the Born postulate without any use of mathematical properties of quantum operators, which allows us to discuss this topic in an introductory course of modern physics. The consistency of quantum mechanics with relativity is also shown for instant disentanglement of an extended composite system.
Abstract A thought experiment is considered on the observation of the instantaneous collapse of an extended wave packet. According to the relativity of simultaneity, such a collapse being instantaneous in some reference frame must be a lasting process in other frames. But according to quantum mechanics, collapse is instantaneous in any frame. The probabilistic nature of quantum-mechanical phenomena eliminates any contradictions between these two apparently conflicting statements. It is shown that the consistency of quantum collapse with relativity follows directly from the Born postulate without any use of mathematical properties of quantum operators, which allows us to discuss this topic in an introductory course of modern physics. The consistency of quantum mechanics with relativity is also shown for instant disentanglement of an extended composite system.
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.”
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.
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.
The nonlocal action of a measurement performed on a quantum entangled particle can determine the quantum state of a distant entangled particle instantly. Since the relativistic simultaneity of events is frame dependent therefore, a physically valid question arises, does the nonlocal action at a distance determine the quantum state of the distant particle in its past, when quantum state collapse is observed from a different inertial frame of reference? From the relativity of simultaneity, Lorentz invariance of the quantum entangled state of photons under consideration and the validity of Bell's theorem in all inertial frames of reference, it is demonstrated that the measurement-induced collapse of a quantum entangled state also determines the quantum state of a distant photon in its past, provided one of the photons is located in the future. The past and future are defined with respect to the time of quantum state collapse in the rest frame of a quantum state measurement device.
Abstract: Everett demonstrates the appearance of collapse, within the context of the unitary linear dynamics. However, he does not state clearly how observers are to have determinate measurement records, hence 50 years of debate. This, however, is inherent. He defines the observer as the record of observations, which, naturally, is the record of correlations established with the physical environment. As in Rovelli's Relational Quantum Mechanics, the correlations record is the sole determinant of the effective physical environment, here the quantum mechanical frame of reference: due to multiple realisation of the functional identity of the observer, the physical environment is a simultaneity of all the physical environments in which it is instantiated, a 'universe superposition', in which only the environment correlated with the observer by observations is determinate. This effects a discrete and idiosyncratic physical environment for each version of an observer, in which determinate measurement records are recorded. Quantum mechanics is on this view fully relational, demonstrated as not only viable but necessary by Rovelli & Laudisa. The quantum mechanical frame of reference is Everett's 'Relative State', and on Tegmark's 'inside view', the time evolution follows the standard von NeumannDirac formulation. Thus observers get precisely the measurement records predicted by the standard formulation, but since objectively there is only the appearance of collapse, there is neither a measurement problem nor a disparity with relativity. The linear dynamics and the collapse dynamics are directly experienced, as the passage of time and the making of observations, respectively. 1
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.