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.
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.
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.
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.”
In special relativity theory the physical quantities are generally expressed as function of the velocity. In the particular case of an extended object, the factor 1/gamma of Lorentz contraction of its length in the direction of motion is written as a function of the velocity of the extended object. The same happens with the Lorentz factor gamma of time interval dilation of a moving clock. In this paper we show that when gamma is written as a function of the relativistic energy of the considered object the resulting expressions for the length and for the time interval suggest that the contraction of length as well as the dilation of the time interval are manifestations of the wave behavior of matter.
A picture of dynamical collapse of the wave function which is relativistic and time symmetric is presented. The part of the model which exhibits these features is the set of collapse outcomes. These play the role of matter distributed in space and time. It is argued that the dynamically collapsing quantum state, which is both foliation dependent and follows a time-asymmetric dynamics, is not fundamental: it represents a state of information about the past matter distribution for the purpose of estimating the future matter distribution. It is also argued from the point of view of collapse models that both special and general relativistic considerations point towards a discrete spacetime structure and that gravity may not need to be quantised to give a theory that is consistent with quantum matter.
ABSTRACT The emergence of quantum entanglement correlations across spatially separated measurement regions renders the interpretation of the relationship between quantum mechanics and relativistic causality a core problem in quantum foundations [Einstein et al., 1935; Bell, 1964]. In this study, two entangled particles are modeled not as two independent physical objects in Minkowski spacetime, but as a joint quantum state in configuration space. The relative space and time coordinates of the joint state are defined via: and the ideal space-time correlation limit assumed in the model is expressed as: This limit is not a general definition of quantum entanglement, but an idealized geometric assumption representing strong correlation in the relative coordinates of the joint state within the proposed model. In this approach, physical spacetime is treated as a geometric structure representing the projection of the joint quantum state onto observable spacetime coordinates. To ensure the projection is Lorentz-covariant, the light-like interval: is employed as the constitutive geometric condition of the model. This condition is accepted not as a mandatory Minkowski interval between physical measurement events, but as the mathematical postulate of the proposed projection geometry. The dynamic scale parameter of the model is grounded in total relativistic quantum energy instead of rest mass, establishing a dimensionless Planck-scaling factor defined as: To encompass both massive and massless systems, quantum energy density is defined via the energy density component of the stress-energy tensor relative to an observer. The required consistency condition for covariant energy-momentum conservation is derived in its general form. Furthermore, modeling the proposed geometric effect as a dimensionless metric perturbation yields a phenomenological first-order geometric phase correction defined as: where is the energy-dependent reduced wavelength. Under fixed and finite , the vanishing of the proposed correction in the low-energy regime relative to the Planck scale () demonstrates that the geometric effect added by the model to standard low-energy quantum mechanics becomes negligible. This study proposes a testable theoretical model aimed at explaining the spatiotemporal correlations of quantum entanglement within a Lorentz-covariant, energy-scaled, and phenomenological geometric framework.
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.