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Proof of the Existence of Universal Temporal Order in Spacetime

Shen Gao

Published Feb 15, 2026• 0 citations
Publisher

Abstract

There are two issues concerning hidden variables in quantum mechanics: 1.Whether the outcomes of quantum measurements are hidden variables has long been debated. Experiments violating Bell's inequalities have essentially refuted local hidden variable theories. 2.Quantum entanglement provides nonlocal effects that alter wave functions. However, these changes cannot transmit signals, making the exact time of such nonlocal effects a hidden variable. Theories about hidden variables are difficult to verify experimentally due to their unobservability. This paper connects these two hidden variable theories in quantum mechanics, proposing the spacetime relationship that nonlocal effects from entanglement must satisfy to prevent quantum measurement outcomes from being local hidden variables. It further outlines the spacetime relationship that any causal effects should adhere to. Based on this, the paper demonstrates the universal temporal order between relativistic spacelike events. On this foundation, it integrates the locally deterministic relativistic spacetime structure with the nonlocal phenomena of probabilistic quantum mechanics, thereby establishing the universal ordered spacetime structure. key words: ordered spacetime structure ; local hidden variable ; nonlocal effects; uncertainty principle;

DOI
10.5281/zenodo.18649662

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There are two issues concerning hidden variables in quantum mechanics: 1.Whether the outcomes of quantum measurements are hidden variables has long been debated. Experiments violating Bell's inequalities have essentially refuted local hidden variable theories. 2.Quantum entanglement provides nonlocal effects that alter wave functions. However, these changes cannot transmit signals, making the exact time of such nonlocal effects a hidden variable. Theories about hidden variables are difficult to verify experimentally due to their unobservability. This paper connects these two hidden variable theories in quantum mechanics, proposing the spacetime relationship that nonlocal effects from entanglement must satisfy to prevent quantum measurement outcomes from being local hidden variables. It further outlines the spacetime relationship that any causal effects should adhere to. Based on this, the paper demonstrates the universal temporal order between relativistic spacelike events. On this foundation, it integrates the locally deterministic relativistic spacetime structure with the nonlocal phenomena of probabilistic quantum mechanics, thereby establishing the universal ordered spacetime structure. key words: ordered spacetime structure ; local hidden variable ; nonlocal effects; uncertainty principle;
There are two issues concerning hidden variables in quantum mechanics: 1.Whether the outcomes of quantum measurements are hidden variables has long been debated. Experiments violating Bell's inequalities have essentially refuted local hidden variable theories. 2.Quantum entanglement provides nonlocal effects that alter wave functions. However, these changes cannot transmit signals, making the exact time of such nonlocal effects a hidden variable. Theories about hidden variables are difficult to verify experimentally due to their unobservability. This paper connects these two hidden variable theories in quantum mechanics, proposing the spacetime relationship that nonlocal effects from entanglement must satisfy to prevent quantum measurement outcomes from being local hidden variables. It further outlines the spacetime relationship that any causal effects should adhere to. Based on this, the paper demonstrates the universal temporal order between relativistic spacelike events. On this foundation, it integrates the locally deterministic relativistic spacetime structure with the nonlocal phenomena of probabilistic quantum mechanics, thereby establishing the universal ordered spacetime structure.
It is well known that there is a freedom-of-choice loophole or superdeterminism loophole in Bell's theorem. Since no experiment can completely rule out the possibility of superdeterminism, it seems that a local hidden variable theory consistent with relativity can never be excluded. In this paper, we present a new analysis of local hidden variable theories. The key is to notice that a local hidden variable theory assumes the universality of the Schroedinger equation, and it permits that a measurement can be in principle undone in the sense that the wave function of the composite system after the measurement can be restored to the initial state. We propose a variant of the EPR-Bohm experiment with reset operactions that can undo measurements. We find that according to quantum mechanics, when Alice's measurement is undone after she obtained her result, the correlation between the results of Alice's and Bob's measurements depends on the time order of these measurements, which may be spacelike separated. Since a local hidden variable theory consistent with relativity requires that relativistically non-invariant relations such as the time order of spacelike separated events have no physical significance, this result means that a local hidden variable theory cannot explain the correlation and reproduce all predictions of quantum mechanics even when assuming superdeterminism. This closes the major superdeterminism loophole in Bell's theorem.
What guarantees the "peaceful coexistence" of quantum nonlocality and special relativity? The tension arises because entanglement leads to locally inexplicable correlations between distant events that have no absolute temporal order in relativistic spacetime. This paper identifies a relativistic consistency condition that is weaker than Bell locality but stronger than the no-signaling condition meant to exclude superluminal communication. While justifications for the no-signaling condition often rely on anthropocentric arguments, relativistic consistency is simply the requirement that joint outcome distributions for spacelike separated measurements (or measurement-like processes) must be independent of their temporal order. This is necessary to obtain consistent statistical predictions across different Lorentz frames. We first consider ideal quantum measurements, derive the relevant consistency condition on the level of probability distributions, and show that it implies no-signaling (but not vice versa). We then extend the results to general quantum operations and derive corresponding operator conditions. This will allow us to clarify the relationships between relativistic consistency, no-signaling, and local commutativity. We argue that relativistic consistency is the basic physical principle that ensures the compatibility of quantum statistics and relativistic spacetime structure, while no-signaling and local commutativity can be justified on this basis.
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.
The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all physical processes have a definite causal structure. While indefinite causal processes have previously been experimentally shown, these proofs relied on the quantum description of the experiments. Yet, the same experimental data could also be compatible with definite causal structures within different descriptions. Here, we present the first demonstration of indefinite temporal order outside of quantum formalism. We show that our experimental outcomes are incompatible with a class of generalised probabilistic theories satisfying the assumptions of locality and definite temporal order. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality using entangled temporal order. This provides experimental evidence that there exist correlations in nature which are incompatible with the assumptions of locality and definite temporal order.
Abstract Quantum mechanics predicts faster-than-light information transportation in order to satisfy quantum entanglement experimental results. Such a prediction violates the locality principle and Bell’s inequality. Quantum mechanisms also state that the world is intrinsically probabilistic. Such an idea was not welcome by many scientists including Einstein, Podolsky and Rosen. To resolve such a dilemma, the ”Many-world” theory was presented by Hugh Everett in 1975. Such a theory asserts that the universal wave function is real and that there is no wave function collapse. Also, it states that all possible outcomes of quantum measurements are physically realized in other parallel universes. Besides, in quantum mechanics, the observer effect defines a state transition of quantum objects. Such a phenomenon affirms that quantum objects behave differently depending on being observed or not. In this paper, we present few assumptions based on which we build a classical hidden-variable-based system that can violate Bell’s inequality. Therefore, adopting similar assumptions in explaining quantum entanglement could lead to a better explanation of quantum mechanics without violating the locality principle or adopting such weird assumptions. Hence, one can conclude that extending Quantum Mechanism by a set of similar hidden variables can resolve such a paradox and predict the quantum entanglement experimental results without violating the locality principle.