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arXiv:2209.07867 · Quantum

Time symmetry in quantum theories and beyond

John H. Selby, Maria E. Stasinou, Stefano Gogioso, Bob Coecke

Published Sep 30, 2026• 1 citation
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Abstract

There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.

DOI
10.22331/q-2026-09-30-2221

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There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of processes. We present the process theory of quantum physics, QPhys, which treats classical systems as internal to quantum theory. We provide three ways to incorporate time symmetry in QPhys. The first restricts the process theory of QPhys to one that satisfies an additional retrocausality constraint. The second is a novel approach, which extends the notions of causality and retrocausality to apply to systems along with processes. Utilizing this approach, we create a toy model for particle physics , where the causal and retrocausal systems correspond to particles and anti-particles respectively. The third approach extends QPhys to a supertheory that satisfies neither a causality nor a retrocausality constraint. To avoid unphysical predictions we modify either its composition rule or its processes.
In arXiv:1707.08641, Tim Maudlin claims to construct a counterexample to the result of Proc. Roy. Soc. A vol. 473, iss. 2202, 2017 (arXiv:1607.07871), in which it was shown that no realist model satisfying a certain notion of time-symmetry (in addition to three other assumptions) can reproduce the predictions of quantum theory without retrocausality (influences travelling backwards in time). In this comment, I explain why Maudlin's model is not a counterexample because it does not satisfy our time-symmetry assumption. I also explain why Maudlin's claim that one of the Lemmas we used in our proof is incorrect is wrong.
Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.
Abstract We investigate two types of temporal symmetry in quantum mechanics. The first type, time symmetry, refers to the inclusion of opposite time orientations on an equivalent physical footing. The second, event symmetry, refers to the inclusion of all time instants in a history sequence on an equivalent physical footing. We find that recent time symmetric interpretations of quantum mechanics fail to respect event symmetry. Building on the recent fixed-point formulation (FPF) of quantum theory, we formulate the notion of an event precisely as a fixed point constraint on the Keldysh time contour. Then, considering a sequence of measurement events in time, we show that both time and event symmetry can be retained in this multiple-time formulation of quantum theory. We then use this model to resolve conceptual paradoxes with time symmetric quantum mechanics within an ‘all-at-once’, atemporal picture.
Philosophical analyses of causation take many forms but one major difficulty they all aim to address is that of the spatiotemporal continuity between causes and their effects. Bertrand Russell in 1913 brought the problem to its most transparent form and made it a case against the notion of causation in physics. The issue highlighted in Russell's argument is that of temporal contiguity between cause and effect. This tension arises from the imposition of a spectrum of discrete events occupying spacetime points upon a background of spacetime continuum. An immediate and natural solution is to superpose instead spatiotemporally continuous entities, or processes, on the spacetime continuum. This is indeed the process view of physical causation advocated by Wesley Salmon and Phil Dowe. This view takes the continuous trajectories of physical objects (worldlines) as the causal connection whereby causal influences in the form of conserved quantities are transported amongst events. Because of their reliance on spatiotemporal continuity, these theories have difficulty when confronted with the discontinuous processes in the quantum domain. This thesis is concerned with process theories. It has two parts. The first part introduces and criticizes these theories, which leads to my proposal of the History Conserved Quantity Theory with Transmission. The second part considers the extension of the idea of causal processes to quantum physics. I show how a probability distribution generated by the Schrodinger wavefunction can be regarded as a conserved quantity that makes the spacetime evolution of the wavefunction a quantum causal process. However, there are conceptual problems in the interpretation of the wavefunction, chiefly to do, as I shall argue, with the difference in the behaviours of probabilistic potentials between quantum and classical physics. I propose in the final chapter, the Feynman Path Integral formulation of quantum mechanics (with the Feynman histories) as an alternative approach to incorporating the probabilistic potentials in quantum physics. This account of how to introduce causal processes in quantum mechanics fares better, I claim, than the previous one in dealing with the situational aspect of quantum phenomena that requires the consideration of events at more than one time.
Collapse models are modifications of quantum theory where the wave function is treated as physically real and the collapse of the wave function is a physical process. This appears to introduce a time reversal asymmetry into the dynamics of the wave function since the collapses affect only the future state. This paper challenges this conclusion, showing that in three different examples of time asymmetries associated with collapse models, if the physically real part of the model can be reduced to the locations in space and time about which collapses occur, then such a model works both forward and backward in time, in each case satisfying the Born rule. Despite the apparent asymmetry of the collapse process, these models in fact have time reversal symmetry. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.
Microscopic quantum laws are time-symmetric: nothing in the Schrödinger equation or its relativistic extensions distinguishes future from past. Yet measurements produce irreversible records, an apparently one-way causal flow, and the familiar notion that causes precede effects. Within the Quantum Time-Symmetric Interpretation (QTSI), this asymmetry is not fundamental but emergent. Isolated quantum systems are described by a two-component temporal state containing forward- and backward-propagating amplitudes. Their mixing, governed by a parameter Δ(ϕ)Δ(ϕ)Δ(ϕ), defines a retrocausal coherence time τRC(ϕ)τ_{RC}(ϕ)τRC​(ϕ) beyond which advanced components are suppressed. As the system couples to amplifying environments characterized by a macroscopic parameter ϕϕϕ, Δ(ϕ)Δ(ϕ)Δ(ϕ) decreases and the backward component is dynamically eliminated, giving rise to classical causality and effective collapse. QTSI aligns naturally with time-symmetric approaches from Wheeler--Feynman, Aharonov, and Price, agrees with all weak-measurement and quantum eraser results in their operational regimes, and predicts specific signatures in temporal echoes and chaotic cavities. Detailed formal and experimental developments appear in the Supplementary Addenda.