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Physics World

How quantum physics is challenging causality

Hamish Johnston

Published Nov 1, 2025• 0 citations
Publisher

Abstract

In the fourth of our series of truly weird quantum effects, Hamish Johnston becomes a casual observer of the bizarre situation in which the causal order of events are in a quantum superposition.
DOI
10.1088/2058-7058/38/10/20

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We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. We show that the current quantum switch experimental implementations do not feature superpositions of causal orders between spacetime events, and that these superpositions can only occur in the context of superposed gravitational fields. We also discuss a recently introduced operational notion of an event, which does allow for superpositions of respective causal orders in flat spacetime quantum switch implementations. We construct two observables that can distinguish between the quantum switch realisations in classical spacetimes, and gravitational switch implementations in superposed spacetimes. Finally, we discuss our results in the light of the modern relational approach to physics.
Parts VIII–XI of this series reduced the program to a single missing object: a quantum measure μ(C) over causal histories. This Part XII specifies that object, realizes it in prototype, and tests whether it selects the observed effective spacetime dimension. The fundamental object is a Hermitian, positive, bi-additive Sorkin decoherence functional D(A,B) with physical measure μ(A)=D(A,A); classical measures obey the two-event sum rule I2=0, while quantum measures have I2≠0 but obey the Sorkin triple sum rule I3=0. An explicit such measure is constructed on the growth histories of small causal sets and verified numerically to satisfy I3=0 to machine precision while I2≠0. The fourth gate is sharpened beyond the standard Lorentzian-continuum requirement: the measure must concentrate on causal orders carrying coherent local proper time (a stable interval volume–proper-time law), the distinctive addition of this program. A systematic test on controlled ensembles then asks whether any non-circular intrinsic ingredient selects the 3+1 sector, with a uniformly negative result. The free measure is dominated by the entropic Kleitman–Rothschild phase (d_MM ≈ 2.37); proper-time coherence with propagation escapes that phase but settles on the effective 2+1 sector; the Benincasa–Dowker quantum phase produces only seed-unstable windows that vanish at the physically natural phase scale; and the Pauli–Jordan operator and the Sorkin–Johnston state, though intrinsic and phase-based, are monotone in dimension. A circularity audit shows that every selector whose optimum lies at four dimensions either inserts the dimension (local gravitational degrees of freedom, bound-matter stability, a (d−4)² term) or was tuned to it. The honest conclusion is that proper-time coherence explains the exit from the entropic phase but not the final 3+1 selection: the bare measure with coherence predicts an effective 2+1 phase, and the open problem is localized as the emergence of the third spatial direction (2+1 → 3+1). This yields a falsifiable prediction and identifies the missing object as a covariant, Bell-causal growth law whose continuum limit would fix the gravitational phase normalization. Supplementary Python scripts reproducing all numerical tests are included.
The process-matrix formalism describes quantum processes without assuming a fixed global causal order, but the physical meaning of indefinite causal order remains open. We address this question within histories theory, where temporal ordering and dynamical evolution are distinct structures. We show that the decoherence functional admits coherent superpositions of dynamics. In measurement settings, under suitable factorization conditions, these generate process matrices. Thus, we identify process-matrix indefinite causal order as an operationally restricted realization of the more general phenomenon of superposition of dynamics. Histories theory also admits a distinct kinematical notion of indefinite order, in which the ordering of physical events is itself a history observable. The resulting distinction between event order and intervention order clarifies the relation between indefinite causal order, quantum dynamics, and spacetime structure.