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arXiv:2610.29804

Conservation in Every Quantum Measurement Outcome?

E. Okon, D. Sudarsky, M. Wiedemann

quant-phphysics.hist-phSubmitted Oct 21, 2026• Announced Oct 22, 2026• 0 citations
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Abstract

In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.

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17 pages

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In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.
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Conservation principles are essential to describe and quantify dynamical processes in all areas of physics.Classically, a conservation law holds because the description of reality can be considered independent of an observation (measurement).In quantum mechanics, however, invasive observations change quantities drastically, irrespective of any classical conservation law.One may hope to overcome this nonconservation by performing a weak, almost noninvasive measurement.Interestingly, we find that the nonconservation is manifest even in weakly measured correlations if some of the other observables do not commute with the conserved quantity.Our observations show that conservation laws in quantum mechanics should be considered in their specific measurement context.We provide experimentally feasible examples to observe the apparent nonconservation of energy and angular momentum.
Because quantum measurements have probabilistic outcomes they can seem to violate conservation laws in individual experiments. Despite these appearances, strict conservation of momentum, orbital angular momentum, and energy can be shown to be consistent with the assumption that the entangling interactions that constitute measurements induce a real collapse of the wave function. The essential idea is that measured systems always have some pre-existing entanglement relations with (usually larger) systems, and that apparent changes in conserved quantities in the measured system are correlated with compensating changes in these larger systems. Since wave function collapse is mediated by entanglement relations a full accounting of the relevant quantities requires a computation over all interacting, entangled systems. The demonstrations by Gemmer and Mahler[1], and by Durt[2,3], that entanglement is a generic result of interaction are central to the argument. A stochastic collapse equation based on interaction potentials is described and shown to guarantee conservation of the relevant quantities at all stages of evolution.
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