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Prespacetime journal

Causality is inconsistent with quantum field theory

Fred Wolf

Published Jan 1, 2010• 1 citation
OpenAlex

Abstract

It is shown that the usual quantum field theoretical argument for the vanishing of the commutator (VC) for spacelike separated fields implying causality is not tenable. For VC to be tenable negative energy antiparticles traveling forward in time must exist and negative energy particles traveling backward in time are not allowed. Hence VC denies the existence of positive energy antiparticles.

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Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non‐vanishing probabilities for both negative energy particles in the forward‐through‐time direction and positive energy antiparticles in the backwards‐through‐time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.

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It is shown that the usual quantum field theoretical argument for the vanishing of the commutator (VC) for spacelike separated fields implying causality is not tenable. For VC to be tenable negative energy antiparticles traveling forward in time must exist and negative energy particles traveling backward in time are not allowed. Hence VC denies the existence of positive energy antiparticles.
Causality in quantum field theory means the vanishing of commutators for spacelike separated fields (VCSSF). I will show that VCSSF is not tenable. For VCSSF to be tenable, and therefore, to have both retarded and advanced propagators vanish in the elsewhere, a superposition of negative energy antiparticle and positive energy particle propagators, traveling forward in time, and a superposition of negative energy particle and positive energy antiparticle propagators, traveling backward in time, are required. Hence VCSSF predicts non‐vanishing probabilities for both negative energy particles in the forward‐through‐time direction and positive energy antiparticles in the backwards‐through‐time direction. Therefore, since VCSSF is unrealizable in a stable universe, tachyonic propagation must occur in denial of causality.
It is shown that the correlations predicted by relativistic quantum field theory in locally normal states between projections in local von Neumann algebras cA(V1),cA(V2)\\cA(V_1),\\cA(V_2)cA(V1​),cA(V2​) associated with spacelike separated spacetime regions V1,V2V_1,V_2V1​,V2​ have a (Reichenbachian) common cause located in the union of the backward light cones of V1V_1V1​ and V2V_2V2​. Further comments on causality and independence in quantum field theory are made.
This paper provides a mechanism-first, non-mathematical clarification of why negative energy solutions of relativistic quantum equations—most notably those arising from Dirac’s formulation—are never physically realized. Rather than modifying existing theories or introducing new physics, the work demonstrates that the exclusion of negative energy states is a necessary consequence of established physical constraints: thermodynamics (specifically the Second Law), locality, causality, and local energy conservation. By grounding physical existence in the requirements for causal interaction and irreversible state change, the paper shows that negative energy states fail at the coupling stage of any realizable interaction and are therefore structurally excluded from the physical manifold. The framework explains why standard Quantum Field Theory procedures such as normal ordering, renormalization, and the reinterpretation of antiparticles are mathematically effective while remaining physically mandatory. The result is a foundational consistency explanation that resolves the negative energy problem without equations, speculation, or modification of existing physical law.
We compare the relativistic time evolution of an initially localized quantum particle obtained from the relativistic Schr\"odinger, the Klein-Gordon and the Dirac equations. By computing the amount of the spatial probability density that evolves outside the light cone we quantify the amount of causality violation for the relativistic Schr\"odinger Hamiltonian. We comment on the relationship between quantum field theoretical transition amplitudes, commutators of the fields and their bilinear combinations outside the light cone as indicators of a possible causality violation. We point out the relevance of the relativistic localization problem to this discussion and comment on ideas about the supposed role of quantum field theory as a vehicle of making a theory causal by introducing antiparticles.
Causal quantum theory is an umbrella term for ordinary quantum theory modified by two hypotheses: state vector reduction is a well-defined process, and strict local causality applies. The first of these holds in some versions of Copenhagen quantum theory and need not necessarily imply practically testable deviations from ordinary quantum theory. The second implies that measurement events which are spacelike separated have no nonlocal correlations. To test this prediction, which sharply differs from standard quantum theory, requires a precise definition of state vector reduction. Formally speaking, any precise version of causal quantum theory defines a local hidden variable theory. However, causal quantum theory is most naturally seen as a variant of standard quantum theory. For that reason it seems a more serious rival to standard quantum theory than local hidden variable models relying on the locality or detector efficiency loopholes. Some plausible versions of causal quantum theory are not refuted by any Bell experiments to date, nor is it evident that they are inconsistent with other experiments. They evade refutation via a neglected loophole in Bell experiments---the collapse locality loophole---which exists because of the possible time lag between a particle entering a measurement device and a collapse taking place. Fairly definitive tests of causal versus standard quantum theory could be made by observing entangled particles separated by $\ensuremath{\approx}0.1$ light seconds.