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AIP conference proceedings

Causality Is Inconsistent With Quantum Field Theory

Fred Alan Wolf, Daniel P. Sheehan

Published Jan 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1063/1.3663723

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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.
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.
n a recent series of papers [1, 2, 3] of this author, we generalized quantum field theory to any curved spacetime. More in particular, in [1] we derived the spin statistics theorem without appealing to anything isomorphic to the vanishing of the field (anti-)commutatation relations at spacelike distances. The correct propagators were derived by means of other principles and no reference towards an operational approach has ever been made; this casts into doubt the operational principle of quantum causality since up till now it is widely believed to constitute a necessity rather than just an axiom added to the theory.
Tachyons are Scalar Bosons that reside in our fourth dimensional spatial Universe. They are point particles with zero mass, zero charge, and zero spin. Based on the Lorentz Transformation for v > c, tachyons can travel backwards in time to enter our third dimensional spatial Universe and can travel faster than light speed, to transmit information instantaneously between two entangled particles, to change their spin values from a superposition state to a definitive up and down state. We will show that the laws of Quantum Mechanics can be retro-causal while the laws of Classical Mechanics must be causal.
Quantum mechanics implies the existence of correlations which cannot be described by any local theory. These nonlocal correlations possibly suggest the existence of particles traveling faster than light (tachyons). But the potential paradoxes associated with their existence imply that, even i f these tachyons do exist, it should not be possible to control them in a manner necessary for human superluminal (faster than light) communication. Indeed, the unitary nature of the time development operator precludes the possibility of using non-local correlations to communicate superluminally within the quantum formalism. A simplified model which preserves unitary time development i s shown to be useful in studying 'thought experiments' which appear init ially to allow for superluminal communication. The consistency of quantum mechanics is questioned when measurements of retarded fields are considered. I f certain idealized measurements are possible in principle, then the quantum formalism appears inconsistent. I f the measurements are not possible in principle, then 'state reduct ion' (non-unitary time evolution of the state operator) in a pragmatic sense can be said to have occurred. The suggestion that tachyons be used to explain the non-local correlations i s abandoned in favor of another model whose philosophy is supported by the tenets of relativity theory. Such a model may imply the existence of a more general quantum theory where a quantum system itself can be taken as a (generalized) frame of reference.
The Common Cause Principle in algebraic relativistic quantum field theory Algebraic quantum field theory (AQFT) predicts correlations between projections A, B lying in von Neumann algebras A ( V 1 ), A ( V 2 ) associated with spacelike separated spacetime regions V 1 , V 2 in Minkowski spacetime. These spacelike correlations predicted by AQFT lead naturally to the question of the status of Reichenbach's Common Cause Principle within AQFT. The aim of this chapter is to investigate the problem of status of Reichenbach's Common Cause Principle within AQFT. Since the correlated projections belong to algebras associated with spacelike separated regions, a direct causal influence between them is excluded by the Special Theory of Relativity. Consequently, compliance of AQFT with Reichenbach's Common Cause Principle would mean that for every correlation between projections A and B lying in von Neumann algebras A ( V 1 ) and A ( V 2 ), respectively, associated with spacelike separated spacetime regions V 1 , V 2 , there must exist a projection C possessing the probabilistic properties that qualify it to be a Reichenbachian common cause of the correlation between A and B . However, since observables and hence also the projections in AQFT must be localized, one also has to specify the spacetime region V with which the von Neumann algebra A(V) is associated that contains the common cause C . Intuitively, the region V should be disjoint from both V 1 and V 2 but should not be causally disjoint from them in order to leave room for a causal effect of C on the events A and B so that C can account for the correlation between A and B .