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No place for particles in relativistic quantum theories?

Rob Clifton

Published Sep 23, 2009• 2 citations
Publisher

Abstract

Abstract It is a widespread belief, at least within the physics community, that there is no relativistic quantum theory of (localizable) particles; and, thus, that the only relativistic quantum theory is a theory of fields. This belief has received much support in recent years in the form of rigorous no­go theorems by Malament (1996) and Hegerfeldt (1998a,b). In particular, Hegerfeldt shows that in a generic quantum theory (relativistic or non­relativistic), if there are states with localized particles, and if there is a lower bound on the system’s energy, then superluminal spreading of the wavefunction must occur. Similarly, Malament shows the inconsistency of a few intuitive desiderata for a relativistic quantum mechanics of (localizable) par­

DOI
10.1093/oso/9780199270156.003.0008

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Abstract It is a widespread belief, at least within the physics community, that there is no relativistic quantum theory of (localizable) particles; and, thus, that the only relativistic quantum theory is a theory of fields. This belief has received much support in recent years in the form of rigorous no­go theorems by Malament (1996) and Hegerfeldt (1998a,b). In particular, Hegerfeldt shows that in a generic quantum theory (relativistic or non­relativistic), if there are states with localized particles, and if there is a lower bound on the system’s energy, then superluminal spreading of the wavefunction must occur. Similarly, Malament shows the inconsistency of a few intuitive desiderata for a relativistic quantum mechanics of (localizable) par­
David Malament (1996) has recently argued that there can be no relativistic quantum theory of (localizable) particles. We consider and rebut several objections that have been made against the soundness of Malament's argument. We then consider some further objections that might be made against the generality of Malament's conclusion, and we supply three no-go theorems to counter these objections. Finally, we dispel potential worries about the counterintuitive nature of these results by showing that relativistic quantum field theory itself explains the appearance of “particle detections.”
Several recent arguments purport to show that there can be no relativistic, quantum-mechanical theory of localizable particles and, thus, that relativity and quantum mechanics can be reconciled only in the context of quantum field theory. We point out some loopholes in the existing arguments, and we provide two no-go theorems to close these loopholes. However, even with these loopholes closed, it does not yet follow that relativity plus quantum mechanics exclusively requires a field ontology, since relativistic quantum field theory itself might permit an ontology of localizable particles supervenient on the fundamental fields. Thus, we provide another no-go theorem to rule out this possibility. Finally, we allay potential worries about this conclusion by arguing that relativistic quantum field theory can nevertheless explain the possibility of "particle detections," as well as the pragmatic utility of "particle talk."
Preface. In defense of dogma: why there cannot be a relativistic quantum mechanics of (localizable) particles D.B. Malament. Just how radical is hyperplane dependence? G. Fleming. Is there superluminal causation in relativistic quantum field theory? M. Redei. EPR, relativity, and the GHZ experiment C. Pagonis, et al. Hidden quantum non-locality N.D. Mermin. Royer's measurements - the rise and fall of (yet another) signalling scheme I. Pitowsky. Tails of Schrodinger's cat D.Z. Albert, B. Loewer. Wavefunction collapse models with nonwhite noise P. Pearle. The emergence of classical properties from quantum mechanics L.E. Ballentine. Relativism S. Saunders. Wave and particle concepts in quantum field theory P. Teller. The conceptual relation between standard quantum mechanics and quantum field theory D. Robinson. What measurement problem? J.T. Cushing. Bovine metaphysics: remarks on the significance of the gravitational phase effect in quantum mechanics H.R. Brown. Exotic (quixotic?) applications of Bohm theory R. Weingard. Complementarity and the orthodox (Dirac-von Neumann) interpretation of quantum mechanics J. Bub. Logical reflections on the Kochen-Specker theorem J.L. Bell. Construction of quantum mechanics via commutative operations S. Kochen.
Although the concept of localization in non-relativistic quantum mechanics is mathematically well-defined there is no obvious and unambiguous way to generalize it to relativistic quantum theory. After a brief review of localization in quantum mechanics the Newton-Wigner localization scheme is introduced and it is shown by the example of a massive spinless system how it leads to a position operator with seemingly unphysical properties. This motivated the development of several theorems which claim to rule out the existence of localizable particles. A particularly important one of them is presented and its validity discussed. In the last section however it is shown that if localization is considered with respect to spacelike hyperplanes, the properties of the Newton-Wigner position operators are not necessarily unphysical and localizable particles can exist.
Abstract The well-definedness of particles of any kind depends on the limits, approximations, or other conditions that may or may not be involved, for example, whether there are interactions and whether ostensibly related energy is localizable. In particular, their theoretical status differs between its non-relativistic and relativistic versions: One can properly define interacting elementary particles in single-system non-relativistic quantum mechanics, at least in the case of non-zero mass systems; by contrast, one is severely challenged to define even these properly in the relativistic quantum field theories that now underlie the study of particle physics. Here, the impact of localizability on this status is reviewed in relation to the work of Paul Busch on positive operator valued measures that significantly probes the relevance of quantum unsharpness to it.
Quantum foundations are still unsettled, with mixed effects on science and society. By now it should be possible to obtain consensus on at least one issue: Are the fundamental constituents fields or particles? As this paper shows, experiment and theory imply that unbounded fields, not bounded particles, are fundamental. This is especially clear for relativistic systems, implying that it's also true of nonrelativistic systems. Particles are epiphenomena arising from fields. Thus, the Schrödinger field is a space-filling physical field whose value at any spatial point is the probability amplitude for an interaction to occur at that point. The field for an electron is the electron; each electron extends over both slits in the two-slit experiment and spreads over the entire pattern; and quantum physics is about interactions of microscopic systems with the macroscopic world rather than just about measurements. It's important to clarify this issue because textbooks still teach a particles- and measurement-oriented interpretation that contributes to bewilderment among students and pseudoscience among the public. This article reviews classical and quantum fields, the two-slit experiment, rigorous theorems showing particles are inconsistent with relativistic quantum theory, and several phenomena showing particles are incompatible with quantum field theories.