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arXiv:quant-ph/0508202

Photon wave function

Iwo Białynicki‐Birula

Published Aug 26, 2005• 106 citations
arXivHTMLPDF

Abstract

Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, the photon wave function exists as long as it can be precisely defined and made useful.

DOI
10.48550/arxiv.quant-ph/0508202

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Photon wave function is a controversial concept. Controversies stem from the fact that photon wave functions can not have all the properties of the Schroedinger wave functions of nonrelativistic wave mechanics. Insistence on those properties that, owing to peculiarities of photon dynamics, cannot be rendered, led some physicists to the extreme opinion that the photon wave function does not exist. I reject such a fundamentalist point of view in favor of a more pragmatic approach. In my view, the photon wave function exists as long as it can be precisely defined and made useful.
This chapter describes the photon wave function, and explains the basic properties of a well-defined mathematical object—a six-component function of space-time variables—that describes the quantum state of the photon. The most essential property that does not hold for the photon wave function is that the argument of the wave function cannot be directly associated with the position operator of the photon. The position operator for the photon simply does not exist. However, one should remember that for massive particles also, the true position operator exists only in the nonrelativistic approximation. The concept of localization associated with the Newton-Wigner position operator is not relativistically invariant. The photon wave function is not restricted to the wave mechanics of photons. The same wave functions also appear as mode functions in the expansion of the electromagnetic field operators.
Few photon systems are best described by their wave function rather than by the usual quantum field formalism. Until recently, the existence of a wave function for photons has been an object of controversy. Important breakthrough happened during the last ten years, sharpening the wave function concept and giving it a precise definition. We show how the photon wave function proposed by Bialynicki-Birula and Sipe connects to experimentally measurable quantities such as multi-photon quantum correlation functions and use it to investigate space-time entanglement of photon pairs produced in parametric down-conversion.
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probability rule are replaced with intrinsic properties of the theory, i.e. decoherence and relative frequency, respectively. Interpretation of the wave function as a faithful representation of the reality naturally emerges, although quantum reality has a peculiar feature which distinguishes it from classical reality.
Abstract We consider the interpretation of quantum mechanics on the basis of the so-called ‘pilot-wave’ concept from the point of view of its adequacy in the light of both already-realized and possible and gedanken experiments, including those that involve photons. It is shown that this concept, despite undoubtedly being useful, can hardly ensure compliance of quantum-theory predictions with the postulate that particle coordinates and velocities objectively exist, while splitting the wave function into empty and nonempty wave packets seems to contradict to the results of feasible experiments and their interpretations.
In recent years it has become evident that the primary concept of the photon has multiple interpretations, with widely differing secondary connotations. Despite the all-pervasive nature of this concept in science, some of the ancillary properties with which the photon is attributed in certain areas of application sit uneasily alongside those invoked in other areas. Certainly the range of applications extends far beyond what was envisaged in the original conception, now entering subjects extending from elementary particle physics and cosmology through to spectroscopy, statistical mechanics and photochemistry. Addressing this diverse context invites the question: What is there, that it is possible to assert as incontrovertibly true about the photon? Which properties are non-controversial, if others are the subject of debate? This paper describes an attempt to answer these questions, establishing as far as possible an irreducible core of what can rightly be asserted about the photon, and setting aside some of what often is, but should never be so asserted. Some of the more bewildering difficulties and differences of interpretation owe their origin to careless descriptions, highlighting a need to guard semantic precision; although simplifications are frequently and naturally expedient for didactic purposes, they carry the risk of becoming indelible. Focusing on such issues, the aim is to identify how much or how little about the photon can be regarded as truly non-controversial.
There are two opposing points of view on the nature of light: the first one manifests the wave-particle duality as a fundamental property of the nature; the second one claims that photons do not exist and the light is a continuous classical wave, while the so-called “quantum” properties of this field appear only as a result of its interaction with matter. In this paper we show that many quantum phenomena which are traditionally described by quantum electrodynamics can be described if light is considered within the limits of classical electrodynamics without quantization of radiation. These phenomena include the double-slit experiment, the photoelectric effect, the Compton effect, the Hanbury Brown and Twiss effect, the so-called multiphoton ionisation of atoms, etc. We show that this point of view allows also explaining the “wave-particle duality” of light in Wiener experiments with standing waves. We show that the Born rule for light can easily be derived from Fermi’s golden rule as an approximation for low-intense light or for short exposure time. We show that the Heisenberg uncertainty principle for “photons” has a simple classical sense and cannot be considered as a fundamental limitation of accuracy of simultaneous measurements of position and momentum or time and energy. We conclude that the concept of a “photon” is superfluous in explanation of light-matter interactions.