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Journal of the Optical Society of America

“Test for the nonexistence of photons” and “Photoelectric counting measurements as a test for the existence of photons”

Sherman Karp

Published Sep 1, 1979• 0 citations
Publisher

Abstract

In recent articles by this author, [ S. Karp , Statistical properties of ensembles of classical wave packets, J. Opt. Soc. Am.65, 421 ( 1975); S. Karp , Test for the nonexistence of photons, J. Opt. Soc. Am.66, 1421 ( 1976)], a radiation model was proposed that could lead to the identification of certain classical properties of the field, based upon photoelectric counting experiments. Mandel [ L. Mandel , Photoelectric counting measurements as a test for the existence of photons, J. Opt. Soc. Am.67, 1101 ( 1977)] responded by asserting that “It follows that for any field for which a classical wave description exists, in the sense that the phase-space density ϕ({ν}), and therefore P(u), are non-negative it is impossible to distinguish between photons and light waves in photoelectric counting experiments.” This statement is based upon the derivation of similar photoelectron counting equations using quantum and classical techniques. It is the mathematically loose associations and subsequent rigid physical interpretation implied in relating the two equations that is under contention. It seems to us that the model-computation-effect approach to physics is still solvent. In particular, if we can model an effect as small as the radiation from an individual electron and produce a predictable effect, then the physics underlying the model must be seriously considered.

DOI
10.1364/josa.69.001309

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In recent articles by this author, [ S. Karp , Statistical properties of ensembles of classical wave packets, J. Opt. Soc. Am.65, 421 ( 1975); S. Karp , Test for the nonexistence of photons, J. Opt. Soc. Am.66, 1421 ( 1976)], a radiation model was proposed that could lead to the identification of certain classical properties of the field, based upon photoelectric counting experiments. Mandel [ L. Mandel , Photoelectric counting measurements as a test for the existence of photons, J. Opt. Soc. Am.67, 1101 ( 1977)] responded by asserting that “It follows that for any field for which a classical wave description exists, in the sense that the phase-space density ϕ({ν}), and therefore P(u), are non-negative it is impossible to distinguish between photons and light waves in photoelectric counting experiments.” This statement is based upon the derivation of similar photoelectron counting equations using quantum and classical techniques. It is the mathematically loose associations and subsequent rigid physical interpretation implied in relating the two equations that is under contention. It seems to us that the model-computation-effect approach to physics is still solvent. In particular, if we can model an effect as small as the radiation from an individual electron and produce a predictable effect, then the physics underlying the model must be seriously considered.
It is pointed out that it is impossible to distinguish between photons and classical wave packets by measurement of photoelectric counting statistics for any state of a light beam for which a classical description exists. Therefore, an experiment with a thermal light source recently proposed by Karp as a test for the existence of photons can yield no information on this question, even if it should be able to distinguish between two different statistical models of a light beam. The quantum nature of the optical field can, however, be inferred from other photoelectric measurements, some of which are briefly discussed.
Extending the concept of the classical addition of wave packets to that of a random ensemble, a hypothesis has been proposed that treats the classical field as such an ensemble. Computations of the resulting field envelope and short-term counting statistics were also made. As a consequence, a test was proposed that would essentially measure the “shot noise” inherent in such a model and differentiate it from the discreteness resulting from the photodetection process. In this paper the test is examined in terms of the resources and environment necessary to perform it.
The photoelectric effect, the Compton effects, and now anticorrelation experiments have been claimed to prove that light consists of particles flying through a void. However the particle model is decisively falsified by the known wave qualities of electromagnetic radiation. Quantum Electrodynamics also uses spreading wave amplitudes; not flying particles. The evidence indicates that light is a wave and electrons are electromagnetic wave-structures that absorb and emit light in discrete wave-packets. These wave-quanta are emitted directionally and then spread in space in proportion to their wavelength. Their waves superposition with all other waves in space. In low intensity experiments, the waves that an electron in a photodetector absorbs come from the superpositioning of the source wave-quanta and background radiation. The importance of background radiation is evidenced by "dark counts". Treating electrons and the quanta they absorb and emit as particles when they are composed of waves is the source of all the paradoxes, unreality and confusion in Quantum Mechanics. The word "photon" should be replaced by "quantum" in the description of this particular electronic process. The conceptual model presented here explains the known phenomena without producing paradoxes and unifies quantum and classical electromagnetics.
A relation is derived between the probability distribution of the integrated intensity of light incident on a photoelectric detector and that of the emission of n photoelectrons in a time interval (t, t + T) from the properties of a quantized electromagnetic field. Both the direct and the inverse relations are derived, thereby enabling the statistical properties of light to be determined from photoelectric measurements. An explicit expression is given for the coefficients for calculating the moments ( W k) by means of the moments (n J) (] = 1, 2 ..... k). The correctness of the operations in which generalized functions occur is confirmed by some direct calculations. The significance of photoelectric detectors has been increasing of late. Since their response is proportional to the intensity of incident light (to the square of the amplitude of light) (more exactly, to the local mean time value of the intensity), one speaks of quadratic detectors. These detectors are of basic importance in the theory of the coherence of the electromagnetic field, since if we place N such detectors into N different points in space and if we lead the outputs of these detectors to the correlator we can measure the correlation (coherence) effects of the 2N-th order in the given field [1]. Such correlation measurements provide information on the energy distribution in the radiation spectrum [2], the angular dimensions of stars [3], and the state of polarization [4] and also enable the phase of physically important functions (e.g. the scattering amplitudes) [5] to be determined. Although in such experiments the properties of photoelectrons are studied rather than of photons, they reflect the basic properties of photons. Let the probability distribution Of the emission of n photoelectrons in a time interval (t, t + T) be p(n, T, t) - p(n) and let the probability distribution of the quantity W(T, t) = W = J'tt+r I(t') dr', where I(t) is the intensity of linearly polarized light incident on the photodetector (for simplicity we assume that the sensitivity of the photocathode is a = 1), be P(W). The quantity W can be regarded as a classical characteristic of the field, the quantity n represents the quantum characteristic of the field. Then, on the basis of such a semi-classical description, in which the field is described classically, but its interaction is described quantum-wise, one can derive the following relation [6]
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.
The idea of the photon has stirred the imaginations of physicists ever since 1905 when Einstein originally proposed the use of light quanta to explain the photoelectric effect. This concept is formalized in the quantum theory of radiation, which has had unfailing success in explaining the interaction of electromagnetic radiation with matter, seemingly limited only by the ability of physicists to perform the indicated calculations. Nevertheless, it has its conceptual problems—various infinities and frequent misinterpretations. Consequently an increasing number of workers are asking, “to what extent is the quantized field really necessary and useful?” In fact the experimental results of the photoelectric effect were explained by G. Wentzel in 1927 without the quantum theory of radiation. Similarly most electro-optic phenomena such as stimulated emission, reaction of the emitted field on the emitting atom, resonance fluorescence, and so on, do not require the quantization of the field for their explanation. As we will see, these processes can all be quantitatively explained and physically understood in terms of the semiclassical theory of the matter–field interaction in which the electric field is treated classically while the atoms obey the laws of quantum mechanics. The quantized field is fundamentally required for accurate descriptions of certain processes involving fluctuations in the electromagnetic field: for example, spontaneous emission, the Lamb shift, the anomalous magnetic moment of the electron, and certain aspects of blackbody radiation. (The Compton effect also fits here, but see later under references 8b and c.) Here we will outline how the photon concept originated and developed, where it is not required and is often misused, and finally where it plays an essential role in the understanding of physical phenomena. In our discussion we will attempt to give a logically consistent definition of the word “photon”—a statement far more necessary than one might think, for so many contradictory uses exist of this elusive beast. In particular consider the original coining of the word by G. N. Lewis: “[because it appears to spend] only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains an important structural element within the atom…, I therefore take the liberty of proposing for this hypothetical new atom which is not light but plays an essential part in every process of radiation, the name photon!” (our exclamation point). Clearly the present usage of the word is very different.