In this chapter, we examine some of the principal attributes of electromagnetic radiation that feature in photons. At the outset, it is worth asserting that the photon concept owes its legitimacy to the quantum theory of light. As we shall see in later chapters, the photon is formally regarded as a quantum of excitation of any specific optical mode. In the literature, one can find occasional mentions of photons qualified by an adjective, such as dipole photons, electric photons, ballistic photons, etc.,* These should be regarded as potentially misleading because each alludes to a property that is more correctly associated with a particular kind of phenomenon. Even if the distinction between "real" and "virtual" photons represents one of the most widely used descriptors, it does not signify a clear-cut difference. We thus begin by listing the following photon properties, all of which can be involved in specific forms of optical interaction, with the exception of the first.
In this chapter, we examine some of the principal attributes of electromagnetic radiation that feature in photons. At the outset, it is worth asserting that the photon concept owes its legitimacy to the quantum theory of light. As we shall see in later chapters, the photon is formally regarded as a quantum of excitation of any specific optical mode. In the literature, one can find occasional mentions of photons qualified by an adjective, such as dipole photons, electric photons, ballistic photons, etc.,* These should be regarded as potentially misleading because each alludes to a property that is more correctly associated with a particular kind of phenomenon. Even if the distinction between "real" and "virtual" photons represents one of the most widely used descriptors, it does not signify a clear-cut difference. We thus begin by listing the following photon properties, all of which can be involved in specific forms of optical interaction, with the exception of the first.
It has been observed that every photon is, in a sense, virtual - being emitted and then sooner or later absorbed. As the motif of a quantum radiation state, the photon shares these characteristics of any virtual state: that it is not directly observable; and that it can signify only one of a number of indeterminable intermediates, between matter states that are directly measurable. Nonetheless, other traits of real and virtual behavior are usually quite clearly differentiable. How 'real', then, is the photon? To address this and related questions it is helpful to look in detail at the quantum description of light emission and absorption. A straightforward analysis of the dynamic electric field, based on quantum electro-dynamics, reveals not only the entanglement of energy transfer mechanisms usually regarded as 'radiative' and 'radiationless'; it also gives significant physical insights into several other electromagnetic topics. These include: the propagating and non-propagating character in electromagnetic fields; near-zone and wave-zone effects; transverse and longitudinal character; the effects of retardation, manifestations of quantum uncertainty and issues of photon spin. As a result it is possible to gain a clearer perspective on when, or whether, the terms 'real' and 'virtual' are helpful descriptors of the photon.
This chapter discusses electromagnetic waves and photons. It begins by reviewing some basic ideas on the properties of waves, introducing the wave properties of radiation. There are several reasons for starting with a discussion of electromagnetic radiation. Historically, it was in this area that the quantum theory first developed. The applications of the light-quantum hypothesis, as it was first called, also provide key pieces of evidence for the quantization of energy in atoms and molecules. The chapter then looks at the evidence for the wave nature of light and of X-rays, before putting these two forms of radiation into the context of electromagnetic radiation in general. It also considers Albert Einstein's analysis of the photoelectric effect. Finally, the chapter assesses the statistical nature of photons.
Light occupies a special position in our attempts to understand nature both classically and quantum mechanically. We recall that Newton, who made so many fundamental contributions to optics, championed a particle description of light and was not favorably disposed to the wave picture of light. However, the beautiful unification of electricity and magnetism achieved by Maxwell clearly showed that light was properly understood as the wave-like undulations of electric and magnetic fields propagating through space. The central role of light in marking the frontiers of physics continues on into the twentieth century with the ultraviolet catastrophe associated with black-body radiation on the one hand and the photoelectric effect on the other. Indeed, it was here that the era of quantum mechanics was initiated with Planck's introduction of the quantum of action that was necessary to explain the black-body radiation spectrum. The extension of these ideas led Einstein to explain the photoelectric effect, and to introduce the photon concept. It was, however, left to Dirac to combine the wave-and particlelike aspects of light so that the radiation field is capable of explaining all interference phenomena and yet shows the excitation of a specific atom located along a wave front absorbing one photon of energy. In this chapter, following Dirac, we associate each mode of the radiation field with a quantized simple harmonic oscillator, this is the essence of the quantum theory of radiation.
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.
A richly diverse range of phenomena and applications, frequently in the context of laser applications, owe their means of operation to the properties of the photon. Yet, since the arrival of the laser, the distinctive and often paradoxical nature of the photon has become more than ever evident, and what the optics community now understands by a ‘photon’ has become richer – certainly less simple, than Einstein’s original conception. There has been a marked expansion in the pace of development since the now familiar derivative term ‘photonics’ first emerged, and in much current theory any dividing line between ‘real’ and ‘virtual’ photons proves to be illusory. So if, in this technical sense, no photon can ever be regarded as entirely real, one is drawn to deeper questions of whether the photon is ‘real’ in the broader sense of reality. Some would argue that electromagnetic fields are closer to irreducible reality. Yet whether we elect to describe optical phenomena in terms of fields or photons, neither represents what is actually measured. The surest ground has to be found where theory is cast in terms that explain or predict actual observations, under given conditions. It is consistent with the path integral formulation of quantum mechanics that derivations should not prescribe what intervenes between setup and measurement, but instead allow for all possibilities. Indeed, one of the beauties of the associated mathematics is its capacity to home in on possibilities that most closely conform to post-event physical interpretation. Still, we can ask: how much do or can we know about the photon itself? How much information could this entity contain or convey? And, how essential is a photonic formulation of theory? This study focuses on some of the key issues.
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.