The wave-particle description of matter and radiation, implicit in the quantum theory, has long been accepted-if at times imperfectly understood-by professional physicists, but often even a qualitative description is lacking at school level. Often too, the examples chosen to illustrate the effects involved utilize unreal situations or dated photographs and experimental details which leave much to be desired. This note illustrates the oscillatory description of matter by considering recent data (obtained in high energy physics experiments) involving the scattering of subnuclear particles.
The wave-particle description of matter and radiation, implicit in the quantum theory, has long been accepted-if at times imperfectly understood-by professional physicists, but often even a qualitative description is lacking at school level. Often too, the examples chosen to illustrate the effects involved utilize unreal situations or dated photographs and experimental details which leave much to be desired. This note illustrates the oscillatory description of matter by considering recent data (obtained in high energy physics experiments) involving the scattering of subnuclear particles.
It has already been noted (section 2.8) that high frequency electromagnetic radiation can exhibit particle-like behaviour. For example, in the sensitive type of detector known as a photomultiplier tube (described in Wehr and Richards, Physics of the Atom , 2nd edn, Addison-Wesley, section 10.5), a beam of low-intensity X-rays is detected as a sequence of isolated sharp pulses, such as would be produced by a stream of particles arriving at the detector. As was pointed out, it is not surprising that it is usually high-frequency radiation which travels in particle form; as shown in figure 2.39, a wave group of high-frequency radiation can be compressed into a very short time span. However, when we speak of a particle, we mean something more than an entity which arrives in a short time span. A particle has a definite size, or more exactly it has a well-defined energy and momentum. It was discovered around about 1900 that the same is true of an X-ray wave packet: all packets of a given frequency radiation carry the same energy and momentum. This revolutionary discovery means that we must treat the wave packets as particles on exactly the same footing as more familiar particles such as electrons. The electromagnetic particle is called a photon . There is a wealth of experimental evidence which may be used to define the properties of a photon. We shall be highly selective, however, and simply present two particularly clear-cut experiments, the photoelectric effect and Compton scattering, which enable one to define the energy and momentum of the photon in terms of the frequency and wave number of the corresponding wave. These experiments will be described in detail in section 4.1.
As we have seen in Section 8.4, the basis of our perception of an objective reality is statistical mechanics and field theory. These are routinely used in equilibrium and nonequilibrium statistical thermodynamics (see, for example, Calzetta & Hu [59]), which govern the macroscopic laws of everyday life. Thus the quantum theory of fields must be the fundamental description of Nature. Therefore, the simpler quantum mechanics of particles is necessarily a derived description. This chapter discusses the extent to which a particle picture of matter and radiation is appropriate. In relativistic quantum field theory, particles appear only as asymptotic excitations of the fields. The quantum particle concept therefore makes mathematical (and intuitive) sense only under very special circumstances, namely in those where a system actually behaves like particles do: - As quasiparticles, they are useful in the domain, where the geometric optics perspective applies. - Before and after a scattering event in a dilute gas or a particle collider ring, particles can be considered as being essentially free. During the very short interaction time itself, the scattering process cannot be described by a particle picture, but needs a hydromechanical description or a kinetic description via Kadanoff-Baym equations. Already at the very beginning of modern quantum mechanics, when Born found his probability interpretation, the scattering process of single particles in an external classical field was understood (see Section 14.1 of the Appendix) to be a wave process relating initially and finally stationary particles, freely moving in their center of mass frame. It is a historical accident that one continues to use the name particle in the many microscopic situations, where it is grossly inappropriate to think of it with the classical meaning of a tiny bullet moving through space. When we restrict the use of the particle concept to where it is appropriate, or when we do not think of particles as “objects”, in both cases all mystery is gone, and the foundations become fully rational. The inappropriate focus on the particle aspect of quantum mechanics created the appearance of mystery; common sense is restored by focussing instead on the field aspect. To substantiate the above summary view, we give in Section 12.1 an analysis of the photoelectric effect and in Section 12.2 a review of the origin of particle tracks. This leads in Section 12.3 to a discussion about the reality of particles. In the remainder of the chapter, we discuss the relation between fields and particles in more detail. Section 12.4 poses the problem how the nonrelativistic multiparticle description arises from relativistic quantum field theory. Section 12.5 considers the case of free quantum fields, and Section 12.6 the case of interacting quantum fields. Section 12.7, the final section, discusses the semiclassical view of quasiparticles in the approximation familiar from geometric optics.
The fundamental fact for quantum physics which has emerged from experimental investigations in the field is a double duality of wave and particle concepts. The wave theory of light, firmly grounded by the wave explanations of interference and diffraction and by Maxwell’s electromagnetic theory of light waves, is now recognized as giving but one aspect of the nature of radiation. The corpusclar aspect of radiation is revealed in the photoelectric effect and in the Compton effect. In these effects Planck’s constant appears as a universal constant which connects the wave and particle modes of description of the same radiation.
Having just described electromagnetic radiation as a wave, it may seem a bit peculiar to embark on a particle description of that radiation. Perhaps it will help to recall from Chapter 2 that our perception of something depends in part on the means we use to perceive it and that we used a specific experiment (interference) to define the wave property. There is no reason to believe that one human-invented experiment is the only one that can be used to describe electromagnetic radiation. In fact, the Einstein photoelectric effect, described next, is consistent with light being a particle.
The long history of the dispute among physicists as to whether matter is composed of particles or waves is reviewed. A turning point came at the dawn of the 20th century in the form of the de Broglie momentum-wavelength and Bohr/Planck energy frequency relations. It was on this basis that Schrödinger developed a quantum mechanical differential equation whose solution came to be known as a wave function. The Born Interpretation of these functions holds that their absolute square constitutes a probability distribution which has been used successfully to make predictions of the properties of the system under discussion. It is pointed out that the phenomenon of light refraction played a key role in the development of both Newton’s corpuscular theory of light and the competing theory of Huygens which looks upon light as consisting exclusively of waves. It is shown that Newton’s failure to predict the decrease in the speed of light as it passes from air into water was not because of his belief in the particle composition of light, but rather because he not did anticipate that the mass of a photon changes upon entering a medium of higher index of refraction n. By assuming that the energy E of light is equal pc/n, where p is the momentum of the photons and c is the speed of light in free space, it is shown that the experimental dependence of the speed the light on its wavelength as it passes through a transparent medium is derived successfully through the use of Hamilton’s Canonical Equations and Newton’s Second Law of Kinetics. It is suggested that the relationship between particles and waves can be understood by noting that the localized properties of matter exhibit themselves in experiments such as the photoelectric effect where attention can be concentrated on the behavior of a single particle. The corresponding wave properties occur when large numbers of particles are observed under exactly similar circumstances, as for example in electron diffraction. ...........
When in the spring of 1926 Erwin Schrödinger set out the form of the equation for wave propagation and drew important conclusions from it, in some very elegant work which appeared to develop the ideas which I had introduced in 1923–24 (de Broglie 1924), he really profoundly modified the ideas which had guided me two years earlier in my original research. For his idea was that although the ψ wave which he was introducing was still a true physical wave propagated in space and time, it would not have any single area of high field concentration which could be a particle; whereas in my original concept I assumed that the coexistence of waves and particles, perceived by Einstein in 1905 in respect of light in his theory of light quanta, should be extended to all types of particle in the form of the coexistence of a physical wave with a particle incorporated in it.