Wave-corpuscle

ATOMIC PHYSICS (8th edition). Max Born. Nobel laureate s lucid treatment of kinetic theory of gases, elementary particles, nuclear atom, wave-corpuscles, atomic structure and spectral lines, much more. Over 40 appendices, bibliography. 495pp. 5X x 8X. 65984-4 Pa. 11.95... 

We add. in conclusion a few general remarks on tlie philosophical side of the question. In the first place it is clear that the dualism, wave-corpuscle, and the indeterminateness essentially involved therein,. 

We propose that this may account for the duality of particle and wave. When a mass is observed, time has been stripped away, leaving a frozen 3-spatial snapshot, which we will see as (having been) a particle (simplest case). That occurs just after major (observable) photon emission from the masstime state. Immediately another observable photon is absorbed, and so state mt occurs. The particle of mass actually oscillates at a very high rate between the m and mt states—so high a rate that by arranging the interaction conditions one may interact with it either as a wave (react predominantly in the mt state) or as a corpuscle (react predominately in the m state). Mass as it exists is actually an oscillation or wave between m and mt states. Every differential piece of the mass is also in oscillation between (dm) and (dm)(dt) states. 

The major point is that mass does not emit photons masstime does. Mass travels through time by an extremely high oscillation between corpuscle-like state m and wave-like state mt. 

The electron is the quintessential particle in electrochemistry. But it has turned out that its properties bear within them a mystery, the nature of which is still debated. For Davidson and Germer (1927), and then G. P. Thompson (1928) found that the corpuscles that J. J. Thompson (1897) had measured possessed a Jekyl and Hyde character. Material corpuscles they could be (with definite mass and charge) but lo —they could also behave as if they were waves. 

The idea of a wave function of a fixed number of corpuscles... 

So far then as experiment has thus far gone, Einstein s equation seems to be an exact statement of the energies of emission of corpuscles under the influence of light waves. 

The initial state will be represented, complete with the uncertainties which it involves, by a certain initial form of the associated wave. The later changes of the wave can be predicted exactly by the equations of Wave Mechanics but this does not mean an absolute Determinism for the corpuscle, since knowledge of the wave at every instant only enables us to assign certain probabilities to the various hypotheses tenable as to the position and momentum of the corpuscle. In a word, then, while the older Mechanics claimed to apply exact and inexorable laws to every phenomenon. 

The relationships to electromagnetic waves postulated by the German physicist Heinrich Rudoph Hertz led to the work of the English physicist Sir Joseph John Thomson in 1897, which is often linked to the actual discovery of the electron [26]. The measurement of the e/m and m of the corpuscles called electrons by Thompson settled this controversy. Electrons were at least particles, but other studies suggested that they were also electromagnetic radiation. Thompson described his conclusions as follows ... 

The ideas which we have arrived at in the preceding chapters with regard to the structure of matter all rest on the possibility of demonstrating the existence of fast-moving particles by direct experiment, and indeed of making their tracks immediately visible, as in the Wilson cloud chamber. These experiments put it beyond doubt that matter is composed of corpuscles. We are now to learn of experiments which just as definitely seem to be only reconcilable with the idea that a molecular or electronic beam is a wave train. Before we enter upon this, however, we shall briefly recall the main facts of wave motion in general, using the phenomena of optical dift raction as a concrete example. 

In the Compton scattering we have therefore a typical example of a process in which radiation behaves like a corpuscle of well-defined energy (and momentum) an explanation by the wave theory of the experimental results which we have described seems absolutely impossible. On the other hand, interference phenomena are quite irreconcilable with the corpuscular view of radiation. Until a few years ago, to explain this contradiction in the theory of light seemed to be beyond the bounds of possibility. 

In the preceding sections we have had a series of facts l)rolight before us which seem to indicate unequivocally that not only light, but also electrons and matter, behave in some cases like a wave process, in other cases like pure corpuscles. How are these contradicjtory aspects to be reconciled ... 

Quite independently of the line of thought just explained, the problem of atomic structure has been attacked with the lielp of the ideas developed in the preceding chapter. According to the hypothesis of de Broglie (p. 79), to every corpuscle thenj corresponds a wave, the wave-length of which, in the case of rectilinear motion of the corpuscle, is connected with the momentum by the relation... 

We have already mentioned the interpretation of the wave function given by the author (p. 83). Let the proper function corresponding to any state be then dv is the probability that the electron (regarded as a corpuscle) is in the volume element dv. 

It might appear that wave mechanics involves a one-sided preference for the wave standpoint, and that the introduction of the corpuscle concept is therefore only made possible by the artificial importation of the statistical interpretation. As against that, it may be remarked, while the matrix or quantum mechaixics of Heisenberg, briefly outlined above, is in complete agreement with wave mechanics in its content, and only differs from it in the form of presentation, still in its methods it attaches itself rather to corpuscular mechanics. 

The true philosophical import of the statistical interpretation has already been explained in 7 (p. 82). It consists in the recognition that the wave picture and the corpuscle picture are not mutually exclusive, but are two complementary ways of considering the same process—a process whose accessibility to intuitive apprehension is never complete, but always subject to certain limitations given by the principle of uncertainty. Here we have only one more important point to mention. The uncertainty relations, which we have obtained simply by contrasting with one another the descriptions of a process in the language of waves and in that of corpuscles, may also be rigorously deduced from the formalism of quantum mechanics—as exact inequalities, indeed for instance, between the co-ordinate q and momentum p we have the relation... 

---