Relational Approach To Quantum Physics - Analysis of Particle and Wave Concepts in Terms of Frames of Detection

Analysis of Particle and Wave Concepts in Terms of Frames of Detection

From the above discussion, it is shown that an outcome of detection (an event) specifies only a relationship between that object and a certain detection; however it is not sufficient to consider only the result of an individual detection. The real significance of our detections arises from the fact that the properties of physical objects can be regularized and ordered in terms of frames of detection. For example, in a particle detection frame of light, one arranges a series of photodetectors in the propagation direction, by which one can define invariant quantities such as the velocity of the light signal propagation c (emission and absorption). This allows one not only to establish a 'trajectory' but also relate it to a portion of energy, E, and momentum, p, (a photon), transferred from a light field to a detector, to form a particle picture (p = E/c).

There also exists a wave frame of detection, where, for example, light is divided into two paths so as to interfere with each other. To measure and analyze such an effect, one also needs to place an array of detectors on the interfering plane, from which one can infer an additional set of quantities such as the frequency, wavelength, and also the phase velocity from the interference fringes; thus one constructs a wave picture. However, as far as Newtonian mechanics is concerned, such a wave frame of detection seems to be not necessary, and with the localizability discussed above, it makes sense to ascribe only the concept of particle to the cases investigated in the Newtonian domain.

Of course, all this experience depends on the condition that the de Broglie wavelength is so small that on the ordinary scale of distance and time, the wave modulation in the detection can be neglected; this is equivalent to assuming an infinitely small wavelength of matter. When a finite de Broglie wavelength is taken into account, new problems of 'wave-particle duality' do in fact arise, which ran through the famous Bohr-Einstein debate and is still a key issue in recent discussions.

In terms of detection frames, the implications of the relational approach implies that there is, in fact, no absolute significance to particle and wave pictures, but rather, their meaning is fundamentally dependent on how a frame of detection is constructed, i.e., on the observer. However, this concept of 'relativity', can only be expressed in precise quantitative form by Glauber's theory of light detection that logically unifies the two pictures of particle and wave.

From the relational viewpoint, physical phenomena in the quantum theory of light detection are described in terms of fields and their detection, which are organized, ordered, and structured so as to correspond to the characteristics of radiation systems that are being studied. In the aforementioned theory, de Broglie's concepts are now manifested by, in terms of annihilation operator (and creation operator ) as field amplitudes modulated by phase factors (and the conjugated ). The key point that we wish to establish is that, contains information concerning the propagation properties of light in both the particle and wave frames of detection since on the one hand, the propagation characteristics of the operators and, which physically describe the absorption and emission of light, indicate a particle frame of detection where the light signal travels at the speed c. On the other hand, the phase factor , implies a wave frame of detection, regulated by interference effects in the detection. It seems clear then that in the quantum theory of light detection, the particle and wave pictures are united as two sets of relative features of the same field in different frames of detection; thus they can be related to each other in such a way that Eq. (1) is left invariant - the principle of relativity. This unification can be characterized by a term called particle-wave rather than 'particle or/and wave', the hyphen emphasizing the new kind of unification.

It should be noted that in spite of the above-described unification of particle and wave pictures brought about in the quantum theory of detection, there remains a rather important and peculiar distinction between them, resulting from the fact that and are operators but the phase factors are c-numbers. On the basis of this distinction, it also clear that the modulation by the phase factors in the probability expression of Eq. (2) at a velocity (the phase velocity) greater than c, for example, in de Broglie matter systems, in no way confuses us on the maximum speed of propagation of the signals, provided that a signal propagation is physically described by the annihilation and creation operators and .