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Discussion and Conclusions

The quantum concept used by de Broglie to associate a frequency to a particle is a consequence of Wien’s displacement law. This law is in turn, a consequence of some kind of invariance of the spectrum of blackbody radiation. The invariance in question can be conceived at different levels, two of which may be involved in our subject matter. First, there is the invariance to some fundamental isotropic space expansion. Secondly there is the invariance with respect to the relativistic frequency transformation. Inasmuch as they lead to common conclusion about the spectrum of blackbody radiation, the two types of invariance are perhaps limiting cases of broader invariance that we may have to take into consideration in order to correctly assess the physicality of de Broglie frequency. Along this line of reasoning De Broglie may have committed a transgression with respect to the last type of invariance, when associating the frequency with the energy, for the very idea of quantum does already contain the transformation of frequency in its background.

Thus, in our opinion, when dealing with assessing the de Broglie’s frequency, the essential fact is to forget about quantum, at least in its by now classical perception. Here, recalling what hard time had de Broglie in order to prove that the photon has a mass, might be of real help. This process of dismissal of the quantum as classically understood has two replicas. The first one is to push the radicalism so far as to forget even about frequency. As we have shown in the present work, it leads us in the realm of some space transformations that may be responsible for the birth of Special Relativity itself. The second replica is to study the deep consequences of the statistic involved in the measurement process. Here the Theoretical Statistics should undertake the issue. As we have shown it certainly leads to another idea of quantum, also touched by de Broglie himself. Interestingly enough the two approaches meet in their final result: the quantum produced by statistical approach does not depend upon frequency, which is the fundamental premise of the velocity space approach. We hope to be able to publish a future work on this subject.

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