5.2.3 Ontological Probabilities
The same mismatch between what a constituent of matter is and what we take it for in our theory is responsible for the strange conception that such an object is not fully anywhere and has only a given probability of being fully at the location where its presence will actually be observed by an appropriate detection apparatus. To see that, consider again the Davisson-Germer predicated observation of electrons scattering off a crystal. The electron which explains this measurement is a giving together from unity of the particle postulated by J.J. Thomson and a von Laue wave. Although de Broglie had already attempted to conceive of such a unity, he only succeeded in thinking of it as an association of two pre-existing entities, a particle whose motion was rectilinear and uniform and a stationary, monochromatic wave, the momentum and the wavelength of which had to satisfy:
if the association was to remain invariant under a Lorentz transformation. The manner in which such an association was to be implemented ontologically remained however largely unspoken and the issue continued to concern de Broglie, on and off, for much of his life.
What stopped him from visualizing the syndosis as anything else but a formal association was the lack of any reference to a specific explanation. Had he tried, for instance, to conceive of the association within the context of something like the Davisson-Germer measurement, he may have been able to realize that the particle which explained the functioning of the electron gun could behave as the wave which explained its scattering off the crystal if, and only if, the particle was also present at points other than the rectilinear trajectory on which it was sent forth from the manufacturing gun. But, if it was thus to be present everywhere, the particle could not fully be anywhere; it could only partially be there. On the other hand, however, the electron has its own individuality which requires it to be all there when observed. The mathematical representation of such a strange situation is a probability, not the probability which counts the frequency with which a given member appears in a family of its peers, but an ontological probability which describes the manner of being of that particle. Constrained however to speak only the language which describes objects of experience, quantum mechanics was led to imagine the object which explains the Davisson-Germer experiment as a particle which has only a specified probability of being observed anywhere but collapses upon one place when observed to be there. In the event, that probability follows the shape of a von Laue wave whose wavelength is related to the momentum of that particle by the de Broglie’s relation. Again, the statistical nature of quantum mechanics reflects the true ontology of a quantum object in a language which fails to accept that such an object is a syndosis, not a synthesis of particle and wave.