An interpretation for the wave function
We present an interpretation of the wave function which gets rid of the probabilities and which transforms the wave function collapse into a principle of symmetry breaking. We are aware that there are other possibilities to answer this problem. 1) the “decoherence” interpretation is certainly very very nice 2) it might be a much be better move to just stop trying to avoid probabilistic interpretations and instead turn the fact that physics has become entirely statistical into a advantage.
We are investing 2) at the moment, while we are very conscious that 1) is most appropriate for a “pure physics”.
At one point Descartes in its meditations said something like : the world could as well be destroyed and re-created at each instant of time… One idea came that the particules could as well not exist when they were not interacting. In this case the probabilities would cease to be a problem. For example the wave function would not represent the probability of presence of the particule, since there would be no particle to be present in the first place.
We can first imagine a particle, with the deterministic interpretation that the wave function guides its trajectory (instead of being a probability of its presence), and we can superpose on this image Descartes’s idea that the particule didn’t exist along this trajectory (would be destroyed just entering the trajectory and re-created at the end).
The present article is simplified, there is no discussion concerning the link between this interpretation and presocratic philosophers who ask the question : Is the universe empty ? But all these ideas are linked in one way or another.
Also since Heisenberg, physics describes the world dynamically. What Aristotle called substance is now a dynamical substance (the description in terms of “static” quantities have been replaced by the description of “dynamical” creation and annihilation operators).
In one word we went from a (static) substance defined by “what is out there” to “a principle of interaction”. We can thus define the (dynamical) substance to be “the principle of interaction” that is to be “what happens”. The true question still is: why should we associate to the fundamental variables of a theory, something called the reality of the world? Making the departure between what is imaginary and what is real is an interesting question which clearly doesn’t involve physics only.