Hi
@PeroK!
Your objections relate to certain metaphysical assumptions that you take for granted, but which RQM rejects.
First, I would like to briefly summarize the essence of the relational interpretation. Taking events/interactions as the central element, if information exists about the occurrence of event ##a##, quantum theory allows us to calculate the probability of event ##b## occurring, that is, the transition probability ##P(b|a) = \bra{a}e^{-iHt}\ket{b}##. Within this conceptual framework, the wave function is simply a tool for obtaining such probabilities. Consequently, there is no single wave function that can be assigned to an electron, since different physical systems may have interacted with it differently in the past.
To answer you, I will consider an extremely simple case: a source that emits an electron at time ##t_1## and a screen that detects it at time ##t_2##, assuming ##t_2 > t_1##.
PeroK said:
One could argue that if the electron does not exist between measurements, then it cannot be described by a state or wave-function (or anything) between measurements. And, if its state does not exist between measurements, then its state cannot evolve between measurements.
As I said before, there is no problem in defining a wave function that allows calculating the probabilities that the electron that was emitted at ##t_1## will be detected later on the screen at an instant ##t_2##. Once again, within RQM, the wave function allows us to calculate correlations between events that occur at different times.
PeroK said:
This is, therefore, not a cornerstone of QM. As QM does indeed entail the evolution of a state or wave-function between measurements. There is always a wave-function.
That's true, of course. What changes is the interpretation of the wave function.
PeroK said:
There is also something of a problem that if an electron does not exist, then why does a measurement bring an electron into existence, instead of any other elementary particle? If an electron ceases to exist, then there is no reason why an electron with predictable properties should be produced by a measurement. If an electron was created in a specific spin state, then ceases to exist, then how does the measuring device manage to create an electron with the expected spin measurement?
Or, indeed, why does it not detect a proton or neutron or any other particle?
A non-existent electron is mathematically equivalent to a non-existent proton.
The fact that the electron is nowhere between two measurements, that it has no physical properties, that it "doesn't exist," does not mean that we cannot define a wave function that allows us to predict future events based on the certainty of having detected an electron with certain physical properties in the past. As I mentioned earlier, the discrepancy arises because you interpret the correlation between the emission of an electron at ##t_1## and its detection at ##t_2## as requiring some physical entity to continuously propagate information between the two events. By doing this, you are assigning an ontic status to the wave function. This is precisely what RQM rejects.
If we know that an electron was emitted at time ##t_1##, the probability that the detection event on the screen involves two electrons or a proton is excluded because the transition probability is zero for such processes. This is all consistent with orthodox/textbook QM.
PeroK said:
As others have suggested, you would really need to get a direct opinion from Rovelli himself on this point. The idea that things do not exist between measurements is indeed widespread in popular science. He may simply be copying a well-worn popularisation.
I really don't think it's necessary, as this topic has been sufficiently analyzed in the numerous texts written on RQM. In any case, I would like to add that, as with other interpretations, there are internal debates within RQM. The question of whether or not entities exist between measurements is a subject of debate. From a philosophical perspective, there is what is called structural realism. For those who are interested, a relatively recent article on this topic is
this one by Laura Candiotto. Furthermore, there is a very recent
paper by Rovelli that presents a "fresh look" on RQM, analyzing the possibility of understanding the theory as the description of continuous processes of measurement/interaction between physical systems. The relational nature of the interpretation is maintained, but not the discontinuous, event-based ontology.
Lucas.