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I am reading an article about the interpretation of quantum mechanics called Relational Quantum Mechanics, and I come across an idea:

RQM is based on an ontology given by physical systems described by physical variables, as in classical mechanics. The difference with classical mechanics is that (a) variables take value only at interactions and (b) the values they take are only relative to the (other) system affected by the interaction. Here “relative” is in the same sense in which velocity is a property of a system relative to another system in classical mechanics. The world is therefore described by RQM as an evolving network of sparse relative events, described by punctual relative values of physical variables.

Second, quantum mechanics describes the world in terms of values of variables at specific discrete times. This second aspect of discreteness is directly accounted for by the sparse (or “flash”) ontology of RQM. The history of a quantum particle, for instance, is neither a continuous line is spacetime (as in classical mechanics), nor a continuous wave function on spacetime. Rather, with respect to any other system it is a discrete set of interactions, each localized in spacetime.

After all, this directly contradicts the mathematical apparatus of quantum field theory, according to which the interaction is constant and continuous, and particles do not exist in a "naked" state. How, then, does relational quantum mechanics explain the interaction of fields in a vacuum state, and what determines at what moment the particles will interact?

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  • $\begingroup$ I think it may be a good idea to separate this out into two separate questions. Firstly there is the question of how does the notion of discrete measurement times (which is used, though normally non-essential, in all interpretations of QM) emerge in a framework with, in principle, continuous interactions between the system and the measurement apparatus (such as QFT). Separately there is a question of how does RQM deal with continuous measurement setups (which is an interesting question but does not have much to do with QFT spesifically). $\endgroup$ Commented Jun 17, 2021 at 14:33
  • $\begingroup$ @BySymmetry As far as I know, in classical interpretations, the interaction of quantum particles and measurement with a macroscopic device are two completely different things. The first concerns the intermediate state, which in any case is described by the wave function-path integral-Feynman diagrams, and the second is the probabilistic result of the addition of all intermediate amplitudes. And in the interval there are no probabilities, there is a deterministic evolution of a quantum system. $\endgroup$ Commented Jun 17, 2021 at 14:38

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I think it's true that there is an open question about the story RQM wants to tell about continous (measurement) interactions. In particular, since it holds on to the collapse postulate, it is at least not obvious how it deals with continuous interactions that (as a matter of fact) do NOT give rise to quantum Zeno effects (freezing of dynamics of the observed system). This seems to be a general problem for collapse interpretations, in fact.

Concerning the question when an interaction occurs, Rovelli has published his views in this paper, maybe that's of help?

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  • $\begingroup$ I don't think that constant interaction with the environment can lead to the Zeno effect. This interaction, although continuous and constant, is not so strong; therefore, the off-diagonal elements of the density matrix tend to zero, but do not become exactly zero. And measurement with a specialized device is a rather strong interaction. $\endgroup$ Commented Dec 7, 2021 at 12:30
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    $\begingroup$ I'm not sure I fully understand your point, but mine is that according to RQM, any interaction between two systems S and S' makes the quantum state of S' relative to S (there are no absolute states in RQM) collapse onto one of the eigenstates of the relevant variable. If this happens continuously, won't we get a Zeno effect? $\endgroup$
    – TRi
    Commented Dec 7, 2021 at 15:58
  • $\begingroup$ I understood. But in the same place the states are relative. A system that has collapsed in relation to one system will not collapse in relation to another. $\endgroup$ Commented Dec 7, 2021 at 16:02
  • $\begingroup$ Right. But still, S will dynamically freeze relative to S', no? $\endgroup$
    – TRi
    Commented Dec 7, 2021 at 16:20
  • $\begingroup$ Yes. Therefore, in this interpretation, the interaction is not constant and continuous, which contradicts the QFT. $\endgroup$ Commented Dec 7, 2021 at 16:23

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