Relational Quantum Mechanics

A very interesting paper on the interpretation of quantum mechanics has appeared yesterday:

Relational EPR
Matteo Smerlak, Carlo Rovelli

The article attempts to explain the EPR experiment using the relational interpretation of quantum mechanics championed by Rovelli (presented here and here). The main idea of the relational interpretation is that a quantum state is not an "absolute" description of a system, but only relative to a given observer, and that a same system may be described at the same time by many different states. For example, in the "Wigner’s Friend" version of the Schroedinger Cat paradox, one observer inside a box makes a measurement of a quantum system and sees a definite result, while for a second observer outside the box the whole system including the first observer is still in an indeterminate "superposition" state. The relational interpretation has a simple description of the situation: the state is collapsed relative to the first observer and superposed relative to the second observer. (In contrast, the better known "many worlds" interpretation would say that the "true" state is the superposed one and that the first observer’s impression is a kind of illusion produced by the "branching" of his consciousness. The relational interpretation is more "democratic"; none of the descriptions is privileged.) A key feature of the relational interpretation is that according to it any quantum system can be called an "observer"; counscious beings have no special status, and any interaction can be a "measurement". If system A is first in a superposition state Ia1> + Ia2> (with respect both to a system B and to an external system C) and then interacts only with system B, relative to C the global state may be now Ia1>Ib1> + Ia2>Ib2>, even though relative to B one of the options has “actualized” and the state is now Ia1>Ib1>.

I think this is a quite elegant solution to the measurement problem. It does not involve any change in the testable predictions of QM, unlike the models with a physical wavefunction collapse; it does not involve extra physical baggage like hidden variables models do, and it does not involve the extra ontological baggage of the many worlds interpretation. (From the point of view of the relational interpretation, the many worlds interpretation would seem to privilege as the only "true" state one which is not relative to any particular observer; God’s point of view, so to say. I think that the relationist should deny that there is any such state, like a "wavefunction of the universe". This should have implications for quantum cosmology.) Even more attractive, for me at least, is that the interpretation is not instrumentalistic: quantum mechanics is not merely a tool for calculating and predicting but a true description of how the world works; the description must be done from the "point of view" of some physical system, but there is no privileged choice for the reference system (much like the situation with reference frames in special relativity).

One criticism that comes to mind is that the relational interpretation is not very clear on which events count as "interactions" or "measurements". In the situation described above, in which system B "measures" system A and changes its state relative to it, at what time does this change occur exactly? From the external point of view no change has occurred: relative to an external observer the whole state has evolved continuously into a superposition. So there is a question that seems real enough, "Exactly when did B's state relative to A change?" but to which quantum mechanics provides no answer and no experiment will ever shed light on. This seems strange; if Rovelli has a good answer to this question, I am not aware of it.

As applied to the EPR experiments discussed in this paper, the apparent paradox in the usual formulation of quantum mechanics is that a measurement in system A (which "collapses" and changes its state) can produce an instantaneous change in the state of a system B entangled with A, even if B is spacelike separated from A and so no physical signal can carry the information of the collapse. The solution, using the relational interpretation, is explained in the article in the following way: If observer O makes a measurement on A, then the state of A relative to O changes, and ipso facto the state of B relative to O insofar as B and A are entangled, but this change in the state of B is not problematic as it only reflects the information available to O. The state of B relative to the observer O' who is measuring it remains uncollapsed when O measures A if O and O’'are spacelike separeted. But after O' measures B, when O and O’ meet to compare results (it is stressed that this comparison is also a physical interaction, involving a measurement), they are garanteed to find the correlations predicted by quantum mechanics. Relative to O, the measurement of O' (comparison of results with him) will always yield O' to be in the state of having measured the opposite spin to the one measured by O, if the original state was a singlet.

One noteworthy feature of the paper is that it quotes Wittgenstein! Propositions 1.1, 2.01, 2.011 y 2.0121 of the Tractatus. Not very common in your average physics paper! The reason for me remarking this is that I was fascinated by the Tractatus at one period of my life and organised a reading group for it with some friends. I'm sad to report it only lasted one meeting.

There is an ongoing discussion of this paper at Christine Dantas' blog.