Tuesday, February 20, 2007

Wigner's Friend and Perspectivist Quantum Theory

As discussed at the end of the last post in my series on quantum mechanics, I want to explore the ideas contained in Paul Merriam’s recent paper to see if his proposal for “quantum relativity” can address the challenges faced by the relational interpretation of quantum mechanics. But first I want to double back a bit by looking at Merriam’s previous (1997) paper on the philosophy of QM: called “On the Relativity of Quantum Superpositions,” it was included in an edition of an online journal called Metaphysical Review.

In this paper Merriam independently (to all appearances) arrived at the same general position as in the relational interpretation primarily identified with Carlo Rovelli. He also began to explore the idea of using relativity theory as a guide to further development of the relational view. To lay the groundwork, the paper begins by invoking the “Wigner’s friend” scenario and showing how it leads to the view he described as “Perspectivist Quantum Theory”.

Eugene Wigner, to highlight a certain aspect of quantum theory, presented an idealized thought experiment (a short account of this written by Henry Stapp can be found here). In the “Wigner’s friend” scenario, an experimenter (the friend) is performing a measurement on a quantum system that will result in one of two outcomes: the original example invokes an atomic state that will emit a visible photon either into the eye of the experimenter or elsewhere (Merriam’s paper imports Schrödinger’s’ cat into his version). A second experimenter (Wigner) is stationed outside the sealed laboratory where the measurement will take place. Inside the laboratory, from the perspective of Wigner’s friend, the experiment will collapse the quantum state into one of the two outcomes and the friend will observe the photon or not. To Wigner on the outside, the physical description of the state in the lab will be a superposition of the two scenarios, where the friend observes the photon and where she does not.

Wigner used the thought experiment to support his view that human consciousness was intimately bound up with quantum measurement: for him, it might make sense to view the two outcomes in the lab as being in superposition if the measurement was performed by an inanimate apparatus of some kind, but he believed that the consciousness of the human friend would have engendered collapse whether or not the he (the second observer) made contact with the situation in the lab. However, there is no part of quantum theory itself which makes any such special provision for human consciousness.

Merriam wants to take QM seriously as a description of nature, and notes the theory itself says nothing about applying only to microscopic or simple or non-conscious systems. QM doesn’t magically dissolve into classical reality at some objective threshold (there is no “Heisenberg cut”). The states of what’s happening inside the lab as known to Wigner and Wigner’s friend differ. This difference cannot be “swept under the rug”. What the Wigner’s friend example is telling us is that QM gives a true physical description relative to the observing/measuring system. “What prediction is made depends on which system is doing the predicting.” Quantum states are well defined only when relativized to a particular system. Quantum theory is an intransitive theory.

Next Merriam considers a comparison of this situation to that of relativity theory: “A quantum description of the state of the system is relative to the system doing the describing just as the description of a system in terms of space and time is relative to the motion (and gravity) of the describing system”. The question is whether we can build on this analogy in a useful way.

In considering the situation, note again that there is no reason to think QM is anything other than “democratic” in nature (my label). As Merriam says: “In QM, there is no ‘ontological’ difference between an experimenter and an electron…” From the point of view of the electron, the experimenter is in superposition between interactions. The next move is to postulate that Quantum Mechanics holds for the points of view of all quantum systems. We then note that while quantum states viewed from different points of view will differ, the perspectives of two systems must match up when they interact. The theory to be developed must be based ultimately on the interactions between systems. The interactions are the pivot to link things together. (This is a point stressed by Rovelli: the interactions are the fundamental entities; quantum states lack objective existence). So, we have a situation where we postulate that QM gives correct physical descriptions from a point of view, but there is a plurality of points of view. A theory of quantum relativity would note that “simultaneity” means two concurrent observations involving the same observer. Since systems’ perspective will match during an interaction, this may form the basis of extending the theory. For instance, the time interval between two succeeding interactions between two systems must match.

It is with this point that the paper ends. Merriam presses the idea of quantum relativity further in the next paper, which I will discuss in a further post.

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