Feynman and Everett

A couple of years ago I gave a talk at the Institute for Quantum Information at Caltech about the origin of probability -- i.e., the Born rule -- in many worlds ("no collapse") quantum mechanics. It is often claimed that the Born rule is a consequence of many worlds -- that it can be derived from, and is a prediction of, the no collapse assumption. However, this is only true in a particular (questionable) limit of infinite numbers of degrees of freedom -- it is problematic when only a finite number of degrees of freedom are considered.

After the talk I had a long conversation with John Preskill about many worlds, and he pointed out to me that both Feynman and Gell-Mann were strong advocates: they would go so far as to browbeat visitors on the topic. In fact, both claimed to have invented the idea independently of Everett.

Today I noticed a fascinating paper on the arXiv posted by H.D. Zeh, one of the developers of the theory of decoherence:

Feynman's quantum theory

H. D. Zeh

(Submitted on 21 Apr 2008)

A historically important but little known debate regarding the necessity and meaning of macroscopic superpositions, in particular those containing different gravitational fields, is discussed from a modern perspective.

The discussion analyzed by Zeh, concerning whether the gravitational field need be quantized, took place at a relativity meeting at the University of North Carolina in Chapel Hill in 1957. Feynman presents a thought experiment in which a macroscopic mass (source for the gravitational field) is placed in a superposition state. One of the central points is necessarily whether the wavefunction describing the macroscopic system must collapse, and if so exactly when. The discussion sheds some light on Feynman's (early) thoughts on many worlds and his exposure to Everett's ideas, which apparently occurred even before their publication (see below).

Nowadays no one doubts that large and complex systems can be placed in superposition states. This capability is at the heart of quantum computing. Nevertheless, few have thought through the implications for the necessity of the "collapse" of the wavefunction describing, e.g., our universe as a whole. I often hear statements like "decoherence solved the problem of wavefunction collapse". I believe that Zeh would agree with me that decoherence is merely the mechanism by which the different Everett worlds lose contact with each other! (And, clearly, this was already understood by Everett to some degree.) Incidentally, if you read the whole paper you can see how confused people -- including Feynman -- were about the nature of irreversibility, and the difference between effective (statistical) irreversibility and true (quantum) irreversibility.

Zeh: ... Quantum gravity, which was the subject of the discussion, appears here only as a secondary consequence of the assumed absence of a collapse, while the first one is that "interference" (superpositions) must always be maintained. ... Because of Feynman's last sentence it is remarkable that neither John Wheeler nor Bryce DeWitt, who were probably both in the audience, stood up at this point to mention Everett, whose paper was in press at the time of the conference because of their support [14]. Feynman himself must have known it already, as he refers to Everett's "universal wave function" in Session 9 – see below.

... Toward the end of the conference (in the Closing Session 9), Cecile DeWitt mentioned that there exists another proposal that there is one "universal wave function". This function has already been discussed by Everett, and it might be easier to look for this "universal wave function" than to look for all the propagators. Feynman said that the concept of a "universal wave function" has serious conceptual difficulties. This is so since this function must contain amplitudes for all possible worlds depending on all quantum-mechanical possibilities in the past and thus one is forced to believe in the equal reality [sic!] of an infinity of possible worlds.

Well said! Reality is conceptually difficult, and it seems to go beyond what we are able to observe. But he is not ready to draw this ultimate conclusion from the superposition principle that he always defended during the discussion. Why should a superposition not be maintained when it involves an observer? Why “is” there not an amplitude for me (or you) observing this and an amplitude for me (or you) observing that in a quantum measurement – just as it would be required by the Schrödinger equation for a gravitational field? Quantum amplitudes represent more than just probabilities – recall Feynman’s reply to Bondi’s first remark in the quoted discussion. However, in both cases (a gravitational field or an observer) the two macroscopically different states would be irreversibly correlated to different environmental states (possibly including you or me, respectively), and are thus not able to interfere with one another. They form dynamically separate “worlds” in this entangled quantum state.

... Feynman then gave a resume of the conference, adding some "critical comments", from which I here quote only one sentence addressed to mathematical physicists:

Feynman: "Don't be so rigorous or you will not succeed."

(He explains in detail how he means it.) It is indeed a big question what mathematically rigorous theories can tell us about reality if the axioms they require are not, or not exactly, empirically founded, and in particular if they do not even contain the most general axiom of quantum theory: the superposition principle. It was the important lesson from decoherence theory that this principle holds even where it does not seem to hold. However, many modern field theorists and cosmologists seem to regard quantization as of secondary or merely technical importance (just providing certain "quantum corrections") for their endevours, which are essentially performed by using classical terms (such as classical fields). It is then not surprising that the measurement problem never comes up for them. How can anybody do quantum field theory or cosmology at all nowadays without first stating clearly whether he/she is using Everett’s interpretation or some kind of collapse mechanism (or something even more speculative)?

Previous posts on many worlds quantum mechanics.