If the decision-theoretic argument works, then a rational agent should expect to find herself in a branch which respects quantum statistics, so it should not surprise her to find herself in such a branch. Perhaps there is some measure according to which “most” observers are in branches where quantum statistics aren’t respected, but that measure is not one that should guide the expectations of rational agents, so I don’t see why it should be surprising that we are not typical observers in the sense of typicality associated with that measure.
It’s sounding like a Boltzmann brain… the observer who happens to have memories of Born-friendly statistics should still be blasted into random pieces in the next moment.
I haven’t pinned down the logic of it yet, but I do believe this issue—that the validity of quantum statistics is required for anything about observed reality to have any stability—seriously, even fatally, undermines Wallace’s argument. Consider your assumption 2, “Arbitrary quantum superpositions can be prepared”. This is the analogue, in the decision-theoretic argument, of Bohr’s original assumption that there is a classical world which provides the context of quantum measurements. That assumption is unsatisfactory if we are trying to explain, solely in terms of quantum mechanics, how a “classical world” manages to exist. It looks the same for Wallace: he is presupposing the existence of a world stable enough that an agent can exist in it, interact with it, and perform actions with known outcomes. We are told that we can get this from Schrodinger dynamics alone, but Schrodinger dynamics will also produce nonzero amplitudes for all the configurations where the world has dissolved into plasma. Since we are trying to justify the Born rule interpretation of those amplitudes, we can’t neglect consideration of these disintegrating-world branches just because the amplitude is small; that would be presupposing the conclusion. Also, observer selection won’t help, because there will be branches where the observer survives but the apparatus disintegrates.
It all sounds absurd, but this results directly from trying to talk about physical processes, without using the part of QM that gives us the probabilities. When we do use that part, we can safely say that the spontaneous disintegration of everyday objects is, not impossible, but so utterly unlikely that it is of no practical interest. When we try to describe reality without it, then all possible futures start on an equal footing, and most of them end in plasma. I just do not see how the argument can even get started.
The decision-theoretic argument is not supposed to prove everything. It’s supposed to explain why agents living in environments that have so far been stable should set their credences according to the Born probabilities. So, yes, there are presuppositions involved. But I don’t see how this is a devastating problem for Everettianism.
You brought up Boltzmann brains. It turns out that our best cosmological models predict that most observers in the universe will be Boltzmann brains. The universe will gradually approach an eternally expanding cold de Sitter phase, and thermal fluctuations in quantum fields will produce an infinity of Boltzmann brain type observers. Do you think this is a devastating objection to cosmology? I think the appropriate tack is to recognize anthropics as an important issue that we need to work on understanding, but in the meantime proceed with using those cosmological models under the assumption that we are not Boltzmann brain type observers.
Much of the evidence for quantum mechanics is statistical in nature. Relative frequency data summarizing the results of repeated experiments is compared to probabilities calculated from the theory; close agreement between the observed relative frequencies and calculated probabilities is taken as evidence in favour of the theory. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to this sort of reasoning. Since, on the Everett interpretation, all outcomes with nonzero amplitude are actualized on dierent branches, it is not obvious that sense can be made of ascribing probabilities to outcomes of experiments, and this poses a prima facie problem for statistical inference. It is incumbent on the Everettian either to make sense of ascribing probabilities to outcomes of experiments in the Everett interpretation, or to find a substitute on which the usual statistical analysis of experimental results continues to count as evidence for quantum mechanics, and, since it is the very evidence for quantum mechanics that is at stake, this must be done in a way that does not presuppose the correctness of Everettian quantum mechanics. This requires an account of theory conrmation that applies to branching-universe theories but does not presuppose the correctness of any such theory. In this paper, we supply and defend such an account. The account has the consequence that statistical evidence can confirm a branching-universe theory such as Everettian quantum mechanics in the same way in which it can confirm a non-branching probabilistic theory.
If the decision-theoretic argument works, then a rational agent should expect to find herself in a branch which respects quantum statistics, so it should not surprise her to find herself in such a branch. Perhaps there is some measure according to which “most” observers are in branches where quantum statistics aren’t respected, but that measure is not one that should guide the expectations of rational agents, so I don’t see why it should be surprising that we are not typical observers in the sense of typicality associated with that measure.
It’s sounding like a Boltzmann brain… the observer who happens to have memories of Born-friendly statistics should still be blasted into random pieces in the next moment.
I haven’t pinned down the logic of it yet, but I do believe this issue—that the validity of quantum statistics is required for anything about observed reality to have any stability—seriously, even fatally, undermines Wallace’s argument. Consider your assumption 2, “Arbitrary quantum superpositions can be prepared”. This is the analogue, in the decision-theoretic argument, of Bohr’s original assumption that there is a classical world which provides the context of quantum measurements. That assumption is unsatisfactory if we are trying to explain, solely in terms of quantum mechanics, how a “classical world” manages to exist. It looks the same for Wallace: he is presupposing the existence of a world stable enough that an agent can exist in it, interact with it, and perform actions with known outcomes. We are told that we can get this from Schrodinger dynamics alone, but Schrodinger dynamics will also produce nonzero amplitudes for all the configurations where the world has dissolved into plasma. Since we are trying to justify the Born rule interpretation of those amplitudes, we can’t neglect consideration of these disintegrating-world branches just because the amplitude is small; that would be presupposing the conclusion. Also, observer selection won’t help, because there will be branches where the observer survives but the apparatus disintegrates.
It all sounds absurd, but this results directly from trying to talk about physical processes, without using the part of QM that gives us the probabilities. When we do use that part, we can safely say that the spontaneous disintegration of everyday objects is, not impossible, but so utterly unlikely that it is of no practical interest. When we try to describe reality without it, then all possible futures start on an equal footing, and most of them end in plasma. I just do not see how the argument can even get started.
The decision-theoretic argument is not supposed to prove everything. It’s supposed to explain why agents living in environments that have so far been stable should set their credences according to the Born probabilities. So, yes, there are presuppositions involved. But I don’t see how this is a devastating problem for Everettianism.
You brought up Boltzmann brains. It turns out that our best cosmological models predict that most observers in the universe will be Boltzmann brains. The universe will gradually approach an eternally expanding cold de Sitter phase, and thermal fluctuations in quantum fields will produce an infinity of Boltzmann brain type observers. Do you think this is a devastating objection to cosmology? I think the appropriate tack is to recognize anthropics as an important issue that we need to work on understanding, but in the meantime proceed with using those cosmological models under the assumption that we are not Boltzmann brain type observers.
Anyway, the kind of problem you’re raising now is not one that Wallace’s decision-theoretic argument is intended to solve. This paper by Greaves and Myrvold might be relevant to your concerns, but I haven’t read it yet: http://philsci-archive.pitt.edu/4222/1/everett_and_evidence_21aug08.pdf
The abstract: