What happens when collapse doesn't happen in collapse theories?

On collapse theories like GRW, Quantum Mechanics proceeds deterministically according to the Schroedinger Equation until a random "hitting" event occurs, when collapse occurs. There is a frequency parameter f that controls how often hitting events tend to happen. They tend to happen much more frequently when there are large amounts of matter involved than when there are small.

Nonetheless, the hitting events are random. Thus the physics of collapse theories implies that it is physically possible, with a non-zero (but presumably tiny) probability, that no hitting event happen in the universe over the next year, and hence no collapse happens over a year. Since this is physically possible, it should make sense to ask: What would it be like if this happened? Indeed, if we live in an infinite multiverse governed by a collapse theory with the same frequency everywhere, we can be confident that such no-collapse years do occur.

So what would it be like if no collapse occurred? I can think of three plausible proposals:

• Nothing: A (nomic or metaphysical) precondition of consciousness is a brain in a pure, or at least close to pure, quantum state, so in a no-collapse year, once everybody's brain states came to have a sufficient superposition of states (from the preferred basis), nobody would be conscious. However, after that year passed, there would be a collapse, and there would be false but plausible memories corresponding to the outcome of the collapse.
• Everett: For that no-collapse year, we would be living as if in a branching Everett-style multiverse. Either we would be experiencing different things in different branches, or we would have counterparts in different branches experiencing different things. Then with the collapse at the end of the year, all the branches but one would disappear.
• Weird: We would be having strange superposed experiences, perhaps quite unlike anything we can imagine. We would have superposed neural memory states. Then at the end of the year, when collapse occurred, our memories would also collapse, and we would end up with an ordinary set of memories corresponding to one component of the superpositions.

Here's one curious feature of all three proposals: At the end of the year, we would be back to business as usual, seemingly with normal memories of the past year. We would have no way of telling after the fact that we had a year with no collapse. On the Nothing proposal, we would have no way of telling during the no-collapse year, either, since we wouldn't be conscious during it. On the Everett proposal, some of our counterparts or branched selves would be having strange, improbable experiences. On the Weird proposal, we would be having strange experiences, but then we would have no memory of them.

If we take the Everett proposal, then the GRW theorist does not avoid the metaphysical oddness of persons in a branching multiverse—her only special contribution is to say that this oddness is unlikely to occur. If we take the Weird proposal, then the collapse theorist still has to deal with the metaphysical and psychological oddness of Schroedinger's cat phenomena—again, her only contribution is to say that such phenomena are unlikely. If these difficulties are really serious metaphysical problems, then the GRW theorist does not avoid them. A die that turns into a square circle once it rolls a million heads is not any less metaphysically problematic than a plain and simple square circle.

I suspect the Nothing approach is the best one for the GRW theorist. For instance, Nothing combined with compact-support-collapse helps with the infamous tails problem for collapse theories (see this for a nice discussion of the tails problem; alas, my suggestion doesn't help with the relativistic problems the author points out). For maybe we are conscious only at those instants when the wavefunctions have compact support. This is good reason to opt for the Nothing proposal if one has a collapse theory.

But the Nothing approach leads to a strange sceptical hypothesis, namely that I have not been conscious over the past week, notwithstanding apparent memories from yesterday. For remember that the collapse theories have a free parameter, f, which governs the frequency of collapses. If that parameter is low enough, then collapses will be rare, say once a month in my vicinity. And what reason do I have on the Nothing proposal to suppose that f isn't that low? The apparent memories of continuous past consciousness are exactly what I would expect with a low parameter, since the apparent memories are induced by the collapse of superposed neural states. We do have some constraints on f. For instance, f had better not be so low that it's surprising why anybody is ever conscious. Maybe there are some stronger constraints than that, though this is not clear to me. But there is no reason given the Nothing proposal to deny a value of f that yields once-per-month collapses.

The Everett proposal may well lead to a sceptical worry about low values of f as well. For how do we know that we're not right now in a no-collapse period?

The Weird proposal does not lead to this sceptical worry that f might be low. For on the Weird proposal, given a low f it's surprising that my current conscious state is non-weird, and so that's evidence against Weird plus a very low value of f. But Weird is weird.

The above sceptical worries about low values of f are ameliorated if in addition to being collapse theorists we are theists. For God likely wouldn't want us to have too many misleading memories, and hence would likely make f high enough to prevent misleading memories.

A wacky metaphysics of time for deterministic physics

Consider a deterministic physical theory on which for each t>0 there is a time-evolution operator U_t on set of all instantaneous states of the universe (i.e., global phase space), so that if u is the state of the universe at time t₁, then U_tu is the evolved state of the universe at t₁+t. For example, Everett-style no-collapse quantum mechanics or Newtonian physics without situations like Norton's dome.

Suppose there is a first moment of time, call it time 0. Here, then, is an odd metaphysics to go with the theory. The universe fundamentally has some initial state. Then what it is for the universe to be in state v at a time t>0 is nothing else than for v to equal U_tu₀, where u₀ is the initial state.

For a simple example, suppose that we have a simple Newtonian theory with point particles and no forces. Then what it is for a particle to be at location x at time t>0 just is for the particle to have an initial momentum p₀, initial location x₀ and initial mass m₀ such that x=x₀+(p₀/m)t.

On this wacky metaphysics, later states are not caused by the initial state, but are metaphysically grounded in the initial state.

What are the merits of this kind of a weird theory? Well, it has a lot of fundamental simplicity:

• Fundamental reality is only three dimensional, and facts about later times are just mathematically derivative from the fundamental facts.
• At the fundamental level of description there is no such thing as time.
• There is no need for causation, laws of nature or nomic simplicity. Temporal evolution just is a matter of metaphysical necessity. Later states reduce to earlier ones.

Yet, we can have genuine explanatory relations between times. If the U_t operator has the right kind of mathematical definition in terms of differential equations, we will be able to say that the state of the universe at time t₂ is explained by the state of the universe at an earlier t₁ which in turn is explained by the state at time 0. The explanation is reductive or metaphysical rather than nomic. Thus the number of types of explanation is reduced.

This is, of course, very wacky. But if one doesn't take our intuitions about modality (say, the metaphysical possibility of miracles, which is ruled out on this account), the fundamental existence of persons, free will, and the like, and one has a deterministic theory, it is hard to avoid falling into a theory like this. Simplicity does, after all, strongly favor it.

The above formulation assumes an initial moment of time, but I think one can formulate it in terms of limiting conditions if one's deterministic theory doesn't have an initial moment.

I've noticed that for a while I've been unconsciously pursuing a curious research project. The research question is something like this: If one throws anthropocentric intuitions to the winds, what sort of interpretations of physics would one take seriously? Call this the estrangement (ostranenie) project. The point of the project is to take estranging approaches to their logical conclusion, and see where they lead. The lesson I am drawing is that when one abandons the kinds of anthropocentric approaches that Aristotelian metaphysics uses, one must go much further, and much stranger, than most people are willing to go.

If you're going to be a Platonist dualist, why not be an idealist?

Let's try another exercise in philosophical imagination. Suppose Platonism and dualism are true. Then consider a theory on which our souls actually inhabit a purely mathematical universe. All the things we ever observe—dust, brains, bodies, stars and the like—are just mathematical entities. As our souls go through life, they become "attached" to different bits and pieces of the mathematical universe. This may happen according to a deterministic schedule, but it could also happen an indeterministic way: today you're attached to part of a mathematical object A₁, and tomorrow you might be attached to B₂ or C₂, instead. You might even have free will. One model for this is the traveling minds story, but with mathematical reality in the place of physical reality.

This is a realist idealism. The physical reality around us on this story is really real. It's just not intrinsically different from other bits of Platonic mathematical reality. The only difference between our universe and some imaginary 17-dimensional toroidal universe is that the mathematical entities constituting our universe are connected with souls, while those constituting that one are not.

One might wonder if this is really a form of idealism. After all, it really does posit physical reality. But physical reality ends up being nothing but Platonic reality.

The view is akin to Tegmark's ultimate ensemble picture, supplemented with dualism.

Given Platonism and dualism, this story is an attractive consequence of Ockham's Razor. Why have two kinds of things—the physical universe and the mathematical entities that represent the physical universe? Why not suppose they are the same thing? And, look, how neatly we solve the problem of how we have mathematical knowledge—we are acquainted with mathematical objects much as we are with tables and chairs.

"But we can just see that chairs and tables aren't made of mathematical entities?" you may ask. This, I think, confuses not seeing that chairs and tables are made of mathematical entities with seeing that they are not made of them. Likewise, we do not see that chairs and tables are made of fundamental particles, but neither do we see that they are not made of them. The fundamental structure of much of physical reality is hidden from our senses.

So what do we learn from this exercise? The view is, surely, absurd. Yet given Platonism and dualism, Ockham's razor strongly pulls to it. Does this give us reason to reject Platonism or dualism? Quite possibly.

The traveling minds interpretation of indeterministic theories

I'm going to start by offering a simple way—likely not original, but even if so, not very widely discussed—of turning an indeterministic physical theory into a deterministic physical theory with an indeterministic dualist metaphysics. While I do not claim, and indeed rather doubt, that the result correctly describes our world, the availability of this theory has some rather interesting implications for the mind-body and free will and determinism debates.

Start with any indeterministic theory that we can diagram as a branching structure. The first diagram illustrates such a theory. The fat red line is how things go. The thin black dotted lines are how things might have gone but didn't. At each node, things might go one way or another, and presumably the theory specifies the transition probabilities—the chances of going into the different branches. The distinction between the selected branches and the unselected branches is that between the actual and the merely possible.

The Everett many-worlds interpretation of Quantum Mechanics then provides us with a way of making an indeterministic theory deterministic. We simply suppose that all the branches are selected. When we get to a node, the world splits, and so do we its observers. All the lines are now fat and red: they are all taken. There are some rather serious probabilistic problems with the Everett interpretation—it works best if the probabilities of each branch coming out of a node are equal, but in general we would not expect this to be true. Also, there are serious ethics problems, since we don't get to affect the overall lot of humankind—no matter which branch we ourselves take, there will be misery on some equally real branches and happiness on others, and we can do nothing about that.

To solve the probabilistic problems, people introduce the many-minds interpretation of the many-worlds interpretation. Each person has infinitely many minds. When we get to a branch point, each mind indeterministically "chooses" (i.e., is selected to) an outgoing branch according to the probabilities in the physics. Since there are infinitely many of these minds, at least in the case where there are finitely many branches coming out of a node we will expect each outgoing branch to get infinitely many of the minds going along it. So we're still splitting, and we still have the ethics problems since we don't get to affect the overall lot of humankind—or even of ourselves (no matter which branch we go on, infinitely many of our minds will be miserable and infinitely many will be happy).

But now I want to offer a traveling minds interpretation of the indeterministic theory. On the physical side, this interpretation is just like the many-worlds interpretation. It is a dualist interpretation like the many-minds one: we each have a non-physical mind. But there is only one mind per person, as per common sense, and minds never split. Moreover our minds are all stuck together: they always travel together. When we come to a branching point, the physical world splits just as on the many-worlds interpretation. But the minds now collectively travel together on one of the outgoing branches, with the probability of the minds taking a branch being given by the indeterministic theory.

In the diagram, the red lines indicate physical reality. So unlike in the original indeterministic theory, and like in the many worlds interpretation, all the branches are physically real. But the thick red lines and the filled-in nodes, indicate the observed branches, the ones with the minds. (Of course, if God exists, he observes all the branches, but here I am only talking of the embodied observers.) On the many-worlds interpretation, all the relevant branches were not only physically real, but also observed. Presumably, many of the unobserved branches have zombies: they have an underlying physical reality that is very much like the physical reality we observe, but there are no minds.

The traveling minds interpretation solves the probability problems. The minds can travel precisely according to the probabilities given by the physics. Traveling minds as generated in the above way will have exactly the same empirical predictions as the original indeterministic theory. (In particular, one can build traveling minds from a Copenhagen-style consciousness-causes-collapse interpretation of Quantum Mechanics, or a GRW-style interpretation.)

Traveling Minds helps a lot with the ethics problem that many-worlds and many-minds faced. For although physical reality is deterministically set, it is not set which part of physical reality is connected with the minds. We cannot affect what physical reality is like, but we can affect which part of physical reality we collectively experience. And that's all we need. Note that "we" here will include all the conscious animals as well: their minds are traveling as well. In fact, as a Thomist, I would be inclined to more generally make this a "traveling forms" theory. Thus the unselected branches not only have zombies, but they have physical arrangements like those of a tree, but it's not a tree but just an arrangement of fields or particles because it lacks metaphysical form. But in the following I won't assume this enhanced version of the theory.

Now while I don't endorse this theory or interpretation—I don't know if it can be made to fit with hylomorphic metaphysics—I do want to note that it opens an area of logical space that I think a lot of people haven't thought about.

Traveling minds is an epiphenomenalist theory (no mind-to-physics causation) with physical determinism, and is as compatible with the causal closure of the physical as any physicalist theory (it may be that physicalist theories themselves require a First Cause; if so, then so will the traveling minds theory). Nonetheless, it is a theory that allows for fairly robust alternate possibilities freedom. While you cannot affect what physical reality is like, you can affect what part of physical reality we collectively inhabit, and that's almost as good. We have a solution to the mind-to-world causation problem for dualism (not that I think it's an important problem metaphysically speaking).

I expect that I and other philosophers have incautiously said many things about things like epiphenomenalism, determinism and causal closure that the traveling minds theory provides a counterexample to. For instance, while traveling minds is a version of epiphenomenalism, it is largely untouched by the standard objections to epiphenomenalism. For instance, one of the major arguments against epiphenomenalism is that if minds make no causal difference, then I have no reason to think you have a mind, since your mind makes no impact on my observations. But this argument fails because it assumes incorrectly that the only way for your mind to make an impact on my observations is by affecting physical reality. But your mind can also make an impact on my observations by leaving physical reality unchanged, and simply affecting which part of physical reality we are all collectively hooked up to.