Might there have been less randomness earlier?

In my previous post, I noted that a branching view of possibility, when continued into an infinite past, leads to the counterintuitive consequence that there is less and less randomness the further back we go.

In this post I want to note that this counterintuitive consequence may in fact be right even with a finite past, given a certain interpretation of quantum mechanics.

Start with the naive consciousness causes collapse (ccc) interpretation of quantum mechanics. On naive ccc, at each moment of time, the laws of nature prevent the world to evolve into a superposition of states that differ with respect to consciousness. Thus, there cannot be a superposition between one’s feeling hot and one’s not feeling hot, or between a cat being aware of its surroundings and a cat being asleep or dead. This is assured by constant collapse with respect to a global consciousness operator C.

Unfortunately, as it stands this is untenable, because it corresponds to a setup where there is constant observation of C, and constant observation of an observable precludes change with respect to that observable by the quantum Zeno effect. In other words, if we had naive ccc, then conscious states would never change, which is empirically absurd.

Here is one way to fix this problem. Suppose that there are special moments in time, which I’ll poetically call “cosmic heartbeats”. Collapse with respect to C only occurs at cosmic heartbeats. If the cosmic “heart rate” is not very fast (i.e., the spacing between the heartbeats is big enough), then the quantum Zeno effect will be negligible, and we needn’t worry about it. And we hypothesize that consciousness only occurs at cosmic heartbeats.

But now let’s consider the history of our universe. In the early universe, the only way to get a non-empty consciousness state is by some ridiculously unlikely feat of quantum tunnelling generating a Boltzmann brain or the like. Thus the only randomness we will have in the early universe will be that induced by pruning away the components of the global wavefunction corresponding to such ridiculously unlikely feats. And that is only a tiny bit of randomness. But as things evolve, we get components of the wave function with significant weight corresponding to the evolution of various conscious critters. Now the periodic collapse will be “deciding” between states of comparable likelihood (e.g., life on earth versus life on some other planet formed from some of the same materials orbiting the sun) rather than just pruning away extremely unlikely options.

One would need to know a lot more physics (and perhaps neuroscience?) to figure out what the cosmic heartrate needs to be to make the theory work. An upper bound is given by the quantum Zeno effect: if the cosmic heartrate is too fast, then we could predict a slowdown of consciousness. A lower bound is given by introspection: the cosmic heartrate had better be at least as fast as the speed at which our conscious states are observed to change.

I wonder if a similar decrease of randomness in the past wouldn’t be predicted by GRW collapse theories.

Superpositions of conscious states

Consider this thesis:

1. Reality is never in a superposition of two states that differ with respect to what, if anything, observers are conscious of.

This is one of the motivators for collapse interpretations of quantum mechanics. Now, suppose that S is an observable that describes some facet of conscious experience. Then according to (1), reality is always in some eigenstate of S.

Suppose that at the beginning t₀ of some interval I of times, reality is in eigenstate ψ₀. Now, suppose that collapse does not occur during I. By continuity considerations, then, over I reality cannot evolve to a state orthogonal to ψ₀ without passing through a state that is a superposition of ψ₀ and something else. In other words, over a collapse-free interval of time, the conscious experience that is described by S cannot change if (1) is true.

What if collapse happens? That doesn’t seem to help. There are two plausible options. Either collapses are temporally discrete or temporally dense. If they are temporally dense, then by the quantum Zeno effect with probability one we have no change with respect to S. If they are temporally discrete, then suppose that t₁ is the first time after t₀ at which collapse causes the system to enter a state ψ₁ orthogonal to ψ₀. But for collapse to be able to do that, the state would have had to have assigned some weight to ψ₁ prior to the collapse, while yet assigning some weight to ψ₀, and that would violate (1).

(There might also be some messy story where there are some temporally dense and some temporally isolated collapse. I haven’t figured out exactly what to say about that, other than that it is in danger of being ad hoc.)

So, whether collapse happens or not, it seems that (1) implies that there is no change with respect to conscious experience. But clearly the universe changes with respect to conscious experience. So, it seems we need to reject (1). And this rejection seems to force us into some kind of weird many-worlds interpretation on which we have superpositions of incompatible experiences.

There are, however, at least two places where this argument can be attacked.

First, the thesis that conscious experience is described by observables understood (implicitly) as Hermitian operators can be questioned. Instead, one might think that conscious states correspond to subsets of the Hilbert space, subsets that may not even be linear subspaces.

Second, one might say that (1) is false, but nothing weird happens. We get weirdness from the denial of (1) if we think that a superposition of, say, seeing a square and seeing a circle is some weird state that has a seeing-a-square aspect and a seeing-a-circle aspect (this is weird in different ways depending on whether you take a multiverse interpretation). But we need not think that. We need not think that if a quantum state ψ₁ corresponds to an experience E₁ and a state ψ₂ corresponds to an experience E₂, then ψ = a₁ψ₁ + a₂ψ₂ corresponds to some weird mix of E₁ and E₂. Perhaps the correspondence between physical and mental states in this case goes like this:

1. when |a₁| ≫ |a₂|, the state ψ still gives rise to E₁

2. when |a₁| ≪ |a₂|, the state ψ gives rise to E₂

3. when a₁ and a₂ are similar in magnitude, the state ψ gives rise to no conscious experience at all (or gives rise to some other experience, perhaps one related to E₁ and E₂, or perhaps one that is entirely unrelated).

After all, we know very little about which conscious states are correlated with which physical states. So, it could be that there is always a definite conscious state in the universe. I suppose, though, that this approach also ends up denying that we should think of conscious states as corresponding in the most natural way to the eigenvectors of a Hermitian operator.

Collapse and the continuity of consciousness

One version of the quantum Zeno effect is that if you collapse a system’s wavefunction with respect to a measurement often enough, the measurement is not going to change.

Thus, if observation causes collapse, and you look at a pot of water on the stove often enough, it won’t boil. In particular, if you are continuously (or just at a dense set of times) observing the pot of water, then it won’t boil.

But of course watched pots do boil. Hence:

• If observation causes collapse, consciousness is not temporally continuous (or temporally dense).

And the conclusion is what we would expect if causal finitism were true. :-)