Is the MWI symmetric in time?

Question

Reading the blog of Sean Carroll (I recognize he isn't the only voice) has made me more sympathetic to the notion of many worlds, but reading Susskind (also not the only voice) has made me think that time-reversibility is important.

I understand that collapse theories aren't reversible, but I've been wondering about the MWI. Does decoherence of worlds occur "backwards"?

I'm trying to imagine this, and I'm coming up with weird mental images wherein several different quantum states cohere into the same one, but this doesn't really make sense and there doesn't seem to be any reason for it to occur. Yet if it doesn't occur, (it seems to me) that MWI is not time-symmetric as (it seems to me) it should be.

Have a lot of other people thought about this before? What do they have to say?

EDIT: Is this, and other reversibility concerns in QM, related to our other familiar asymmetry -- entropy? Or is that crazy?

Answer 1

Yes, the many-worlds interpretation is supposed to be time symmetric.

Consider this toy example with a particle than can be in either of the states $\left|1\right\rangle$ or $\left|2\right\rangle$. Additionally, we denote the no particle state as $\left|0\right\rangle$.

The particle gets emitted by our source $S$ that can be in its ground state $\left|S_0\right\rangle$, in a state $\left|S_1\right\rangle$ ready to emit a particle in state $\left|1\right\rangle$ or in a state $\left|S_2\right\rangle$ ready to emit a particle in state $\left|2\right\rangle$.

Eventually, the particle gets absorbed by a detector $D$ that can be in its ground state $\left|D_0\right\rangle$, in a state $\left|D_1\right\rangle$ after absorption of a particle in state $\left|1\right\rangle$ or in a state $\left|D_2\right\rangle$ after absorption of a particle in state $\left|2\right\rangle$.

Let the time evolution of the states of interest be given by the discrete steps $$ \left|S_1\right\rangle\otimes\left|0\right\rangle\otimes\left|D_0\right\rangle \longrightarrow \left|S_0\right\rangle\otimes\left|1\right\rangle\otimes\left|D_0\right\rangle \longrightarrow \left|S_0\right\rangle\otimes\left|0\right\rangle\otimes\left|D_1\right\rangle $$ and $$ \left|S_2\right\rangle\otimes\left|0\right\rangle\otimes\left|D_0\right\rangle \longrightarrow \left|S_0\right\rangle\otimes\left|2\right\rangle\otimes\left|D_0\right\rangle \longrightarrow \left|S_0\right\rangle\otimes\left|0\right\rangle\otimes\left|D_2\right\rangle $$ Note that this is not how unitary time evolution works in quantum mechanics, and I'll get back to that at the end.

So, what happens if we start out in a state $\left|S_1\right\rangle + \left|S_2\right\rangle$?¹ $$ \left(\left|S_1\right\rangle+\left|S_2\right\rangle\right)\otimes\left|0\right\rangle\otimes\left|D_0\right\rangle \\\longrightarrow \left|S_0\right\rangle\otimes\left(\left|1\right\rangle+\left|2\right\rangle\right)\otimes\left|D_0\right\rangle \\\longrightarrow \left|S_0\right\rangle\otimes\left|0\right\rangle\otimes\left(\left|D_1\right\rangle+\left|D_2\right\rangle\right) $$

This is symmetric in source and detector and time symmetry is manifest. However, in our subjective experience, we only ever see detectors in a state $\left|D_1\right\rangle$ or $\left|D_2\right\rangle$ - we have no concept of a detector in a superposition of states $\left|D_1\right\rangle+\left|D_2\right\rangle$, its pointer indicating two values simultaneously.

Some people argue (or at the very least, have done so historically) that the state must have collapsed through one of the (non-unitary) physical processes $$ \left(\left|1\right\rangle+\left|2\right\rangle\right)\otimes\left|D_0\right\rangle \longrightarrow \left|0\right\rangle\otimes\left|D_1\right\rangle $$ or $$ \left(\left|1\right\rangle+\left|2\right\rangle\right)\otimes\left|D_0\right\rangle \longrightarrow \left|0\right\rangle\otimes\left|D_2\right\rangle $$

Others claim that the 'collapse' is merely apparent, a Bayesian update of our information about the world, and the quest for ways to achieve objective collapse is indicative of a fundamental misunderstanding of the nature of reality as revealed by modern physics.

Proponents of the MWI argue that the most sensible resolution is to consider the observer (including their subjective state of mind) as intrinsically liked to $D$, ie we can consider the detector with its macroscopically distinct pointer states as a proxy for the relevant parts of the environment. The asymmetry arises because the observer was blind to the microscopic state of the source, but sensitive to the macroscopic state of the detector, and a time reversal would include a process of memory erasure.

It should be noted that the toy model I presented is cheating, which is why I had deleted my answer:

Emission and absorption are not just given by unitary time evolution like $$ U(t_i, t_f) \left( \left|S_1\right\rangle\otimes\left|0\right\rangle \right) = \left|S_0\right\rangle\otimes\left|1\right\rangle $$

Instead, we're dealing with stochastic processes (the source could in principle stay in its excited state indefinitely), and there's already a 'collapse' implied by the discrete time evolution of the toy model that was glossed over.

However, I suspect the line of reasoning I presented here would make sense in a consistent histories approach to the many-worlds interpretation.

For now, I'll leave the answer as-is - I'm not sure I can come up with a better one without a few sessions of late-night (or beer-fueled) philosophizing...

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¹ we ignore issues of phase and normalization

Answer 2

The MWI interprets quantum physics roughly as follows:

1. Everything everywhere and at all times evolves via Schrodinger's equation.

2. What constitutes physical reality, and is described by quantum physics, is not so much a set of things as a set of correlations.

An example of item 2 here is given by entangled states. When a particle decay results in the death of a cat, for example, then the final situation is not one in which cat is alive or dead, but rather one in which there is a correlation between the state of the particle and the state of the cat, says MWI. This seems plausible at first, but in order to make it consistent one has to also solve the preferred basis problem and make sense of the concept of probability.

I feel that since one has to solve the preferred basis problem anyway, one may as well say there is just one branch as say there are vast numbers of branches and all but one of them are irrelevant to our present and future experience. The latter claim does not sound like good physics to me. This makes MWI, for me, not a strong contender for a correct account of physics. But it is not easy to argue convincingly for either view in our present state of knowledge.

The main thing in answer to your question is that in view of item (1) above, the MWI interpretation is time-reversible. (I can't resist adding that I personally don't think the physical universe is time-reversible, so to me this is a major weakness of MWI, but I don't have a sufficiently persuasive model to resolve this debate.)

If one takes some physical process and runs it backwards, then we get weird things such as broken eggs coming back together and leaping off the floor. But any view of physics should conclude that time running backwards is weird, simply because it genuinely would be weird as soon as processes of sufficient complexity are involved. So it is ok that the MWI suggests very odd things would happen if we applied a time-reversal to the dynamics of the universe. The MWI interpretation would account for the odd observations in the same way that classical physics would account for reducing entropy in a time-reversed dynamics: one would say there were many very special correlations in the conditions from which the time-reversed dynamics set out (the conditions which were final conditions really, but which we are turning into initial conditions in this thought-experiment).