# Is the MWI symmetric in time?

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.

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

• MWI is perfectly time-symmetric, just like every other formalism of quantum mechanics. The irreversibility is a second-law-type thing; it's very unlikely for two distinct 'worlds' to recohere for the same reason you won't see an egg uncook itself. – knzhou Jun 27 '16 at 3:43
• Both in thermodynamics/statistical mechanics and relativity. Think about the consequences of the speed of light for a local observer: the local observer can't catch a light wave (or, for that matter, any other massless field). This automatically creates a fundamentally irreversible loss of state information for any local definition of physics. MWI comes at this with "god's eye" by proposing a completely irrelevant (since unmeasurable) global wave function. It then analyzes this without any consequences for what would really happen if god measured this entity: a quantum zeno. – CuriousOne Jun 27 '16 at 3:55
• Thats a really interesting thought. Can you elaborate on the meaning of "quantum zeno"? – Devin Patterson Jun 27 '16 at 4:00
• en.wikipedia.org/wiki/Quantum_Zeno_effect. It's basically the consequence of repetitive measurements. Every measurement of a system puts it into a new initial state. If the time evolution of the state is slow compared to the rate of the measurement, the system will stay near the initial state forced on it by the measurement. When the rate increases towards infinity (i.e. the measurement becomes continuous), then the state will essentially be frozen. – CuriousOne Jun 27 '16 at 4:04
• The measurements in QM are self-evidently irreversible motls.blogspot.com/2016/05/… as logical steps and whatever is claimed to replace them must be irreversible as well. What the MWI advocates say is that they "want" some "theory" or "interpretation" that is completely reversible but it's obvious that nothing of the sort may exist. No "MWI theory" exists mathematically - it's just a collection of propaganda and wishful thinking. Irreversibility is a nice window to see that all realist replacements for QM must be wrong. – Luboš Motl Jun 27 '16 at 5:19

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...

1 we ignore issues of phase and normalization

• Hi, thanks for the answer. So, in reverse, the detector emits the superposed state |1⟩+|2⟩ which decoheres into sources S1 and S2? Doesn't this imply that I came, with certainty, from either the S1 branch or the S2 branch (rather than a superposition thereof)? Doesn't this replace the branching quantum universe with a bunch of non-intersecting classical ones? I hope I haven't gotten too confused. – Devin Patterson Jun 27 '16 at 20:40