[nessus42]

> It should be noted, however, that the Everett interpretation does have one issue: it's not clear why probabilities should work the way they do.

Yes, back when I studied this topic seriously, this was an issue. E.g., if you toss a quantum coin that has a 1/3 chance of coming up heads and 2/3 chance of coming up tails, this seems to result in only two "worlds". And if there are two worlds, why are the observed probabilities then not .5/.5 rather than .3333/.6667?

I didn't mention this in my OP because (1) that would have been something of a deep-dive for a summary post, and (2) there were ideas being floated about to solve this problem back when I was studying this, but I don't know how these ideas ultimately panned out.

I'm surely curious as to what the current best ideas are about this issue.

[int_19h]

Why can't it result in three worlds, two of which are indistinguishable?

[nessus42]

Well, maybe it does. Only there really aren't separate worlds in the Everett Interpretation. It only seems that way to our superpositioned brains.

At some point this debate becomes a bit too confusing for me. All I can report is that the experts fretted over this.

[jostylr]

In a perfectly mathematically coherent version of Everett: https://arxiv.org/abs/0903.2211, the idea is to integrate out the wave function to get a mass density on 3 space. This mass density on 3-space is a mess at any particular moment, but one can witness its evolution over time to pick out particular correlated histories. There is no particular splitting into separate worlds. And, indeed, the whole picture of discrete spin measurements is misleading. It is always spatial measurement stuff ultimately going on and so plenty of smearing.

The relevant probabilities are not derived by number of "worlds". Pick some particular moment and correlated history, look backwards (what is recorded in the current "configuration") at experiments, and one should see the proper statistics appearing in the "vast majority" of experiences.

However, there will be plenty of experimenters who see wrong statistics. Everett predicts this with certainty. There is a "world", according to this, that just split from the moment I am writing this, in which all future experiments have spin up coming up 100% of the time from that moment on. Over time, we all end up correlated with this as the experimenters report their fantastical findings.

If they truly believe in Everett's theory, they would accept that they just happen to be in the branch where this happens. In Bohmian mechanics, they would say something else is going on. The odds of seeing something like that in Bohmian mechanics are so vastly, incomprehensibly small, that it is more likely to see cracked eggs reassembling themselves from random thermal motions. But in Everett, it happens with certainty to some universe.

This is the difference. Bohmian mechanics can be readily falsified based on statistical outcomes of experiments. Perhaps not with 100% certainty, but certainly with 100% practical certainty. Everett can never be falsified based on statistics. It could be falsified if something that was supposed to happen with a literal 100% certainty failed to happen, but with anything statistical, it simply can't because the theory says it does happen.

One could modify the theory to cut out the "outlier" worlds. This is, in some sense, what GRW with a mass density ontology does.

[nessus42]

I guess I am unclear on one of your points: Let's say we toss a fair quantum coin many, many times. In the Everett Interpretation, yes, there is a "world" in which that coin has always come up heads. But our chance of finding ourselves in that world is vanishingly small.

In the Bohm Interpretation, that coin could always come up heads too, but again with a vanishingly small probability.

So they seem equivalent experimentally to me. (And to the experts who have written entire books on the subject.)

Max Tegmark came up with a way to experimentally determine if the Everett Interpretation is correct. (I believe it was Tegmark who came up with this.) It has a high cost for the experimenter, though!

What you do, is rig a gun to a fair quantum coin, so when you pull the trigger, the gun fires 50% of the time. Now shoot yourself in the head with it many, many times. If you end up surviving many rounds of this, you can be pretty darn certain that the Everett Interpretation is correct.

Never mind the billions of other versions of yourself that you murdered to discover the truth!

[tlb]

For this to work, the gun has to terminate your consciousness before the state of the coin can become entangled with the world. Objects as large as guns cannot (currently) be kept in an unentangled state for the milliseconds required for a bullet to do its work. If it were possible, the entire gun-bullet-head system would need to be cooled to microkelvin temperatures, at which guns or consciousness don't work.

[nessus42]

I don't understand your comment. In the Everett Interpretation, the wave function never collapses. Everything is always entangled. "Decoherence", however, causes the perception that the wave function collapses, and consequently this interpretation is often called the "Many World Interpretation", because the theory results in a different "world" (for all intents and purposes) for every possible outcome.

Hence, in the Everett Interpretation, if you shoot yourself using such a quantum gun, every time you pull the trigger, there will end up being one "world" in which the gun didn't go off and one world in which you put a bullet in your head.