I Many worlds and high-amplitude anomaly branches

[durant35]

A question came up to my mind while thinking about probabilities and Born rule in the context of the Everettian approach.

It is often said that anomalies/maverick branches where the experiments go horribly wrong and crazy stuff happens have a negligible amplitude/measure so they really don't matter. It is also said that most of the measure in the Everettian approach gets the Born rule right and that most of the measure will see righ distributions.

But here is where I find a problem. Suppose we do a quantum experiment with odds being stacked like 70% for outcome A and 30% for outcome B, with their correspoding measures. There is certainly a branch where outcome A happens many, many, many times in a row without outcome B at all - and what's weird is that that branch will have a higher measure than any of the branches where Born rule holds.

Is my reasoning right, and how can we say that the repeated, exaggerated occurence of outcomes with a higher probability is a statistical deviation itself - or a maverick branch in the MWI context, despite having a higher amplitude than "normal branches"?

Thanks in advance

 

[stevendaryl]

A question came up to my mind while thinking about probabilities and Born rule in the context of the Everettian approach.

It is often said that anomalies/maverick branches where the experiments go horribly wrong and crazy stuff happens have a negligible amplitude/measure so they really don't matter. It is also said that most of the measure in the Everettian approach gets the Born rule right and that most of the measure will see righ distributions.

But here is where I find a problem. Suppose we do a quantum experiment with odds being stacked like 70% for outcome A and 30% for outcome B, with their correspoding measures. There is certainly a branch where outcome A happens many, many, many times in a row without outcome B at all - and what's weird is that that branch will have a higher measure than any of the branches where Born rule holds.

Is my reasoning right, and how can we say that the repeated, exaggerated occurence of outcomes with a higher probability is a statistical deviation itself - or a maverick branch in the MWI context, despite having a higher amplitude than "normal branches"?

Thanks in advance

If I understand your question correctly, you're asking how we distinguish between:

1. A "normal" world that just happens to be having a statistically unlikely run.
2. A "maverick" world where the probabilities are different from those computed by the Born rule.

I'm pretty sure that there is no distinction at all. Maybe I'm misunderstanding the question.

 

[durant35]

If I understand your question correctly, you're asking how we distinguish between:

1. A "normal" world that just happens to be having a statistically unlikely run.
2. A "maverick" world where the probabilities are different from those computed by the Born rule.

I'm pretty sure that there is no distinction at all. Maybe I'm misunderstanding the question.

I think you are understanding it correctly. So you would say that any statistically unlikely run, despite the possible scenario where 'likelier' outcomes (like in my example) can happen can be considered a maverick branch. What happens with the amplitude? It gets dominated by the worlds where Born rule holds?

 

[PeterDonis]

I'm pretty sure that there is no distinction at all.

I would say something even stronger than that: there aren't even two possibilities ("normal" world with unlikely run, vs. "anomaly" world) to begin with. In each world, a particular distribution of outcomes is observed, and the only data on which to base any conclusions about probabilities is the distribution of outcomes. It makes no sense to say that the probabilities are "really" X but we observed distribution of outcomes Y.

AFAIK, how to obtain the Born rule in the MWI is considered one of the key unsolved problems for that interpretation.

 

[eloheim]

But here is where I find a problem. Suppose we do a quantum experiment with odds being stacked like 70% for outcome A and 30% for outcome B, with their correspoding measures. There is certainly a branch where outcome A happens many, many, many times in a row without outcome B at all - and what's weird is that that branch will have a higher measure than any of the branches where Born rule holds.

So I may be way off on a tangent here, and if I'm completely misinterpreting your question then my apologies.

But taking the example of the 70/30 A/B experiment, just in a regular, classical probability sense. I'm imagining doing 5 iterations here. The chance of getting all 5 A's would be (by my admittedly fallible reasoning) 16.8%.

Furthermore, these given odds would seem to peg the expected number of B's for 5 turns to be "1.5". So if we take, for example, a 'well-behaved' run to be one with 1 or 2 B's out of 5, I get 14 out of the 32 possible sequences to fit this criteria, and the chance of getting one of these 'typical' results is 66%.

I'm not sure anything seems off-kilter about such a distribution of outcomes, and I'm not sure how a quantum or MWI context for this experiment is supposed to change the expected, or actual, results. Maybe if nothing else this can help (hopefully) clarify the question a little?