MWI and macroscopic probability

[durant35]

I have a long-standing question regarding the fundamental nature of macroscopic QM in combination with MWI.

First, generally speaking, what does the Born rule say about macroscopic objects and experiments (without superfluids and other traditional examples of quantum behavior on the large scale)? It seems that events around us evolve deterministically, that we can predict the future with much accuracy. In reality, if every variable was known would the Born rule give a 99.9999 probability for a specific outcome that would be considered a normal sequence in classical mechanics?

Which leads me to MWI. If every possibility occurs in that interpretation, does that mean that at each macroscopic branching point there is a 99.999% probability outcome and every other branch is a low probability/amplitude one which can be regarded as a fluctuation from the classical mechanics sequence? And that's why we never observe those low probability events but only high probability branches and outcomes.

Thanks in advance.

 

[secur]

It's a good question which gets at one of the two big problems with MWI.

First, the Born rule simply gives the probability of each possible outcome, in regular QM. As you say in ordinary macro-world situation the probability of the classical path is very close to 1. But the key issue has little to do with Born rule, rather it's how does that particular path's probability get so large. Let's ignore that. Another wrinkle: when the macro event is caused by a quantum event there can be multiple macro alternatives with large probabilities. For instance when you measure particle's spin the apparatus will say either +1 or -1 (e.g. via a pointer on a dial) and each (typically) has probability 1/2. Ignore that also. You're thinking of a normal macro event, like throwing a ball. The actual trajectory followed is overwhelmingly likely. Nevertheless, according to QM, there's a very tiny chance that any other conceivable trajectory might occur. The ball might land on the moon, for instance.

Which leads me to MWI. As you say, MWI must also give the correct probabilities, but it can't use the Born rule, since all possible paths are taken with probability 1. The only reasonable mechanism for encoding the correct probabilities is the number of paths for each alternative. The very likely path must have 99.99999.. times as many instances as the unlikely ones. But what does that mean? The total number of paths is a high order of infinity. 99% of infinity is the same as .01%: they're both infinity. So we must define a probability measure on the enormous space of alternatives which allows the "density" of paths to be compared. Such that the likely path is much more "dense" in the space. It turns out that's not easy.

Consider one of the unlikely paths: the ball lands on the moon. According to MWI that really does happen, in some universe. Then that universe, of course, continues to evolve along infinitely many paths. Now, MWI conserves information, which is equivalent to time-reversibility. What this means, that "one" path - ball on moon - actually must itself consist of a huge infinity of "sub-paths", one for every way the universe evolves after this unlikely event. No matter how unlikely it must contain as many alternative "sub-paths" as the likely one!

Given these difficulties it may be impossible for MWI researchers to come up with a satisfactory answer to your question. They haven't done so yet.

 

[durant35]

It's a good question which gets at one of the two big problems with MWI.

First, the Born rule simply gives the probability of each possible outcome, in regular QM. As you say in ordinary macro-world situation the probability of the classical path is very close to 1. But the key issue has little to do with Born rule, rather it's how does that particular path's probability get so large. Let's ignore that. Another wrinkle: when the macro event is caused by a quantum event there can be multiple macro alternatives with large probabilities. For instance when you measure particle's spin the apparatus will say either +1 or -1 (e.g. via a pointer on a dial) and each (typically) has probability 1/2. Ignore that also. You're thinking of a normal macro event, like throwing a ball. The actual trajectory followed is overwhelmingly likely. Nevertheless, according to QM, there's a very tiny chance that any other conceivable trajectory might occur. The ball might land on the moon, for instance.

Which leads me to MWI. As you say, MWI must also give the correct probabilities, but it can't use the Born rule, since all possible paths are taken with probability 1. The only reasonable mechanism for encoding the correct probabilities is the number of paths for each alternative. The very likely path must have 99.99999.. times as many instances as the unlikely ones. But what does that mean? The total number of paths is a high order of infinity. 99% of infinity is the same as .01%: they're both infinity. So we must define a probability measure on the enormous space of alternatives which allows the "density" of paths to be compared. Such that the likely path is much more "dense" in the space. It turns out that's not easy.

Consider one of the unlikely paths: the ball lands on the moon. According to MWI that really does happen, in some universe. Then that universe, of course, continues to evolve along infinitely many paths. Now, MWI conserves information, which is equivalent to time-reversibility. What this means, that "one" path - ball on moon - actually must itself consist of a huge infinity of "sub-paths", one for every way the universe evolves after this unlikely event. No matter how unlikely it must contain as many alternative "sub-paths" as the likely one!

Given these difficulties it may be impossible for MWI researchers to come up with a satisfactory answer to your question. They haven't done so yet.

That is an excellent answer and it went along the lines of explanation that I was expecting. Thanks for you patience in writing it down and your effort.