Many worlds and probability amplitude. What does it represent?

[JDude13]

Is there any statement which perfectly captures what the probability amplitude, in the many worlds interpretation, represents?
To say that there is an x chance of y happening is non-sensical because, according to the interpretation, y WILL happen in at least one universe.
To say that there is an x chance that I, as an observer, will end up in a universe in which y happens is non-sensical because the interpretation says that “I” will split into several “I”s, each as real and as bound to my history as I am.
So what does probability represent in the many worlds interpretation?

 

[Fredrik]

It represents the approximate relative frequency with which an experimenter must observe a particular result in a long series of measurements on systems that have been prepared in almost exactly the same way, to be allowed (by the rules of science) to consider the theory of quantum mechanics to not have been falsified.

That kind of sucks for the experimenters in branches where the results keep contradicting the predictions, but that's almost certainly not our problem.

 

[JDude13]

It represents the approximate relative frequency with which an experimenter must observe a particular result in a long series of measurements on systems that have been prepared in almost exactly the same way, to be allowed (by the rules of science) to consider the theory of quantum mechanics to not have been falsified.

But the "experimenter", before an experiment, experiences every outcome of the experiment.
So the probability amplitude only describes the system after experimentation has taken place? What does the amplitude mean to the experimenter beforehand?

To say it represents the frequency of an observer observing a specific outcome is non-sensical because, according to the many worlds theory, the observer observes all of the possible outcomes.

After you have taken a number of measurements you can say that it represents the frequency which you observed the outcome but beforehand all descriptions of the significance of the probability amplitude are non-sensical... according to the many worlds theory.

 

[Bill_K]

Ok, I'll try answering this, making a prediction beforehand with probability one that you'll declare it to be non-sensical. It's true, in the many worlds interpretation there will be a universe with every possible outcome. And the observer will find himself in one out of this set of universes, with equal probability. But the universes occur with a frequency distribution governed by the probability amplitude that appears in the wavefunction.

 

[Fyzix]

Bill K, so what happens in a situation where it's 99,9% likely that outcome A will occur and 00,1% that B will occur?
Surely if MWI was correct the universe would still split into 2 universes... If we repeat this a thousand times, why would you always get the same observed result, namely 999 vs 1 ?

 

[Fredrik]

But the "experimenter", before an experiment, experiences every outcome of the experiment.

I wouldn't say that. An experience is a single sequence of well-defined memory states, so a physical system that appears in different branches as persons with different experiences, doesn't have experiences of its own.

So the probability amplitude only describes the system after experimentation has taken place? What does the amplitude mean to the experimenter beforehand?

The same thing as after the fact. It's an instruction that tells him how to test if the theory's predictions agree with experiments.

To say it represents the frequency of an observer observing a specific outcome is non-sensical because, according to the many worlds theory, the observer observes all of the possible outcomes.

Observations are experiences, and experiences are had in the branches, not in the "omnium". (That's what Penrose calls the physical system that can be described as a collection of "worlds").

...according to the many worlds theory.

There's no such thing as many-worlds theory. It's at best an interpretation, and it doesn't even have a definition that people agree on. So it's hard to use "it" to prove anything, because it's not clear what "it" is. This is also a problem for me when I try to explain these things. What I mean by "the MWI" isn't going to be the same thing as what the person I'm talking to means by "the MWI".

 

[Fredrik]

Bill K, so what happens in a situation where it's 99,9% likely that outcome A will occur and 00,1% that B will occur?
Surely if MWI was correct the universe would still split into 2 universes... If we repeat this a thousand times, why would you always get the same observed result, namely 999 vs 1 ?

I don't think there's anything in QM that justifies the popular picture of how the universe "splits in two". The probabilities certainly don't have anything to do with branch counting.

 

[Fyzix]

yes, but even if you are talking about the splitting version of MWI (DeWitt, Deutsch, Everett) or the decoherence approach, you'd still get this result, meaning the current MWI's can't be true.

Unless you are going to claim that there exist MORE branches with outcome A instead of B "just because" we need it to fit our model, aka religion.

 

[Fredrik]

Unless you are going to claim that there exist MORE branches with outcome A instead of B "just because" we need it to fit our model, aka religion.

What I'm claiming is that the probabilities don't have anything to do with the numbers of branches of each kind.

 

[Fyzix]

So you are proposing some sort of completley new MWI?

 

[Fredrik]

I don't think of it as something new. Essentially it's just QM plus the idea that what QM describes is in fact reality. (The alternative would be that it's a "fictional" physical system that just happens to be a very useful tool when we want to predict probabilities of possible results of experiments).

 

[Fyzix]

So you currently believe in this MWI?

but how would it explain the situation I used earlier?
Why would you still observe 1 vs 999 instead of always 50/50 in such a scenario with only 2 alternative outcomse?

 

[Fredrik]

So you currently believe in this MWI?

No, I think I prefer the option that QM is just a set of rules that tells us how to calculate probabilities of possible results of experiments, not a description of what actually happens. But I believe that the only way to interpret QM as a description of what actually happens is in terms of many worlds.

but how would it explain the situation I used earlier?
Why would you still observe 1 vs 999 instead of always 50/50 in such a scenario with only 2 alternative outcomse?

I don't have an answer completely worked out. I believe that the idea that one world splits in two is false, and that the number of worlds with a given result isn't well-defined (or at least not finite).