The discussion revolves around the Many Worlds Interpretation (MWI) of quantum mechanics, particularly focusing on how it handles scenarios with unequal probabilities, such as the Schrödinger's cat thought experiment. Participants explore the implications of making observations at different times and the resulting universe splits, as well as the mathematical underpinnings of these probabilities.
Participants express differing views on the interpretation of probabilities in MWI, with no consensus reached on how to handle unequal probabilities or the implications of continuous outcomes. The discussion remains unresolved regarding the nature of "worlds" and the mathematical framework supporting these interpretations.
Some participants highlight the limitations of the discussion, including the dependence on definitions of "world" and the unresolved mathematical steps in relating probabilities to outcomes in MWI.
Huh? What's ridiculous about it?kered rettop said:A single particle whose wave function contains the reflected photon and the transmitted photon in equal proportions???? Quite ridiculous!
I don't know if there is a unique answer to this among MWI proponents. Some view the relative weights of the branches as a "measure" of the worlds, others don't.Sherwood Botsford said:How does the many worlds interpretation deal with events where there are two possible outcomes with unequal probability. Or worse, when the probabiliy ratio is an irrational number?
No, it isn't. You don't need to have just two states. All you need is two orthogonal subspaces of the cat's Hilbert space. Each subspace could contain zillions of states, as long as all of the states in the "alive" subspace are orthogonal to all of the states in the "dead" subspace.PeroK said:There is, in any case, no uniquely identifiable state that corresponds to a dead cat. Nor to a live cat. To suppose there are only two states seems to invoke the "magic split" mentioned above.
I was being ironic, for goodness sake!PeterDonis said:Huh? What's ridiculous about it?
You can sum the timed dead-cat worlds together to create a single timeless one so I'm not sure what the point is that you think I ought to address.PeterDonis said:You are missing the point. The point is that this operator you speak of is a different operator if we apply it at different times. In the Heisenberg picture this is obvious. And if you are trying to count "worlds", you have to take that into account; you can't just say "well, the cat is either dead or alive", because different times of death for the cat are macroscopically distinguishable, so they count as different worlds.
You are not addressing this point at all.
Please describe, in QM terms, your proposed measurement to determine whether a cat is alive or dead?jbergman said:I have to agree with @kered rettop 's analysis of the situation.
The article at https://plato.stanford.edu/entries/qm-manyworlds/ is a brilliant primer for anyone wanting to understand the MWI interpretation of QM. In particular, the section on the preferred basis problem talks about the partitioning of hilbert space into worlds in order to represent a quantum state.
I just wanted to say that understanding MWI in the Heisenberg picture is a nontrivial exercise. I've been meaning to get around to reading Kuyper and Deutsch's paper on it, https://arxiv.org/abs/2008.02328PeterDonis said:You are missing the point. The point is that this operator you speak of is a different operator if we apply it at different times. In the Heisenberg picture this is obvious. And if you are trying to count "worlds", you have to take that into account; you can't just say "well, the cat is either dead or alive", because different times of death for the cat are macroscopically distinguishable, so they count as different worlds.
You are not addressing this point at all.
That was not at all clear from your post. I would strongly suggest either avoiding irony or making it much clearer when you are doing it.kered rettop said:I was being ironic, for goodness sake!
No, you can't. You can't "sum" worlds; they are macroscopically distinguishable and they can't interfere with each other.kered rettop said:You can sum the timed dead-cat worlds together to create a single timeless one
I will have to search the literature to answer this. I think this is an important question to get the right answer to.PeroK said:Please describe, in QM terms, your proposed measurement to determine whether a cat is alive or dead?
Please describe how this act of measurement results in the cat being alive or dead. I.e. the appropriate eigenstate of your observable.
What if a test on a cat involved a biopsy - taking a small sample of the cat and processing it in a lab? Does that meet the criteria of a measurement in QM. Suppose you get the result back a day later. When was the cat measured - when the biopsy was taken, when the lab processed the sample or when you got the results?
PS if you take a biopsy, is it still the same cat that's left alive or dead?
This needs discussing properly.PeterDonis said:No, you can't. You can't "sum" worlds; they are macroscopically distinguishable and they can't interfere with each other.
If you say so. I may start another thread to get the point clarified, if that's OK.PeterDonis said:This is not your thread and your posts are rapidly approaching the point where they are doing more harm than good to the OP's understanding. Please take heed.
If you can give a reference as a basis for your claim that "worlds" can be added, sure.kered rettop said:This needs discussing properly.
Only if you have a valid reference.kered rettop said:I may start another thread to get the point clarified, if that's OK.