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Wikipedia says > While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circ

Wikipedia says > While it has been claimed that Born's law can be derived from the many-worlds interpretation, the existing proofs have been criticized as circular. So it seems you aren't alone in feeling this way. Edit: Forgot the link - https://en.wikipedia.org/wiki/Born_rule https://en.wikipedia.org/wiki/Born_rule

n4r9 7y ago
Interesting. Following through the citations, this statement seems to be based on two quite old articles which criticise a different Born rule formulation based on frequency analysis: https://link.springer.com/article/10.1007%2FBF02058273 https://link.springer.com/article/10.1007%2FBF02058273 https://arxiv.org/pdf/quant-ph/0409144.pdf https://arxiv.org/pdf/quant-ph/0409144.pdf The latter article is more recent at 2005 but as far as I can tell Carroll's self-locating uncertainty ideas weren't introduced until around 2014.
- lisper 7y ago
  Here's a blog post I wrote about this recently: http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html http://blog.rongarret.info/2019/07/the-trouble-with-many-wor... The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also introduces an "invisible pink unicorn", i.e. a concept that, according to the theory, has physical significance but cannot be measured. In the case of MWI that concept is branch weights. [UPDATE] The critique I wrote is based on Wallace (https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718). Carroll's argument appears to be somewhat different. I'm just now working my way through his paper (https://arxiv.org/abs/1405.7577 https://arxiv.org/abs/1405.7577) but I'd be very surprised if it did not also have some untenable assumption hidden in there somewhere.
  - n4r9 7y ago
    Adrian Kent has a lengthy and detailed overview of MWIs pre-2009 which may interest you [0]. He discusses Wallace's formulation, contrasts it with other formulations and touches on branching indifference. He also has a more recent (and much more brief) article which refers to the Self-locating Uncertainty arguments [1]. I have previously come across Deutsch's formulation in terms of information flow [2], along with what seemed like a very strong criticism from Wallace and Christopher Timpson [3] that his model was not gauge-invariant. [0] https://arxiv.org/pdf/0905.0624.pdf https://arxiv.org/pdf/0905.0624.pdf [1] https://arxiv.org/abs/1408.1944 https://arxiv.org/abs/1408.1944 [2] https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf [3] http://users.ox.ac.uk/~bras2317/dhshort2.pdf http://users.ox.ac.uk/~bras2317/dhshort2.pdf
    - lisper 7y ago
      Thanks for the pointers. (This is turning into quite the little rabbit hole.)
  - Strilanc 7y ago
    What do you think of the simplified argument here: https://algassert.com/post/1902 https://algassert.com/post/1902 ? Basically: ground the definition of probability into a reversible classical circuit then use that circuit's quantum behavior to generalize the definition to quantum (while assuming as few things as possible). In this case the assumptions are "limiting to amplitude 1 must mean limiting to probability 1" and no signalling.
    - lisper 7y ago
      Thanks for bringing that to my attention. My initial reaction is that the argument appears sufficiently cogent to merit respectful consideration. I predict that if someone were to dig into it, they'd find a question-begging assumption hidden somewhere. (The alternative is that this is a major breakthrough in physics, and my Bayesian prior on that is low.) But where that assumption is hiding is not immediately obvious to me. Looking for it seems like a worthwhile exercise.
      - Strilanc 7y ago
        I don't think the argument is novel, it's just a cut down counting/frequency argument. So any objections to those would presumably port over.
        lisper 7y ago
        I dunno, I think you might be selling it short. This argument seems to be based on the mathematical continuity of probabilities, which is not something I can recall ever seeing before.

n4r9 7y ago

Interesting. Following through the citations, this statement seems to be based on two quite old articles which criticise a different Born rule formulation based on frequency analysis: https://link.springer.com/article/10.1007%2FBF02058273 https://link.springer.com/article/10.1007%2FBF02058273 https://arxiv.org/pdf/quant-ph/0409144.pdf https://arxiv.org/pdf/quant-ph/0409144.pdf The latter article is more recent at 2005 but as far as I can tell Carroll's self-locating uncertainty ideas weren't introduced until around 2014.

lisper 7y ago
Here's a blog post I wrote about this recently: http://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html http://blog.rongarret.info/2019/07/the-trouble-with-many-wor... The TL;DR is that the critics are correct. Deriving the Born rule begs the question because it makes an unjustified assumption (branching indifference) and also introduces an "invisible pink unicorn", i.e. a concept that, according to the theory, has physical significance but cannot be measured. In the case of MWI that concept is branch weights. [UPDATE] The critique I wrote is based on Wallace (https://arxiv.org/abs/0906.2718 https://arxiv.org/abs/0906.2718). Carroll's argument appears to be somewhat different. I'm just now working my way through his paper (https://arxiv.org/abs/1405.7577 https://arxiv.org/abs/1405.7577) but I'd be very surprised if it did not also have some untenable assumption hidden in there somewhere.
- n4r9 7y ago
  Adrian Kent has a lengthy and detailed overview of MWIs pre-2009 which may interest you [0]. He discusses Wallace's formulation, contrasts it with other formulations and touches on branching indifference. He also has a more recent (and much more brief) article which refers to the Self-locating Uncertainty arguments [1]. I have previously come across Deutsch's formulation in terms of information flow [2], along with what seemed like a very strong criticism from Wallace and Christopher Timpson [3] that his model was not gauge-invariant. [0] https://arxiv.org/pdf/0905.0624.pdf https://arxiv.org/pdf/0905.0624.pdf [1] https://arxiv.org/abs/1408.1944 https://arxiv.org/abs/1408.1944 [2] https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf https://arxiv.org/ftp/quant-ph/papers/9906/9906007.pdf [3] http://users.ox.ac.uk/~bras2317/dhshort2.pdf http://users.ox.ac.uk/~bras2317/dhshort2.pdf
  - lisper 7y ago
    Thanks for the pointers. (This is turning into quite the little rabbit hole.)
- Strilanc 7y ago
  What do you think of the simplified argument here: https://algassert.com/post/1902 https://algassert.com/post/1902 ? Basically: ground the definition of probability into a reversible classical circuit then use that circuit's quantum behavior to generalize the definition to quantum (while assuming as few things as possible). In this case the assumptions are "limiting to amplitude 1 must mean limiting to probability 1" and no signalling.
  - lisper 7y ago
    Thanks for bringing that to my attention. My initial reaction is that the argument appears sufficiently cogent to merit respectful consideration. I predict that if someone were to dig into it, they'd find a question-begging assumption hidden somewhere. (The alternative is that this is a major breakthrough in physics, and my Bayesian prior on that is low.) But where that assumption is hiding is not immediately obvious to me. Looking for it seems like a worthwhile exercise.
    - Strilanc 7y ago
      I don't think the argument is novel, it's just a cut down counting/frequency argument. So any objections to those would presumably port over.
      - lisper 7y ago
        I dunno, I think you might be selling it short. This argument seems to be based on the mathematical continuity of probabilities, which is not something I can recall ever seeing before.