13 ms·

Where Quantum Probability Comes From

97 points by eaguyhn 7y ago

nabla9 7y ago
This is related to his research. His latest podcast goes to it more deeply (there is a transcript): https://www.preposterousuniverse.com/podcast/2019/09/09/63-solo-finding-gravity-within-quantum-mechanics/ https://www.preposterousuniverse.com/podcast/2019/09/09/63-s... The goal is to derive emergent spacetime and gravity from quantum mechanics. Some features of their theory: * Finite dimensional Hilbert space. Quantum field theory gets boot. * Spacetime is entangled degrees of freedom in a way that semi-classical spacetime geometry emerges. Things are local because they are entangled not the other way around. * Spacetime expands because initially untangled degrees of freedom become entangled with the rest of the the universe.
- v77 7y ago
  His book just came out this week as well.
n4r9 7y ago
Carroll is a big advocate of the Many Worlds Interpretation, so it's nice to see some other interpretations getting a decent hearing in this article as well as a decent treatment of some academic concerns about MWI. That's a testament to his humility as a researcher. I must admit I struggle with the MWI Born rule derivations based on rational credence. I don't see why proving that one ought to assign credence in such and such a way is sufficient to prove that that's the way nature is. It feels too much like deriving an "is" from an "ought", although in a slightly different way than what Hume objected to!
- pure-awesome 7y ago
  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
- crdrost 7y ago
  Yeah, I mean, at this scale you’re not going to prove how nature is from any of this. What MWI is saying is that if you admit a really difficult view of the cosmos, then you can regard the Born rule as part of Schrödinger evolution—but it is kind of only possible because you punted the details into that difficult view of the cosmos. (And then the MWI-supporters come in full force and argue that actually the view is not so “difficult” after all.) Backing up, the problem is that you have these different approaches—depending on how you count them you could maybe group them broadly and say there are 3-4, or as large as a dozen or two—that are all mathematically identical. They all predict the Born rule, but suggest different ways that Nature really fundamentally would act to produce that rule. Since they are mathematically identical, it is provable that there is no way to choose between them. As a result, the one which steps the most out of peoples’ ways to enable experimental results, has better “genes” for its own reproduction in the publication of papers. And that has just been the Copenhagen interpretation: you the experimentalist have a soul and when that soul measures the world the nice unitary evolution of the world comes crashing down with probabilities given by the Born rule. Contrast with pilot-wave theories where you have to work out a whole separate equation that doesn’t do anything which makes any further observational impact. The basic issue that we are facing is that while the notion of souls seems laughable for fashionable sciencey people, it also seems in some distressing way inevitable. You take Many Worlds for instance, you admit the reality of every single possibility of the entire universe as a much broader multiverse. An equation, the Schrödinger equation, essentially works over, say, a Planck time to create a vector field on top of this, saying “This instant is followed by that instant is followed by that instant.” In the middle of that, what uniquely qualifies my experience here and now as I know such experience must exist? I do not perceive a multiverse; I perceive a changing universe. And MWI says “well actually there are a million yous, frozen in time, all perceiving changing universes. Your experience of motion through time is actually kind of a lie.” This is not a unique problem to QM; it happened much earlier with special relativity where we discovered that you are actually a rope of worldlines thrusting through a static four-dimensional Lorentzian manifold, every part of that rope being presumably in a separate conscious state, perceiving itself as moving through time but we “on the outside” can see that there is no unique present defined such that it can wash over all of the ropes simultaneously. MWI just happens to facilitate the same basic “unrolling of time” because it has already unrolled all of possibility-space. And to fix it you need something—I’m calling it a soul, you can get fancy—which “zips along the worldline” and contains my conscious experience, or you need to argue that my experience is an illusion, or you need some “universe-soul” to act like a coherent “present moment” for all of us, or the like. It all kind of sucks. There is a nice perspective sitting in the middle of this due to Andreas O. Tell [1], and it is pleasantly agnostic while still doing something like what MWI is doing to try and derive the Born rule from normal wavefunction evolution. In brief, he says: “use the state-matrix formalism for QM, and take a completely agnostic view of what the cosmos is and how it behaves. Still if you have a local information-processing system which is embedded in the cosmos and changing, then it receives information and must update its model of the universe. Its model of the universe must necessarily come down to a list of wavefunctions with a list of weightings, but there is a freedom-of-perspective which allows you to choose the wavefunction with the highest weight as “the” one that you think the system is in. New data just forces these weights to cross in size, causing the Born rule when you try to determine whether those weights will cross over and the system will be in the new state.” In some sense then we can live in a very Copenhageny world where we are changing data-processors uniquely present in some space and time, but we can use Schrödinger evolution to derive the Born rule just the same as the many-worlds interpretation does, but rather than committing to its plethora of different universes we might be able to just remain non-committal about what is in the rest of the universe, beyond what I see in it. [1] https://arxiv.org/abs/1205.0293 https://arxiv.org/abs/1205.0293
- kovrik 7y ago
  I was always wondering about MWI and couldn't find the answer to one question. AFAIK Everett never mentioned Many Worlds in his paper. What he was talking about was a Universal Wave Function. In that sense, 'world' is just a 'quantum system', not 'Universe'. At what stage we started calling it Many Worlds? When scientists say Many Worlds, do they actually mean Worlds as physical 'parallel universes' that pop up into existence? Or they only mean that those are probable outcomes of our measurement (probable histories) that never actually happened (only one of them happened - the one we end up being it)?
  - millstone 7y ago
    In MWI, all Worlds are physically real and may interfere with each other.
    - sliken 7y ago
      Sounds like that would be a testable hypothesis, right? How exactly would they interfere?
      - millstone 7y ago
        All QM interpretations require interference. This is demonstrated by the two-slit experiment (for example). In this experiment, an electron passing through the two-slit shield generates an interference pattern. But if you detect which slit the electron passes through, you destroy the pattern. Why? In textbook/Copenhagen interpretation, we say that when the electron passes through the slits the wavefunction has not yet been measured. But with the detector in place, you collapse the wavefunction to an eigenvector of position. By the uncertainty principle, the momentum uncertainty is now very high, so the electron shoots off in a random direction and cannot be expected to follow any pattern. In MWI, we start with the interference pattern. But adding the detector does not "collapse" anything - instead it introduces lots of degrees of freedom. The particle passes through both the left and right slits, but the degrees of freedom ensure there is no fixed relative phase delta between these possibilities. The detector turns waves into "static noise", and so any interference pattern is lost. Both options are realized, but cannot detect the other possibility: distinct Worlds. The key point is that MWI has no special role for measurement. The left-slit and right-slit worlds interfere, but with the detector in place the pattern is destroyed: the interference is uncoordinated and averages to zero, so undetectable. Whereas in textbook/Cophenhagen QM we say that the measurement results in a single outcome.
Simon_says 7y ago
In a shocking turn of events Quanta Magazine features an author who’s heard of the Many Worlds Interpretation.
- mercer 7y ago
  If I were to write an edgy/snarky comment bot for HN, I imagine its comment history would resemble yours to a tee. That's not particularly a criticism nor a compliment, btw.
  - Simon_says 7y ago
    Nice. You’re a better programmer than I, though.
    - mercer 7y ago
      What makes you think that's the case?
      - Simon_says 7y ago
        It follows from you programming snark as well as I think it. I’m sure it’s possible, but it seems like a hard problem to me.
        homonculus1 7y ago
        lmao
        keiru 7y ago
        I wonder if one could earn a living as a professional shitposter for AI training purposes.
EGreg 7y ago
Isn’t space and time considered continuous? What about the Planck distance then? What’s that all about? It seems to me that on a microscopic level and small time scales, a small change in input will lead to a small change in output. This is certainly true in classical mechanics, but what about quantum mechanics? Are the quanta the result of a continuous process? Can an subatomic particle wind up on mars, exceeding the speed of light? with a certain probability? HERE is what bothers me. The instability of certain physical problems (small change in input leads to large changes in output, like where a pencil is going to fall if stood on its tip). How can this happen if the composition of continuous functions is continuous??? In mathematics we have abstractions such Real Numbers and infinite sequences of functions that can converge to discontinuous and even really weird functions in the limit. But in the real world it seems that we have some sort of minimum, like planck distance, or simple measurement error, that preclude us from reversing a process after a certain point. Maybe THAT is where unstable problems on the macro scale come from?? Pilot Wave Theory seems to say that everything is deterministic and the uncertainty in Quantum Mechanics comes from us being unable to observe the process that leads to the result. But PWC requires us to abolish the idea of locality, which to me is a special case of continuity. Anyway can someone please explain this to me? As it regards quantum mechanics? Leslie Lamport’s paper caused a big watershed moment for me and I’m still reeling from it: https://lamport.azurewebsites.net/pubs/buridan.pdf https://lamport.azurewebsites.net/pubs/buridan.pdf
canjobear 7y ago
If you'd like an intuitive introduction to the actual technical details of quantum probability: https://www.math3ma.com/blog/a-first-look-at-quantum-probability-part-1 https://www.math3ma.com/blog/a-first-look-at-quantum-probabi...
grumpy8 7y ago
I love this website so much (quantamagazine.org). The design is great and the articles are amazing.
danbruc 7y ago
In contrast with frequentism, in Bayesianism it makes perfect sense to attach probabilities to one-shot events, such as who will win the next election, or even past events that we’re unsure about. Does frequentism really require actually performing the experiment? Or is imagining doing the experiment good enough? I would say »Candidate X will win the next election with a probability of Y percent.« is just a shorthand for »The following sets of states and possible evolutions of those states are compatible with my knowledge about the world and in Y percent of the cases candidate X wins the next election.« which seems not to different from a coin flip where the different outcomes are also due to imperfect knowledge of the initial state. The difference is that it is easy to sample the set of initial states for a coin flip by just repeatedly flipping a coin from slightly different initial states due to human imperfections in doing this task. Sampling the initial states of an election in the same way is obviously not possible and I have admittedly no real clue how people arrive at a meaningful number in practice. A similar example seems to be the probability of rain at some place some time into the future in which case it is possible to sample the set of initial states by running a weather model repeatedly.
- 6gvONxR4sf7o 7y ago
  I interpret it as a reference system. To a frequentist, a probabilistic statement is "this coin flip is 50% heads in reference to this set of coin flips." Your elements of the statement are the event, the probability, and the reference set of events.
laser 7y ago
There's something that has deeply irked me for many years about these MWI probability constructions, and that is the largely glossed over fact that there's sort of a non-local numerical awareness and computation within the wave function necessary to construct the number of branches in proper ratio required to maintain self-consistency in the MWI universe. Additionally, this number of branches is incomprehensibly larger than simply splitting the universe once for every quantized event, and results in unwieldy levels of duplication of identical branches. The reason for this is that if we take the most improbable outcome of a given wave function and say “This highly improbable branch occurs once”, we are immediately contradicted, as the next least improbable event is virtually certainly a non-integer ratio to the former. So, we give the wave function numerical factoring / self-resolving capabilities and instead, the least and second least improbable branches occur the number of times necessary to maintain status as whole integers with correct relative ratio. But then, that only resolves two possible events on the wave function, and so with the third least improbable event, almost certainly not an integer ratio to the first or the second, we must repeat this step again of multiplying the number of branches for the least and second least improbable, to maintain a consistent integer ratio for our types of branches. As you can see, as you follow this up through all the possible branch outcomes, to express their corresponding probabilities in whole integers counts of quantum outcomes, you essentially have to engage in a massive computation of finding common factors all the way up. Further, even the least improbable event will require an incomprehensible number of duplicate branches, and the most probable events will have an even more innumerable count of duplicate branches still. The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist, but then you have seeming contradictions in observable discreteness and it’s not clear it’s truly even MWI anymore. Disclosure: I’m not a physicist, and it's quite plausible that I don’t know what I’m talking about.
- madhadron 7y ago
  > The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist That's what it is. A measurement is coupling a quantum event to a statistically irreversible process. The total wave function that results has two major lobes. There's no split on measurement. That's why it's appealing: it makes no reference to classical mechanics in the formulation.
macawfish 7y ago
I'm not an expert, but one of the most exciting realizations I've had over the last few years is just how close quantum theory is to various "ordinary" kinds of probability theory, including Kolmogorov's classical theory. Now probability theory is not so boring for me. Quantum physics has inspired so much work in other fields! Check out this guy's work for examples: https://scholar.google.com/citations?user=wdhkzPMAAAAJ&hl=en https://scholar.google.com/citations?user=wdhkzPMAAAAJ&hl=en I don't agree with Khrennikov's interpretation of quantum mechanics (he's a realist whereas I tend to appreciate the more "mystical" feeling interpretations of quantum mechanics), but he and others' work on the connections between quantum physics and classical probability theory, as well as on non-physics applications of quantum theoretic tools, is crazy thought provoking.

97 points by eaguyhn 7y ago

This is related to his research. His latest podcast goes to it more deeply (there is a transcript): https://www.preposterousuniverse.com/podcast/2019/09/09/63-solo-finding-gravity-within-quantum-mechanics/ https://www.preposterousuniverse.com/podcast/2019/09/09/63-s... The goal is to derive emergent spacetime and gravity from quantum mechanics. Some features of their theory: * Finite dimensional Hilbert space. Quantum field theory gets boot. * Spacetime is entangled degrees of freedom in a way that semi-classical spacetime geometry emerges. Things are local because they are entangled not the other way around. * Spacetime expands because initially untangled degrees of freedom become entangled with the rest of the the universe.

v77 7y ago
His book just came out this week as well.

n4r9 7y ago

Carroll is a big advocate of the Many Worlds Interpretation, so it's nice to see some other interpretations getting a decent hearing in this article as well as a decent treatment of some academic concerns about MWI. That's a testament to his humility as a researcher. I must admit I struggle with the MWI Born rule derivations based on rational credence. I don't see why proving that one ought to assign credence in such and such a way is sufficient to prove that that's the way nature is. It feels too much like deriving an "is" from an "ought", although in a slightly different way than what Hume objected to!

pure-awesome 7y ago
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
crdrost 7y ago
Yeah, I mean, at this scale you’re not going to prove how nature is from any of this. What MWI is saying is that if you admit a really difficult view of the cosmos, then you can regard the Born rule as part of Schrödinger evolution—but it is kind of only possible because you punted the details into that difficult view of the cosmos. (And then the MWI-supporters come in full force and argue that actually the view is not so “difficult” after all.) Backing up, the problem is that you have these different approaches—depending on how you count them you could maybe group them broadly and say there are 3-4, or as large as a dozen or two—that are all mathematically identical. They all predict the Born rule, but suggest different ways that Nature really fundamentally would act to produce that rule. Since they are mathematically identical, it is provable that there is no way to choose between them. As a result, the one which steps the most out of peoples’ ways to enable experimental results, has better “genes” for its own reproduction in the publication of papers. And that has just been the Copenhagen interpretation: you the experimentalist have a soul and when that soul measures the world the nice unitary evolution of the world comes crashing down with probabilities given by the Born rule. Contrast with pilot-wave theories where you have to work out a whole separate equation that doesn’t do anything which makes any further observational impact. The basic issue that we are facing is that while the notion of souls seems laughable for fashionable sciencey people, it also seems in some distressing way inevitable. You take Many Worlds for instance, you admit the reality of every single possibility of the entire universe as a much broader multiverse. An equation, the Schrödinger equation, essentially works over, say, a Planck time to create a vector field on top of this, saying “This instant is followed by that instant is followed by that instant.” In the middle of that, what uniquely qualifies my experience here and now as I know such experience must exist? I do not perceive a multiverse; I perceive a changing universe. And MWI says “well actually there are a million yous, frozen in time, all perceiving changing universes. Your experience of motion through time is actually kind of a lie.” This is not a unique problem to QM; it happened much earlier with special relativity where we discovered that you are actually a rope of worldlines thrusting through a static four-dimensional Lorentzian manifold, every part of that rope being presumably in a separate conscious state, perceiving itself as moving through time but we “on the outside” can see that there is no unique present defined such that it can wash over all of the ropes simultaneously. MWI just happens to facilitate the same basic “unrolling of time” because it has already unrolled all of possibility-space. And to fix it you need something—I’m calling it a soul, you can get fancy—which “zips along the worldline” and contains my conscious experience, or you need to argue that my experience is an illusion, or you need some “universe-soul” to act like a coherent “present moment” for all of us, or the like. It all kind of sucks. There is a nice perspective sitting in the middle of this due to Andreas O. Tell [1], and it is pleasantly agnostic while still doing something like what MWI is doing to try and derive the Born rule from normal wavefunction evolution. In brief, he says: “use the state-matrix formalism for QM, and take a completely agnostic view of what the cosmos is and how it behaves. Still if you have a local information-processing system which is embedded in the cosmos and changing, then it receives information and must update its model of the universe. Its model of the universe must necessarily come down to a list of wavefunctions with a list of weightings, but there is a freedom-of-perspective which allows you to choose the wavefunction with the highest weight as “the” one that you think the system is in. New data just forces these weights to cross in size, causing the Born rule when you try to determine whether those weights will cross over and the system will be in the new state.” In some sense then we can live in a very Copenhageny world where we are changing data-processors uniquely present in some space and time, but we can use Schrödinger evolution to derive the Born rule just the same as the many-worlds interpretation does, but rather than committing to its plethora of different universes we might be able to just remain non-committal about what is in the rest of the universe, beyond what I see in it. [1] https://arxiv.org/abs/1205.0293 https://arxiv.org/abs/1205.0293
kovrik 7y ago
I was always wondering about MWI and couldn't find the answer to one question. AFAIK Everett never mentioned Many Worlds in his paper. What he was talking about was a Universal Wave Function. In that sense, 'world' is just a 'quantum system', not 'Universe'. At what stage we started calling it Many Worlds? When scientists say Many Worlds, do they actually mean Worlds as physical 'parallel universes' that pop up into existence? Or they only mean that those are probable outcomes of our measurement (probable histories) that never actually happened (only one of them happened - the one we end up being it)?
- millstone 7y ago
  In MWI, all Worlds are physically real and may interfere with each other.
  - sliken 7y ago
    Sounds like that would be a testable hypothesis, right? How exactly would they interfere?
    - millstone 7y ago
      All QM interpretations require interference. This is demonstrated by the two-slit experiment (for example). In this experiment, an electron passing through the two-slit shield generates an interference pattern. But if you detect which slit the electron passes through, you destroy the pattern. Why? In textbook/Copenhagen interpretation, we say that when the electron passes through the slits the wavefunction has not yet been measured. But with the detector in place, you collapse the wavefunction to an eigenvector of position. By the uncertainty principle, the momentum uncertainty is now very high, so the electron shoots off in a random direction and cannot be expected to follow any pattern. In MWI, we start with the interference pattern. But adding the detector does not "collapse" anything - instead it introduces lots of degrees of freedom. The particle passes through both the left and right slits, but the degrees of freedom ensure there is no fixed relative phase delta between these possibilities. The detector turns waves into "static noise", and so any interference pattern is lost. Both options are realized, but cannot detect the other possibility: distinct Worlds. The key point is that MWI has no special role for measurement. The left-slit and right-slit worlds interfere, but with the detector in place the pattern is destroyed: the interference is uncoordinated and averages to zero, so undetectable. Whereas in textbook/Cophenhagen QM we say that the measurement results in a single outcome.

Simon_says 7y ago

In a shocking turn of events Quanta Magazine features an author who’s heard of the Many Worlds Interpretation.

mercer 7y ago
If I were to write an edgy/snarky comment bot for HN, I imagine its comment history would resemble yours to a tee. That's not particularly a criticism nor a compliment, btw.
- Simon_says 7y ago
  Nice. You’re a better programmer than I, though.
  - mercer 7y ago
    What makes you think that's the case?
    - Simon_says 7y ago
      It follows from you programming snark as well as I think it. I’m sure it’s possible, but it seems like a hard problem to me.
      - homonculus1 7y ago
        lmao
      - keiru 7y ago
        I wonder if one could earn a living as a professional shitposter for AI training purposes.

EGreg 7y ago

Isn’t space and time considered continuous? What about the Planck distance then? What’s that all about? It seems to me that on a microscopic level and small time scales, a small change in input will lead to a small change in output. This is certainly true in classical mechanics, but what about quantum mechanics? Are the quanta the result of a continuous process? Can an subatomic particle wind up on mars, exceeding the speed of light? with a certain probability? HERE is what bothers me. The instability of certain physical problems (small change in input leads to large changes in output, like where a pencil is going to fall if stood on its tip). How can this happen if the composition of continuous functions is continuous??? In mathematics we have abstractions such Real Numbers and infinite sequences of functions that can converge to discontinuous and even really weird functions in the limit. But in the real world it seems that we have some sort of minimum, like planck distance, or simple measurement error, that preclude us from reversing a process after a certain point. Maybe THAT is where unstable problems on the macro scale come from?? Pilot Wave Theory seems to say that everything is deterministic and the uncertainty in Quantum Mechanics comes from us being unable to observe the process that leads to the result. But PWC requires us to abolish the idea of locality, which to me is a special case of continuity. Anyway can someone please explain this to me? As it regards quantum mechanics? Leslie Lamport’s paper caused a big watershed moment for me and I’m still reeling from it: https://lamport.azurewebsites.net/pubs/buridan.pdf https://lamport.azurewebsites.net/pubs/buridan.pdf

canjobear 7y ago

If you'd like an intuitive introduction to the actual technical details of quantum probability: https://www.math3ma.com/blog/a-first-look-at-quantum-probability-part-1 https://www.math3ma.com/blog/a-first-look-at-quantum-probabi...

grumpy8 7y ago

I love this website so much (quantamagazine.org). The design is great and the articles are amazing.

danbruc 7y ago

In contrast with frequentism, in Bayesianism it makes perfect sense to attach probabilities to one-shot events, such as who will win the next election, or even past events that we’re unsure about. Does frequentism really require actually performing the experiment? Or is imagining doing the experiment good enough? I would say »Candidate X will win the next election with a probability of Y percent.« is just a shorthand for »The following sets of states and possible evolutions of those states are compatible with my knowledge about the world and in Y percent of the cases candidate X wins the next election.« which seems not to different from a coin flip where the different outcomes are also due to imperfect knowledge of the initial state. The difference is that it is easy to sample the set of initial states for a coin flip by just repeatedly flipping a coin from slightly different initial states due to human imperfections in doing this task. Sampling the initial states of an election in the same way is obviously not possible and I have admittedly no real clue how people arrive at a meaningful number in practice. A similar example seems to be the probability of rain at some place some time into the future in which case it is possible to sample the set of initial states by running a weather model repeatedly.

6gvONxR4sf7o 7y ago
I interpret it as a reference system. To a frequentist, a probabilistic statement is "this coin flip is 50% heads in reference to this set of coin flips." Your elements of the statement are the event, the probability, and the reference set of events.

laser 7y ago

There's something that has deeply irked me for many years about these MWI probability constructions, and that is the largely glossed over fact that there's sort of a non-local numerical awareness and computation within the wave function necessary to construct the number of branches in proper ratio required to maintain self-consistency in the MWI universe. Additionally, this number of branches is incomprehensibly larger than simply splitting the universe once for every quantized event, and results in unwieldy levels of duplication of identical branches. The reason for this is that if we take the most improbable outcome of a given wave function and say “This highly improbable branch occurs once”, we are immediately contradicted, as the next least improbable event is virtually certainly a non-integer ratio to the former. So, we give the wave function numerical factoring / self-resolving capabilities and instead, the least and second least improbable branches occur the number of times necessary to maintain status as whole integers with correct relative ratio. But then, that only resolves two possible events on the wave function, and so with the third least improbable event, almost certainly not an integer ratio to the first or the second, we must repeat this step again of multiplying the number of branches for the least and second least improbable, to maintain a consistent integer ratio for our types of branches. As you can see, as you follow this up through all the possible branch outcomes, to express their corresponding probabilities in whole integers counts of quantum outcomes, you essentially have to engage in a massive computation of finding common factors all the way up. Further, even the least improbable event will require an incomprehensible number of duplicate branches, and the most probable events will have an even more innumerable count of duplicate branches still. The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist, but then you have seeming contradictions in observable discreteness and it’s not clear it’s truly even MWI anymore. Disclosure: I’m not a physicist, and it's quite plausible that I don’t know what I’m talking about.

madhadron 7y ago
> The only way I can see to escape this madness with MWI seems to be give up on the notion of truly separate branches, and instead treat these “many worlds” as a stream of overlapping world-ish-nesses in which discrete outcomes don’t actually even exist That's what it is. A measurement is coupling a quantum event to a statistically irreversible process. The total wave function that results has two major lobes. There's no split on measurement. That's why it's appealing: it makes no reference to classical mechanics in the formulation.

macawfish 7y ago

I'm not an expert, but one of the most exciting realizations I've had over the last few years is just how close quantum theory is to various "ordinary" kinds of probability theory, including Kolmogorov's classical theory. Now probability theory is not so boring for me. Quantum physics has inspired so much work in other fields! Check out this guy's work for examples: https://scholar.google.com/citations?user=wdhkzPMAAAAJ&hl=en https://scholar.google.com/citations?user=wdhkzPMAAAAJ&hl=en I don't agree with Khrennikov's interpretation of quantum mechanics (he's a realist whereas I tend to appreciate the more "mystical" feeling interpretations of quantum mechanics), but he and others' work on the connections between quantum physics and classical probability theory, as well as on non-physics applications of quantum theoretic tools, is crazy thought provoking.