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Armchair physicist here, and yet: > The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is

Armchair physicist here, and yet: > The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic, axioms of quantum theory, together with the non-probabilistic part of classical decision theory. Well this seems crazy! We can drop the Born rule axiom, because you (a game theorist) will make the same decisions whether the universe is deterministic or probabilistic? The difference is crucial, right? A PRNG requires hidden state: exfiltrate the state and predict all future results. But there is no room in the wavefunction + Schrödinger equation for such state: you either augment it (Bohmian mechanics) or accept the essential probabilistic nature. Probabilistic predictions cannot be obtained from deterministic axioms, just like PRNGs cannot produce true randomness. How does Deutsch resolve this?

danbmil99 7y ago
There is no way to prove that a supposedly random source of information is not effectively a PRNG. Similarly, the Born rule must apply unless and until we learn that there is some deterministic process that QM reduces to, and even then, unless we know how the PRNG was 'seeded', we must progress _as if_ the process was in fact random. The deep point here is, arguably, randomness is in the eye of the observer.
- millstone 7y ago
  I'm not sure what you mean by "effectively" a PRNG, but the big objection here is the EPR paradox. A true RNG can be stateless, but a PRNG necessarily requires state. So where is that state? It's not in the wavefunction, so we must introduce new axioms: non-local variables, or super-determinism, etc. Yuck! The MWI program is eliminating the objectionable "part two" of QM: probabilistic measurements and wavefunction collapse. But it's no progress if the replacements are even worse!
  - vincent-toups 7y ago
    "non-local variables, or super-determinism, etc. Yuck!" All of these things are less philosophically objectionable to me than the idea that all outcomes (in some sense) "occur" or that the true substance of the universe is an inaccessible, linearly evolving, quantum mechanical wave function. I mean seriously - the latter is an enormous enlargement and modification of our ontology. Non-locality and super-determinism are actually much less objectionable. Indeed, before quantum mechanics, we were essentially _certain_ that determinism would win the day. And we only need to jettison one of them, of which non-locality seems the most plausible. In that view, spacetime emerges from some underlying non-local dynamics. This isn't particularly hard to imagine (see a Smolin paper called "Nonlocal beables" or something like that).
    - joycian 7y ago
      Thanks for calling out how the Canon interpretations of QM do not not actually save us from much of the problems that are objected to in other interpretations. Sometimes I feel like everyone just repeats what they heard as a student. Smolin's work looks interesting, thanks for the recommendation.
      - vincent-toups 7y ago
        I knew the Phd would come in handy eventually.
- lixtra 7y ago
  > There is no way to prove that a supposedly random source of information is not effectively a PRNG. Maybe no practical way. But a finite state PRNG will be periodic while a true RNG won’t. And the length of the non observed period gives you an estimate of the minimal size of state.
  - pixl97 7y ago
    It can be periodic but unbounded.
  - danbmil99 7y ago
    What would be the period of a 4096 bit pseudo-random number generator iterating at a time scale commensurate with the plank length? I haven't done the math, but the answer is, a long, long, long time.
lisper 7y ago
Deutsch is a many-worlder so he would say there is nothing to resolve because there is no randomness. Everything in the time-evolution of the multiverse is deterministic.
- millstone 7y ago
  Thanks for the writeup, I enjoyed it very much. How does Deutsch connect this view to experimental results? Is the idea that all results are realized, or is my choice of experiment itself predetermined?
  - kd5bjo 7y ago
    My layman’s understanding is that all results are realized many times. The values that we usually interpret as probabilities are really the proportion of universes in which the event occurs; a 95% probably of an experimental outcome means that if we sampled 100 worlds that are successors of the one in which the experiment occurred, 95 of them would have produced that outcome and 5 wouldn’t. We perceive this as randomness due to the weak anthropoic principle: from our perspective, there is only one universe and things actually occurred in only one way, because there’s no interaction between worlds after the split; at every opportunity, we effectively draw one random result from the distribution because all of the other worlds don’t contain us, they contain copies of us.
    - TheOtherHobbes 7y ago
      That means branch counting matters, which means there has to be some way for the universes to communicate the results of branch counting with each other. Otherwise there's no mechanism for probability to arise. If you try to fall back to the position that the probabilities are somehow inherent in the interaction between all the universes, then you may as well dispense with the universes and just say the probabilities are defined by a hidden non-local (i.e. not Bell-violating) interaction in this universe. Because otherwise you still have to explain how a split (or differential propagation or whatever you want to call it) in one location generates an entire universe instantaneously - i.e. faster than c - while preserving state that is beyond the event horizon of the current location. There's a kind of sleight of hand about the argument. You can just about imagine multiple copies of a single particle existing along a foliated timeline. But when MWI people say "What splits is the wavefunction of the universe" they're just handwaving. The wavefunction of the universe doesn't exist as a testable abstraction, and even if it did, are we supposed to believe that it's the only physical entity discovered so far that can ignore relativistic limits? And even if that were true, it implies that the wavefunction of the universe is somehow perfectly deterministic - which is unproven at best. Those are all very strong claims to be making. In fact (IMO) there's a strong whiff of handwavy nonsense about the idea. But I have the luxury of not doing this for a living, and I'm very happy to be proved wrong by people who do. Observer independence - and observer relevance - seems to be a separate problem.

danbmil99 7y ago

There is no way to prove that a supposedly random source of information is not effectively a PRNG. Similarly, the Born rule must apply unless and until we learn that there is some deterministic process that QM reduces to, and even then, unless we know how the PRNG was 'seeded', we must progress _as if_ the process was in fact random. The deep point here is, arguably, randomness is in the eye of the observer.

millstone 7y ago
I'm not sure what you mean by "effectively" a PRNG, but the big objection here is the EPR paradox. A true RNG can be stateless, but a PRNG necessarily requires state. So where is that state? It's not in the wavefunction, so we must introduce new axioms: non-local variables, or super-determinism, etc. Yuck! The MWI program is eliminating the objectionable "part two" of QM: probabilistic measurements and wavefunction collapse. But it's no progress if the replacements are even worse!
- vincent-toups 7y ago
  "non-local variables, or super-determinism, etc. Yuck!" All of these things are less philosophically objectionable to me than the idea that all outcomes (in some sense) "occur" or that the true substance of the universe is an inaccessible, linearly evolving, quantum mechanical wave function. I mean seriously - the latter is an enormous enlargement and modification of our ontology. Non-locality and super-determinism are actually much less objectionable. Indeed, before quantum mechanics, we were essentially _certain_ that determinism would win the day. And we only need to jettison one of them, of which non-locality seems the most plausible. In that view, spacetime emerges from some underlying non-local dynamics. This isn't particularly hard to imagine (see a Smolin paper called "Nonlocal beables" or something like that).
  - joycian 7y ago
    Thanks for calling out how the Canon interpretations of QM do not not actually save us from much of the problems that are objected to in other interpretations. Sometimes I feel like everyone just repeats what they heard as a student. Smolin's work looks interesting, thanks for the recommendation.
    - vincent-toups 7y ago
      I knew the Phd would come in handy eventually.
lixtra 7y ago
> There is no way to prove that a supposedly random source of information is not effectively a PRNG. Maybe no practical way. But a finite state PRNG will be periodic while a true RNG won’t. And the length of the non observed period gives you an estimate of the minimal size of state.
- pixl97 7y ago
  It can be periodic but unbounded.
- danbmil99 7y ago
  What would be the period of a 4096 bit pseudo-random number generator iterating at a time scale commensurate with the plank length? I haven't done the math, but the answer is, a long, long, long time.

lisper 7y ago

Deutsch is a many-worlder so he would say there is nothing to resolve because there is no randomness. Everything in the time-evolution of the multiverse is deterministic.

millstone 7y ago
Thanks for the writeup, I enjoyed it very much. How does Deutsch connect this view to experimental results? Is the idea that all results are realized, or is my choice of experiment itself predetermined?
- kd5bjo 7y ago
  My layman’s understanding is that all results are realized many times. The values that we usually interpret as probabilities are really the proportion of universes in which the event occurs; a 95% probably of an experimental outcome means that if we sampled 100 worlds that are successors of the one in which the experiment occurred, 95 of them would have produced that outcome and 5 wouldn’t. We perceive this as randomness due to the weak anthropoic principle: from our perspective, there is only one universe and things actually occurred in only one way, because there’s no interaction between worlds after the split; at every opportunity, we effectively draw one random result from the distribution because all of the other worlds don’t contain us, they contain copies of us.
  - TheOtherHobbes 7y ago
    That means branch counting matters, which means there has to be some way for the universes to communicate the results of branch counting with each other. Otherwise there's no mechanism for probability to arise. If you try to fall back to the position that the probabilities are somehow inherent in the interaction between all the universes, then you may as well dispense with the universes and just say the probabilities are defined by a hidden non-local (i.e. not Bell-violating) interaction in this universe. Because otherwise you still have to explain how a split (or differential propagation or whatever you want to call it) in one location generates an entire universe instantaneously - i.e. faster than c - while preserving state that is beyond the event horizon of the current location. There's a kind of sleight of hand about the argument. You can just about imagine multiple copies of a single particle existing along a foliated timeline. But when MWI people say "What splits is the wavefunction of the universe" they're just handwaving. The wavefunction of the universe doesn't exist as a testable abstraction, and even if it did, are we supposed to believe that it's the only physical entity discovered so far that can ignore relativistic limits? And even if that were true, it implies that the wavefunction of the universe is somehow perfectly deterministic - which is unproven at best. Those are all very strong claims to be making. In fact (IMO) there's a strong whiff of handwavy nonsense about the idea. But I have the luxury of not doing this for a living, and I'm very happy to be proved wrong by people who do. Observer independence - and observer relevance - seems to be a separate problem.