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I have a question about wave function collapse, especially tied into many worlds. Let's say that a photon in the double slit experiment could travel straight to

by bmh100 10y ago

I have a question about wave function collapse, especially tied into many worlds. Let's say that a photon in the double slit experiment could travel straight to a detector, go at a 15 degree angle, or go at a 30 degree angle. Those 3 particles exist simultaneously, leading them to interfere with each other. Does the straight particle "split off" from the other universe right when it reaches the detector? Are the two angled photons left in the "original" universe in a partially collapsed wave function? When does the wave function fully collapse, when the longest possible path has been completed? If I point the double slit at The Great Void, is it possible the wave function would never collapse because the particle would never be detected? Note: I understand that a wave function of just 3 photons or photons that travel in straight lines could not cause an interference pattern.

lisper 10y ago
I'm not a subscriber to the many-worlds interpretation so I'm not the right person to defend it, partly for this very reason: the question of when one universe "splits off" doesn't actually have an answer, for the same reason that the question of "when does a measurement actually happen?" doesn't actually have an answer. Many-worlds and Copenhagen both have this rhetorical problem: they want to draw a sharp line when something "happens" (collapse, universe-split) and there is no such sharp line. The transition from quantum to classical is gradual, not abrupt. It typically happens very fast (picosecods or femtoseconds to get to the point where the state of the system is no longer distinguishable from a classical state) which is why it appears to be an abrupt transition, but it's not. This is one of the many reasons that I find the QIT/zero-worlds interpretation to be the most satisfactory. It and decoherence are the only ones that don't have this problem. But decoherence is too mathy :-)
- nhaehnle 10y ago
  IANAP, but I think part of the problem with MWI is that popularizers of it wanted to sound cool by calling it the Many-Worlds Interpretation in the first place. The idea was originally known as the Theory of the Universal Wave Function, which makes a lot more sense as long as you're unafraid of mathematics. There is no "splitting off" of universes; I agree with you that that wouldn't make much sense. Instead, the observer simply becomes entangled with the observed physical system during the measurement process. This entanglement is a gradual process, though it certainly happens very quickly. This basically pushes all the weirdness out of quantum mechanics and into the fact that we just don't understand consciousness very well. Why don't we perceive the full linear combination of quantum states? And can we somehow map our subjective experience of probability and statistics to what happens in the Universal Wave Function? It's much easier to ignore that weirdness, since we're used to ignoring it in our daily lives anyway. It's also a more parsimonious interpretation than the others, because it doesn't postulate anything special about us (the "observers"). (This does not mean that consciousness is a quantum or even meta-physical phenomenon. Quite the opposite, actually: I find that the mystery lies more in why consciousness is unable to perceive quantum states despite existing in a universe that has quantum physics.)
  - lisper 10y ago
    > Why don't we perceive the full linear combination of quantum states? My personal belief is that it is because consciousness is a classical information-processing phenomenon. In other words, we can only directly perceive things that can be described as real numbers rather than complex numbers because we are Turing machines, and Turing machines are classical.
    - bmh100 10y ago
      Then wouldn't an appropriately constructed sensor be able to record the full linear combination of quantum states?
      - lisper 10y ago
        No, because records are necessarily classical. This is because of the no-cloning theorem. You cannot copy quantum information, only classical information.
    - nhaehnle 10y ago
      That's an interesting thought, especially with the addendum of the no-cloning theorem. This fits with a Hofstadter-like perspective that consciousness is about "strange loops", where we somehow repeatedly evaluate simplified models of the world including yourself. Doing such repeated evaluations requires (at least partial) "cloning" of the state of the world outside for the purpose of evaluation, and cloning quantum states is impossible, hence consciousness must be a classical phenomenon. I like that line of argument. Note: I wouldn't state it as being unable to perceive things that can be described as complex numbers, but rather complex linear combinations.
- loup-vaillant 10y ago
  Wait a minute, since when is there any difference between Many Worlds and Decoherence? I always assumed they referred to the same interpretation, do they not?
  - lisper 10y ago
    There are actually three different ideas in play here: decoherence as described by Zurek, the relative-state interpretation as described by Everett, and the popular account of the universe "splitting" when a measurement is made. All three of these are different, at least rhetorically, even though at a high enough conceptual level they all amount to the same thing.
jostylr 10y ago
I have never understood what the classic Many World Interpretation actually is. Splitting of universes has the same problem as collapse and probabilities become rather nebulous since presumably all possibilities do happen, after all. But there is a version of it which does make sense: https://arxiv.org/abs/0903.2211 https://arxiv.org/abs/0903.2211 The basic question for all theories is, "what is fundamentally real?" and the wave function of quantum mechanics just doesn't work in that role. This is why Bohmian mechanics adds particles; that is what is real in that theory. But to make a MW theory, one can integrate out the wave function to create a mass density function on 3-space. In any given instance, this is a mess and useless. But if you watch it evolve, then you could see multiple different stories evolving. And those are the different "worlds". There is no splitting, just regimes that are no longer relevant.
- loup-vaillant 10y ago
  > I have never understood what the classic Many World Interpretation actually is. There's little to understand: at its core, Many Worlds is real close to "shut up and calculate". The only significant assumption is that the wave function as described by the math is real. And when the math says there are 2 non-interacting blobs, well, this translates to 2 universes. That's about it. As for why people seems to reject it instinctively, it's probably because our subjective experience is linear —or mono-threaded. However, linear histories aren't contradictory with trees. Imagine a Git History that never merges: each leaf is the product of a linear set of modifications, a perfectly clean history. From that final commit's perspective, other branches might as well not exist. You'd need merges to break that illusion, and our universe doesn't have macro-merges —we only observe them at a very small scale, for instance with photon interference.
  - bmh100 10y ago
    Doesn't that also require at least one additional dimension of spacetime to separate the two universes?
  - lisper 10y ago
    > Imagine a Git History that never merges That is a really excellent analogy. It is also important to understand that there is a reason we don't have "macro merges", and that is because some irreversible process is required to create classical information, which is what we (the entities having this conversation) are actually made of. See: http://blog.rongarret.info/2014/10/parallel-universes-and-arrow-of-time.html http://blog.rongarret.info/2014/10/parallel-universes-and-ar...

by bmh100 10y ago

lisper 10y ago

I'm not a subscriber to the many-worlds interpretation so I'm not the right person to defend it, partly for this very reason: the question of when one universe "splits off" doesn't actually have an answer, for the same reason that the question of "when does a measurement actually happen?" doesn't actually have an answer. Many-worlds and Copenhagen both have this rhetorical problem: they want to draw a sharp line when something "happens" (collapse, universe-split) and there is no such sharp line. The transition from quantum to classical is gradual, not abrupt. It typically happens very fast (picosecods or femtoseconds to get to the point where the state of the system is no longer distinguishable from a classical state) which is why it appears to be an abrupt transition, but it's not. This is one of the many reasons that I find the QIT/zero-worlds interpretation to be the most satisfactory. It and decoherence are the only ones that don't have this problem. But decoherence is too mathy :-)

nhaehnle 10y ago
IANAP, but I think part of the problem with MWI is that popularizers of it wanted to sound cool by calling it the Many-Worlds Interpretation in the first place. The idea was originally known as the Theory of the Universal Wave Function, which makes a lot more sense as long as you're unafraid of mathematics. There is no "splitting off" of universes; I agree with you that that wouldn't make much sense. Instead, the observer simply becomes entangled with the observed physical system during the measurement process. This entanglement is a gradual process, though it certainly happens very quickly. This basically pushes all the weirdness out of quantum mechanics and into the fact that we just don't understand consciousness very well. Why don't we perceive the full linear combination of quantum states? And can we somehow map our subjective experience of probability and statistics to what happens in the Universal Wave Function? It's much easier to ignore that weirdness, since we're used to ignoring it in our daily lives anyway. It's also a more parsimonious interpretation than the others, because it doesn't postulate anything special about us (the "observers"). (This does not mean that consciousness is a quantum or even meta-physical phenomenon. Quite the opposite, actually: I find that the mystery lies more in why consciousness is unable to perceive quantum states despite existing in a universe that has quantum physics.)
- lisper 10y ago
  > Why don't we perceive the full linear combination of quantum states? My personal belief is that it is because consciousness is a classical information-processing phenomenon. In other words, we can only directly perceive things that can be described as real numbers rather than complex numbers because we are Turing machines, and Turing machines are classical.
  - bmh100 10y ago
    Then wouldn't an appropriately constructed sensor be able to record the full linear combination of quantum states?
    - lisper 10y ago
      No, because records are necessarily classical. This is because of the no-cloning theorem. You cannot copy quantum information, only classical information.
  - nhaehnle 10y ago
    That's an interesting thought, especially with the addendum of the no-cloning theorem. This fits with a Hofstadter-like perspective that consciousness is about "strange loops", where we somehow repeatedly evaluate simplified models of the world including yourself. Doing such repeated evaluations requires (at least partial) "cloning" of the state of the world outside for the purpose of evaluation, and cloning quantum states is impossible, hence consciousness must be a classical phenomenon. I like that line of argument. Note: I wouldn't state it as being unable to perceive things that can be described as complex numbers, but rather complex linear combinations.
loup-vaillant 10y ago
Wait a minute, since when is there any difference between Many Worlds and Decoherence? I always assumed they referred to the same interpretation, do they not?
- lisper 10y ago
  There are actually three different ideas in play here: decoherence as described by Zurek, the relative-state interpretation as described by Everett, and the popular account of the universe "splitting" when a measurement is made. All three of these are different, at least rhetorically, even though at a high enough conceptual level they all amount to the same thing.

jostylr 10y ago

I have never understood what the classic Many World Interpretation actually is. Splitting of universes has the same problem as collapse and probabilities become rather nebulous since presumably all possibilities do happen, after all. But there is a version of it which does make sense: https://arxiv.org/abs/0903.2211 https://arxiv.org/abs/0903.2211 The basic question for all theories is, "what is fundamentally real?" and the wave function of quantum mechanics just doesn't work in that role. This is why Bohmian mechanics adds particles; that is what is real in that theory. But to make a MW theory, one can integrate out the wave function to create a mass density function on 3-space. In any given instance, this is a mess and useless. But if you watch it evolve, then you could see multiple different stories evolving. And those are the different "worlds". There is no splitting, just regimes that are no longer relevant.

loup-vaillant 10y ago
> I have never understood what the classic Many World Interpretation actually is. There's little to understand: at its core, Many Worlds is real close to "shut up and calculate". The only significant assumption is that the wave function as described by the math is real. And when the math says there are 2 non-interacting blobs, well, this translates to 2 universes. That's about it. As for why people seems to reject it instinctively, it's probably because our subjective experience is linear —or mono-threaded. However, linear histories aren't contradictory with trees. Imagine a Git History that never merges: each leaf is the product of a linear set of modifications, a perfectly clean history. From that final commit's perspective, other branches might as well not exist. You'd need merges to break that illusion, and our universe doesn't have macro-merges —we only observe them at a very small scale, for instance with photon interference.
- bmh100 10y ago
  Doesn't that also require at least one additional dimension of spacetime to separate the two universes?
- lisper 10y ago
  > Imagine a Git History that never merges That is a really excellent analogy. It is also important to understand that there is a reason we don't have "macro merges", and that is because some irreversible process is required to create classical information, which is what we (the entities having this conversation) are actually made of. See: http://blog.rongarret.info/2014/10/parallel-universes-and-arrow-of-time.html http://blog.rongarret.info/2014/10/parallel-universes-and-ar...