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So when does decoherence happen? Provide a formula for it. That is what people struggle with in quantum mechanics, MWI just deflects the question. Without a for

So when does decoherence happen? Provide a formula for it. That is what people struggle with in quantum mechanics, MWI just deflects the question. Without a formula for when this phenomena happens any "interpretation" is just nonsense, except as a tool to get towards that formula.

russdill 4y ago
There's no yes/no equation as decoherence is statistical in nature.
- Jensson 4y ago
  Statistics also has formulas... This is the problem with MWI gospel, people come and say that it solves all the math but it leaves gaping holes like this. And you didn't even solve the randomness, since as you say it is "statistical", although that is just a theory we currently have no formula for this. Calling it a wave function collapse is much more honest since it accurately describes the situation, that we have no clue at what it is, why or when it happens. All we know how to do is calculate what possibly happens when we know that a wave function collapse will happen in a certain way.
DiogenesKynikos 4y ago
The mathematical framework for modeling decoherence involves coupling an isolated system to a thermal bath, described by a density matrix. Decoherence is a phenomenon that's been studied mathematically and experimentally, not simply an interpretation or hand-waving.
- _0w8t 4y ago
  This notion does not explain how the thermal bath appears. I.e. why the system interacts with a particular bath and not a superposition of such baths? At best the decoherence can try to explain how appearance of a sufficiently big classical object may trigger appearance of other objects, but it does not explain how the initial object appears.
  - lmm 4y ago
    > This notion does not explain how the thermal bath appears. The point of the bath is it's a generic model of a large system with lots of states and interactions. > I.e. why the system interacts with a particular bath and not a superposition of such baths? The bath can be in a superposition state at the start, that's fine. (Indeed the whole model would be pretty useless otherwise).
    - _0w8t 4y ago
      Again, models of decoherence assume existence of an external bath resembling classical state. By interacting with it the system becomes classical itself if it is and the bath is sufficiently big. But it does not explain how that external bath appears. In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function. Then the idea of the decoherence is that perhaps during evolution of this big wave function it is possible to find a subsystem that looks like it is approximately decoherent during some time interval. Then one claim that our visible universe is just such subsystem. The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears. Perhaps we have not tried hard enough or this is a really difficult problem, but at this point I am rather skeptical that decoherence is the right approach at all.
      - layer8 4y ago
        I don’t think it’s black & white, either coherent or decoherent, for subsystems. It’s rather a scale. In that sense there may not be discrete “worlds”, but rather a continuum of them, matching the degree to which particles are entangled or not entangled, and in superposition or not in superposition.
      - lmm 4y ago
        > models of decoherence assume existence of an external bath resembling classical state They don't assume it's classical. They assume it's a system with lots of states and interactions, because if you want to have a model of "the external universe" then you have to have some kind of concept of what that looks like. > In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function. Sure; the point is that if you split the universe into "these two entangled particles" and "the rest of the universe", because you want to understand how we observe that entanglement "decaying" as the particles interact with the rest of the universe, then you can model that as "these two entangled particles" interacting with "a thermal bath". > The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears. This is nonsense? Wavefunctions generally have a lot of structure and decomposing them into smaller subsystems and functions happens all the time.
lmm 4y ago
Decoherence of a system happens when the entropy of entanglement is maximal, so if you want a formula then it's S(Tr_a(p_ab)) -> N/e. In practice a complex system is probably never fully decoherent, but the separability is small enough to not matter; if we're being truly rigorous we work with it as a limit, similar to how we use the "classical limit" in other parts of QM or other contexts. (Analogy: imagine saying "Relativity doesn't explain how we live in a Newtonian world. If relativity is valid, it should be able to say at exactly what speed motion becomes nonrelativistic. Provide a formula for it")
- Jensson 4y ago
  Relativity is a real formula, you just say that decoherence seems to correlate with entropy and then gave a formula for entropy. We don't have a formula for decoherence. Any explanation for decoherence that doesn't help us find a formula for it is nonsense. Here is a better theory than MWI: We live in a simulation, the computer is optimized so when there are too complex interactions in an area it simplifies the state into some probable untangled version. This theory predicts that decoherence thus happens at certain computational complexity levels, that is something we could try to find and test experimentally making this theory more scientific than MWI. MWI doesn't lead anywhere, it isn't science, it is just nonsense. I'm not saying my theory here is a good one, but it is better than MWI which isn't a high bar.
  - lmm 4y ago
    > Relativity is a real formula Relativity is a real formula and the classical limit is a real phenomenon, but there's no formula for when a relativistic situation "becomes classical". > you just say that decoherence seems to correlate with entropy and then gave a formula for entropy If the observed system and the observer/external universe are fully entangled (i.e. their entropy of entanglement is maximal) then decoherence has occurred and all observations of the observed system by that observer will be indistinguishable from if the system were not in superposition. That is a mathematical fact that falls right out of the equations. So I don't know what else you're asking for.

russdill 4y ago

There's no yes/no equation as decoherence is statistical in nature.

Jensson 4y ago
Statistics also has formulas... This is the problem with MWI gospel, people come and say that it solves all the math but it leaves gaping holes like this. And you didn't even solve the randomness, since as you say it is "statistical", although that is just a theory we currently have no formula for this. Calling it a wave function collapse is much more honest since it accurately describes the situation, that we have no clue at what it is, why or when it happens. All we know how to do is calculate what possibly happens when we know that a wave function collapse will happen in a certain way.

DiogenesKynikos 4y ago

The mathematical framework for modeling decoherence involves coupling an isolated system to a thermal bath, described by a density matrix. Decoherence is a phenomenon that's been studied mathematically and experimentally, not simply an interpretation or hand-waving.

_0w8t 4y ago
This notion does not explain how the thermal bath appears. I.e. why the system interacts with a particular bath and not a superposition of such baths? At best the decoherence can try to explain how appearance of a sufficiently big classical object may trigger appearance of other objects, but it does not explain how the initial object appears.
- lmm 4y ago
  > This notion does not explain how the thermal bath appears. The point of the bath is it's a generic model of a large system with lots of states and interactions. > I.e. why the system interacts with a particular bath and not a superposition of such baths? The bath can be in a superposition state at the start, that's fine. (Indeed the whole model would be pretty useless otherwise).
  - _0w8t 4y ago
    Again, models of decoherence assume existence of an external bath resembling classical state. By interacting with it the system becomes classical itself if it is and the bath is sufficiently big. But it does not explain how that external bath appears. In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function. Then the idea of the decoherence is that perhaps during evolution of this big wave function it is possible to find a subsystem that looks like it is approximately decoherent during some time interval. Then one claim that our visible universe is just such subsystem. The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears. Perhaps we have not tried hard enough or this is a really difficult problem, but at this point I am rather skeptical that decoherence is the right approach at all.
    - layer8 4y ago
      I don’t think it’s black & white, either coherent or decoherent, for subsystems. It’s rather a scale. In that sense there may not be discrete “worlds”, but rather a continuum of them, matching the degree to which particles are entangled or not entangled, and in superposition or not in superposition.
    - lmm 4y ago
      > models of decoherence assume existence of an external bath resembling classical state They don't assume it's classical. They assume it's a system with lots of states and interactions, because if you want to have a model of "the external universe" then you have to have some kind of concept of what that looks like. > In universe-as-a-wave-function there is no external bath. The system as whole is always coherent and is described by a single wave function. Sure; the point is that if you split the universe into "these two entangled particles" and "the rest of the universe", because you want to understand how we observe that entanglement "decaying" as the particles interact with the rest of the universe, then you can model that as "these two entangled particles" interacting with "a thermal bath". > The trouble is that so far nobody came up with a model where such temporary approximately classical subsystem appears. This is nonsense? Wavefunctions generally have a lot of structure and decomposing them into smaller subsystems and functions happens all the time.

lmm 4y ago

Decoherence of a system happens when the entropy of entanglement is maximal, so if you want a formula then it's S(Tr_a(p_ab)) -> N/e. In practice a complex system is probably never fully decoherent, but the separability is small enough to not matter; if we're being truly rigorous we work with it as a limit, similar to how we use the "classical limit" in other parts of QM or other contexts. (Analogy: imagine saying "Relativity doesn't explain how we live in a Newtonian world. If relativity is valid, it should be able to say at exactly what speed motion becomes nonrelativistic. Provide a formula for it")

Jensson 4y ago
Relativity is a real formula, you just say that decoherence seems to correlate with entropy and then gave a formula for entropy. We don't have a formula for decoherence. Any explanation for decoherence that doesn't help us find a formula for it is nonsense. Here is a better theory than MWI: We live in a simulation, the computer is optimized so when there are too complex interactions in an area it simplifies the state into some probable untangled version. This theory predicts that decoherence thus happens at certain computational complexity levels, that is something we could try to find and test experimentally making this theory more scientific than MWI. MWI doesn't lead anywhere, it isn't science, it is just nonsense. I'm not saying my theory here is a good one, but it is better than MWI which isn't a high bar.
- lmm 4y ago
  > Relativity is a real formula Relativity is a real formula and the classical limit is a real phenomenon, but there's no formula for when a relativistic situation "becomes classical". > you just say that decoherence seems to correlate with entropy and then gave a formula for entropy If the observed system and the observer/external universe are fully entangled (i.e. their entropy of entanglement is maximal) then decoherence has occurred and all observations of the observed system by that observer will be indistinguishable from if the system were not in superposition. That is a mathematical fact that falls right out of the equations. So I don't know what else you're asking for.