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I skimmed the article, and admittedly didn't understand much. Action principles and path integrals are unfortunately one step above where my knowledge of physic

I skimmed the article, and admittedly didn't understand much. Action principles and path integrals are unfortunately one step above where my knowledge of physics stops. But seeing a headline that reads, "Our reality may be a sum of all possible realities", I wonder whether the point is to (a) explain new experiments, (b) develop simpler mathematics, (c) close the gap between intuition and theory, or (d) whether this is all unfalsifiable speculation. A charitable interpretation might be (c), but a skeptic within me thinks that this might be (d).

whatshisface 4y ago
Path integrals are for (a) and (b), but take that with the knowledge that Feynman came up with them maybe 70 or so years ago, so that anything we say about it now tends towards (c) and (d) by virtue of a lot of the (a) and (b) questions already being taken care of.
babyshake 4y ago
Sometimes the discussion I observe among scientific experts resembles the type of discourse I've seen from Marvel fans debating the finer points about multiverses and incursions within their comic book canon.
skissane 4y ago
I think one problem here - physics and the philosophy of physics are two different things, but a lot of people (even professional physicists) fail to treat them as distinct in practice. So long as we are talking about math, observation and experiment, that’s physics. But many of these “multiverse theories” are moving beyond that into philosophy, because they are not about the math, but rather how to interpret it; not only are existing observations or experiments are insufficient to determine their truth or falsehood, but we often have no idea of any practically feasible way to test them. There’s nothing wrong with doing philosophy-but let’s be honest when we are doing it, rather than pretending it is still just physics. Furthermore, your average professional physicist has indubitable expertise in physics, their expertise in philosophy (even the philosophy of physics) is much more variable.
- evanb 4y ago
  If you have a quantum-mechanical system that you describe by specifying a Hamiltonian, I can always write down an exactly equivalent path integral. A failure of equivalence between these two descriptions would be extremely exciting, as it'd be evidence of some paradigm beyond quantum mechanics.
  - ImHereToVote 4y ago
    Can you do that for two systems that interfere? I think that is where the multiverse stuff comes from.
    - evanb 4y ago
      Well, it depends on what you mean by "two systems". If they are described by one Hamiltonian the result is one path integral. In a relativistic quantum field theory, for example, one may describe systems of any number of particles. The path integral captures all the interference effects.
  - skissane 4y ago
    The mathematical equivalence of Hamiltonians and path integrals, by itself, doesn't tell us anything about a "multiverse", however. Since the mid-20th century, many philosophers have come to analyse everyday talk about possibility in terms of "possible worlds" or "possible universes". However, those who invented that language (such as Carnap and Kripke) weren't claiming that all those possible worlds were just as actual as this one – that claim only arose later (David Lewis). Similarly, the originators of the path integral formulation of QM (Dirac and Feynman) weren't claiming that all those paths were "equally real". By contrast, the majority of proponents of "multiverse" theories, are claiming those other "universes" are ultimately just as real as this one, as as opposed to merely being some theoretical construct, a mathematical metaphor. You can understand these "paths" in two ways – either as just a useful mathematical tool for analysing past observations and experimental results, and predicting future ones, but passing no judgement on their ultimate ontological status; or, as a claim that in some sense, all these paths "really exist". And, if you adopt the later reading, you can then argue whether they are all "equally real", or maybe one of them is "actual" and the others "non-actual", or even just maybe that some are "more actual" than others. Nothing wrong with those debates – but when we start engaging in them, we are no longer doing physics proper, we are doing the philosophy of physics.
wyager 4y ago
At some level this is just the application of wave mechanics to reality. "A vibration on a guitar string is just the sum of the vibrations of its harmonics." You are decomposing a system into a mathematically favorable basis, performing a calculation in that basis, and recovering the original basis (by linearity). You can do this in a hamiltonian way (find the eigenvectors of the hamiltonian, decompose your system into those, step them forward [easy] and add them back together) or in a lagrangian way (treat each point in the system as the source of a sort of spherical wavefront). Feynman is doing the latter - he's just asking "what if we treated other fields the same way we know we can treat the EM field via Huygens-Fresnel?" Calculate the progression of wavefronts through the field, using euler-lagrange to find the parts of the wavefront that don't fade away into random noise. So, in the framing of your question, I think it's mostly B and C, with maybe a bit of D (it's not clear if we have any kind of tool besides aesthetic preference to distinguish between extrinsically equivalent models). However, your framing might be a bit uncharitable.
- evanb 4y ago
  If we falsified quantum mechanics we might expect some formalisms (Hamiltonian, Lagrangian, path integral, whatever) to continue to work while others don't. So it's perfectly possible to falsify the idea that path integrals do not describe the world; doing so would demonstrate a failure of quantum mechanics and would be extremely exciting to physicists.

whatshisface 4y ago

Path integrals are for (a) and (b), but take that with the knowledge that Feynman came up with them maybe 70 or so years ago, so that anything we say about it now tends towards (c) and (d) by virtue of a lot of the (a) and (b) questions already being taken care of.

babyshake 4y ago

Sometimes the discussion I observe among scientific experts resembles the type of discourse I've seen from Marvel fans debating the finer points about multiverses and incursions within their comic book canon.

skissane 4y ago

I think one problem here - physics and the philosophy of physics are two different things, but a lot of people (even professional physicists) fail to treat them as distinct in practice. So long as we are talking about math, observation and experiment, that’s physics. But many of these “multiverse theories” are moving beyond that into philosophy, because they are not about the math, but rather how to interpret it; not only are existing observations or experiments are insufficient to determine their truth or falsehood, but we often have no idea of any practically feasible way to test them. There’s nothing wrong with doing philosophy-but let’s be honest when we are doing it, rather than pretending it is still just physics. Furthermore, your average professional physicist has indubitable expertise in physics, their expertise in philosophy (even the philosophy of physics) is much more variable.

evanb 4y ago
If you have a quantum-mechanical system that you describe by specifying a Hamiltonian, I can always write down an exactly equivalent path integral. A failure of equivalence between these two descriptions would be extremely exciting, as it'd be evidence of some paradigm beyond quantum mechanics.
- ImHereToVote 4y ago
  Can you do that for two systems that interfere? I think that is where the multiverse stuff comes from.
  - evanb 4y ago
    Well, it depends on what you mean by "two systems". If they are described by one Hamiltonian the result is one path integral. In a relativistic quantum field theory, for example, one may describe systems of any number of particles. The path integral captures all the interference effects.
- skissane 4y ago
  The mathematical equivalence of Hamiltonians and path integrals, by itself, doesn't tell us anything about a "multiverse", however. Since the mid-20th century, many philosophers have come to analyse everyday talk about possibility in terms of "possible worlds" or "possible universes". However, those who invented that language (such as Carnap and Kripke) weren't claiming that all those possible worlds were just as actual as this one – that claim only arose later (David Lewis). Similarly, the originators of the path integral formulation of QM (Dirac and Feynman) weren't claiming that all those paths were "equally real". By contrast, the majority of proponents of "multiverse" theories, are claiming those other "universes" are ultimately just as real as this one, as as opposed to merely being some theoretical construct, a mathematical metaphor. You can understand these "paths" in two ways – either as just a useful mathematical tool for analysing past observations and experimental results, and predicting future ones, but passing no judgement on their ultimate ontological status; or, as a claim that in some sense, all these paths "really exist". And, if you adopt the later reading, you can then argue whether they are all "equally real", or maybe one of them is "actual" and the others "non-actual", or even just maybe that some are "more actual" than others. Nothing wrong with those debates – but when we start engaging in them, we are no longer doing physics proper, we are doing the philosophy of physics.

wyager 4y ago

At some level this is just the application of wave mechanics to reality. "A vibration on a guitar string is just the sum of the vibrations of its harmonics." You are decomposing a system into a mathematically favorable basis, performing a calculation in that basis, and recovering the original basis (by linearity). You can do this in a hamiltonian way (find the eigenvectors of the hamiltonian, decompose your system into those, step them forward [easy] and add them back together) or in a lagrangian way (treat each point in the system as the source of a sort of spherical wavefront). Feynman is doing the latter - he's just asking "what if we treated other fields the same way we know we can treat the EM field via Huygens-Fresnel?" Calculate the progression of wavefronts through the field, using euler-lagrange to find the parts of the wavefront that don't fade away into random noise. So, in the framing of your question, I think it's mostly B and C, with maybe a bit of D (it's not clear if we have any kind of tool besides aesthetic preference to distinguish between extrinsically equivalent models). However, your framing might be a bit uncharitable.

evanb 4y ago
If we falsified quantum mechanics we might expect some formalisms (Hamiltonian, Lagrangian, path integral, whatever) to continue to work while others don't. So it's perfectly possible to falsify the idea that path integrals do not describe the world; doing so would demonstrate a failure of quantum mechanics and would be extremely exciting to physicists.