3 ms·

These are fun questions to ask. If you take away everything in the thought experiment except a single hydrogen ion, what can it rotate about? What does rotati

These are fun questions to ask. If you take away everything in the thought experiment except a single hydrogen ion, what can it rotate about? What does rotation mean in a universe without anything except a single atom? What does inertia mean without respect to something else? Can such a particle have a velocity?

whatshisface 9y ago
If all you have is a single hydrogen ion (proton? I assume you mean H+), then you will always be able to choose a coordinate system where it is neither moving nor rotating. You can also do this if there is a universe outside. Alternatively, you can choose a coordinate system where the particle is rotating, accelerating, or moving however you like. Your choice will be determined by the goals you have. (Without the laws of motion, there is no reason to prefer even intertial frames over nonintertial ones.)
- state_less 9y ago
  Yep, I was thinking about a proton. I probably should have been more explicit. Is the particle moving or is the coordinate system? It seems, like you say, to be arbitrary. Without something else in the universe, the particle could have any rotation, velocity, inertia, etc... depending on which coordinate system you choose. The coordinate system seems to be layered on, from a universe where the idea of space and time were more useful.
  - vorg 9y ago
    There must be something else in the Universe to observe the single proton for it to have rotation, etc, according to quantum physics. Extend this idea to the centrifugal force on the water in the bucket in a Universe with nothing else in it, and the centrifugal force is similarly both there and not there, in a quantum superposition until observed. The value of Planck's constant is thus a function of the large-scale distribution of energy in the Universe, rather than a fixed property of spacetime itself.
    - testestx 9y ago
      > There must be something else in the Universe to observe the single proton for it to have rotation, etc, according to quantum physics. No, according to the Copenhagen interpretation.
      - whatshisface 9y ago
        Even in the Copenhagen interpretation states can have well-defined angular momenta before wavefunction collapse.
        vorg 9y ago
        I thought in QM you couldn't know both the degree of rotation and the direction of the axis for a particle. If so, I wouldn't call that "well-defined".
  - frutiger 9y ago
    > It seems, like you say, to be arbitrary. Note that in general relativity, which allows inertial and non-inertial reference frames as equally valid, there is some non-arbitrary motion of objects that is independent of the choice of frame. These are the so-called tidal gravitational effects that cannot be transformed away in any frame, and are easiest described as curvature of spacetime due to stress-energy.
    - raattgift 9y ago
      Small point: in General Relativity you can have a vacuum solution of the Einstein Field Equations with arbitrary curvature; a test object can probe that curvature despite the absence of any (other) stress-energy. A smaller point: "motion" and "tidal...effects" each implicitly chooses a splitting (in particular a 1+3 threading) of spacetime into space and time. That's fine; it's really hard for general relativity to confront observation without doing some splitting, and implicitly threading is standard behaviour (Synge does this in his textbook, for example, when discussing 3-velocity and spatial distance and offering up his world function biscalar; note that this is different from explicitly applying a 1+3 formalism). Your central point is right though: coordinate transformations or arbitrary choices of splittings -- 1+3 threading or 3+1 slicings are examples -- cannot get rid of real curvature.
      - state_less 9y ago
        Out of curiosity, where is the spacetime curvature coming from in the single particle universe? And if the particle curves spacetime, what effect does it have on itself?
        raattgift 9y ago
        In General Relativity, spacetime itself can be curved by its very nature. Vacuum solutions which are exact solutions of the Einstein Field Equations (the core set of partial differential equations of General Relativity; the EFEs), have been the subject of extensive research since the 1920s. A test particle is one with negligible mass and extent, and thus does not itself perturb the curvature of the background vacuum spacetime. If a real particle is electrically neutral, extremely low mass, and nearly pointlike, then in a vacuum spacetime it should behave very much like a test particle. Moreover, for microscopic real objects, which aren't truly pointlike and which may not be wholly chargeless, it is impractically hard to tell at a large enough spatial distance that it's not a test particle. So a test particle or test field does not source the spacetime curvature -- it just rides along the background spacetime, which is arbitrarily curved by its nature. We can extend the notion to a test field that is almost wholly massless, like a single-electron quantum field. The test field sits on the background, but doesn't influence the background's dynamics. Real quantum fields, like test fields, permeate the whole of spacetime. However they tend to have abundant stress-energy in them, so source some of the curvature of the whole spacetime, and typically not uniformly. One can fix a gauge (like how one calibrates an air-pressure altimeter) that lets one talk about the inherent curvature of the background spacetime and the contribution to the total curvature of the lowest density of the quantum field. Typically the background is chosen to be some exact vacuum solution of the EFEs with corrections added via something like perturbation theory; flat spacetime, Schwarzschild and Robertson-Walker expanding spacetimes are popular backgrounds, depending on what one is studying. Sometimes, though one wants to think about an electron rather than some characteristic set of numbers in some all-over-spacetime fields. In that case one (probably implicitly) fixes a gauge that lets one talk about the electron as an independent object that generates an electromagnetic field which, because that has some nonzero stress-energy (zero being set by our gauging choices and being found sufficiently far from our electron) it influences the background curvature of the spacetime (the background again being set by our gauging choices). In either paradigm, one might want to think about, in reverse order, the gravitational back-reaction of the electron (and its EM field)'s gravitational footprint on itself, or the gravitational back-reaction of the overdensities in the all-over-spacetime (classical or quantum) fields on the regions of spacetime they are found in. "Gravity gravitates" is the problem: this arises from the EFEs' non-linearity. Fortunately, for a single electron these back-reactions will be very small, because electrons in either paradigm have very little stress-energy, so their contribution to any curvature will thus be so extremely tiny that it will be practically immeasurable, so there is basically no hope of measuring higher-order contributions (that is, the electron's gravitational influence's own influence on the curvature). Negiligibility saves a lot of headaches, because working with gravitational backreaction is hard.
- raattgift 9y ago
  > ... rotating, accelerating ... there is no reason to prefer even intertial frames over nonintertial ones.) There's a whole set of excellent reasons to prefer to work in inertial frames where possible, most of them having to do with calculational burden. Our case here is essentially flat electrovac with a test field - do you really want to work in Rindler or Born coordinates or worse if you don't have to? You're free to do so if you're feeling masochistic (or doing it as a learning exercise), just as you're free go further and solve Maxwell's equations in curved spacetime in arbitrary coordinates with the vector potentials in some arbitrary gauge (\partial_{\mu} A^{\nu} \neq 0). And with "proton?" then you might as well dive into QCD as well. Unnecessary extra work is surely a good reason to prefer to use the simpler maths where the results will be indistinguishable. > Without the laws of motion I don't understand this point. Are you ditching the action principle somehow?
  - whatshisface 9y ago
    > > Without the laws of motion There are no meaningful potentials in the one-particle universe that the OP described. However the particle is "really moving," you could just invent a coordinate system to make it "move" however you like. Even introducing EM would bump you up to at least two particles! The only reasonable one particle universe would be one where the partice was coupled to nothing. (It is under the "try to interpret it as they meant it" doctrine that I go from a proton to a particle that doesn't leave behind a disturbed field when it accelerates.)

whatshisface 9y ago

If all you have is a single hydrogen ion (proton? I assume you mean H+), then you will always be able to choose a coordinate system where it is neither moving nor rotating. You can also do this if there is a universe outside. Alternatively, you can choose a coordinate system where the particle is rotating, accelerating, or moving however you like. Your choice will be determined by the goals you have. (Without the laws of motion, there is no reason to prefer even intertial frames over nonintertial ones.)

state_less 9y ago
Yep, I was thinking about a proton. I probably should have been more explicit. Is the particle moving or is the coordinate system? It seems, like you say, to be arbitrary. Without something else in the universe, the particle could have any rotation, velocity, inertia, etc... depending on which coordinate system you choose. The coordinate system seems to be layered on, from a universe where the idea of space and time were more useful.
- vorg 9y ago
  There must be something else in the Universe to observe the single proton for it to have rotation, etc, according to quantum physics. Extend this idea to the centrifugal force on the water in the bucket in a Universe with nothing else in it, and the centrifugal force is similarly both there and not there, in a quantum superposition until observed. The value of Planck's constant is thus a function of the large-scale distribution of energy in the Universe, rather than a fixed property of spacetime itself.
  - testestx 9y ago
    > There must be something else in the Universe to observe the single proton for it to have rotation, etc, according to quantum physics. No, according to the Copenhagen interpretation.
    - whatshisface 9y ago
      Even in the Copenhagen interpretation states can have well-defined angular momenta before wavefunction collapse.
      - vorg 9y ago
        I thought in QM you couldn't know both the degree of rotation and the direction of the axis for a particle. If so, I wouldn't call that "well-defined".
- frutiger 9y ago
  > It seems, like you say, to be arbitrary. Note that in general relativity, which allows inertial and non-inertial reference frames as equally valid, there is some non-arbitrary motion of objects that is independent of the choice of frame. These are the so-called tidal gravitational effects that cannot be transformed away in any frame, and are easiest described as curvature of spacetime due to stress-energy.
  - raattgift 9y ago
    Small point: in General Relativity you can have a vacuum solution of the Einstein Field Equations with arbitrary curvature; a test object can probe that curvature despite the absence of any (other) stress-energy. A smaller point: "motion" and "tidal...effects" each implicitly chooses a splitting (in particular a 1+3 threading) of spacetime into space and time. That's fine; it's really hard for general relativity to confront observation without doing some splitting, and implicitly threading is standard behaviour (Synge does this in his textbook, for example, when discussing 3-velocity and spatial distance and offering up his world function biscalar; note that this is different from explicitly applying a 1+3 formalism). Your central point is right though: coordinate transformations or arbitrary choices of splittings -- 1+3 threading or 3+1 slicings are examples -- cannot get rid of real curvature.
    - state_less 9y ago
      Out of curiosity, where is the spacetime curvature coming from in the single particle universe? And if the particle curves spacetime, what effect does it have on itself?
      - raattgift 9y ago
        In General Relativity, spacetime itself can be curved by its very nature. Vacuum solutions which are exact solutions of the Einstein Field Equations (the core set of partial differential equations of General Relativity; the EFEs), have been the subject of extensive research since the 1920s. A test particle is one with negligible mass and extent, and thus does not itself perturb the curvature of the background vacuum spacetime. If a real particle is electrically neutral, extremely low mass, and nearly pointlike, then in a vacuum spacetime it should behave very much like a test particle. Moreover, for microscopic real objects, which aren't truly pointlike and which may not be wholly chargeless, it is impractically hard to tell at a large enough spatial distance that it's not a test particle. So a test particle or test field does not source the spacetime curvature -- it just rides along the background spacetime, which is arbitrarily curved by its nature. We can extend the notion to a test field that is almost wholly massless, like a single-electron quantum field. The test field sits on the background, but doesn't influence the background's dynamics. Real quantum fields, like test fields, permeate the whole of spacetime. However they tend to have abundant stress-energy in them, so source some of the curvature of the whole spacetime, and typically not uniformly. One can fix a gauge (like how one calibrates an air-pressure altimeter) that lets one talk about the inherent curvature of the background spacetime and the contribution to the total curvature of the lowest density of the quantum field. Typically the background is chosen to be some exact vacuum solution of the EFEs with corrections added via something like perturbation theory; flat spacetime, Schwarzschild and Robertson-Walker expanding spacetimes are popular backgrounds, depending on what one is studying. Sometimes, though one wants to think about an electron rather than some characteristic set of numbers in some all-over-spacetime fields. In that case one (probably implicitly) fixes a gauge that lets one talk about the electron as an independent object that generates an electromagnetic field which, because that has some nonzero stress-energy (zero being set by our gauging choices and being found sufficiently far from our electron) it influences the background curvature of the spacetime (the background again being set by our gauging choices). In either paradigm, one might want to think about, in reverse order, the gravitational back-reaction of the electron (and its EM field)'s gravitational footprint on itself, or the gravitational back-reaction of the overdensities in the all-over-spacetime (classical or quantum) fields on the regions of spacetime they are found in. "Gravity gravitates" is the problem: this arises from the EFEs' non-linearity. Fortunately, for a single electron these back-reactions will be very small, because electrons in either paradigm have very little stress-energy, so their contribution to any curvature will thus be so extremely tiny that it will be practically immeasurable, so there is basically no hope of measuring higher-order contributions (that is, the electron's gravitational influence's own influence on the curvature). Negiligibility saves a lot of headaches, because working with gravitational backreaction is hard.
raattgift 9y ago
> ... rotating, accelerating ... there is no reason to prefer even intertial frames over nonintertial ones.) There's a whole set of excellent reasons to prefer to work in inertial frames where possible, most of them having to do with calculational burden. Our case here is essentially flat electrovac with a test field - do you really want to work in Rindler or Born coordinates or worse if you don't have to? You're free to do so if you're feeling masochistic (or doing it as a learning exercise), just as you're free go further and solve Maxwell's equations in curved spacetime in arbitrary coordinates with the vector potentials in some arbitrary gauge (\partial_{\mu} A^{\nu} \neq 0). And with "proton?" then you might as well dive into QCD as well. Unnecessary extra work is surely a good reason to prefer to use the simpler maths where the results will be indistinguishable. > Without the laws of motion I don't understand this point. Are you ditching the action principle somehow?
- whatshisface 9y ago
  > > Without the laws of motion There are no meaningful potentials in the one-particle universe that the OP described. However the particle is "really moving," you could just invent a coordinate system to make it "move" however you like. Even introducing EM would bump you up to at least two particles! The only reasonable one particle universe would be one where the partice was coupled to nothing. (It is under the "try to interpret it as they meant it" doctrine that I go from a proton to a particle that doesn't leave behind a disturbed field when it accelerates.)