4 ms·

Also, yes, gravitational waves travel at c.

deleted 9y ago
[deleted]
Filligree 9y ago
(Caution: Pedantry ahead.) Gravitational waves are believed to travel at C, the theory says they should travel at C, and we're slowly narrowing in on C in measurements, but our ability to measure gravity waves is poor enough that we aren't yet quite sure. Which is one thing this observation would fix, assuming it's real.
- raattgift 9y ago
  General Relativity (GR) is a metric theory of gravitation, with one metric to which everything couples. In GR gravitational waves (GW) have lightlike worldlines. Consequently, a source emitting both electromagnetic and gravitational radiation will have its GWs and EMWs (or more generally its optical image and the direction in which things indicating its gravitational influence point) line up. This has been well-tested observationally, for example by watching the deflection of light from distant objects (like quasars) around Jupiter (whose mass, orbit, and distance from us are all very well characterized). However, one can write down a bimetric theory of gravitation with different couplings. It's possible to write down a bimetric theory in which gravitational waves move more slowly or more quickly than electromagnetic waves. It was fairly popular some years to take this kind of approach to solve some cosmological problems relating to the homogeneity within the horizon [1]. These were often cast as "variable speed of light", for aesthetic reasons fixing the speed of the gravitational interaction. However, it is perfectly reasonable to call the same models "variable speed of gravitational radiation" fixing the speed of light, as one has many freedoms with respect to coordinate conditions in General Relativity. The problem is that these "variable speed of gravitational radiation" theories do not match observations of the galaxy-filled parts of the universe that we can see, and also does not match what we see in the Cosmic Microwave Background. (Some bimetric models fail to match the results of laboratory-scale physics experiments too.) Viable bimetric theories thus have the second metric decay in the very very early universe, such that in the galaxy-filled epoch the speeds of light and gravitational radiation are identical, and physics becomes (outside of the very early universe) indistinguishable from their "standard" single-metric General Relativity based generally covariant formulations. Such decaying-bimetric theories usually are designed to do away with cosmic inflation, but it becomes difficult to distinguish between cosmic inflation and viable bimetric-decay models because the observables eventually have to become identical, and the time at which they can differ gets pushed back further as we develop observatories which can resolve objects at ever higher redshifts, or as we can get better data on the anisotropies of the CMB. > we're slowly narrowing in on C in measurements We should determine c empirically, but we have already done so to exquisite precision. However, we can also fix c to some exact value (e.g. the CODATA value, or 1) and be mindful of the side effects of doing so. This is, by far, the most common approach; you will be hard-pressed to find any formulation of a physical law which introduces uncertainty into the value of c, although it's certainly doable. The fixed CODATA value is extremely good. The relative uncertainty in the speed of light is principally driven by the uncertainties in interferometry, which at the time of the 1983 redefinition of the metre was less than 0.1 part per billion (and is now less than a part per trillion, and so for all practical purposes is unimportant at scales of the observable universe). Finally, one should note that in a general curved spacetime, while the constant factor "c" arises everywhere, it can only be taken as a speed when comparing two objects that co-occupy exactly the same infinitesimal point in spacetime. Comparing the speeds of distant objects is something that one should avoid in General Relativity. However, everywhere in every spacetime, in vacuum conditions one should find the same "c" as the upper limit of relative speeds of objects just as they enter, co-occupy, and exit the same point. - -- [1] https://www.wikiwand.com/en/Horizon_problem https://www.wikiwand.com/en/Horizon_problem
  - pcnix 9y ago
    I must admit, I really enjoyed reading your comments on this thread. Good work, and thanks for the effort!
  - Koshkin 9y ago
    What are the side effects of fixing the value of c?
    - raattgift 9y ago
      Let's flip the question and ask what happens if we let the value of c depend on the location in spacetime. Ellis provides a "short checklist of issues that should be satisfactorily handled by" theories that have a value of c that depends on location in spacetime. https://arxiv.org/abs/astro-ph/0703751 https://arxiv.org/abs/astro-ph/0703751 The tl;dr version is that relativistic physical theories will need revising because in the face of a location-dependent c, and in particular the problem arises because we necessarily break lengths and durations when c is not everywhere-and-everywhen identical. More narrowly observables like spectral lines are sensitive to ratios involving the quantity hc which are taken to be constant. Since cosmological redshifting of spectral lines fits in a substantial web of observables related to distance (e.g. angular diameter, surface brightness) we can practically rule out variation in hc to a very high redshift (z > 10). You might instead be asking what happens if c is the same everywhere but we've settled on a very slightly wrong value of c. The answer is that this will almost be absorbed into our system of units, in particular in various ratios involving hc. If we change the value of c to the slightly improved value, we also probably slightly change things like the fine structure constant and the electron-to-proton mass ratio, which are dimensionless quantities with ratios involving hc. These dimensionless quantities are good checks on the many ways in which we might measure c empirically.
  - Filligree 9y ago
    > We should determine c empirically, but we have already done so to exquisite precision. As interesting as that is, what I meant we're narrowing down is the speed of gravity -- that is, that it's almost certainly equal to C. Not that we're narrowing down C itself, it's way more convenient to define that as 1. Since you're here, though... the horizon problem. I can kind of understand the logic that makes it a problem, but... If you have the same initial conditions everywhere, and the same laws of physics, wouldn't you expect everything we can see of the universe to look similar even if there hasn't been any communication? That seems like an obvious implication of having deterministic physics, and sure, "same initial conditions" is a big assumption -- but I never see this hypothesis offered.
- Koshkin 9y ago
  > we're slowly narrowing in on C in measurements Interesting... I thought that c = 299,792,458 m/s exactly. So what are we are actually measuring here? The meter and/or the second?
  - ekimekim 9y ago
    I believe the OP meant that they're narrowing in on being confident that gravitational waves travel at C, not narrowing in on a more precise value of C. That said, if we do obtain a more precise value of C, the definition that changes is the meter. The second is defined in terms of energy states of a caesium atom.
    - Filligree 9y ago
      Right you are. I wrote that a bit ambiguously.

deleted 9y ago

[deleted]

(Caution: Pedantry ahead.) Gravitational waves are believed to travel at C, the theory says they should travel at C, and we're slowly narrowing in on C in measurements, but our ability to measure gravity waves is poor enough that we aren't yet quite sure. Which is one thing this observation would fix, assuming it's real.

raattgift 9y ago
General Relativity (GR) is a metric theory of gravitation, with one metric to which everything couples. In GR gravitational waves (GW) have lightlike worldlines. Consequently, a source emitting both electromagnetic and gravitational radiation will have its GWs and EMWs (or more generally its optical image and the direction in which things indicating its gravitational influence point) line up. This has been well-tested observationally, for example by watching the deflection of light from distant objects (like quasars) around Jupiter (whose mass, orbit, and distance from us are all very well characterized). However, one can write down a bimetric theory of gravitation with different couplings. It's possible to write down a bimetric theory in which gravitational waves move more slowly or more quickly than electromagnetic waves. It was fairly popular some years to take this kind of approach to solve some cosmological problems relating to the homogeneity within the horizon [1]. These were often cast as "variable speed of light", for aesthetic reasons fixing the speed of the gravitational interaction. However, it is perfectly reasonable to call the same models "variable speed of gravitational radiation" fixing the speed of light, as one has many freedoms with respect to coordinate conditions in General Relativity. The problem is that these "variable speed of gravitational radiation" theories do not match observations of the galaxy-filled parts of the universe that we can see, and also does not match what we see in the Cosmic Microwave Background. (Some bimetric models fail to match the results of laboratory-scale physics experiments too.) Viable bimetric theories thus have the second metric decay in the very very early universe, such that in the galaxy-filled epoch the speeds of light and gravitational radiation are identical, and physics becomes (outside of the very early universe) indistinguishable from their "standard" single-metric General Relativity based generally covariant formulations. Such decaying-bimetric theories usually are designed to do away with cosmic inflation, but it becomes difficult to distinguish between cosmic inflation and viable bimetric-decay models because the observables eventually have to become identical, and the time at which they can differ gets pushed back further as we develop observatories which can resolve objects at ever higher redshifts, or as we can get better data on the anisotropies of the CMB. > we're slowly narrowing in on C in measurements We should determine c empirically, but we have already done so to exquisite precision. However, we can also fix c to some exact value (e.g. the CODATA value, or 1) and be mindful of the side effects of doing so. This is, by far, the most common approach; you will be hard-pressed to find any formulation of a physical law which introduces uncertainty into the value of c, although it's certainly doable. The fixed CODATA value is extremely good. The relative uncertainty in the speed of light is principally driven by the uncertainties in interferometry, which at the time of the 1983 redefinition of the metre was less than 0.1 part per billion (and is now less than a part per trillion, and so for all practical purposes is unimportant at scales of the observable universe). Finally, one should note that in a general curved spacetime, while the constant factor "c" arises everywhere, it can only be taken as a speed when comparing two objects that co-occupy exactly the same infinitesimal point in spacetime. Comparing the speeds of distant objects is something that one should avoid in General Relativity. However, everywhere in every spacetime, in vacuum conditions one should find the same "c" as the upper limit of relative speeds of objects just as they enter, co-occupy, and exit the same point. - -- [1] https://www.wikiwand.com/en/Horizon_problem https://www.wikiwand.com/en/Horizon_problem
- pcnix 9y ago
  I must admit, I really enjoyed reading your comments on this thread. Good work, and thanks for the effort!
- Koshkin 9y ago
  What are the side effects of fixing the value of c?
  - raattgift 9y ago
    Let's flip the question and ask what happens if we let the value of c depend on the location in spacetime. Ellis provides a "short checklist of issues that should be satisfactorily handled by" theories that have a value of c that depends on location in spacetime. https://arxiv.org/abs/astro-ph/0703751 https://arxiv.org/abs/astro-ph/0703751 The tl;dr version is that relativistic physical theories will need revising because in the face of a location-dependent c, and in particular the problem arises because we necessarily break lengths and durations when c is not everywhere-and-everywhen identical. More narrowly observables like spectral lines are sensitive to ratios involving the quantity hc which are taken to be constant. Since cosmological redshifting of spectral lines fits in a substantial web of observables related to distance (e.g. angular diameter, surface brightness) we can practically rule out variation in hc to a very high redshift (z > 10). You might instead be asking what happens if c is the same everywhere but we've settled on a very slightly wrong value of c. The answer is that this will almost be absorbed into our system of units, in particular in various ratios involving hc. If we change the value of c to the slightly improved value, we also probably slightly change things like the fine structure constant and the electron-to-proton mass ratio, which are dimensionless quantities with ratios involving hc. These dimensionless quantities are good checks on the many ways in which we might measure c empirically.
- Filligree 9y ago
  > We should determine c empirically, but we have already done so to exquisite precision. As interesting as that is, what I meant we're narrowing down is the speed of gravity -- that is, that it's almost certainly equal to C. Not that we're narrowing down C itself, it's way more convenient to define that as 1. Since you're here, though... the horizon problem. I can kind of understand the logic that makes it a problem, but... If you have the same initial conditions everywhere, and the same laws of physics, wouldn't you expect everything we can see of the universe to look similar even if there hasn't been any communication? That seems like an obvious implication of having deterministic physics, and sure, "same initial conditions" is a big assumption -- but I never see this hypothesis offered.
Koshkin 9y ago
> we're slowly narrowing in on C in measurements Interesting... I thought that c = 299,792,458 m/s exactly. So what are we are actually measuring here? The meter and/or the second?
- ekimekim 9y ago
  I believe the OP meant that they're narrowing in on being confident that gravitational waves travel at C, not narrowing in on a more precise value of C. That said, if we do obtain a more precise value of C, the definition that changes is the meter. The second is defined in terms of energy states of a caesium atom.
  - Filligree 9y ago
    Right you are. I wrote that a bit ambiguously.