6 ms·

But the arms are predicted to vary in those cases by the same theory that LIGO is confirming: our rotation causes frame dragging, and there's some weird Sun-Ear

• axilmar 8y ago
  By aether, do you mean an underlying medium that allows forces to be propagated? I guess that using that definition, there is an 'aether'. The difference with the rejected concept of aether is that this "aether" is deformable by gravity, whereas the rejected one is not.
  • raattgift 8y ago
    > underlying medium that allows forces to be propagated General Relativity is a local theory concerned with the mechanisms that generate the metric, the geodesics implied by the metric, and the coupling of objects to those geodesics. The relevant forces are those which accelerate objects into non-geodesic motion (or boost them from one geodesic to another). Those are local[1] as well: electromagnetism and the nuclear interactions. There's nothing like a luminiferous aether or underlying medium in the Standard Model, even if you look funnily at the gauge bosons -- they obey Lorentz covariance. I made a couple of sibling comments to yours, one of which deals directly with your comment's parent's idea of a gravitational aether. - -- [1] RM Wald, _Quantum Field Theory on Curved Spacetime and Black Hole Thermodynamics_ (University of Chicago Press, 1994). Cf. the top of page 6 of Hollands & Wald 2014, https://arxiv.org/abs/1401.2026 https://arxiv.org/abs/1401.2026
    • NotAnEconomist 8y ago
      Isn't every "field" in QFT basically an aether?
      • raattgift 8y ago
        Please tell me what you mean by aether, as rigorously as you can, and then I can give you an answer to the question which seems to be bedevilling you. Meanwhile I can guess at what you're asking: The Standard Model (a QFT) has interacting quantum fields obeying purely local dynamics. The behaviour "here-and-now" depends on the field-values "here". It does not depend on field-values "now" but far from "here". Moreover, the Standard Model is Lorentz-invariant, meaning its laws hold in any inertial frame of reference, thus the scare quotes in the previous sentence. The luminiferous aether that Michelson & Morley were looking to measure was motivated by finding a single special (and universal, or at least covering the whole solar system) inertial frame of reference in which Maxwell's equations hold exactly. No such frame exists; there is a huge democracy of inertial frames in which relativistic electrodynamics is exact in the classical limit. ( https://en.wikipedia.org/wiki/Preferred_frame https://en.wikipedia.org/wiki/Preferred_frame )
  • NotAnEconomist 8y ago
    > By aether, do you mean an underlying medium that allows forces to be propagated? I guess that using that definition, there is an 'aether'. That's what an 'aether' is -- that background medium which the interaction is happening within. My conception of it is that Michelson-Morley disproved an infinitely rigid aether, which was the conception at the time and squared with Newtonian physics because it's equivalent to an infinite speed of information. Einstein then corrected the aether models to account for the finite speed of information through the aether, and the impacts that aether waves have on causality. My impression has always been that dropping 'aether' was merely a branding move, rather than anything technical about the term. (Not that I fault scientists for this, it's politically savvy -- but it's weird to see their marketing used as arguments decades later.)
• raattgift 8y ago
  > My mental model of this is that it perturbs the aether ("spacetime") through which it travels, radiating waves which carry energy out of the system. Is there a different one? Yes, and I'll get to that in my third last paragraph below. Two isolated compact objects in mutual orbit generate a spacetime-filling "tumbling barbell" dynamical metric (as opposed to static or stationary; the two weights on the ends of the notional bar eventually collide), and gravitational radiation is simply a piece of the dynamical spacetime. Let's slice the spacetime into spacelike hypervolumes indexed by time, and call our sources B and b, and our observer O. Let's take two times, t_| and t_-. Pipes or hyphens are the not-really-there bar of the barbell connecting the weighted ends; in the schematic below - and | have essentially identical spatial length. t_-: B---b O t_|: B | | O | b In a full 3+1 formalism of General Relativity we'd calculate the geodesics generated by B and b. More on that later. However, since O is weakly stressed and moving very slowly compared to c, and B and b are moving slowly with respect to c, we are firmly in the weak field limit and can linearize [1]. In effect we can think pretty Newtonian: what attractive force does O feel? If O is a planet with its equator is on the extended line of the barbell at t_- then observers in the upper hemisphere will measure a gravitational attraction pointing equator-wards. Conversely, at t_| the same observers will measure a gravitational attraction pointing away from the equator. Since Bb is tumbling (suppose it's clockwise about the middle hyphen or vertical bar in this case), the attraction sweeps equatorwards and anti-equatorwards, and we'll also see the times when the positions of B and b are essentially reversed in the two time-slices above. The frequency of the changes from anti-equatorwards to equatorwards (in our schematic, that's the maximum stretch/squeeze) is the detection frequency, the periodic change in amplitude depends on how circular or elliptic the tumbling is, the amplitude grows as the orbit decays, and the amplitude itself depends on the masses and the distances among the objects. Feynman's "sticky bead" [2] visualization is probably helpful here. If we replace our polar observers on O, and O itself, with a long pole (perpendicular to O's equator, which means we are perpendicular to the "bar" at t_-) with a couple of beads able to slide north-and-south, then as we approach t_- we expect the north bead to slide south, and the south bead to slide north. As we approach t_- we expect the north bead to slide north, and the south bead to slide south. The beads oscillate north-and-south matching the Bb orbit. If there is friction between the pole and the beads, heat is generated. If we make the pole vanish and let the beads sit in space at the same positions they would be on the pole, we can see that their behaviour is simply geodesic; over short timescales the deviation from purely timelike geodesic motion is neglibible (over long timescales they may crash into each other or get drawn into the Bb system, since tumbling barbell metrics are collapsing spacetimes). The geodesics are curved in a patch of local Cartesian coordinates with the origin at the centre of the pole at some moment in time. In the full GR picture the heat from the "sticky beads" on the pole is because the pole pulls the beads off their geodesics. Moving objects out of free-fall (i.e., off geodesics) requires work. This is a local phenomenon, General Relativity being a local theory. However, the full GR picture is a bear to work with, and as there are several reasonable choices for slicing the 4-spacetime into 3+1 and as at astronomical distances post-Newtonian corrections are small, linearized gravity is the formalism of choice, and that choice drives vocabulary (and intuitions, especially in experiment design) somewhat. In effect, our BbO schematic system is similar to a https://en.wikipedia.org/wiki/Cavendish_experiment https://en.wikipedia.org/wiki/Cavendish_experiment apparatus. Finally, "... carry energy out of the system ..." depends on the system. In the full GR theory in our toy model above, the system is the entire spacetime. We could measure an energy at spacelike or lightlike infinity and see that it's constant [3]. However, if we measure in a region of spacetime encircling Bb but not O (or our sticky beads, or freely floating beads) then energy is clearly leaving that region. But what's special about that region, physically? Nothing. General Relativity does its thing, with moving masses generating curvature (which you can represent as perturbations of a static background), and curvature determining geodesic motion versus accelerated motion (which you can represent as moving sources dumping momentum into spacetime, and spacetime dumping momentum into matter, and that's about as close to an aether as you can get, but it is UNLIKE the luminiferous aether in crucial ways [4]). - -- [1] https://en.wikipedia.org/wiki/Linearized_gravity https://en.wikipedia.org/wiki/Linearized_gravity which is where perturbations of a non-dynamical background enter formally [2] https://en.wikipedia.org/wiki/Sticky_bead_argument https://en.wikipedia.org/wiki/Sticky_bead_argument [3] We can rely on the https://en.wikipedia.org/wiki/Peeling_theorem https://en.wikipedia.org/wiki/Peeling_theorem to let us use Bondi mass M_B; cf. http://www2.phys.canterbury.ac.nz/ACGRG5/talks/Scholtz~Martin.pdf http://www2.phys.canterbury.ac.nz/ACGRG5/talks/Scholtz~Marti... [4] http://www-history.mcs.st-andrews.ac.uk/Extras/Einstein_ether.html http://www-history.mcs.st-andrews.ac.uk/Extras/Einstein_ethe... - pay close attention to the clause after the comma in the second-last sentence there. Einstein's main point is that flat spacetime is simply a special case of a general curved spacetime where the curvature is dominated by the sources (matter) or the absence thereof. Also, it's important to remember that nobody's splitting up of 4-spacetime into 3+1 space+time is "most right"; in our toy model above we have chosen a particular foliation and have not introduced any pesky relativistic observers. That we can use a background (especially flat spacetime) and perturb against that does not mean the background is physically privileged.
• raattgift 8y ago
  I just noticed this: > our rotation causes frame dragging Not exactly; it's the choice of accelerated coordinates and pretending that the coordinates are freely-falling that manifests seemingly odd coordinate-dependent physical effects. One can resolve these by switching to freely-falling coordinates, or by not pretending that the accelerated coordinates are freely-falling. In practice this means doing Special Relativity calculations only in the Special background of the theory, and using the full covariant physics otherwise. One can treat the Lense-Thirring effect as a distortion of a Special Relativistic background (or a different static background, like Schwarzschild), or one can determine the actual background from the distribution of stress-energy. The first choice leads one to conclusions like the precession of test objects in polar orbits around axisymmetric bodies with nonzero angular momentum, and applying that to Earth and a satellite. The second choice is more work, because angular momentum and axisymmetry are only two of the departures from Schwarzschild in the system. Crucially the contributions from surface bumps, masscons, the distribution of matter in the satellite, and so on are all small enough that it's fair to ignore them in the second case. The difference is that the second case simply correctly calculates out the geodesic the satellite occupies in the real spacetime, while the latter calculates out an orbit that is simply wrong for the real configuration of the system and then applies corrections by bringing in pseudo-forces. In the weak field limit, one can get completely correct coordinate-dependent results taking the former approach. Additionally, analogies arise in this approach that can lead to interesting intuitions. However, one should always check to make sure that the intuitions can be explained in terms of coordinate-independent formulations of physics. > weird Sun-Earth orbital relativistic effects If you calculate out the geodesics, no; all the parts of Earth down to its individual molecules and below "want" to travel on geodesics sourced by the system and do so unless the stronger three forces interfere with that "want" (and in bulk Beiglböck and Dixon show that the Earth has a coordinate-independent centre-of-mass that does travel on a timelike geodesic, and you arrive at it by considering the vector position of each particle). This is a lot of work. So instead, you can use a background like Kerr (or Schwarzschild or Minkowski) and correct the failure of the parts of the Earth (or the planet in the large) to travel on the geodesics of these backgrounds. The correction is typically done by introducing pseudoforces, pseudofields, and dynamics and potentials in these. They're pseudo because they vanish entirely in at least one frame of reference. (see https://en.wikipedia.org/wiki/Fictitious_force https://en.wikipedia.org/wiki/Fictitious_force which is pretty decent). > gravitational aether One could do perturbative General Relativity by choosing Minkowski (flat) spacetime as the background \eta [0], and then recovering all the real motions of objects in a perturbation field h. That field, h, is a pseudofield with its own potentials and dynamics. It's just a set of first-order corrections to the background metric. The real metric g will be an expansion: g = \eta + h + O(h^2) + O(h^3) + ... where O(h^x) are higher-order correcting terms, and those are negligible for systems where stresses are weak and speeds are slow compared to c. It is reasonable to think of h as having the properties of an aether in some cases: it can walk and quack like a real field, like the electromagnetic one in Maxwell's theory. However it can also be made to vanish entirely without removing matter and the gravitational potentials they source, and it is a pseudofield in the more fundamental theory of General Relativity. The Maxwell electromagnetic field is always present (you can only get rid of it by removing all charges and potentials), and obviously related fields are still there in the more fundamental theories of QED and the Standard Model (a QFT). The specific theory of the luminiferous aether theory that Michelson-Morley surprised themselves by falsifying was that the aether was stationary and the Earth moved through it. There were comparable theories of a gravitational aether (https://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation https://en.wikipedia.org/wiki/Mechanical_explanations_of_gra...) that have never recovered many fairly easily observed behaviours of gravitating masses, so there was never really a surprisingly failed direct test of them. - -- [0] More generally, as someone raised this with me before, one can write g^{(0)}_{\mu\nu} for an arbitrary choice of background instead of abusing the notation \eta_{\mu\nu} which (out of context) generally means only the Minkowski metric. I leave out the greek-lettered indices above.