With the caveat that I have nothing to do with ligo and so don't know much...
I think that during this ligo run (it just turned back on in April-ish) they expect to find roughly 1 event per week. So this will be fairly common! [1] is a nice summary of what they have found so far.
For people here interested in the engineering side of LIGO, it is absolutely mind blowing. The effect of the gravitational waves is tiny (fractions of the size of a proton change in length) and so there are so many things that need to be incredibly tightly controlled for. I went to a talk on this a year or so ago, but can't find the slides... Here's a summary [2] and the wikipedia page also has some info.
The gravitational waves in question have no quantum properties, either because they have so many quantum numbers in them that classical behaviour is recovered, or because they are classical “all the way down”. LIGO, its siblings, and their foreseeable successors are unlikely to help resolve this.
The results have already constrained the space of quantum gravity theories from which General Relativity must be recoverable, but that is not the same as preferring (much less indicating) any particular approach to quantum gravity that will be consistent with LIGO et al.’s results.
That said, LIGO’s detector itself relies upon the details of quantum mechanics, as it is also sensitive to quantum noise from its immediate environment. However the quantum mechanics in question are purely local, and have nothing to do with distant events like binary black hole mergers. (LIGO is not sensitive to those distant quantum mechanics — it’s either outright blind to them, or at best they blur into classicality — and it’s hard to envisage a human-buildable detector that would be sensitive to their gravitational influence within our solar system).
Is there such a thing as real phenomena that's classical “all the way down”, as you have put it? If yes, which such phenomena is easiest to understand?
I was under the impression that all of classical physics was special cases of quantum and relativistic physics, just like the relativistic equations of motion "degrade" into classical equations of motion when we postulate that all velocities involved are much lower than the speed of light.
In this sense "classical" means "not quantum". General relativity is "classic" in the sense that position and momentum are variables rather than operators. They have real values rather than functions.
So it's distinct from "classical" meaning "Newtonian" (or, perhaps "Newtonian + Maxwellian"), which is the sense in which "all of classical physics was special cases of quantum and relativistic physics".
Yes, all true, but we have the Hamiltonian formulation (e.g. https://arxiv.org/abs/1505.01403 which is a nice book chapter) which “… is also the starting point for the canonical quantization program, which constitutes one main approach to the as yet unsolved problems of Quantum Gravity. In this approach one tries to make essential use of the Hamiltonian structure of the classical theory in formulating the corresponding quantum theory.” From there you could jump to https://en.wikipedia.org/wiki/Canonical_quantum_gravity which has references.
Nobody knows. Gravitation might be classical “all the way down”. Dark Matter might not be quantum-mechanical. Few people really expect this though: either would be a surprise because as you say, for known macroscopic behaviours of matter they’re almost certainly
> special cases of [relativistic] quantum
and quantum mechanical objects even when doing funny quantum mechanical things will generate stress-energy and thus the stress-energy tensor (and thus the Einstein gravitational tensor) must reflect that. Unfortunately the obvious easy ways to do this (averaging the stress-energy tensor, quantum corrections to the metric using perturbation theory, second-quantizing the Hamiltonian formulation of General Relativity (cf. objections in near the start of [1]) …) have run into difficult problems. Mostly, however, the problems arise only when curvature is strong, and such strong curvature is hidden from us. These approaches work well for practically all the physics of uncollapsed stars, and a considerable amount of physics even in neutron stars. Thus we tend to say that we have various ways to turn classical General Relativity into an effective field theory [2].
We know — and can and do prove within our solar system — how errors arise in equations of motion that do not take relativistic speeds or non-flat spacetime backgrounds into account. In fact, we have some mathematical theorems about that, and reflect them in post-Newtonian formalisms and expansions, and have ample observational and experimental evidence supporting them. As a result, we can talk about the Newtonian limit and the flat-space limit of General Relativity, and we can derive the theories associated with those limits from the more fundamental theory of General Relativity (recovering Newtonian gravitation requires some extra tricks, and it’s those that help show why Newtonian gravitation is wrong; one is that the propagation of Newtonian gravitation is superluminal (technically infinitely fast) and this is contradicted by experiment (e.g. precession of Mercury’s orbit, MESSENGER, Hulse-Taylor, LIGO)).
Unfortunately we’re not as sure about the “errors” in classical matter theories as we fail to take quantum properties into account. It is a principle, rather than something stronger. In https://en.wikipedia.org/wiki/Correspondence_principle one finds: “This concept is somewhat different from the requirement of a formal limit”. We do not know how to derive numerous classical theories from quantum mechanics, correspondence principle notwithstanding, and so while one can claim that e.g. Navier-Stokes (“NS”) can be derived from the Standard Model, nobody has actually shown how to do this mathematically. Indeed, quantum theories of dissipative physics of all sorts are at best exceedingly rare [1], so in NS’s case viscosity has no derivation from quantum principles.
We don’t need anything at Planck energies to see a conflict between quantum field theories (QFTs) and General Relativity in the face of non-classical behaviour of matter which generates a strong signal in the stress-energy tensor. The main problem is that that such behaviours are “washed out” by the rest of the stress-energy tensor’s coupling to matter that is “in the classical limit”, and we don’t yet know how to recover classical physics from QFTs.
The interesting-to-theorists quantum gravity stuff is near the centres of neutron stars and black holes, and in the distant past of our universe: all regions we have yet to be figure out how to explore. And all those regions are surrounded by extremely hot and noisy matter: the ultradense nuclear pasta and hot atmosphere and so forth in neutron stars, the accretion regions of black holes, and the “fog” of the surface of last scattering (and the equivalent for neutrinos and possibly equivalent(s) for other non-charged particles or whatever the hell dark matter is). The closest neutron stars and black holes are already a depressingly long way away by RADAR-distance, so there’s no real hope of soon sending a probe close to them to try to gather up and report back observations. So theorists who want to abolish General Relativity’s gravitational singularity, or alternatively quantum things like unitarity, are struggling to extract (even in principle) signal from noisy relics of these extreme-and-hidden things.
However, there is still interesting stuff possible to test near us: if we can develop a laboratory-based object with strongly non-classical behaviour even at sufficient mass to influence lab gravimeters (that is, it will rise above the background stress-energy) then there are all sorts of things we can do to test theories of quantum gravity. We expect that semiclassical gravity will be blown away by such an experiment (there is a member of https://www.npl.washington.edu/eotwash/node/1 here on HN, for instance). An example might be to bring a milligram-or-more coherent mass into a superposition for at least a few milliseconds and see which way an array of lab gravimeters point. That’s already a difficult experiment! (the subsection heading is wildly optimistic, but explains the expected result of such an experiment: https://en.wikipedia.org/wiki/Semiclassical_gravity#Experime... )
I’m not certain the Planck length is anything more than mixing some physical constants into a unit of length, rather than something important to nature. It is interesting to see Planck-scale dimensionful units are frame-invariant — they might not be, which is the premise of Doubly-Special Relativity, for instance. On the other hand, Special Relativity and its deformations might not be the right tool anyway, as a Planck scale object may generate enough spacetime curvature (by virtue of the Planck scale object’s local stress-energy) to blow away the global symmetries of the flat spacetime that form the background for these theories (which are NOT background-independent!). We’re not going to be probing Planck scale objects in the near future, and so there are few limits on speculative theories other than re-re-re-reconfirmations of local Lorentz invariance at lower (stress-)energies in a variety of backgrounds, including that of the Standard Model of Cosmology (the red-shifting of spectra from supernovae, the Lyman-alpha forest, and so on), that of effectively flat spacetime (labs on earth, and in space vehicles around the solar system), and that of significantly curved spacetime (spectra of neutron stars, for instance). And that same information is also evidence favouring one QFT: the Standard Model of Particle Physics (“SM”), which incorporates Lorentz invariance (but not gravitation, so SM is background-dependent, and enjoys the fact that General Relativity predicts the correct background for SM in every sufficiently small region in the universe, even if the background between SM-event-at-A and SM-observer-at-B is such that a region covering A and B is clearly not flat spacetime []).
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[] we can adapt to that by using generally covariant physical theories; unfortunately not all physical theories have been “promoted” into general covariance, and anyway tensors are hard so people will use cut-downs of generally covariant theories adapted to some special background. One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds.
>One can study gauge fixing to figure out how well this works for physical theories, and whether the “comma-goes-to-semicolon” rule of “promoting” theories into general covariance actually ends up with something that works in an arbitrary background. Lots of perfectly-good-here-on-Earth physical theories fall apart in different spacetime backgrounds.
What? What is this "comma-goes-to-semi-colon" rule of "promoting" theories. This is either some superdense jargon I haven't been in the right place to encounter, or the research world has entered far stranger realms of symbolic representation than I've imagined possible.
Seriously, what am I missing? I'm assuming it has something to do with proving the consistency of theoretical frameworks by correlating them with empirical confirmation, but I'm not 100% sure I'm not stripping out important nuance.
Comma and semicolon typographical notation for partial resp. covariant derivatives. The comma is used to indicate a partial derivative: V^{\alpha}_{\comma\beta} = \partial_{\beta}V_{\alpha}. The semicolon V^{\alpha}_{\semicolon\beta} turns somewhat complicatedly (via Christoffel symbols) into \nabla{\beta}V^{\alpha}. There’s more detail at https://en.wikipedia.org/wiki/Covariant_derivative#Notation
These notations are reflected in “comma-goes-to-semicolon” which is discussed in MTW chapter 20 & 22 (esp. §22.4, Electrodynamics in Curved Spacetime) and other textbooks. Carroll’s online lecture notes at https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll... discusses it briefly starting with the paragraph beginning “Our next task is to show how the remaining laws of physics…” and in particular (starting with) that paragraph’s penultimate sentence.
Even more briefly, we need generally covariant physics to escape the flat spacetime background into general curved spacetime and still get sensible electromagnetism and so on.
Even more briefly: the semicolon indicates a valid tensor equation, showing that we are fine when the basis vectors are not constant. Switching , to ; when it works hides away a bunch of work with Christoffel symbols, and what makes it work is the Equivalence Principle. Semicolon-goes-to-comma always works by gauge fixing, but unfortunately V^{a}_{,b} -> V^{a}_{;b} sometimes doesn’t; doing the full expansion by hand (well, or with modern automation) is one way to see if your physical theory is really generally covariant/background independent.
> superdense
Yes! As an example, and I haven’t really done more than scrub through it, and he really doesn’t go into any details beyond what you’d get in a standard textbook:
Putting the extra typographical dot on top of the , giving a ; can literally represent several pages of dense equations.
> jargon
Yes! A lot of writing that turns out to generally be really mechanical has been squashed out of General Relativity through the years. Unfortunately the notation itself — as typography — tends to “leak out”, so we talk about indices being in the basement or upstairs, Greek vs Roman, etc etc.
I think that during this ligo run (it just turned back on in April-ish) they expect to find roughly 1 event per week. So this will be fairly common! [1] is a nice summary of what they have found so far.
For people here interested in the engineering side of LIGO, it is absolutely mind blowing. The effect of the gravitational waves is tiny (fractions of the size of a proton change in length) and so there are so many things that need to be incredibly tightly controlled for. I went to a talk on this a year or so ago, but can't find the slides... Here's a summary [2] and the wikipedia page also has some info.
1 - https://www.sciencenews.org/article/ligo-virgo-made-5-likely... 2 - https://www.engineering.com/Education/EducationArticles/Arti...