Einstein's description of gravity just got much harder to beat

Although there is some history about which empirical results were elevated into postulates of General Relativity, the history of the theory's discovery and development is pretty irrelevant to the two key features of General Relativity as a theory for our universe. They are: the Einstein tensor of curvature is constantly proportional to the stress-energy-momentum tensor of matter, and the universe's spacetime is a Lorentzian manifold with a vanishing torsion tensor. These two theoretical features produce dramatic consequences which are physically testable.

The two basic avenues of attack of General Relativity as a theory accurately describing our universe: undermine local Lorentz invariance (if it's wrong then we aren't in a torsion-free 4-dimensional pseudo-Riemannian space), or undermine the strong equivalence principle (specifically the universality of free-fall, which means that inertial mass and (passive) gravitational mass are always identical) which would blow apart the proportionality of curvature to matter.

The first line of attack tests the consequence that locally -- within a laboratory, say, whether that's on the ground, on the ISS, or on the moon -- physics which aren't dependent on gravitation are compatible with Special Relativity. Since the Standard Model of Particle Physics is governed by Special Relativity and is extremely sensitive to deviations from it, and is totally silent on the subject of gravitation, tests of the Standard Model of Particle Physics are also probes of this consequence, which is called local Lorentz invariance. Proof that results of Standard Model experiments differ during odd minutes from those obtained during even minutes, or that such experiments produce different results when the ISS is over the northern hemisphere rather than over the southern hemisphere, would call into question universal local Lorentz invariance. These tests happen often, and a lot of attentionis generated whenever a claim is made which violates local Lorentz invariance. Practically all such claims have been found to have been wrong. https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_vi...

The second avenue is to look for cases where black holes or neutron stars travel on different orbits from ordinary stars, planets, asteroids, people, or flecks of paint falling off spacecraft. Observational evidence favours this part of General Relativity, which implies that the gravitational constant G is truly a universal constant (the same everywhere and at all times and in all systems of matter), and that there is no long range interaction that applies to all mass-energy including the Standard Model and whatever dark matter is. 8 pi G (where c is set to 1) is the constant of proportionality between the tensors mentioned above, and it's not General Relativity if that constant is not the same at all times and in all places. (This exact proportionality also protects the components of the Einstein curvature tensor: it's not General Relativity if you allow the Riemann scalar ("R") to vary, and there are plenty of alternatives which propose to vary R: these are f(R) gravity theories and most conflict pretty violently with what we observe in the universe (technically General Relativity is an f(R) gravity where f is the identity function).

These two postulates of General Relativity produce numerous consequences which are unavoidable, and so there is a wide range of tests of General Relativity that are implicitly tests of these two postulates. These consequences can be described parametrically in such a way that alternatives to General Relativity can have their consequences assessed: deviations from General Relativity in most of these parameters is strongly constrained by observation and experiment, and it is maddeningly difficult to produce an alternative to GR that survives this kind of theoretical analysis. It's easy to shoot down most f(R), f(G), or f(c) theories using a parameterized Taylor-like expansion, for example. It's a pity, because a number of such theories would significantly simplify the description of the hot dense phase of the universe about 13.8 billion years in our past.

Worse, so far nobody has found a parameter extracted from General Relativity which is contradicted by observational or experimental evidence, and most tests of such parameters are in accord with General Relativity to better than a fraction of a percent, and in many in some cases to much better than a part in a billion (we have some statistics from the Hulse-Taylor system that constrain to within one part in 10^20 some preferred-frame effects that touch on local Lorentz invariance and the universality of free fall).

The problem is that General Relativity itself is mathematically complete and the maths say that gravitational interactions are entirely dependent on the distribution of matter (in the most general sense), and there's lots of detail we don't know about how matter is distributed or how exactly a lot of it works, including in the Standard Model at extremely high energies and also at extremely low energies (e.g. justifying infrared cutoffs on soft photons). Modifying General Relativity as an approach to make extreme-energy particle physics simpler has tended to produce a lot of dead ends.

I was an artist for a while. It wasn't that artists couldn't depict depth. Fashion, religious instructon, and to a lesser extent materials, is what decided which paintings and frescoes lasted the test of time.

You can still find people who are just as "unchallenged" as a medieval peasant today. Look in rural places of countries like china.

There are some words in people's explanations that always bother me. These are 'just', 'mere', merely' and the like. Why? Because they're not explaining, but explaining away. It's like saying: x is trivial, so it's not as important as you think.

But reality is much more complicated than that. For even simple things are hard to fathom for those not knowing how simple it is.

Now, back to the topic: no, medieval painters' lack of knowledge on how use perspective was not just matter of being stuck at conventions. When everyone is expecting to see a certain thing and you're payed to do that thing, it's not 'just' up to the painter see outside her/his perspective. What I'm saying is that takes a huge leap to break away from all that.

Beware of just explaining away phenomena.

What does this mean? Is it mean that Universe have insufficient rules, so there are phenomena which do not follow any rules? Is it possible to devise an experiment whose results would be totally fundamentally irreproducible?

Or you mean that Universe has strict rules, but human's ways to write these rules are flawed and insufficient to grasp in a full a fractal nature of mythical rules of Universe?

It would be a different situations if the theories actually covered different domains of experiments, but neither define such a restriction (and it wouldn't make much sense to either of them).

So it doesn't have to be a combination of GR and QM, but it does have to be something which is at least as good as GR and QM respectively in their existing domains of explanation.

QM applies to weak forces too.

The gravitational field of a neutrino may be small but it's not zero.

Meh.

"The treatment is purely classical, but motivated by links between acausal structures and quantum theory."

This is not unification of QM and GR, it's a classical construction which the author speculates might lead to such a thing. Such things have been around for a long time; the obvious (and far more progressed) example is string theory.

You can do QM on curved backgrounds, see eg https://ncatlab.org/nlab/show/AQFT+on+curved+spacetimes

That's not a theory of quantum gravity, though.

The usual objection is that test stress-energy fairly generically forms singularities (via Raychaudhuri focusing and Jeans instability mechanisms, for example). Singularities obstruct the determination of the entire spacetime from a "complete sample" of it across a spacelike hypersurface, which makes initial values surfaces approaches containing singularities (very probably) incomplete. The genericity means that most spacetimes are incomplete, and if one thinks a fundamental theory should be able to describe a test universe completely (i.e., every field value everywhere and at every time), this is a problem.

This theoretical problem appears already in a purely classical stress-energy on a Lorentzian spacetime. For all practical purposes this only matters for carefully defined test spacetimes that we care to simulate, rather than for real astrophysical systems in our (Lorentzian) universe. After all we can only describe mathematically-isolated parts of our universe, and with current technology we can only reasonably describe even those with approximations and effective theories. There is no shame in using Newtonian gravitation when planning a moon shot even when you know that you can't use Newtonian gravitation to describe the entire universe or even parts of it like the precession of Mercury's orbit much less the Hulse-Taylor system. There is no shame in using General Relativity in satellite-based navigation systems, either, even if you suspect GR cannot describe some feature of our universe much further afield.

So, let's consider a concrete theoretical example using a Schwarzschild black hole for which we break the time symmetry (i.e., we let its mass vary over time) and whose mass we drive with some classical matter that only negligibly perturbs the exterior part of Schwarzschild spacetime otherwise. With the gentle assumption of the no-hair conjecture being true, one can toss a spherically symmetrical shell of perfectly classical matter (remember this is a probe of theory, rather than a simulation of reality) of mass M into a black hole at the centre of the shell, or two concentric shells of classical matter of mass M/2 each, or three concentric shells of classical matter of mass M/3 each. If one takes a initial values surface (IVS) in the future of this shell-tossing and works backwards to determine the predecessors value surfaces of the IVS, one cannot decide whether one, two, or three shells were thrown in. The black hole singularity at r = r_0 is said to have destroyed the information, or if you like, the information is simply not encoded in the modified Schwarzschild solution described above.

That this is a problem pretty generically in nonvacuum Lorentzian spacetimes is sufficient to make General Relativity, at least in its initial values formulation, a less-than-desirable candidate for a fundamental theory of our universe from which other theories (Newton, Einstein-Maxwell, QCD, Navier-Stokes, etc.) might be derived.

Indeed, taking the position that one might erase quantum weirdness in strong gravity (and not worry much about exactly how by resorting to the slightly-less-gentle assumption of a cosmic censorship conjecture being true, such that strong gravity is always completely enclosed by a horizon) does not repair this problem, even if it might conceivably fix all the questions raised by Hawking radiation. Essentially, you're still left with questions like (simplifying the nuclear physics): given an initial values surface for black hole M at time T_now, when considering time T_slightly_earlier for black hole M_slightly_lower, can one work out whether the increase in mass was due to two deuterons falling in or one helium nucleus falling in? That is, we just have a quantum version of the classical shells above, and the same failure to extend from arbitrary IVSes across a whole fairly-generic spacetime.

We can make it worse by taking a surface T_far_future and M_much_smaller, that is after Hawking radiation has much reduced the mass of our black hole, and discover that we have an apparent violation of unitarity: our quarks and gluons (and electrons and so on) can't still be in the black hole (it's now too light to hide them behind the horizon) and yet there is now a cold gas of photons "carrying" the difference in mass. Lots of very clever people continue to study this "AMPS firewall" problem, which is essentially a theoretical sharpening of the "we lose the ability to describe the entire toy universe when a black hole is involved, and the real universe appears to have black holes in it" problem.

Experiments which provide evidence favouring a generic blocking mechanism that prevents matter from forming gravitational singularities in General Relativity would undoubtedly encourage a great deal of research into GR as a candidate fundamental theory once again. (Geometry-is-fundamental-as-in-stress-energy-is-geometrical-when-you-look-closely extensions of GR are still not dead-ended; just unpopular compared to stress-energy-is-a-specific-gauge-theory-and-geometry-probably-arises-from-it approaches).

Penultimately, a mathematical discovery that proves that gravitational singularities in GR are procedural artifacts arising from things like gauge fixing, and that they vanish with a good choice of gauge (or coordinate condition or whatnot) much like the coordinate singularity at r = r_s in the Schwarzschild solution was eventually found to vanish under different choices of coordinates (none of which makes the infinite Kretschmann scalar (at r = r_0 in Schwarzschild) go away).

Finally, we can just shrug and keep working with GR (and careful approximations) where it's useful and obviously in concordance with observations, and not sweat the fine details we can't in practice measure now anyway. If someone discovers an observational conflict which undermines GR as a theory in specific circumstances, it seems unlikely that GR will stop being used or taught any more than Newton has been abolished from classrooms and lecture halls, mostly because it is such a brilliantly effective theory for why there are very specific and observed-in-detail deviations from Newtonian gravitation. Practically nothing comes anywhere close to the match between GR and experiment and observation, and of those that do, most do worse than plain old Newton (sign reversals are rife) in certain situations : https://en.wikipedia.org/wiki/Alternatives_to_general_relati...

Are you sure that’s where the conflict is?

I think people have done QM with a given curved spacetime, just, where the spacetime manifold isn’t decided based on the distribution of matter and whatnot?

Like, I think that’s where the ideas of Hawking radiation come from?

We don't know whether the planck length is fundamental or not, but current models are in terms of continuous spatial and rotational degrees of freedom (in general). The eigenvalues often are quantized, however.