Actually, it just got easier to beat. What happened was scientists found a new way to measure the effects of gravity that can substantially distinguish between different proposals to unify general relativity with quantum mechanics.
The article says it got "harder" because the theory of general relativity wins every measurement, and that means the search space for potential solutions is much smaller - you have more constraints that you need to fit.
But this is actually a good thing. Finding the right theory is like looking for a needle in a hay stack. These new measurements are the functional equivalent of removing a huge portion of the hay.
Yes, it means there are now fewer places to check, but that's actually what we want. We'll spend less time chasing dead ends because it's easier for us to see they are dead ends sooner.
Thinking like an engine “taking relativity apart” and going over its pieces for flaws, finding a piece that’s broken, but needing such a highly customized piece to maintain consistency of the engine and maybe link it to quantum mechanics hasn’t really done away with the possibility we’ll chase thousands of dead ends first.
I don't disagree with your overarching observations, but it's not so much that there are "pieces" of General Relativity to examine, but rather that the most central two features of the theory produce -- inevitably -- several consequences, all of which seem to be supported by observational and experimental evidence. Adapting the central two features generically leads to a universe noticeably different from what we observe. Likewise, the universe we observe appears to demand General Relativity as a framework for describing it accurately.
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 w...
It's more like the haystack got smaller but we still don't know where the haystack is. The unknown unknowns got even harder to touch. This is all a good thing.
> Despite its successes, Einstein's robust theory remains mathematically irreconcilable with quantum mechanics, the scientific understanding of the subatomic world. Testing general relativity is important because the ultimate theory of the universe must encompass both gravity and quantum mechanics.
Why must the ultimate theory of the universe encompass both? Do we know that there is an ultimate theory of the universe? Could GR and QM be wholly separate with no unifying connection?
> Could GR and QM be wholly separate with no unifying connection?
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?
They give different predictions for the same observed event so both can't be true. For example, since there is no gravity in the standard model (the general QM-model encompassing everything but gravity) and gravity obviously is observed, the theories are fundamentally incompatible.
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).
The color of gold is better explained by an ad-hoc combination of SR, GR, and QM, than by any one of them alone. SR and GR explain the planets' motion better than Newton and Kepler alone. QM explains pi bonds in molecules like benzene better than classical chemistry. GR compensation is required by GPS satellites and receivers.
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.
During brainstorming sessions, I often think about why/how medieval artists couldn't quite grasp how to depict depth in their paintings (as a lateral thinking technique). Being humans living in the world, they obviously experienced and understood that depth existed all around them, but had a hard time grasping the concept as a whole. I feel like we're kind of in a "medieval depth" phase of gravity/spacetime understanding...it's literally all around us, we know something is there, but we can't quite grasp what it even is we're looking for.
Here's a possible explanation that I'd seen somewhere. Up until very recently, humans had had weak ability to think, especially abstract thoughts, and the phrase common today "just think about it", would be meaningless just a few centuries ago. Perhaps the concept of depth in those times would be similar in complexity to 4-dimensional structures today.
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.
That's completely wrong. Humans were just as smart 3000 years ago as they were today. The difference between today and back then is that people were much poorer and didnt receive an education. Their jobs were farming which didnt require things we consider essential like reading or writing which meant they stay unchallenged for their entire life. When you look at the rich elite or rich cities in the past then you see how small the difference between us and the people 3000 years ago is. They were just as smart but there were fewer of them. Nowadays everyone is educated and "rich".
You can still find people who are just as "unchallenged" as a medieval peasant today. Look in rural places of countries like china.
This is a nice theory, but what is the proof? Were people just as smart 30,000 years ago? What about 300,000 or 3 million years ago? How do you set the time scale? When was the boundary when people became smart?
We don't know exact dates of course, but looking at the works of mathematics and philosophy that have survived, we know for sure that humans were capable of abstract thought at least as far back as 4-5000 years ago (for example, during the construction of the Great Pyramid of Giza), and very likely even 12-13000 years ago (during the construction of the megaliths at Gobekli Tepe, for example). Furthermore, we can assume that some time must have passed between the first threads of abstract thought and any achievements due to it that would stand the test of time, though I don't think we can put any hard estimates on this time.
We can look at the genetic changes and timeframe of them, and how certain mutations have spread - novel changes in our species are not that frequent on the historical timescale. People 3000 years ago are the same with respect to their biology, so they have to be "just as smart"; hominids 300,000 years ago are different in some aspects so for them we can't really know how "smart" they were, perhaps they were as smart, perhaps they were not.
Another big factor, I think is communication. Today, discoveries spread almost instantly, all over the world. But back then you had hard to copy manuscript and people had to meet in person using slow and dangerous transportation.
So I think ancient discoverers wasted a lot of time rediscovering things.
> I often think about why/how medieval artists couldn't quite grasp how to depict depth in their paintings (as a lateral thinking technique).
The explanation for that is generally agreed on to have more to do with the aesthetics of early Christianity influencing Medieval practices, more than changes to human perception (source: I have a masters degree in Art History).
Not OP, though mild experience with art history and Christian history, but I suspect OP is talking about the intersection of art and the prevailing religion in Europe at the time (Christianity). Early Christian art was intentionally unrealistic in style specifically because the intent was often symbolism and representation rather than realism (this still holds true today for most Orthodox Christian art[0]). In fact, making it realistic would even border on idolatry (see Iconoclastic Controversy[1]).
That said, up until the European middle ages, nearly all art was that which was commissioned by the church. The style of the time permeated the art that wasn't commissioned by the church. As more non-religious art was commissioned, there was little need to remain working in that style and realism was embraced. I could be wrong, and probably am, but I think Catholicism is the only large Christian denomination that adopted realistic art.
I think depth was already understood by this point, though (see sculptures[2]). Again, I'm not OP, and I'm sure OP will have a more thorough explanation.
Good point. There’s also, to me, a perception of style and technique: there were a lot of stone-based art, made specifically to endure time. Bas-relief, a very fit approach of art for stone-based material had this specific style that got aesthetically and technically translated to paintings and stained glass, for an overall quite consistent style whatever the medium.
You can see the intent on many religious sculptures in medieval churches around e.g France: the technique is precise, so it’d be really easy for a sculptor to just compare and match to a living and breathing model, therefore they chose not to. Contemplating how churches tell stories through imagery, you can see how they used this style for emphasis on specific physical features to elicit strong emotional response instead, not entirely unlike those TVs in stores cranking up contrast to completely unrealistic levels.
This [1] is a painting from 1476. Notice how architecture and landscape has depth, but people are all +- the same size except for Mary and God.
You wouldn't want to draw mere mortals bigger than saints just because they happen to be closer. Peasants (which couldn't read and were the main target of these paintings) could get wrong ideas.
Not exactly what they mentioned, but check this out [1]. It talks about the perception of time in the middle ages, and how merchant time slowly substituted the impractical notions of church time. A professor of mine who was talking about medieval paintings and their ideas of space and time suggested this paper.
I think that art is just overwhelmed by fads. Artists are copying styles off of each other. It's true for any era. Egyptian drawings, medieval paintings, manga or holywood movies or internet memes.
Mimicking reality is rarely the goal that art is optimized for. It's mostly converging to local optimum of one of the current fads.
As others have said, I believe the lack of depth in medieval art is much more a matter of conventions than a matter of lack of theory or physical abilities (see [0]).
The one thing that convinced me of that is the sudden jump in realism in Egyptian art during the reign of Akhenaten (Amarna period, see the famous Nefertiti bust for a great example). The new king asked for more realism and he received it, it just took a reset in conventions.
Don't take this personally. Your comment just gave me an itch I had to scratch.
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.
To expand on this, Pirsig tears apart "just" as a completely useless word which reaffirms the speaker's belief but also trivializes the listener's inability to understand. "just" comes from ancient Latin "ius" and it means "I swear" or "I believe". When somebody says "I was just doing something", they are swearing a light oath that they were doing something.
Back in context, what the parent is saying is that the grandparent provided a "just-so" story: The parent finds it easy to believe that history happened in a way which neatly lines up with the story that they are telling. Did earlier humans know about perspective? Grandparent believes that it's obvious.
The word "just" in "it just took a reset in conventions" was intended as ironical (but it might not come across clearly in the text). A change of conventions is a large change that is no trivial matter to undertake.
Rather it is the belief that they fundamentally must be compatible that is driving this research. Currently we don't know how to answer questions like "what is the gravitational field around a photon?".
Photos by definition don't have a rest mass because they are never at rest. They must always travel at the speed of light, which means they don't experience time, so rest does not even make sense for a photon.
As I understand it (not a physicist), according to GR the Einstein field equations equate the curvature of spacetime to the stress-energy tensor, of which mass is just one component. Photons, having energy, should produce a gravitational field.
If you shine light on an object, the light pushes on the object and the object is accelerated. If the object absorbs the light, there's a certain amount of pressure, and if the object reflects the light, there's even more pressure.
This has practical applications. Optical tweezers are made of light's force acting on small objects. "Optical tweezers are used in biology and medicine (for example to grab and hold a single bacterium or cell like a sperm cell, blood cell or DNA), nanoengineering and nanochemistry (to study and build materials from single molecules), quantum optics and quantum optomechanics (to study the interaction of single particles with light)" (Wikipedia).
Conservation of momentum means the light has mass by definition, and this photon mass can be measured by multiplying the mass and acceleration of the object.
Not only does this mean photons have gravity in the theory of GR, because all mass/energy does, it means they attract each other in a vacuum. In theory, you can make photons orbit each other due to their gravity.
Radiation pressure is due to momentum, not mass. I have no idea where you got that idea, since the same sort of sources that teach you about these concepts are very emphatic about photons being massless.
Here is one of the 3-5 interesting facts I remember from my modern physics class: Two photons going the same direction have no mass, but two photons in different directions do have mass. Unfortunately I don't remember the math well enough to explain it. Maybe this means your right about being able to put photons in orbit around each other.
> Radiation pressure is due to momentum, not mass. I have no idea where you got that idea, since the same sort of sources that teach you about these concepts are very emphatic about photons being massless.
You are right, I was sloppy with language, and accept my downvote honourably :-)
I was talking about what is sometimes called relativistic mass or effective mass (which are considered obsolete terminology), in order to address the GP (brabel)'s belief that photons having zero mass will have zero gravity.
> since the same sort of sources that teach you about these concepts are very emphatic about photons being massless
It depends how old you are; I learned these concepts in the 80s :-)
> Does light have mass? The short answer is "no", but it is a qualified "no"
> Part of this discussion is only concerned with semantics. It might be thought that it would be better to regard the mass of the photons to be their (nonzero) relativistic mass, as opposed to their (zero) invariant mass. We could then consistently talk about the light having mass independently of whether or not it is contained. If relativistic mass is used for all objects, then mass is conserved and the mass of an object is the sum of the masses of its parts. However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation. In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts. Thus, the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero). Relativistic mass is equivalent to energy, which is why relativistic mass is not a commonly used term nowadays.
Energy gravitates. QM tells us systems can be in superposition of energy eigenstates, and we'd like to know what happens to the gravitational field in such cases. For that, we need a quantum theory of gravity.
We have some recipes to go from a classical to a quantum field theory, but they fail for general relativity. For example, GR is not perturbatively renormalizable: For electromagnetism, we only need to determine a finite number of parameters experimentally to (presumably) fix the theory at all energy scales. That doesn't work for general relativity for technical reasons, and we'd have to measure an infinite number of parameters.
Then, there are a couple of conceptual problems, such as GR doing away with a fixed background spacetime, or the so-called problem of time. Different approaches to quantum gravity approach this in different ways (as far as I'm aware, the background normally gets fixed asymptotically in string theory - though don't quote me on that one - whereas loop quantum gravity tackles the issue head on).
By "QM" and "GM", physicists mean our current mathematical models of these theories.
They just don't line up -- QM doesn't have anytging in it which would create relativistic gravity, and GM doesn't contain any weird quantum effects.
Previous attempts to just "glue them together" have always failed, as the maths ends up falling apart and you get stupid results, which clearly don't align with the real world.
I've seen somewhere a clever trick that derives some QM with a small tweak in GR. I can't judge whether the trick makes sense, though. So the trick was to modify the ds2=c2dt2-dx2-dy2-dz2 equation to exp(a cos(wt))ds2=... That extra exp(...) modulation, when combined with Lorentz transforms, produced some basic QM formula. With more wizardry, the author derived the time-dependent Schrodinger equation. Someone who knows GR well could probably tell if GR has "room" for the exp(...) modulation, i.e. that something in GR doesn't fall apart after this addition.
(What follows is a layman's understanding; I have a physics degree but never studied particle physics to the kind of depth required to give an authoritative answer to this question.)
Because any attempt to quantise gravity via the methods that worked for other forces leads to theories which aren’t any use to us. So far all such attempts have led to theories which are not renormalisable. Renormalisation is not an absolute requirement for a useful quantum theory; you can do perfectly good physics in a non renormalisable theory with a high energy cut off. But we only expect quantum gravity effects to be noticeable in high energy / curvature regimes so that's no good to us. We already have a perfectly good low energy theory of gravity that explains all observable phenomena after all: It’s called General Relativity. A non-renormalisable theory that results in infinities that cannot be eliminated in the energy regimes that you hope to probe is not a useful theory.
The other source of difficulty is that existing quantum theories assume a flat spacetime background. Reworking them to account for curved spacetime makes the mathematics much harder, even if you only assume a fixed but curved background.
So we need new ideas, because the existing ideas give infinite answers in the regime where existing theories fail, but even testing such new ideas mathematically is currently challenging & very few people have the mathematical background required.
Not all physicists think they are incompatible. Mark Hadley [0][1] for example suggests that:
"On spacetimes that are not time orientable we construct a U(1) bundle [model of a particle as an asymptotically flat spacetime manifold with a region of non trivial topology where time is not orientable] to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell’s equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path."
"Deriving the U(1) bundle as a measure of the twisting of the time axis is new, as is the application to manifolds that are not time orientable. Like Kaluza Klein theory, it is purely classical, but free of the complications and ad hoc assumptions required by full 5D Kaluza Klein theories. It is remarkable how so much is derived from such a simple construction without additional assumptions."
"The connection with quantum theory is intriguing. Classical structures that are not time orientable have close links with quantum phenomena such as the logical structure [4], particle creation and annihilation [14] and spin half [7] The derivation of Maxwell’s equations and electric charge is just another result from the same premise of non time orientability."
Electric charges are a natural feature of the model, but quantisation only appears naturally for magnetic monopoles (which arise in pairs). However, adding elements of quantum theory to the monopole structures leads to quantisation of electric charge. The simplest such argument uses quantisation of angular momentum, but the argument fails when more than one monopole is introduced. The other approach uses a wavefunction for a charged particle [1, p262]. Uniqueness of the phase of the wavefunction leads to quantisation of charge. This is a tantalising link between the complex phase of the wavefunction and the orientability of spacetime."
In your quote of the abstract, you conveniently left out the last sentence:
"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.
What you quote doesn't deny "no compatability" of the author… (I didnt say it was THE unification theory of QM and GR, you somehow inferred that, why? i dont know) and irrelevant when the author points out where the overlaps lie (what I quoted last). I could add that quote and it would change nothing as far as I'm concerned what the authors stance is on "no compatability". Hell, even in the second quote even mentions "it is purely classical" in reference to the derivation…
Whether something is "more progressed" hardly matters in matters that still have many questions and more reflective of a consensus of the time that progresses one funeral at a time.
> What you quote doesn't deny "no compatability" of the author
What I quote shows that the author knows and acknowledges that he's describing a classical construct. The question of "compatability" (sic) is not even addressed.
> I didnt say it was THE unification theory of QM and GR, you somehow inferred that
I did not. Here's what I wrote: "This is not unification of QM and GR, it's a classical construction". Not the absence of any "THE", whether capitalized or not.
> I could add that quote and it would change nothing as far as I'm concerned what the authors stance is
Because you do not understand what the author is saying. He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones. That does not make it a quantum theory, any more than the discrete eigenfrequencies of a vibrating classical string make a classical model of vibrating strings a quantum theory.
For some reason, you are trying to make it seem like I'm saying that the author is making a quantum theory (i have no idea why you think im saying this), I'm not.
> He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones.
Compared to other physicists who just outright state that there is no compatibility… You can ignore it, but it is an area for further study in regards to non time orientability for others.
> For some reason, you are trying to make it seem like I'm saying that the author is making a quantum theory
No, I am pointing out that you do not understand the paper you misquoted as evidence that "Not all physicists think they [GR and QM] are incompatible".
The author would not have written a paper trying to take a small step toward a solution if he didn't think that there is a problem.
The author acknowledges in the paper where the overlaps lie wrt to EM (coupled to GR) and QM using a classical model that treats particles as an asymptotically flat spacetime manifold with a region of non trivial topology where time is not orientable (but manifold subtracting out the worldtubes of said particles is both space and time oreintable).
Just because he does not say explicitly "[GR and QM] are compatible", does not mean opposite.
If you aren't interested in the that U(1) bundle described in the paper is from utilizing time oreintability from a classical standpoint and not formed from the complex phase of a quantum mechanical wave-function, that's on you.
> Just because he does not say explicitly "[GR and QM] are compatible", does not mean opposite.
It also doesn't mean what you are claiming.
To have a meaningful discussion about the incompatibility of GR with QM, you first need to know how they are incompatible. Reproducing classical electromagnetism with the Kaluza-Klein trick from 1919 [1] has nothing to do with it.
QM deals with unit vectors in a state space, operators acting on those vectors, and observables whose values can not all be known simultaneously [2]. The hole left by the observer's limited knowledge about the state of the system is filled by an intrinsic randomness which does not exist in classical theories.
GR and other classical theories have only observables, their evolution is deterministically determined and the state of the system can in principle be fully known at all times. We have known for a long time that nature does not actually work like this [3].
If you want to claim that GR is compatible with QM, you have to resolve the above contradiction.
What people who actually understand the problem have been trying to do for a long time is:
1) Quantize GR. This is the obvious first thing to try; you treat the problem as analogous to the quantization of classical electromagnetism and hope to create a quantum version of GR, the gravitational equivalent of QED. When you try that, it turns out you can't make the theory renormalizable - the infinities caused by loops in Feynman diagrams can not be brought under control. Trying to fix that leads to things like loop quantum gravity [4]. Weinberg came up with the alternative idea of asymptotic safety, which tries to neuter the problem with a fixed point in the renormalization group flow [5], but proving that it actually works is another story.
2) Come up with a deterministic (i.e. classical) theory underlying QM. Naive approaches involving hidden variables (i.e. trying to explain away our limited knowledge of quantum states as ignorance rather than truly fundamental) died with Bell's theorem. A few brave souls, notably t'Hooft [6] are still trying more sophisticated approaches (I think it would be nice if superdeterminism [7] got more attention).
3) Write down a more fundamental theory which produces both GR and the other known interactions in the appropriate limits (thermodynamic, large number of quanta). Since the other known interactions are empirically known to be quantum mechanical, it is generally believed that this theory will have to be quantum mechanical too. String theory is the obvious example. In principle, you could also imagine a classical (i.e. deterministic) theory along the lines of (2), but I can't think of any example which comes close to actually doing the job.
It's mostly because math prevents them from expressing gravity as a quantum field.
The exactly opposite idea of adjusting QM to directly work in geometry of strongly curved space-time is not pursued much. Not sure why. Maybe because it's hard. Maybe because it would just be an extension of business as usual which isn't attractive. Maybe for some other reason.
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...
1. If they aren't compatible at all something is really off, i.e. what happens to electrons in a gravitation field?
2. We can combine (quantize) gravity, but the problem is that using the tools we have today (Quantum Field Theory) the theory doesn't give meaningful answers. There is a process called renormalization that we use to squeeze an answer out of the theory, but that process don't work for all theories and not gravity.
No. They cover different domains, so their predictions within those domains are consistent (and non-overlapping). It is combining them that is the problem.
QM doesn’t assume space is discrete. It does deal with a number of discrete quantities though.
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.
It means we don't know how to quantize GR. Unlike the standard model of particle physics, it's a classical theory, i.e. a set of equations which tell you deterministically, without any of the inherent uncertainty of QM, how a given initial configuration will evolve.
This becomes a problem when you try to include GR in even simple experimental setups which expose QM's non-classical behavior, like the Stern-Gerlach experiment [1]. What does gravity do before the path chosen by the particle (which is gravitationally attractive) is measured?
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[ 4.1 ms ] story [ 29.3 ms ] threadThe article says it got "harder" because the theory of general relativity wins every measurement, and that means the search space for potential solutions is much smaller - you have more constraints that you need to fit.
But this is actually a good thing. Finding the right theory is like looking for a needle in a hay stack. These new measurements are the functional equivalent of removing a huge portion of the hay.
Yes, it means there are now fewer places to check, but that's actually what we want. We'll spend less time chasing dead ends because it's easier for us to see they are dead ends sooner.
It got easier but “easy” relative ;)
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 w...
"Einstein's description of gravity just got much less likely to be beaten"
Maybe the universe just has a giant if statement.
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.
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.
So I think ancient discoverers wasted a lot of time rediscovering things.
The explanation for that is generally agreed on to have more to do with the aesthetics of early Christianity influencing Medieval practices, more than changes to human perception (source: I have a masters degree in Art History).
That said, up until the European middle ages, nearly all art was that which was commissioned by the church. The style of the time permeated the art that wasn't commissioned by the church. As more non-religious art was commissioned, there was little need to remain working in that style and realism was embraced. I could be wrong, and probably am, but I think Catholicism is the only large Christian denomination that adopted realistic art.
I think depth was already understood by this point, though (see sculptures[2]). Again, I'm not OP, and I'm sure OP will have a more thorough explanation.
[0] https://orthodoxartsjournal.org/topics/iconography/
[1] https://www.britannica.com/event/Iconoclastic-Controversy
[2] https://en.wikipedia.org/wiki/Victorious_Youth
You can see the intent on many religious sculptures in medieval churches around e.g France: the technique is precise, so it’d be really easy for a sculptor to just compare and match to a living and breathing model, therefore they chose not to. Contemplating how churches tell stories through imagery, you can see how they used this style for emphasis on specific physical features to elicit strong emotional response instead, not entirely unlike those TVs in stores cranking up contrast to completely unrealistic levels.
You wouldn't want to draw mere mortals bigger than saints just because they happen to be closer. Peasants (which couldn't read and were the main target of these paintings) could get wrong ideas.
https://upload.wikimedia.org/wikipedia/commons/f/ff/Francesc...
[1] https://journals.sagepub.com/doi/10.1177/053901847000900411 - Church Time and Merchant Time in the Middle Ages - Jacques Le Goff
Mimicking reality is rarely the goal that art is optimized for. It's mostly converging to local optimum of one of the current fads.
The one thing that convinced me of that is the sudden jump in realism in Egyptian art during the reign of Akhenaten (Amarna period, see the famous Nefertiti bust for a great example). The new king asked for more realism and he received it, it just took a reset in conventions.
[0]: https://en.wikipedia.org/wiki/Perspective_(graphical)#Early_...
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.
Back in context, what the parent is saying is that the grandparent provided a "just-so" story: The parent finds it easy to believe that history happened in a way which neatly lines up with the story that they are telling. Did earlier humans know about perspective? Grandparent believes that it's obvious.
[1] https://en.wikipedia.org/wiki/Kugelblitz_(astrophysics)
If you shine light on an object, the light pushes on the object and the object is accelerated. If the object absorbs the light, there's a certain amount of pressure, and if the object reflects the light, there's even more pressure.
This has practical applications. Optical tweezers are made of light's force acting on small objects. "Optical tweezers are used in biology and medicine (for example to grab and hold a single bacterium or cell like a sperm cell, blood cell or DNA), nanoengineering and nanochemistry (to study and build materials from single molecules), quantum optics and quantum optomechanics (to study the interaction of single particles with light)" (Wikipedia).
Conservation of momentum means the light has mass by definition, and this photon mass can be measured by multiplying the mass and acceleration of the object.
Not only does this mean photons have gravity in the theory of GR, because all mass/energy does, it means they attract each other in a vacuum. In theory, you can make photons orbit each other due to their gravity.
Here is one of the 3-5 interesting facts I remember from my modern physics class: Two photons going the same direction have no mass, but two photons in different directions do have mass. Unfortunately I don't remember the math well enough to explain it. Maybe this means your right about being able to put photons in orbit around each other.
This is not limited to photons, although the first part, "no mass" is due to the rest mass of photons being zero.
Two objects of any kind whatsoever have more mass going in different directions than going in the same direction.
You are right, I was sloppy with language, and accept my downvote honourably :-)
I was talking about what is sometimes called relativistic mass or effective mass (which are considered obsolete terminology), in order to address the GP (brabel)'s belief that photons having zero mass will have zero gravity.
> since the same sort of sources that teach you about these concepts are very emphatic about photons being massless
It depends how old you are; I learned these concepts in the 80s :-)
From https://physics.stackexchange.com/a/133380:
> There's no controversy about whether mass increases or not, there's controversy about what you call mass.
Something that may help readers:
From https://www.desy.de/user/projects/Physics/Relativity/SR/ligh...:
> Does light have mass? The short answer is "no", but it is a qualified "no"
> Part of this discussion is only concerned with semantics. It might be thought that it would be better to regard the mass of the photons to be their (nonzero) relativistic mass, as opposed to their (zero) invariant mass. We could then consistently talk about the light having mass independently of whether or not it is contained. If relativistic mass is used for all objects, then mass is conserved and the mass of an object is the sum of the masses of its parts. However, modern usage defines mass as the invariant mass of an object mainly because the invariant mass is more useful when doing any kind of calculation. In this case mass is not conserved and the mass of an object is not the sum of the masses of its parts. Thus, the mass of a box of light is more than the mass of the box and the sum of the masses of the photons (the latter being zero). Relativistic mass is equivalent to energy, which is why relativistic mass is not a commonly used term nowadays.
Relativity deals with so much gravity that spacetime is warped.
Neither is appropriate for the other and they are on opposite sides of the spectrum. Classical physics is useful in the middle at "human" scale.
What would be nice is a simple theory that covers it all. Nothing we currently have is able to stretch to be useful in all situations.
Sean Carroll's _The Big Picture_ was useful for me, as was the older _A Brief History Of Time_ by Stephen Hawking
QM applies to weak forces too.
The gravitational field of a neutrino may be small but it's not zero.
Meh.
We have some recipes to go from a classical to a quantum field theory, but they fail for general relativity. For example, GR is not perturbatively renormalizable: For electromagnetism, we only need to determine a finite number of parameters experimentally to (presumably) fix the theory at all energy scales. That doesn't work for general relativity for technical reasons, and we'd have to measure an infinite number of parameters.
Then, there are a couple of conceptual problems, such as GR doing away with a fixed background spacetime, or the so-called problem of time. Different approaches to quantum gravity approach this in different ways (as far as I'm aware, the background normally gets fixed asymptotically in string theory - though don't quote me on that one - whereas loop quantum gravity tackles the issue head on).
They just don't line up -- QM doesn't have anytging in it which would create relativistic gravity, and GM doesn't contain any weird quantum effects.
Previous attempts to just "glue them together" have always failed, as the maths ends up falling apart and you get stupid results, which clearly don't align with the real world.
Because any attempt to quantise gravity via the methods that worked for other forces leads to theories which aren’t any use to us. So far all such attempts have led to theories which are not renormalisable. Renormalisation is not an absolute requirement for a useful quantum theory; you can do perfectly good physics in a non renormalisable theory with a high energy cut off. But we only expect quantum gravity effects to be noticeable in high energy / curvature regimes so that's no good to us. We already have a perfectly good low energy theory of gravity that explains all observable phenomena after all: It’s called General Relativity. A non-renormalisable theory that results in infinities that cannot be eliminated in the energy regimes that you hope to probe is not a useful theory.
The other source of difficulty is that existing quantum theories assume a flat spacetime background. Reworking them to account for curved spacetime makes the mathematics much harder, even if you only assume a fixed but curved background.
So we need new ideas, because the existing ideas give infinite answers in the regime where existing theories fail, but even testing such new ideas mathematically is currently challenging & very few people have the mathematical background required.
"On spacetimes that are not time orientable we construct a U(1) bundle [model of a particle as an asymptotically flat spacetime manifold with a region of non trivial topology where time is not orientable] to measure the twisting of the time axis. This single assumption, and simple construction, gives rise to Maxwell’s equations of electromagnetism, the Lorentz force law and the Einstein-Maxwell equations for electromagnetism coupled to General relativity. The derivations follow the Kaluza Klein theory, but with the constraints required for connections on a U(1) bundle rather than five spacetime dimensions. The non time orientability is seen to justify and constrain Kaluza Klein theories exactly as required to unify gravitation with electromagnetism. Unlike any other schemes, apparent net electric charges arise naturally because the direction of the electric field reverses along a time reversing path."
"Deriving the U(1) bundle as a measure of the twisting of the time axis is new, as is the application to manifolds that are not time orientable. Like Kaluza Klein theory, it is purely classical, but free of the complications and ad hoc assumptions required by full 5D Kaluza Klein theories. It is remarkable how so much is derived from such a simple construction without additional assumptions."
"The connection with quantum theory is intriguing. Classical structures that are not time orientable have close links with quantum phenomena such as the logical structure [4], particle creation and annihilation [14] and spin half [7] The derivation of Maxwell’s equations and electric charge is just another result from the same premise of non time orientability."
Electric charges are a natural feature of the model, but quantisation only appears naturally for magnetic monopoles (which arise in pairs). However, adding elements of quantum theory to the monopole structures leads to quantisation of electric charge. The simplest such argument uses quantisation of angular momentum, but the argument fails when more than one monopole is introduced. The other approach uses a wavefunction for a charged particle [1, p262]. Uniqueness of the phase of the wavefunction leads to quantisation of charge. This is a tantalising link between the complex phase of the wavefunction and the orientability of spacetime."
[0] https://warwick.ac.uk/fac/sci/physics/staff/academic/mhadley...
[1] https://doi.org/10.1007/s10773-017-3344-4
"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.
The author also doesn't also think very highly of string theory: https://warwick.ac.uk/fac/sci/physics/staff/academic/mhadley...
Whether something is "more progressed" hardly matters in matters that still have many questions and more reflective of a consensus of the time that progresses one funeral at a time.
What I quote shows that the author knows and acknowledges that he's describing a classical construct. The question of "compatability" (sic) is not even addressed.
> I didnt say it was THE unification theory of QM and GR, you somehow inferred that
I did not. Here's what I wrote: "This is not unification of QM and GR, it's a classical construction". Not the absence of any "THE", whether capitalized or not.
> I could add that quote and it would change nothing as far as I'm concerned what the authors stance is
Because you do not understand what the author is saying. He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones. That does not make it a quantum theory, any more than the discrete eigenfrequencies of a vibrating classical string make a classical model of vibrating strings a quantum theory.
> He's presenting a purely classical model which displays some features (in particular charge quantization) also seen in quantum mechanical ones.
Compared to other physicists who just outright state that there is no compatibility… You can ignore it, but it is an area for further study in regards to non time orientability for others.
No, I am pointing out that you do not understand the paper you misquoted as evidence that "Not all physicists think they [GR and QM] are incompatible".
The author would not have written a paper trying to take a small step toward a solution if he didn't think that there is a problem.
Just because he does not say explicitly "[GR and QM] are compatible", does not mean opposite.
If you aren't interested in the that U(1) bundle described in the paper is from utilizing time oreintability from a classical standpoint and not formed from the complex phase of a quantum mechanical wave-function, that's on you.
It also doesn't mean what you are claiming.
To have a meaningful discussion about the incompatibility of GR with QM, you first need to know how they are incompatible. Reproducing classical electromagnetism with the Kaluza-Klein trick from 1919 [1] has nothing to do with it.
QM deals with unit vectors in a state space, operators acting on those vectors, and observables whose values can not all be known simultaneously [2]. The hole left by the observer's limited knowledge about the state of the system is filled by an intrinsic randomness which does not exist in classical theories.
GR and other classical theories have only observables, their evolution is deterministically determined and the state of the system can in principle be fully known at all times. We have known for a long time that nature does not actually work like this [3].
If you want to claim that GR is compatible with QM, you have to resolve the above contradiction.
What people who actually understand the problem have been trying to do for a long time is:
1) Quantize GR. This is the obvious first thing to try; you treat the problem as analogous to the quantization of classical electromagnetism and hope to create a quantum version of GR, the gravitational equivalent of QED. When you try that, it turns out you can't make the theory renormalizable - the infinities caused by loops in Feynman diagrams can not be brought under control. Trying to fix that leads to things like loop quantum gravity [4]. Weinberg came up with the alternative idea of asymptotic safety, which tries to neuter the problem with a fixed point in the renormalization group flow [5], but proving that it actually works is another story.
2) Come up with a deterministic (i.e. classical) theory underlying QM. Naive approaches involving hidden variables (i.e. trying to explain away our limited knowledge of quantum states as ignorance rather than truly fundamental) died with Bell's theorem. A few brave souls, notably t'Hooft [6] are still trying more sophisticated approaches (I think it would be nice if superdeterminism [7] got more attention).
3) Write down a more fundamental theory which produces both GR and the other known interactions in the appropriate limits (thermodynamic, large number of quanta). Since the other known interactions are empirically known to be quantum mechanical, it is generally believed that this theory will have to be quantum mechanical too. String theory is the obvious example. In principle, you could also imagine a classical (i.e. deterministic) theory along the lines of (2), but I can't think of any example which comes close to actually doing the job.
[1] https://en.wikipedia.org/wiki/Kaluza%E2%80%93Klein_theory
[2] https://en.wikipedia.org/wiki/Quantum_mechanics#Mathematical...
[3] https://en.wikipedia.org/wiki/Bell%27s_theorem
[4] https://en.wikipedia.org/wiki/Loop_quantum_gravity
[5] https://en.wikipedia.org/wiki/Asymptotic_safety_in_quantum_g...
[6] https://arxiv.org/abs/1405.1548
[7] https://en.wikipedia.org/wiki/Superdeterminism
The exactly opposite idea of adjusting QM to directly work in geometry of strongly curved space-time is not pursued much. Not sure why. Maybe because it's hard. Maybe because it would just be an extension of business as usual which isn't attractive. Maybe for some other reason.
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...
2. We can combine (quantize) gravity, but the problem is that using the tools we have today (Quantum Field Theory) the theory doesn't give meaningful answers. There is a process called renormalization that we use to squeeze an answer out of the theory, but that process don't work for all theories and not gravity.
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.
This becomes a problem when you try to include GR in even simple experimental setups which expose QM's non-classical behavior, like the Stern-Gerlach experiment [1]. What does gravity do before the path chosen by the particle (which is gravitationally attractive) is measured?
[1] https://en.wikipedia.org/wiki/Stern%E2%80%93Gerlach_experime...
This is exaggeration, they are not badly in conflict with each other, we just have not found a way to unify them, i.e. explain gravity through QM.