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).
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.
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.
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.
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_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...
"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...
"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...
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.
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.