Quantum gravity is a castle in the air

When you spend some time digging into the history of physics, you find yourself uncovering the foundations of physics, and then you come to appreciate a few things. You come to appreciate how gravity works, and why an electron falls down. It isn’t because gravitons are flying back and forth:

Graviton image by Julie Peasley, see http://www.particlezoo.net/

You also come to appreciate that light interacts with light to form electrons and positrons in gamma-gamma pair production. You come to appreciate that the electron is not a point particle, so renormalization is not a good thing. You come to appreciate what Maxwell meant when he talked about the screw nature of electromagnetism, why magnetic monopoles do not exist, and why the electron moves towards the proton. It isn’t because photons are flying back and forth. So you come to appreciate that there are issues with quantum gravity. Let’s take a look at that by going through Sabine Hossenfelder’s blog post on the subject. And I quote:

Einstein’s theory of general relativity is more than a hundred years old, but still it gives physicists headaches. Not only are Einstein’s equations hideously difficult to solve, they also clash with physicists other most-cherished achievement, quantum theory.

I suspect the headaches are because some physicists haven’t read the Einstein digital papers, so they don’t know why light curves downwards. It doesn’t “follow the curvature of spacetime”, or curve downwards because gravitons are flying around. Light curves downwards because the speed of light is spatially variable. Like sonar waves curve downwards when the speed of sound in water decreases with depth. On top of that, some physicists don’t know that the electron falls down because spin is real. See Hans Ohanian’s 1984 paper what is spin? He said “the means for filling the gap have been at hand since 1939, when Belinfante established that the spin could be regarded as due to a circulating flow of energy”. Think of the electron as a dynamical “spinor”, then simplify it to light going around and around. The horizontal component curves downwards, so the electron’s position is displaced downwards. In other words, it falls down. What’s the problem?

Problem is, particles have quantum properties. They can, for example, be in two places at once. These particles also have masses, and masses cause gravity.

Yes, particles have quantum properties. The photon has quantum properties associates with Planck’s constant of action h, hence the photon’s energy is E=hc/λ. And yes, particles can be in two places at once because it’s the wave nature of matter, not the point-particle nature of matter. And yes, matter causes gravity because it’s a concentration of energy. Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. So what’s the problem? There is no problem. So what’s next?

But since gravity does not have quantum properties, no one really knows what’s the gravitational pull of a particle in a quantum superposition. To solve this problem, physicists need a theory of quantum gravity. Or, since Einstein taught us that gravity is really curvature of space-time, physicists need a theory for the quantum properties of space and time.

That’s not a problem. Superposition is just a wave thing. See the Wikipedia article on the superposition principle, which has a section on wave superposition. Like I said, it’s the wave nature of matter. That’s why we have the Heisenberg uncertainty principle, which is “inherent in the properties of all wave-like systems”. That’s why we can diffract electrons. That’s why we can make electrons along with positrons out of gamma photons in gamma-gamma pair production. The photon has a wave nature too. That’s why it curves downwards when the speed of light is spatially variable. So why do we need a theory of quantum gravity? Especially when Einstein told us a gravitational field is a place where space is neither homogeneous not isotropic. He didn’t teach us that gravity is really the curvature of space-time. Spacetime curvature is associated with the tidal force rather than the force of gravity. Next.

It’s a hard problem, even for big-brained people like theoretical physicists. They have known since the 1930s that quantum gravity is necessary to bring order into the laws of nature, but 80 years on a solution isn’t anywhere in sight. The major obstacle on the way to progress is the lack of experimental guidance. The effects of quantum gravity are extremely weak and have never been measured, so physicists have only math to rely on. And it’s easy to get lost in math.

Yes, it’s easy to get lost in maths. Especially when you don’t pay attention to what Einstein said. Or what Schrödinger said. Did big-brained physicists in the 1920s listen to what Schrödinger said on page 26 of his 1926 paper quantization as a problem of proper values, part II? He said “let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. And did they listen to what he said on page 27 about light rays influencing one another and showing remarkable curvature? No. Did they listen to what Charles Galton Darwin said in his 1927 paper on the electron as a vector wave, which talked about a spherical harmonic for the two directions of spin? No. Instead Heisenberg and Pauli and others sidelined Schrödinger and Darwin, and promoted Frenkel’s point-particle electron instead. Then when Oppenheimer talked about the resultant problem of infinities and said the theory was fatally flawed in 1930, they carried on regardless, and promoted the kludge called renormalization as a virtue. I would venture to suggest that quantum gravity isn’t what’s necessary to bring order. It’s understanding what went wrong with quantum electrodynamics in the 1920s and 1930s, why it wasn’t fixed in the 1930s and 1940s, and what’s wrong with it now. Then it’s understanding the photon, and how pair production works, and the electron, and why it moves the way that it does. It goes round in circles in a uniform magnetic field because it’s a dynamical “spinor” that’s subject to precession. Think boomerang. For a positron, think left-handed boomerang. Moving on:

The reason it is difficult to obtain observational evidence for quantum gravity is that all presently possible experiments fall into two categories. Either we measure quantum effects – using small and light objects – or we measure gravitational effects – using large and heavy objects. In both cases, quantum gravitational effects are tiny. To see the effects of quantum gravity, you would really need a heavy object that has pronounced quantum properties, and that’s hard to come by.

What observational evidence of quantum gravity? It’s been around since circa 1960, and there’s still no observational evidence for quantum gravity. Compare and contrast with general relativity, where the first evidence came in May 1919. That was only 3½ years after the theory was published in November 1915. With a war on. Perhaps the reason it is difficult to obtain observational evidence for quantum gravity, is because there isn’t any.

Physicists do know a few naturally occurring situations where quantum gravity should be relevant. But it is not on short distances, though I often hear that. Non-quantized gravity really fails in situations where energy-densities become large and space-time curvature becomes strong. And let me be clear that what astrophysicists consider “strong” curvature is still “weak” curvature for those working on quantum gravity. In particular, the curvature at a black hole horizon is not remotely strong enough to give rise to noticeable quantum gravitational effects.

Was that a little dig at Hawking radiation and its negative energy particles plus particles travelling backwards in time? That’s good, because there is no curvature at a black hole horizon. Einstein said a gravitational field is a place where the speed of light is spatially variable. Nowadays some physicists refer to this as the “coordinate” speed of light, and think the speed of light in vacuo is constant. They don’t know that a gravitational field is a place where there’s a gradient in the speed of light. Or that spacetime curvature is where this gradient changes. So they don’t know about the fly in the ointment: at the black hole event horizon, the speed of light is zero, and it can’t go slower than that. So at the event horizon there is no gravitational field, and no spacetime curvature either. It gets worse.

Curvature strong enough to cause general relativity to break down, we believe, exists only in the center of black holes and close by the big bang. In both cases the strongly compressed matter has a high density and a pronounced quantum behaviour which should give rise to quantum gravitational effects. Unfortunately, we cannot look inside a black hole, and reconstructing what happened at the Big Bang from today’s observation can, with present measurement techniques, not reveal the quantum gravitational behaviour.

Who says general relativity breaks down? It’s the best-tested theory we’ve got, as per Clifford M Will’s excellent paper on the confrontation between general relativity and experiment. It only appears to break down if you ignore what Einstein said and pay too much attention to people like Stephen Hawking. In his 1966 paper on singularities and the geometry of spacetime, Hawking talked of “such a strong gravitational field that even the ‘outgoing’ light rays from it are dragged back”. That’s wrong. In a strong gravitational field, outgoing light rays aren’t dragged back. They speed up even more. Don’t just take my word for it, see what physicsFAQ editor Don Koks says in Is The Speed of Light Everywhere the Same? The answer is no, because light speeds up as it ascends from floor to ceiling. Hawking didn’t understand gravity, so he didn’t understand black holes. Nor did Penrose. That means Penrose-Hawking singularity theorems are wrong. It gets even worse.

The regime where quantum gravity becomes relevant should also be reached in particle collisions at extremely high center-of-mass energy. If you had a collider large enough – estimates say that with current technology it would be about the size of the Milky Way – you could focus enough energy into a small region of space to create strong enough curvature. But we are not going to build such a collider any time soon.

The physicists who talk about the strong curvature regime don’t seem to know about Maxwell saying “light consists of transverse undulations”. Or about Percy Hammond saying: “the field describes the curvature that characterizes the electromagnetic interaction”. Or about a Geometric Model for Fundamental Particles by Batty-Pratt and Racey, who said they’d “made the presumptive leap of assuming photons to be undulations of the space-time structure”. They also talked about a “theory of the continuum that purports to describe matter as a distortion of space in the manner first suggested by W K Clifford”. That’s William Kingdon Clifford, the Clifford algebra Clifford. The author of the 1870 space theory of matter. The Clifford who said “I hold in fact: (1) That small portions of space are in fact of a nature analogous to little hills on a surface which is on the average flat; namely, that the ordinary laws of geometry are not valid in them”. I’m confident enough that as per Schrödinger’s 1926 paper about light rays showing remarkable curvature, the strong curvature regime is where the photon is. Or where the electron is. Or where the proton is. So high-energy particle collisions are missing the point. So what’s the alternative?

Besides strong space-time curvature, there is another case where quantum effects of gravity should become measureable that is often neglected: By creating quantum superpositions of heavy objects. This causes the approximation in which matter has quantum properties but gravity doesn’t (the “semi-classical limit”) to break down, revealing truly quantum effects of gravity. A few experimental groups are currently trying to reach the regime where they might become sensitive to such effects. They still have some orders of magnitude to go, so not quite there yet.

Is that spatial curvature or spacetime curvature? See John Baez and Emory Bunn’s preliminaries article dating from 2006: “Similarly, in general relativity gravity is not really a ‘force’, but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial”. But either way they’ll never be quite there. Light has a quantum nature, and so does an electron, because we make electrons out of photons in gamma-gamma pair production. If the photon didn’t have a quantum nature, electrons wouldn’t be 511keV electrons. But the downward motion of a photon doesn’t have a quantum nature, and nor does the downward motion of an electron. Nor does the downward motion of a brick.

Why don’t physicists study this case closer? As always, it’s hard to say why scientists do one thing and not another. I can only guess it’s because from a theoretical perspective this case is not all that interesting.

Agreed. Quantum superposition is not all that interesting when you know about the wave nature of matter and the superposition of waves.

I know I said that physicists don’t have a theory of quantum gravity, but that is only partly correct. Gravity can, and has been, quantized using the normal methods of quantization already in the 1960s by Feynman and DeWitt. However, the theory one obtains this way (“perturbative quantum gravity”), breaks down in exactly the strong curvature regime that physicists want to use it (“perturbatively non-renormalizable”). Therefore, this approach is today considered merely a low-energy approximation (“effective theory”) to the yet-to-be-found full theory of quantum gravity (“UV-completion”).

Feynman, like his supervisor Wheeler, confused curved spacetime with curved space. He didn’t know that curved spacetime is merely the non-linearity of the inhomogeneity of space, which decreases with distance in line with the inverse square law. DeWitt likened quantum gravity to Yang-Mills theory, waxed lyrical about braneworld, and promoted the many-worlds interpretation of quantum mechanics. Moving swiftly on:

Past the 1960s, almost all research efforts in quantum gravity focused on developing that full theory. The best known approaches are string theory, loop quantum gravity, asymptotic safety, and causal dynamical triangulation. The above mentioned case with heavy objects in quantum superpositions, however, does not induce strong curvature and hence falls into the realm of the boring and supposedly well-understood theory from the 1960s. Ironically, for this reason there are almost no theoretical predictions for such an experiment from either of the major approaches to the full theory of quantum gravity.

As above. Such research efforts didn’t start with the Einstein digital papers, or with Schrödinger’s 1926 paper, or with any attempt to understand how gravity works or how a magnet works. These were mathematical research efforts, not physics research efforts. Ironically, by people who got Lost in Math.

Most people in the field presently think that perturbative quantum gravity must be the correct low-energy limit of any theory of quantum gravity.

The problem with that is perturbation theory and renormalization are touted as virtues, when they aren’t. Perturbation theory merely “comprises mathematical methods for finding an approximate solution to a problem”. Oppenheimer said the theory was fatally flawed in 1930. Renormalization didn’t fix that. It just swept it under the carpet.

A minority, however, holds that this isn’t so, and members of this club usually quote one or both of the following reasons.

I’m in that club, only I’m giving different reasons. Unfortunately most people in the field don’t want you to hear about them. They’ve spent decades on quantum gravity. They are invested in it. They won’t give it up lightly.

The first objection is philosophical. It does not conceptually make much sense to derive a supposedly more fundamental theory (quantum gravity) from a less fundamental one (non-quantum gravity) because by definition the derived theory is the less fundamental one.

But surely quantum gravity isn’t fundamental. Energy is fundamental. Photons are fundamental too. A photon in space is energy propagating through space. Regardless of whether that space is homogeneous or not, it’s the only particle there. There are no gravitons flitting around it like flies round a horse.

Indeed, the quantization procedure for Yang-Mills theories is a logical nightmare. You start with a non-quantum theory, make it more complicated to obtain another theory, though that is not strictly speaking a derivation, and if you then take the classical limit you get a theory that doesn’t have any good interpretation whatsoever. So why did you start from it to begin with it?

Yang-Mills theory is a logical nightmare because there are no actual messenger particles. See the peculiar notion of exchange forces part I and part II by Cathryn Carson. She says the exchange-particle idea began to work its way into QED from the mid-to-late 1930s. And that Heisenberg’s importation of exchange forces into nuclear physics depended essentially on a model of the neutron that was later retracted. She says “the idea now taken as definitional of the concept of force – for quantum field theory, the all-important idea of particle exchange – was not in fact there from the start, but rather worked its way in from somewhere outside”. The electron and the proton aren’t attracted to one another because they’re throwing photons back and forth. Hydrogen atoms don’t twinkle, and magnets don’t shine. In similar vein there are no pions flitting back and forth inside an atomic nucleus, and the nuclear force is said to be a disaster. Moreover gauge theories aren’t gauge theories if the gauge bosons are massive, and if you give them mass via cosmic treacle, you’re flatly contradicting E=mc². Then what’s the point of proposing weak hypercharge when you don’t know what charge is? How can free neutron decay possibly occur because an 80GeV W-boson pops into existence, spontaneously like worms from mud?

Well, the obvious answer is: We do it because it works, and we do it this way because of historical accident not because it makes a lot of sense. Nothing wrong with that for a pragmatist like me, but also not a compelling reason to insist that the same method should apply to gravity.

See Gary Taub’s physicsworld article on Carlo Rubbia and the discovery of the W and Z. It only works if you’re Carlo Rubbia, and you declare that an electron track means you’ve “discovered” the W-boson.

The second often-named argument against the perturbative quantization is that you do not get atomic physics by quantizing water either. So if you think that gravity is not a fundamental interaction but comes from the collective behavior of a large number of microscopic constituents (think “atoms of space-time”), then quantizing general relativity is simply the wrong thing to do.

Gravity is the collective behaviour of a large number of microscopic constituents? What sorcery is this? Go read what Einstein said. There are no atoms of spacetime. Spacetime is an abstract ting that models space at all times. That’s why there is no motion in spacetime. The photon moves through space, not spacetime. It curves downwards because a concentration of energy in the guise of a massive star “conditions” the surrounding space, this effect diminishing with distance. As a result space is neither homogeneous not isotropic, so the speed of light is spatially variable, so light curves downwards like other waves curve downwards when there’s vertical gradient in wave speed. Again, this all comes back to understanding how gravity works.

Those who take this point of view that gravity is really a bulk-theory for some unknown microscopic constituents follow an approach called “emergent gravity”. It is supported by the (independent) observations of Jacobson, Padmanabhan, and Verlinde, that the laws of gravity can be rewritten so that they appear like thermodynamical laws. My opinion about this flip-flops between “most amazing insight ever” and “curious aside of little relevance,” sometimes several times a day.

My opinion about this flip-flops between “pseudoscience” and “garbage”. Gravity is nothing to do with thermodynamics. It’s to do with continuum mechanics. The stress-energy-momentum tensor has a shear stress term. Space is modelled as something akin to a gin-clear ghostly elastic medium, wherein a gravitational field is akin to a pressure gradient in space.

Be that as it may, if you think that emergent gravity is the right approach to quantum gravity, then the question where gravity-as-we-know-and-like-it breaks down becomes complicated. It should still break down at high curvature, but there may be further situations where you could see departures from general relativity.

Gravity doesn’t break down at high curvatures. It stops at the event horizon, because that’s where the speed of light is zero, and it can’t go slower than that. Again, high curvature is to do with electromagnetism, not gravity. A 511keV photon is converted into an electron in gamma-gamma pair production. Again take a tip from Schrödinger’s 1926 paper quantization as a problem of proper values, part II: let us think of a wave group which in some way gets into a small closed path, whose dimensions are of the order of the wave length. Then let’s call it an electron.

Erik Verlinde, for example, interprets dark matter and dark energy as relics of quantum gravity. If you believe this, we do already have evidence for quantum gravity!

I believe that Erik Verlinde doesn’t understand that a gravitational field is space that’s neither homogeneous not isotropic. So I believe that he doesn’t understand dark matter either. Or dark energy. So I don’t believe we already have evidence for quantum gravity. Sorry.

Others have suggested that if space-time is made of microscopic constituents, then it may have bulk-properties like viscosity, or result in effects normally associated with crystals like birefringence, or the dispersion of light.

Space-time isn’t space. It’s a model of space at all times. The map is not the territory. There is no dispersion of light in gravitational lensing. Instead light curves because the speed of light is spatially variable, and that speed is independent of the frequency. Shapiro knew that the speed of light is spatially variable. His 1964 paper concerned what’s now called the Shapiro delay. Wikipedia faithfully quotes what he said: “the speed of a light wave depends on the strength of the gravitational potential along its path”. Why isn’t this common knowledge in the quantum gravity field?

In summary, the expectation that quantum effects of gravity should become relevant for strong space-time curvature is based on an uncontroversial extrapolation and pretty much everyone in the field agrees on it.

Pretty much everyone in the field agrees that the speed of light is constant. They don’t know that  the speed of light is not constant. Or that spacetime curvature is where the gradient in the speed of light changes. Or that spacetime curvature is not spatial curvature.

In certain approaches to quantum gravity, deviations from general relativity could also become relevant at long distances, low acceleration, or low energies. An often neglected possibility is to probe the effects of quantum gravity with quantum superpositions of heavy objects.

You’ll find your “deviations from general relativity” when you read the Einstein digital papers. Then you’ll realize that the people who wrote the general relativity books were doing their own thing, and making it up as they went along. Then they taught it to you.

I hope to see experimental evidence for quantum gravity in my lifetime.

I’m sorry Sabine, but you won’t. Because quantum gravity is detached from the foundations of physics. Instead it’s a castle in the air, floating on hype and hypothesis and misconception. One day it’s all going to come crashing down, so bale out while you can. There are better things to do.


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  1. Marcelino Kemplin

    This post seem really good.

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