New type of gravitational wave detector proposed

The existence of gravitational waves is one of the central predictions of Einstein’s theory of general relativity. Gravitational waves have never been directly observed, though the indirect evidence is so good that Marc Kamionkowski, a theorist at Johns Hopkins University in Baltimore, Maryland, recently said

“We are so confident that gravitational waves exist that we don’t actually need to see one.”

But most scientists for good reasons prefer evidence over confidence, and so the hunt for a direct detection of gravitational waves has been going on for decades. Existing gravitational wave detectors search for the periodic stretching in distances caused by a the gravitational wave’s distortion of space and time itself. For this one has to very precisely measure and compare distances in different directions. Such tiny relative distortion can be detected very precisely by an interferometer.

In the interferometer, a laser beam is sent into each of the directions that are being compared. The signal is reflected and then brought to interfere with itself. This interference pattern is very sensitive to the tiniest changes in distance; the longer the arms of the interferometer, the better. One can increase the sensitivity by reflecting the laser light back and forth several times.

The most ambitious gravitational wave interferometer in planning is the eLISA space observatory, which would ping back and forth laser signals between one mother space-station and two “daughter” stations. These stations would have distances of about 1 mio kilometer. The interferometer would be sensitive to gravitational waves in the mHz to Hz range, a range in which one expects signals from binary systems, probably one of the most reliable sources of gravitational waves. eLisa might or might not be launched in 2028.

In a recent paper now two physicists from Tel Aviv University, Israel, have proposed a new method to measure gravitational waves. They propose not to look for periodic distortions of space, but periodic distortions of time instead. If Einstein taught us one thing, it’s that space and time belong together, and so all gravitational waves distort both together. The idea then is to measure the local passing of time in different locations with atomic clocks to very high precision, and then compare it.

If you recall, time passes differently depending on the position in a gravitational field. Close by a massive body, time goes by slower than farther away from it. And so, when a gravitational wave passes by, the tick rate of clocks, or of atoms respectively, depends on the location in the field of the wave.

The fineprint is that to reach an interesting regime in which gravitational waves are likely to be found, similar to that of eLISA, the atomic clocks have to be brought into distances far exceeding the diameter of the Earth and more like the distance of the Earth to the Sun. So the researchers propose that we could leave behind a trail of atomic clocks on our path around the Sun. The clocks then would form a network of local time-keepers from which the presence of gravitational waves could be read off; the more clocks, the better the precision of the measurement.

Figure from arXiv:1501.00996

It is a very ambitious proposal of course, but I love the vision!

No, the LHC will not make contact with parallel universes

Evidence for rainbow gravity by butterfly
production at the LHC.

The most recent news about quantum gravity phenomenology going through the press is that the LHC upon restart at higher energies will make contact with parallel universes, excuse me, with PARALLEL UNIVERSES. The telegraph even wants you to believe that this would disprove the Big Bang, and tomorrow maybe it will cause global warming, cure Alzheimer and lead to the production of butterflies at the LHC, who knows. This story is so obviously nonsense that I thought it would be unnecessary to comment on this, but I have underestimated the willingness of news outlets to promote shallow science, and also the willingness of authors to feed that fire.

This story is based on the paper:

Absence of Black Holes at LHC due to Gravity's Rainbow
Ahmed Farag Ali, Mir Faizal, Mohammed M. Khalil
arXiv:1410.4765 [hep-th]
Phys.Lett. B743 (2015) 295

which just got published in PLB. Let me tell you right away that this paper would not have passed my desk. I'd have returned it as major revisions necessary.

Here is a summary of what they have done. In models with large additional dimensions, the Planck scale, where effects of quantum gravity become important, can be lowered to energies accessible at colliders. This is an old story that was big 15 years ago or so, and I wrote my PhD thesis on this. In the new paper they use a modification of general relativity that is called "rainbow gravity" and revisit the story in this framework.

In rainbow gravity the metric is energy-dependent which it normally is not. This energy-dependence is a non-standard modification that is not confirmed by any evidence. It is neither a theory nor a model, it is just an idea that, despite more than a decade of work, never developed into a proper model. Rainbow gravity has not been shown to be compatible with the standard model. There is no known quantization of this approach and one cannot describe interactions in this framework at all. Moreover, it is known to lead to non-localities with are ruled out already. For what I am concerned, no papers should get published on the topic until these issues have been resolved.

Rainbow gravity enjoys some popularity because it leads to Planck scale effects that can affect the propagation of particles, which could potentially be observable. Alas, no such effects have been found. No such effects have been found if the Planck scale is the normal one! The absolutely last thing you want to do at this point is argue that rainbow gravity should be combined with large extra dimensions, because then its effects would get stronger and probably be ruled out already. At the very least you would have to revisit all existing constraints on modified dispersion relations and reaction thresholds and so on. This isn't even mentioned in the paper.

That isn't all there is to say though. In their paper, the authors also unashamedly claim that such a modification has been predicted by Loop Quantum Gravity, and that it is a natural incorporation of effects found in string theory. Both of these statements are manifestly wrong. Modifications like this have been motivated by, but never been derived from Loop Quantum Gravity. And String Theory gives rise to some kind of minimal length, yes, but certainly not to rainbow gravity; in fact, the expression of the minimal length relation in string theory is known to be incompatible with the one the authors use. The claims that this model they use has some kind of derivation or even a semi-plausible motivation from other theories is just marketing. If I had been a referee of this paper, I would have requested that all these wrong claims be scraped.

In the rest of the paper, the authors then reconsider the emission rate of black holes in extra dimension with the energy-dependent metric.

They erroneously state that the temperature diverges when the mass goes to zero and that it comes to a "catastrophic evaporation". This has been known to be wrong since 20 years. This supposed catastrophic evaporation is due to an incorrect thermodynamical treatment, see for example section 3.1 of this paper. You do not need quantum gravitational effects to avoid this, you just have to get thermodynamics right. Another reason to not publish the paper. To be fair though, this point is pretty irrelevant for the rest of the authors' calculation.

They then argue that rainbow gravity leads to black hole remnants because the temperature of the black hole decreases towards the Planck scale. This isn't so surprising and is something that happens generically in models with modifications at the Planck scale, because they can bring down the final emission rate so that it converges and eventually stops.

The authors then further claim that the modification from rainbow gravity affects the cross-section for black hole production, which is probably correct, or at least not wrong. They then take constraints on the lowered Planck scale from existing searches for gravitons (ie missing energy) that should also be produced in this case. They use the contraints obtained from the graviton limits to say that with these limits, black hole production should not yet have been seen, but might appear in the upcoming LHC runs. They should not of course have used the constaints from a paper that were obtained in a scenario without the rainbow gravity modification, because the production of gravitons would likewise be modified.

Having said all that, the conclusion that they come to that rainbow gravity may lead to black hole remnants and make it more difficult to produce black holes is probably right, but it is nothing new. The reason is that these types of models lead to a generalized uncertainty principle, and all these calculations have been done before in this context. As the authors nicely point out, I wrote a paper already in 2004 saying that black hole production at the LHC should be suppressed if one takes into account that the Planck length acts as a minimal length.

Yes, in my youth I worked on black hole production at the LHC. I gracefully got out of this when it became obvious there wouldn't be black holes at the LHC, some time in 2005. And my paper, I should add, doesn't work with rainbow gravity but with a Lorentz-invariant high-energy deformation that only becomes relevant in the collision region and thus does not affect the propagation of free particles. In other words, in contrast to the model that the authors use, my model is not already ruled out by astrophysical constraints. The relevant aspects of the argument however are quite similar, thus the similar conclusions: If you take into account Planck length effects, it becomes more difficult to squeeze matter together to form a black hole because the additional space-time distortion acts against your efforts. This means you need to invest more energy than you thought to get particles close enough to collapse and form a horizon.

What does any of this have to do with paralell universes? Nothing, really, except that one of the authors, Mir Faizal, told some journalist there is a connection. In the phys.org piece one can read:

""Normally, when people think of the multiverse, they think of the many-worlds interpretation of quantum mechanics, where every possibility is actualized," Faizal told Phys.org. "This cannot be tested and so it is philosophy and not science. This is not what we mean by parallel universes. What we mean is real universes in extra dimensions. As gravity can flow out of our universe into the extra dimensions, such a model can be tested by the detection of mini black holes at the LHC. We have calculated the energy at which we expect to detect these mini black holes in gravity's rainbow [a new theory]. If we do detect mini black holes at this energy, then we will know that both gravity's rainbow and extra dimensions are correct."

To begin with rainbow gravity is neither new nor a theory, but that addition seems to be the journalist's fault. For what the parallel universes are concerned, to get these in extra dimensions you would need to have additional branes next to our own one and there is nothing like this in the paper. What this has to do with the multiverse I don't know, that's an entirely different story. Maybe this quote was taken out of context.

Why does the media hype this nonsense? Three reasons I can think of. First, the next LHC startup is near and they're looking for a hook to get the story across. Black holes and parallel universes sound good, regardless of whether this has anything to do with reality. Second, the paper shamelessly overstates the relevance of the investigation, makes claims that are manifestly wrong, and fails to point out the miserable state that the framework they use is in. Third, the authors willingly feed the hype in the press.

Did the topic of rainbow gravity and the author's name, Mir Faizal, sound familiar? That's because I wrote about both only a month ago, when the press was hyping another nonsense story about black holes in rainbow gravity with the same author. In that previous paper they claimed that black holes in rainbow gravity don't have a horizon and nothing was mentioned about them forming remnants. I don't see how these both supposed consequences of rainbow gravity are even compatible with each other. If anything this just reinforces my impression that this isn't physics, it's just fanciful interpretation of algebraic manipulations that have no relation to reality whatsoever.

In summary: The authors work in a framework that combines rainbow gravity with a lowered Planck scale, which is already ruled out. They derive bounds on black hole production using existing data analysis that does not apply in the framework they use. The main conclusion that Planck length effects should suppress black hole production at the LHC is correct, but this has been known since 10 years at least. None of this has anything to do with parallel universes.

No, you cannot test quantum gravity with X-ray superradiance

I am always looking for new ways to repeat myself, so I cannot possibly leave out this opportunity to point out yet another possibility to not test quantum gravity. Chris Lee from Arstechnica informed the world last week that “Deflecting X-rays due to gravity may provide view on quantum gravity”, which is a summary of the paper

Gravitational and Relativistic Deflection of X-Ray Superradiance
By Wen-Te Liao and Sven Ahrens

The idea is to shine light on a crystal at frequencies high enough so that it excites nuclear resonances. This excitation is delocalized, and the energy is basically absorbed and reemitted systematically, which leads to a propagation of the light-induced excitation through the crystal. How this propagation proceeds depends on the oscillations of the nuclei, which again depends on the local proper time. If you place the crystal in a gravitational field, the proper time will depend on the strength of the field. As a consequence, the propagation of the excitation through the crystal depends on the gradient of the gravitational field. The authors argue that in principle this influence of gravity on the passage of time in the crystal should be measurable.

They then look at a related but slightly different effect in which the crystal rotates and the time-dilatation resulting from the (non-inertial!) motion gives rise to a similar effect, though much larger in magnitude.

The authors do not claim that this experiment would be more sensitive than already existing ones. I assume that if it was so, they’d have pointed this out. Instead, they write the main advantage is that this new method allows to test both special and general relativistic effects in tabletop experiments.

It’s a neat paper. What does it have to do with quantum gravity? Well, nothing. Indeed the whole paper doesn’t say anything about quantum gravity. Quantum gravity, I remind you, is the quantization of the gravitational interaction, which plays no role for this whatsoever. Chris Lee in his Arstechnica piece explains

“Experiments like these may even be sensitive enough to see the influence of quantum mechanics on space and time.”

Which is just plainly wrong. The influence of quantum mechanics on space-time is far too weak to be measurable in this experiment, or in any other known laboratory experiment. If you figure out how to do this on a tabletop, book your trip to Stockholm right away. Though I recommend you show me the paper before you waste your money.

Here is what Chris Lee had to say about the question what he thinks it’s got to do with quantum gravity:

@skdh @arstechnica no not entirely. Every test of general relativity is trying to find a discrepancy, which is relevant to quantum gravity
— Chris Lee (@exmamaku) March 22, 2015

Deviations from general relativity aren’t the same as quantum gravity. And besides this, for all I can tell the authors haven’t claimed that they can test a new parameter regime that hasn’t been tested before. The reference to quantum gravity is an obvious attempt to sex up the piece and has no scientific credibility whatsoever.

Summary: Just because it’s something with quantum and something with gravity doesn’t mean it’s quantum gravity.

No foam: New constraint on space-time fluctuations rules out stochastic Planck scale dispersion

The most abused word in science writing is “space-time foam.” You’d think is a technical term, but it isn’t – space-time foam is just a catch-all phrase for some sort of quantum gravitational effect that alters space-time at the Planck scale. The technical term, if there is any, would be “Planck scale effect”. And please note that I didn’t say quantum gravitational effects “at short distances” because that is an observer-dependent statement and wouldn’t be compatible with Special Relativity. It is generally believed that space-time is affected at high curvature, which is an observer-independent statement and doesn’t a priori have anything to do with distances whatsoever.

Having said that, you can of course hypothesize Planck scale effects that do not respect Special Relativity and then go out to find constraints, because maybe quantum gravity does indeed violate Special Relativity? There is a whole paper industry behind this since violations of Special Relativity tend to result in large and measurable consequences, in contrast to other quantum gravity effects, which are tiny. A lot of experiments have been conducted already looking for deviations from Special Relativity. And one after the other they have come back confirming Special Relativity, and General Relativity in extension. Or, as the press has it: “Einstein was right.”

Since there are so many tests already, it has become increasingly hard to still believe in Planck scale effects that violate Special Relativity. But players gonna play and haters gonna hate, and so some clever physicists have come up with models that supposedly lead to Einstein-defeating Planck scale effects which could be potentially observable, be indicators for quantum gravity, and are still compatible with existing observations. A hallmark of these deviations from Special Relativity is that the propagation of light through space-time becomes dependent on the wavelength of the light, an effect which is called “vacuum dispersion”.

There are two different ways this vacuum dispersion of light can work. One is that light of shorter wavelength travels faster than that of longer wavelength, or the other way round. This is a systematic dispersion. The other way is that the dispersion is stochastic, so that the light sometimes travels faster, sometimes slower, but on the average it moves still with the good, old, boring speed of light.

The first of these cases, the systematic one, has been constrained to high precision already, and no Planck scale effects have been seen. This has been discussed since a decade or so, and I think (hope!) that by now it’s pretty much off the table. You can always of course come up with some fancy reason for why you didn’t see anything, but this is arguably unsexy. The second case of stochastic dispersion is harder to come by because on the average you do get back Special Relativity.

I already mentioned in September last year that Jonathan Granot gave a talk at the 2014 conference on “Experimental Search for Quantum Gravity” where he told us he and collaborators had been working on constraining the stochastic case. I tentatively inquired if they saw any deviations from no effect and got a head shake, but was told to keep my mouth shut until the paper is out. To make a long story short, the paper has appeared now, and they don’t see any evidence for Planck scale effects whatsoever:

A Planck-scale limit on spacetime fuzziness and stochastic Lorentz invariance violation
Vlasios Vasileiou, Jonathan Granot, Tsvi Piran, Giovanni Amelino-Camelia

What they did for this analysis is to take a particularly pretty gamma ray burst, GRB090510. The photons from gamma ray bursts like this travel over a very long distances (some Gpc), during which the deviations from the expected travel time add up. The gamma ray spectrum can also extend to quite high energies (about 30 GeV for this one) which is helpful because the dispersion effect is supposed to become stronger with high energy.

What the authors do then is basically to compare the lower energy part of the spectrum with the higher energy part and see if they have a noticeable difference in the dispersion, which would tend to wash out structures. The answer is, no, there’s no difference. This in turn can be used to constrain the scale at which effects can set in, and they get a constraint a little higher than the Planck scale (1.6 times) at high confidence (99%).

It’s a neat paper, well done, and I hope this will put the case to rest.

Am I surprised by the finding? No. Not only because I knew the result since September, but also because the underlying models that give rise to such effects are theoretically unsatisfactory, at least for what I am concerned. This is particularly apparent for the systematic case. In the systematic case the models are either long ruled out already because they break Lorentz-invariance, or they result in non-local effects which are also ruled out already. Or, if you want to avoid both they are simply theoretically inconsistent. I showed this in a paper some years ago. I also mentioned in that paper that the argument I presented does not apply for the stochastic case. However, I added this because I simply wasn’t in the mood to spend more time on this than I already had. I am pretty sure you could use the argument I made also to kill the stochastic case on similar reasoning. So that’s why I’m not surprised. It is of course always good to have experimental confirmation.

While I am at it, let me clear out a common confusion with these types of tests. The models that are being constrained here do not rely on space-time discreteness, or “graininess” as the media likes to put it. It might be that some discrete models give rise to the effects considered here, but I don’t know of any. There are discrete models of space-time of course (Causal Sets, Causal Dynamical Triangulation, LQG, and some other emergent things), but there is no indication that any of these leads to an effect like the stochastic energy-dependent dispersion. If you want to constrain space-time discreteness, you should look for defects in the discrete structure instead.

And because my writer friends always complain the fault isn’t theirs but the fault is that of the physicists who express themselves sloppily, I agree, at least in this case. If you look at the paper, it’s full with foam, and it totally makes the reader believe that the foam is a technically well-defined thing. It’s not. Every time you read the word “space-time foam” make that “Planck scale effect” and suddenly you’ll realize that all it means is a particular parameterization of deviations from Special Relativity that, depending on taste, is more or less well-motivated. Or, as my prof liked to say, a paramterization of ignorance.

In summary: No foam. I’m not surprised. I hope we can now forget deformations of Special Relativity.

What physics says about the vacuum: A visit to the seashore.

[Image Source: www.wall321.com]

Imagine you are at the seashore, watching the waves. Somewhere in the distance you see a sailboat — wait, don’t fall asleep yet. The waves and I want to tell you a story about nothing.

Before quantum mechanics, “vacuum” meant the absence of particles, and that was it. But with the advent of quantum mechanics, the vacuum became much more interesting. The sea we’re watching is much like this quantum vacuum. The boats on the sea’s surface are what physicists call “real” particles; they are the things you put in colliders and shoot at each other. But there are also waves on the surface of the sea. The waves are like “virtual” particles; they are fluctuations around sea level that come out of the sea and fade back into it.

Virtual particles have to obey more rules than sea waves though. Because electric charge must be conserved, virtual particles can only be created together with their anti-particles that carry the opposite charge. Energy too must be conserved, but due to Heisenberg’s uncertainty principle, we are allowed to temporarily borrow some energy from the vacuum, as long as we give it back quickly enough. This means that the virtual particle pairs can only exist for a short time, and the more energy they carry, the shorter the duration of their existence.

You cannot directly measure virtual particles in a detector, but their presence has indirect observable consequences that have been tested to great accuracy. Atomic nuclei, for example, carry around them a cloud of virtual particles, and this cloud shifts the energy levels of electrons orbiting around the nucleus.

So we know, not just theoretically but experimentally, that the vacuum is not empty. It’s full with virtual particles that constantly bubble in and out of existence.

Vizualization of a quantum field theory calculation showing virtual particles in the quantum vacuum.
Image Credits: Derek Leinweber

Let us go back to the seashore; I quite liked it there. We measure elevation relative to the average sea level, which we call elevation zero. But this number is just a convention. All we really ever measure are differences between heights, so the absolute number does not matter. For the quantum vacuum, physicists similarly normalize the total energy and momentum to zero because all we ever measure are energies relative to it. Do not attempt to think of the vacuum’s energy and momentum as if it was that of a particle; it is not. In contrast to the energy-momentum of particles, that of the vacuum is invariant under a change of reference frame, as Einstein’s theory of Special Relativity requires. The vacuum looks the same for the guy in the train and for the one on the station.

But what if we take into account gravity, you ask? Well, there is the rub. According to General Relativity, all forms of energy have a gravitational pull. More energy, more pull. With gravity, we are no longer free to just define the sea level as zero. It’s like we had suddenly discovered that the Earth is round and there is an absolute zero of elevation, which is at the center of the Earth.

In best manner of a physicist, I have left out a small detail, which is that the calculated energy of the quantum vacuum is actually infinite. Yeah, I know, doesn’t sound good. If you don’t care what the total vacuum energy is anyway, this doesn’t matter. But if you take into account gravity, the vacuum energy becomes measurable, and therefore it does matter.

The vacuum energy one obtains from quantum field theory is of the same form as Einstein’s Cosmological Constant because this is the only form which (in an uncurved space-time) does not depend on the observer. We measured the Cosmological Constant to have a small, positive, nonzero value which is responsible for the accelerated expansion of the universe. But why it has just this value, and why not infinity (or at least something huge), nobody knows. This “Cosmological Constant Problem” is one of the big open problems in theoretical physics today and its origin lies in our lacking understanding of the quantum vacuum.

But this isn’t the only mystery surrounding the sea of virtual particles. Quantum theory tells you how particles belong together with fields. The quantum vacuum by definition doesn’t have real particles in it, and normally this means that the field that it belongs to also vanishes. For these fields, the average sea level is at zero, regardless of whether there are boats on the water or aren’t. But for some fields the real particles are more like stones. They’ll not stay on the surface, they will sink and make the sea level rise. We say the field “has a non-zero vacuum expectation value.”

On the seashore, you now have to wade through the water, which will slow you down. This is what the Higgs-field does: It drags down particles and thereby effectively gives them mass. If you dive and kick the stones that sunk to the bottom hard enough, you can sometimes make one jump out of the surface. This is essentially what the LHC does, just call the stones “Higgs bosons.” I’m really getting into this seashore thing ;)

Next, let us imagine we could shove the Earth closer to the Sun. Oceans would evaporate and you could walk again without having to drag through the water. You’d also be dead, sorry about this, but what about the vacuum? Amazingly, you can do the same. Physicists say the “vacuum melts” rather than evaporates, but it’s very similar: If you pump enough energy into the vacuum, the level sinks to zero and all particles are massless again.

You may complain now that if you pump energy into the vacuum, it’s no longer vacuum. True. But the point is that you change the previously non-zero vacuum expectation value. To our best knowledge, it was zero in the very early universe and theoretical physicists would love to have a glimpse at this state of matter. For this however they’d have to achieve a temperature of 10¹⁵ Kelvin! Even the core of the sun “only” makes it to 10⁷ Kelvin.

One way to get to such high temperature, if only in a very small region of space, is with strong electromagnetic fields.

In a recent paper, Hegelich, Mourou, and Rafelski estimated that with the presently most advanced technology high intensity lasers could get close to the necessary temperature. This is still far off reality, but it will probably one day become possible!

Back to the sea: Fluids can exist in a “superheated” state. In such a state, the medium is liquid even though its temperature is above the boiling point. Superheated liquids are “metastable,” this means if you give them any opportunity they will very suddenly evaporate into the preferred stable gaseous state. This can happen if you boil water in the microwave, so always be very careful taking it out.

The vacuum that we live in might be a metastable state: a “false vacuum.” In this case it will evaporate at some point, and in this process release an enormous amount of energy. Nobody really knows whether this will indeed happen. But even if it does happen, best present estimates date this event into the distant future, when life is no longer possible anyway because stars have run out of power. Particle physicist Joseph Lykken estimated something like a Googol years; that’s about 10⁹⁰ times the present age of the universe.

According to some theories, our universe came into existence from another metastable vacuum state, and the energy that was released in this process eventually gave rise to all we see around us now. Some physicists, notably Lawrence Krauss, refer to this as creating a universe from “nothing.”


If you take away all particles, you get the quantum vacuum, but you still have space-time. If we had a quantum theory for space-time as well, you could take away space-time too, at least operationally. This might be the best description of a physical “nothing” that we can ever reach, but it still would not be an absolute nothing because even this state is still a mathematical “something”.

Now what exactly it means for mathematics to “exist” I better leave to philosophers. All I have to say about this is, well, nothing.

---

If you want to know more about the philosophy behind nothing, you might like Jim Holt’s book “Why does the world exist”, which I reviewed here. 

This post previously appeared at Starts With a Bang under the title “Everything you ever wanted to know about nothing”.

Can we prove the quantization of gravity with the Casimir effect? Probably not.

Quantum gravity phenomenology has hit the news again. This time the headline is that we can supposedly use the gravitational Casimir effect to demonstrate the existence of gravitons, and thereby the quantization of the gravitational field. You can read this on New Scientist or Spektrum (in German), and tomorrow you’ll read it in a dozen other news outlets, all of which will ignore what I am about to tell you now, namely (surpise) the experiment is most likely not going to detect any quantum gravitational effect.
The relevant paper is on the arxiv

Gravitational Casimir effect
James Q. Quach
Phys. Rev. Lett. 114, 081104 (2015)
arXiv:1502.07429 [gr-qc]

I’m here for you. I went and read the paper. Then it turned out that the argument is based on another paper by Minter et al, which has a whooping 60 pages. Don’t despair, I’m here for you. I went and read that too. It’s only fun if it hurts, right? Luckily my attempted martyrdom wasn’t put to too much test because I recalled after the first 3 pages that I had read the Minter et al paper before. So what is this all about?

The Casmir effect is a force that is normally computed for quantum electrodynamics, where it acts between conducting, uncharged plates. The resulting force is a consequence of the boundary conditions on the plates. The relevant property of the setup in quantum electrodynamics is that the plates are conducting, which is what causes the boundary condition. Then, the quantum vacuum outside the plates is different from the vacuum between the plates, resulting in a net force. You can also do this calculation for other geometries with boundary conditions; it isn’t specific to the plates, this is just the simplest case.

The Casimir effect exists for all quantized fields, in principle, if you have suitable boundary conditions. It does also exist for gravity, if you perturbatively quantize it, and this has been calculated in the context of many cosmological models. Since compactified dimensions are also boundary conditions, the Casmir effect can be relevant for all extra-dimensional scenarios, where it tends to destabilize configurations.

In the new paper now, the author, James Quach, calculates the gravitational Casimir effect with a boundary condition where the fields do not abruptly jump, but are smooth, and he also takes into account a frequency-dependence in the reaction of the boundary to the vacuum fluctuations. The paper is very clearly written, and while I haven’t checked the calculation in detail it looks good to me. I also think it is a genuinely new result.

To estimate the force of the resulting Casmir effect one then needs to know how the boundary reacts to the quantum fluctuations in the vacuum. The author for this looks at two different case for which he uses other people’s previous findings. First, he uses an estimate for how normal materials scatter gravitational waves. Then he uses an estimate that goes back to the mentioned 60 pages paper how superconducting films supposedly scatter gravitational waves, due to what they dubbed the “Heisenberg-Coulomb Effect” (more about that in a moment). The relevant point to notice here is that in both cases the reaction of the material is that to a classical gravitational wave, whereas in the new paper the author looks at a quantum fluctuation.

Quach estimates that for normal materials the gravitational Casimir effect is ridiculously tiny and unobservable. Then he uses the claim in the Minter et al paper that superconducting materials have a hugely enhanced reaction to gravitational waves. He estimates the Casimir effect in this case and finds that it can be measureable.

The paper by Quach is very careful and doesn’t overstate this result. He very clearly spells out that this doesn’t so much test quantum gravity, but that it tests the Minter et al claim, the accuracy of which has previously been questioned. Quach writes explicitly:

“The origins of the arguments employed by Minter et al. are heuristical in nature, some of which we believe require a much more formal approach to be convincing. This is echoed in a review article […] Nevertheless, the work by Minter et al. do yield results which can be used to falsify their theory. The [Heisenberg-Coulomb] effect should enhance the Casimir pressure between superconducting plates. Here we quantify the size of this effect.”

Take away #1: The proposed experiment does not a priori test quantum gravity, it tests the controversial Heisenberg-Coulomb effect.

So what’s the Heisenberg-Coulomb effect? In their paper, Minter et al explain that a in a superconducting material, Cooper pairs aren’t localizable and thus don’t move like point particles. This means in particular they don’t move on geodesics. That by itself wouldn’t be so interesting, but their argument is that this is the case only for the negatively charged Cooper pairs, while the positively charged ions of the atomic lattice move pretty much on geodesics. So if a gravitational wave comes in, their argument, the positive and negative charges react differently. This causes a polarization, which leads to a restoring force.

You probably don’t feel like reading the 60 pages Minter thing, but have at least a look at the abstract. It explicitly uses the semi-classical approximation. This means the gravitational field is unquantized. This is essential, because they talk about stuff moving in a background spacetime. Quach in his paper uses the frequency-dependence from the Minter paper not for the semi-classical approximation, but for the response of each mode in the quantum vacuum. The semi-classical approximation in Quach’s case is flat space by assumption.

Take away #2: The new paper uses a frequency response derived for a classical gravitational wave and uses it for the quantized modes of the vacuum.

These two things could be related in some way, but I don’t see how it’s obvious that they are identical. The problem is that to use the Minter result you’d have to argue somehow that the whole material responds to the same mode at once. This is so if you have a gravitational wave that deforms the background, but I don’t see how it’s justified to still do this for quantum fluctuations. Note, I’m not saying this is wrong. I’m just saying I don’t see why it’s right. (Asked the author about it, no reply yet. I’ll keep you posted.)

We haven’t yet come to the most controversial part of the Minter argument though. That the superconducting material reacts with polarization and a restoring force seems plausible to me. But to get the desired boundary condition, Minter et al argue that the superconducting material reflects the incident gravitational wave. The argument seems to be basically that since the gravitational wave can’t pull apart the negative from the positive charges, it can’t trespass the medium at all. And since the reaction of the medium is electromagnetic in origin, it is hugely enhanced compared to the reaction of normal media.

I can’t follow this argument because I don’t see where the backreaction from the material on the gravitational wave is supposed to come from. The only way the superconducting material can affect the background is through the gravitational coupling, ie through its mass movement. And this coupling is tiny. What I think would happen is simply that the superconducting film becomes polarized and then when the force becomes too strong to allow further separation through the gravitational wave, it essentially moves as one, so no further polarization. Minter et al do in their paper not calculate the backreaction of the material to the background. This isn’t so surprising because backreaction in gravity is one of the thorniest math problems you can encounter in physics. As an aside, notice that the paper is 6 years old but unpublished. And so

Take away #3: It’s questionable that the effect which the newly proposed experiments looks for exists at all.

My summary then is the following: The new paper is interesting and it’s a novel calculation. I think it totally deserves publication in PRL and I have little doubt that the result (Eqs 15-18) is correct. I am not sure that using the frequency response to classical waves is good also for quantum fluctuations. And even if you buy this, the experiment doesn’t test for quantization of the gravitational field directly, but rather it tests for a very controversial behavior of superconducting materials. This controversial behavior has been argued to exist for classical gravitational waves though, not for quantized ones. Besides this, it’s a heuristic argument in which the most essential feature – the supposed reflection of gravitational waves – has not been calculated.

For these reasons, I very strongly doubt that the proposed experiment that looks for a gravitational contribution to the Casimir effect would find anything.