The relevant paper is on the arxiv

**Gravitational Casimir effect**

James Q. Quach

Phys. Rev. Lett. 114, 081104 (2015)

arXiv:1502.07429 [gr-qc]

*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.

## 23 comments:

"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. "I don't have time to check now, but isn't it the case that if you take a sphere with a Schwarzschild radius, the resulting excess outside the horizon is equivalent to the corresponding Hawking radiation?

"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."Obviously, backreaction comes from your blog!

Phillip,

Yes, you can try to interpret black hole radiation by means of Casimir pressure. I was about to mention it, but then I thought it will just distract the reader. I never really liked this analogy anyway. The Hawking effect in its original form relies on the dynamics of the background.

Best,

B.

1) Podkletnov

http://www.freerepublic.com/focus/chat/3169171/posts

http://www.abovetopsecret.com/forum/thread1006701/pg1

2) Gravitation(al radiation) is diddled, inertial properties remain unaltered.

3) Create mass that is only Casimir etalons: A flat annulus rotates above a ring of vacuum deposition sectors alternately placing films of aluminum and 60:40 MgF_2:LiF. 70 nm Al has 93% reflectance 100 - 120 nm, linear expansion 23.1 ppm/°K. MgF_2 has 80% transmittance at 115 nm, refractive index 1.63 at 121 nm, LE 13.7 ppm/°K. LiF has 80% T at 110 nm, RI = 1.777, LE 37.0 ppm/°K. (0.6)(13.7) + (0.4)(37.0) = 23 ppm/°K, matching aluminum. The annulus spins, accumulating hundreds of layers of aluminum reflector and 37 nm fluoride alloy, RI = 1.628, Casimir etalon 120 nm cancellation. Excise a section for a sandwich stack of etalons,

casimatter. Is it observably anomalous? Average d = 2.79 gm/cm^3, 37 wt-% vacuum zero point fluctuation-depleted fluoride alloy.http://www.npl.washington.edu/eotwash/epwhat

Eötvös balance, Equivalence Principle (open leading image in new tab).

4) Repeat, depositing suitably scaled alternating layers of superconductor and insulator or normal conductor. Is it observably anomalous (e.g., cavorite; EP) to static gravitation?

http://rsta.royalsocietypublishing.org/content/372/2026/20140025.full.pdf+html

Cryogenic torsion pendulum

5) Are usable gravitational waves obtained by locally imploding a hollow sphere of depleted uranium, d = 19.05 g/cm^3, plus rebound? If not, how is the proposed effect tested? LIGO remains inert.

The gravity is already quantized in photons. When the stars radiate them, they're losing mass/gravity in pieces..

/*...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?..*/

This doesn't look like quite deep explanation, I've to admit..;-) So, which argument it actually is? Why the superconductors should bounce and reflect the gravitational waves at all....?

@Zephir

The gravity is already quantized in photons.maundering IDIOTMonopole radiation is sourced by a changing monopole moment for a charge q or for a mass m. Charge and mass are conserved. Monopole electromagnetic radiation and monopole gravitational radiation are forbidden

Dipole radiation is sourced by a changing dipole moment. (Punctiliously, the second time derivative of the dipole moment, acceleration) For a pair of charges

d = qr + q'r'

There's nothing special about the derivatives. For a pair of masses, the gravitational dipole moment and its time derivative are

d = mr + m'r'

mv + m'v' = p + p'

By conservation of momentum the second time derivative of the gravitational dipole moment is zero. Go to a center of momentum frame and set the first derivative to zero as well. There is no gravitational "electric dipole" radiation. Consider the analog of "magnetic dipole" radiation. The gravitational equivalent of the magnetic dipole moment for a pair of charges is

M = mv x r + m'v' x r'

("x" is the cross product, "mv" is the "mass current")

But M is the total angular momentum, which is also conserved. There is no gravitational "magnetic dipole" radiation.

The next moment up is quadrupole, with no relevant conservation laws, so gravitational quadrupole radiation is permitted. Thus gravity must be a tensorial (spin-2) interaction and uniformly attractive. Electromagnetism is mediated by spin-1 photons and can be repulsive.

Class. Quantum Grav.174125 (2000)Exactly obtain Maxwell's equations from the Einstein field equation, BUT a long list of caveats inevitably break the analogy with electromagnetism.

From Minter et al.:

``The non-localizability of Cooper pairs, which is ultimately due to the Uncertainty Principle (UP), causes them to undergo non-picturable, non-geodesic motion in the presence of a GR wave. This non-geodesic motion, which is accelerated motion through space, leads to the existence of mass

and charge supercurrents inside a superconductor.''

Hmm .. this sort of statement triggers my crackpot alert.

I'm going to ask a tangential question about Casimir forces. The Casimir QED pressure between two conducting plates doesn't depend on the fine structure constant (i.e. on the strength of the interaction.)

So do all gauge fields induce Casimir pressures of the same strength? If not, how can you tell?

(I think this must be related to the perfectly conducting boundaries--that there's no accessible material that's a perfect "color conductor" for, say, QCD. But I'm not sure of the exact relationship, and you seem like you might be :) )

May this seem as utterly naïve, as I do not have the background, but like many ‘outsiders’ I am also interested in ‘knowing’ a bit more clearly about the Casimir effect (not just for ZPE and the associated ‘controversy’ etc)-Can you kindly explain the following quoted excerpts, if it is not too much to ask, -

You mentioned,- “…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…”. Again, what does ‘such a boundary condition’ and ‘frequency dependence in the reaction of the boundary’ mean physically?

Finally, I was again stuck over these words, -“…In their paper, Minter et al explain…Cooper pairs aren’t localizable and thus don’t move like point particles. This means in particular they don’t move on geodesics….while the positively charged ions of the atomic lattice move pretty much on geodesics…”- why the different behavior for cooper pairs and ions? Is it because cooper pairs are not localizable, (say crudely like the delocalized pi-electrons (Aromatic ring current) of the benzene ring electrons) while positively charged ions in lattice are sort of fixed?

And off-topic, can you someday, if at all, - spare the time/ energy or interest – sort of explain the dynamical Casimir effect?

Thank you.

Jatajata

- It means it's slice of medium (boundary) that has a finite width (is real) and its response depends on the wavelength of the incident gravitational wave (or its frequency respectively)

- Yes, as I wrote it's because the Cooper pairs aren't localizable. You quoted the sentence, so I don't understand why you ask exactly what I wrote. That the ions are 'fixed' isn't so relevant, relevant is that they are localizable (at lest better localizable than the Cooper pairs).

I neither have the time nor the interest to explain the dynamical Casimir effect, sorry. Best,

B.

/* There is no gravitational "electric dipole" radiation. */

The existence of 2-spin component of EM wave doesn't follow from Heaviside-Maxwell theory, which cannot predict the existence of photons without consideration of extradimensional or quantum components ("aether vorticity" for example http://arxiv.org/abs/1502.05926).

But because we can observe the existence of photons, we can also consider the existence of these components and to derive the existence of 2-spin component of EM wave, for example here.

http://rspa.royalsocietypublishing.org/content/462/2071/1987.full

Please, refrain of notes about idiots for future - they're irrelevant for subject and we aren't at Motl's or someone else's uncivilized blog. That is to say, we have ladies here....;)

Regarding the gravitational waves, these waves are fully atemporal, so that they cannot have the direction and reference frame defined in 4D space-time. They must be stationary of fully chaotic and they cannot exhibit a shielding Cassimir force-like effects.

But the gravitational waves and photons aren't the only components of vacuum fluctuations. The dark matter particles (anapoles and high spin photons or "scalar waves") would have chaotic effect with weak repulsive component competing the gravity. IMO these fluctuations ruined the Gravity Probe-B gyroscopes, which were also covered with superconductive layers. But these fluctuations also aren't pure 2-spin quadruple waves in the sense of general relativity, which are attributed to gravitational waves today.

Zephir,

Well, Uncle is correct, there's no gravitational dipole radiation. I think you didn't understand the relevance of his comment to your, uhm, theory that photons are gravitons. Be that as it may, this isn't the place to discuss your ideas, further comments on this will be deleted. Thanks,

B.

Dr. Hossenfelder ,

Thank you for the reply.

I understand a bit better now, esp. it's the concept 'localizable' that matters more than being 'fixed'. It still raises a question, and a few more here and there, ...but overall I liked this piece of writing, as I followed it through.

Maybe if I can earn the chance to get back to college one day, I can appreciate it all better. :)

Thank you all the same, and a lot.

-JJ

I see that James Quach, in his paper, references Raymond Chiao's work at the University of California, Merced. Ray Chiao has been very active in this field of trying to find some type of coupling between Bose-Einstein condensates and gravity waves.

One of my favorite sites for explaining these complex phenomena to laymen, over the last 20 years, is John Cramer's "The Alternate View" Column. Hoping I'm not violating posting rules, here is an article he wrote on Chiao's work in this area in 2009.

http://www.npl.washington.edu/av/altvw149.html

Dear Alice,

Are we in any position at all?

In any position for what?

For background independence.

Sincerely,

Babble Blogger Bob

I recently discovered your blog. It's great to see a physicist countering some of the exaggerated claims we see in science news coverage: "Black holes don't exist", "We can detect gravity quantization", etc. Thank you for your very lucid take on what the science actually says here.

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

Amen!

Sabine Hossenfelder: “… the gravitational Casimir effect to demonstrate the existence of gravitons, and thereby the quantization of the gravitational field.”

The GR (general relativity) is a pure theoretical physics-framework; that is, its validity depends not on any empirical verification. Those verified facts (gravitation lensing, indirect gravitation wave, etc.) does not improve the greatness of GR being a great theoretical framework. In fact, the keeping for the empirical evidences of GR (such as the LIGO, etc.) is the insult for GR.

If GR is wrong, it is wrong on its theoretical foundation. As the gravitation wave is so weak to be detected even with LIGO, it will not play a major role in the STRUCTURE of this universe. Then, why wasting the time on finding it? With such a weak gravitation wave, the GR gravitation FIELD must also be the wrong idea for describing the structure of this universe. Not to say that it cannot be assimilated with QM, it will still be useless even if it could be done.

Some great discussions on this are available at the following links. (https://scientiasalon.wordpress.com/2015/03/10/a-bayesian-approach-to-informal-argument-fallacies/comment-page-1/#comment-12735 and https://scientiasalon.wordpress.com/2015/03/10/a-bayesian-approach-to-informal-argument-fallacies/comment-page-2/#comment-12748 ).

The Minter et al paper was published, Physica E, Volume 42, Issue 3, January 2010, Pages 234–255

This statement is not correct: "The Casimir QED pressure between two conducting plates doesn't depend on the fine structure constant (i.e. on the strength of the interaction.)"

The alpha independent calculation corresponds to alpha going to infinity

http://arxiv.org/abs/hep-th/0503158

http://www.nature.com/nature/journal/v479/n7373/pdf/nature10561.pdf

Suprisingly enough, in this experiment superconductors are used...

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