# A Andrei Lebed, equivalence principle

1. Dec 5, 2015

### bcrowell

Staff Emeritus
Andrei G. Lebed, "Breakdown of the equivalence between gravitational mass and energy for a composite quantum body," http://arxiv.org/abs/1404.4044

[corrected a mistake in the following paragraph]

He seems to argue that hydrogen atoms moving from one region of space to another, with a different gravitational potential, will make transitions from the ground state to an excited state. This violates the equivalence principle. He proposes a space-based experiment to detect the effect.

I suppose this shouldn't be particularly surprising, since semiclassical gravity (a) doesn't seem to work reliably, and (b) has a tendency to produce results that violate the equivalence principle. I'm basing this on my non-specialist impression of the kind of stuff that people like Barcelo do, e.g., http://arxiv.org/abs/0902.0346 . They have to do all kinds of renormalizations, and when they're done they predict dramatic things happening at the event horizon of a black hole, which violates the e.p. My take on it has been that semiclassical gravity is simply bogus and shouldn't be trusted.

Last edited: Jan 8, 2016
2. Dec 6, 2015

### greswd

What about conducting an experiment using a tank of hydrogen in free fall on Earth?

3. Dec 6, 2015

### Staff: Mentor

If this was correct, wouldn't we have already noticed something in interstellar clouds?

4. Dec 6, 2015

### bcrowell

Staff Emeritus
If I'm understanding correctly, he's saying that if you put a hydrogen atom through a change in gravitational potential of $\Delta\phi$, then this has a probability $\sim (\Delta\phi/c)^2$ of kicking it into the n=2 state. (This probability is multiplied by an energy ratio that I think is on the order of 1 for atomic hydrogen.)

This would be a pretty serious violation of the equivalence principle. He talks about a $\Delta\phi$ corresponding to the difference in potential between the earth's surface and (I think) a large distance from the earth. But if we believe in the equivalence principle, then there should be no way to tell whether there is some other, stronger, uniform field superimposed on top of the earth's. In general it's just physically bizarre that he claims that the gravitational potential produces physically observable effects. The e.p. says that only the second derivative of the potential should be observable.

It would be interesting to get someone with good QM chops to look at this and see if it's just obviously wrong. That may be the case, and if so, then that would explain why he publishes this stuff in such obscure journals. Although his calculations are actually pretty simple, I think it takes someone with a very firm grasp on the fundamentals to sniff out a mistake in this kind of novel context.

It's not clear to me whether he's also in effect predicting nonconservation of energy here...??

Although I believe some of those clouds are very cold (so that the expected equilibrium thermal population of the n=2 states may be negligible), they're still exposed to an environment with a lot of hard radiation. Therefore I don't think they're really in a state of thermal equilibrium, are they? I imagine it wouldn't take a lot of ambient UV to produce a non-equilibrium population of 10^-16 in an n=2 state. A secondary issue is that these clouds would contain molecular hydrogen, not atomic hydrogen, but I assume that if his theory were right, it would also predict these anomalous transitions in molecular hydrogen.

If I'm understanding him correctly, then there is no reason that it has to be in free fall. It could be in a moving elevator or contained in a spacecraft whose rockets were thrusting. I think the reason he talks about a spacecraft is that he wants to make a very large change in gravitational potential. (The effect is proportional to the square of that change.) If I'm understanding his prediction correctly, then it even implies that there should be an annual effect in a tabletop experiment, due to the earth's motion in the sun's potential as it goes through its slightly elliptical orbit. Or maybe there would be an effect due to the solar system's motion through the potential due to the Milky Way.

I suppose a calculation is required in order to figure out the conditions of temperature and pressure that would be needed in order to keep a tank of atomic hydrogen gas in a condition where $\lesssim 10^{-16}$ of the atoms are in the n=2 state based on thermal equilibrium, and furthermore where interactions between atoms don't distort the wavefunctions by something on the order of this amount. In fact, this seems like the kind of estimate that Lebed should have done as part of these papers.

Looking back at his claimed result for the probability of a gravitationally induced change of state, he has an additional factor involving energies that I think is of order unity for hydrogen. Let's call this factor F. It's $F=(V/\Delta E)^2$, where $V$ is something like the internal energy of the atom (average KE plus electrical PE), and $\Delta E$ is, in the case he discusses, the energy difference between the n=1 and n=2 states. This makes me wonder why he doesn't consider systems in which this energy ratio is large.

In H2, the rotational transitions are in the infrared, with energies on the order of 0.1 eV, so that I think his energy ratio would be on the order of 10^4, which is a lot better than hydrogen. Of course, it might be hard to prepare a sample of H2 cold enough to keep the first excited rotational state unpopulated -- you'd probably tend to make liquid H2 unless the pressure was very low.

Or what about nuclei? Odd-odd nuclei often have isomeric states with excitation energies on the order of 1 keV (possibly much less in some cases?). The internal energy of a heavy nucleus is $V\sim10^6$ keV or something, so it seems like F would be gigantic. If Lebed's theory is right, why don't we observe very strong anomalous emission of x-rays from odd-odd nuclei? It seems like with an F this large, it should be very easy to detect this in tabletop experiments, based on annual variations in the gravitational potential due to the sun.

Last edited: Dec 6, 2015
5. Dec 7, 2015

### bcrowell

Staff Emeritus
I discussed this by email with a colleague who is much more sophisticated than I am about quantum mechanics. He had some interesting thoughts, which I may quote here if he gives permission.

One of the things we talked about is whether the equivalence principle applies, since the hydrogen atom has a finite spatial extent. My take on it (which he may not agree with) is that we have ways of quantifying how local is local for purposes of the e.p. If an experiment has size $h$, then we expect various effects to scale as $h^n$, where $n$ is greater than zero. I don't see anything in Lebed's analysis that makes $n$ not equal to zero. Its only dependence on the quantum-mechanical object being studied occurs through the energy ratio that I notated as $F$ in #4, and this energy ratio can be of order 1 for systems of various sizes. For example, his result would seem to apply just as much to a nucleus as to an atom, even though the nucleus is smaller by a factor of $10^5$. The reason for this scale-independence is not hard to see. It clearly comes from the fact that the effect is claimed to depend on the value of $\phi$. Any real physics should depend only on $\phi$'s second or higher derivatives.

6. Dec 7, 2015

### bcrowell

Staff Emeritus
My colleague gave me permission to post the following, which I thought was helpful:

Last edited by a moderator: Dec 26, 2015
7. Dec 8, 2015

### Dr. Courtney

I tend to be suspicious when critics base their arguments on things like this instead of basing conclusions on direct repeatable experiments (preferred) or simple theoretical arguments that suggest effects (if present) would have shown up in experiments that are already completed. My suspicion grows when it does not take much digging to reveal that the author has published a number of papers in Phys Rev B and Phys Rev Lett over the past few years.

In later posts the discussion moves more productively toward weighing the paper on its merits, but I hate to see physicists demonstrating strong biases against new ideas because of the publication venue, writing style, and references rather than a careful evaluation of the ideas on their merits. If there are serious and obvious flaws, it seems like it would be a service to the entire community for a competent authority to publish a reply to the paper which would both give the author an opporunity for rebuttal as well as bring an awareness of the serious and obvious flaws (and debate) to the broader community.

But let's take care to debate scientific issues on the merits and not on the publication venue, writing style, or references.

Last edited: Dec 8, 2015
8. Dec 8, 2015

I think the point was that as a non-expert, who would struggle to carefully evaluate the scientific merit due to a lack of background knowledge of the topic, that these issues may raise flags. I do agree with your sentiment however - in the field of neuroscience at least, I've heard several leading scientists say they wouldn't trust the results of a paper if they didn't personally know the senior author.

9. Dec 8, 2015

### bcrowell

Staff Emeritus
Following through in more detail on the ideas in #4, consider the following experiment. We take a sample of 134Cs nuclei, put them in a lead box, and put an x-ray detector in the box. 134 Cs has a first excited state that decays by emission of an 11.2 keV x-ray. The fround state has a lifetime of 2.1 years, and the excited state has a lifetime of 47 ns. The box is stored in a laboratory on the surface of the earth, and we measure the count rate of this x-ray for one year. The null hypothesis is that the count rate is exactly zero.

Now I may be totally misunderstanding Lebed's claims, but my interpretation is that in this situation, he claims that a microscopic system such as a nucleus will, with some probability, go into an excited state and then emit detectable radiation. The probability is given by

$P=yx^2=\left(\frac{V_{2,1}}{E_2-E_1}\right)^2\left(\frac{\Delta\phi}{c^2}\right)^2,$

where $y$ is a shorthand for the unitless square of the energy ratio, and $x$ means the change in gravitational potential in relativistic units. As the earth goes from perihelion to aphelion, we get $x=3.3\times10^{-10}$ (which is about half the value of $x$ that Lebed considers in his proposed near-earth space-based experiment). For 134Cs, we have $E_2-E_1=11.2$ keV for the first excited (5+) state relative to the 4+ ground state. His matrix element $V_{2,1}$ is basically a measure of the internal energy of the system. Using a binding energy per nucleon of 8 MeV, we get an estimate of $V_{2,1}=(134)(8\ \text{MeV})$. Now in reality this matrix element, which is off-diagonal, is going to be less than that value, and if we really wanted to estimate it, we'd have to do a fairly complicated calculation using the nuclear shell model. But these two states in 134Cs are believed to have similar structures (same valence proton and neutron states, just coupled to a different angular momentum), so I'm going to assume that $V_{2,1}$ is still on this order of magnitude, not orders of magnitudes less. We then have $y\sim10^{10}$. The result is $P\sim10^{-9}$, which is much, much larger than the probability in Lebed's design. Although we can't buy or work with a kilomole of 134Cs, a probability of one in a billion is still easily big enough to make the radiation detectable, even with a microcurie sample. The radiation should show a semiannual variation, with the rate being at its maximum around April and October, and reaching a minimum of zero in January and July (perihelion and aphelion).

I think there are three possibilities here: (1) I've misunderstood or misapplied Lebed's prediction. (2) He would agree that this experiment would actually give these results, and it actually would. (3) He would agree with the prediction, but the experiment would give a negative result.

I can't take #2 seriously. It would be not just a violation of the equivalence principle but a gross violation. It also seems to violate conservation of energy. Furthermore, it seems likely that with a little effort one could cook up examples where the predicted effect would be even stronger, and would already have been detected in past experiments.

Last edited: Dec 8, 2015
10. Dec 8, 2015

### marcus

Ben,you mentioned some warning signs in your first post. To follow up I checked his Inspire author profile, but it seems incomplete:
http://inspirehep.net/author/profile/A.G.Lebed.1
It only shows one paper, and there are several on arXiv.
You mentioned the quality of the journals (in those cases where the papers were published)
http://www.degruyter.com/view/j/phys.2013.11.issue-8/s11534-013-0302-5/s11534-013-0302-5.xml
http://www.hindawi.com/journals/ahep/2014/678087/
I also noticed a comment on the abstract page of arXiv:1404.3765 the one Inspire lists:
"arXiv admin note: substantial text overlap with arXiv:1304.6106, arXiv:1311.2627, arXiv:1205.3134"

BTW any comment about the distant similarity between Lebed's idea and the Tolman temperature (1930), aka
the Tolman-Ehrenfest effect? I don't want to suggest any real physical connection but there seems to be a kind of vague parallelism. Deeper is warmer, in a gravitational field. Other readers may want to check it out. I don't have a good link. Here are original source references.
R. C. Tolman, “On the Weight of Heat and Thermal Equilibrium in General Relativity,”
Phys. Rev. 35 (1930) 904–924.

R. C. Tolman and P. Ehrenfest, “Temperature Equilibrium in a Static Gravitational Field,”
Phys. Rev. 36 (1930) no. 12, 1791–1798.

Last edited: Dec 8, 2015
11. Dec 8, 2015

### Dr. Courtney

More complete info is available at the author's faculty page at the University of Arizona:

http://w3.physics.arizona.edu/people/andrei-lebed

At the author's page at the Landau Institute for Theoretical Physics

http://www.itp.ac.ru/en/persons/lebed-andrei-grigorevich/

and at a list of publications compiled from Scopus

http://www.experts.scival.com/arizo...asp?n=Andrei+G+Lebed&u_id=3335&oe_id=1&o_id=4

Prof. Andrei G. Lebed might (or might not) be wrong on this one, but he is an accomplished theoretical physicist.

12. Dec 8, 2015

### Dr. Courtney

Now this is the kind of brainstorming toward an experimental design that I really appreciate. I haven't done a detailed check, but the gist seems in agreement with the paper, and the experiment is much more accessible than the hydrogen in the rocket ship. I can't help but wonder what the author would think and if there is an analogous experiment that might even be easier/cheaper.

13. Dec 10, 2015

### bcrowell

Staff Emeritus
One thing I realized probably doesn't work in #9 is that the two states of the nucleus have different angular momenta, but I think Lebed's operator $\hat{V}$ commutes with angular momentum, so the matrix element involved there vanishes.

14. Dec 11, 2015

### greswd

Is it safe to say that the original UA article is misleading and incorrect?

15. Dec 11, 2015

### Dr. Courtney

It's safe to say that isn't how science works.

If an article makes a theoretical prediction regarding the outcome of an experiment, the only way to say with certainty that the prediction is incorrect is to perform the experiment and get a different result. Alternatively, equivalent experiments that test a substantially similar prediction based on the same ideas may be performed.

But since the ultimate arbiter of competing theories in science is repeatable experiment, all one has if one does not perform an equivalent experiment is a competing theory. Using one theory to say another theory is wrong, because it makes a different prediction regarding the outcome of a proposed experiment is not definitive in science. One theory may be preferred (favored based on evidence until the arbitrating experiment is performed), but it is not safe to conclude with confidence how the arbitrating experiment will turn out.

If science gets to the point that we are "safe" concluding what the outcome of arbitrating experiments will be based only on theoretical arguments, then we are not doing science any more, we are arguing from authority.

16. Dec 11, 2015

### MathematicalPhysicist

Some will argue that we are at the age that this is the trouble with physics.(but it's also seen in maths in obscure math papers which are judged by logic alone).

17. Dec 11, 2015

### Jimster41

One interesting perspective of Stephen Wolfram's (at least part of his perspective - as I understand it) is that simulations and measuring the distance of different simulated outcomes from the observed behavior of the world are useful tools somewhere in between experiment and authority when experiments are very hard to come by. Conway's "Game Of Life" is a good example I think.

Last edited: Dec 11, 2015
18. Dec 15, 2015

### DrDu

I don't see anything in the article which is peculiar to classical mechanical systems (as opposed to quantum mechanical systems). Supose we would bring the earth and the moon very rapidly nearer to the sun. Would the orbit change?

Last edited: Dec 15, 2015
19. Dec 15, 2015

### DrDu

The real problem is maybe the following: While Lebed says that he does not regard tidal effects (which seems ok) there is some more term he neglects: In his Hamiltonian, he regards the nucleus as somehow fixed. But then the gravitational field should polarise the orbit of the electron, so that the center of charge should be somewhat shifted towards the center of earth. When the atom is brought nearer to earth, this polarisation should change, too, and I can imagine that it makes up the claimed effect.

20. Dec 15, 2015

### bcrowell

Staff Emeritus
I assume you meant "as opposed to classical systems?"

The whole thing seems explicitly quantum-mechanical to me...???

I don't think this is right. The effect he's talking about is basically a rescaling of the coordinates by a scalar. That scalar is related to the gravitational potential, which is also a scalar. To get a polarization effect, you would need a vector.

Or if by "polarise" you mean just a spherically symmetric uniform shift, I don't think that's right either, because it would work the same on positive and negative charges in the earth.