Andrei Lebed, equivalence principle

[bcrowell]

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.

Comments?

 

[greswd]

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

 

[DrClaude]

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

 

[bcrowell]

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...??

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

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.

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

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.

 

[bcrowell]

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.

 

[bcrowell]

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

Even if the atoms move near the speed of light, the time for them to physically move from phi = 0 to some finite value is much greater than 1 / the frequency difference in Hydrogen energy levels (at least, any two that are realistically observable). Therefore, the adiabatic approximation should be valid, and the atom will remain in the ground state.

 

[Dr. Courtney]

This seems interesting, but I'm inclined to be suspicious because he publishes in low-quality journals, and his references are to textbooks, his own previous papers, and other people's old papers (a pattern that we often see in junk science, kook papers, and low-quality papers).

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.

 

[madness]

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.

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.

 

[bcrowell]

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.

 

[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.

 

[Dr. Courtney]

Ben,you mentioned some warning signs in your first post. To follow up I checked his Inspire author profile, but it seems incomplete:...

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.

 

[Dr. Courtney]

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.

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.

 

[bcrowell]

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.

 

[greswd]

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

 

[Dr. Courtney]

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

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.

 

[MathematicalPhysicist]

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.

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).

 

[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.

 

[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?

 

[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.

 

[bcrowell]

I don't see anything in the article which is peculiar to quantum 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?

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

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

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.

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.

 

[DrDu]

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

Yes, I corrected this.

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.

True, but this is an effect of the same order as the one he is studying. I don't think you can neglect one and keep the ohter.

 

[bcrowell]

True, but this is an effect of the same order as the one he is studying. I don't think you can neglect one and keep the ohter.

When you say "this is an effect," you imply that you've established the existence of such an effect. You haven't.

 

[DrDu]

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

I am not sure about this. The transition probability he calculates is in sudden approximation, i.e. assuming the atom is brought very quickly to its new position. This is quite the contrary of the adiabatic approximation your colleague mentioned and which I also think to be the correct way to argue.
The transition probabilities Lebed calculates are not peculiar to the transition from state n to the ground state. You may also start with an excited state m and observe transitions from n to m. If m is very large, you are in the classical limit and you are only describing the change of a classical orbit when you suddenly scale coordinates and time as prescribed.

 

[bcrowell]

I am not sure about this. The transition probability he calculates is in sudden approximation, i.e. assuming the atom is brought very quickly to its new position. This is quite the contrary of the adiabatic approximation your colleague mentioned and which I also think to be the correct way to argue.

I agree.

The transition probabilities Lebed calculates are not peculiar to the transition from state n to the ground state. You may also start with an excited state m and observe transitions from n to m. If m is very large, you are in the classical limit and you are only describing the change of a classical orbit when you suddenly scale coordinates and time as prescribed.

I see what you mean. Yes, there are really two big problems with the scaling behavior of his predicted effect:

(1) It doesn't obey the correspondence principle in the sense that as the system gets more classical, his predicted effect gets bigger rather than smaller. The quantity $V_{21}$ is a measure of internal energy, and it grows as you add more particles to the system. Furthermore, the difference $E_2-E_1$ between the energies of the two states can be smaller when the system is bigger (more particles). Since the factor $y$ (in the notation of my #9) goes like like the square of the ratio of these two factors, we can make his predicted effect as big as we wish by going to a system with more particles. In this sense, yes, his result smells classical despite his claim that it's quantum-mechanical.

(2) His effect doesn't scale down with the linear dimensions of the system. This is not physically reasonable for a gravitational effect, which should depend on curvature (the second derivative of the potential, not the potential itself).

In #9 I made up a system that was designed to exploit this scaling behavior in order to produce a reductio ad absurdum, but there was a flaw in my setup because I think we need the two states to have the same angular momentum and parity. Here's a different system that I think works. Buckminsterfullerene (C60) has an excited state at 0.061 eV that is a "breathing" or dilational mode, i.e., a vibration in which the whole molecule expands and contracts: http://www.public.asu.edu/~cosmen/C60_vibrations/mode_assignments.htm . The mode is labeled Ag(1). This mode should have angular momentum 0 and positive parity, which I assume is the same as the ground state, and so I think the matrix element $V_{21}$ between these two states should not vanish because of any selection rules. In fact, the coupling should be very strong, since the motion is physically very similar to the metrical dilation that Lebed invokes in order to predict his effect. So I would think that the matrix element would be on the order of the internal energy of the system. In hydrogen, this energy scale is the 14 eV of the Rydberg constant. Scaling Z up by 6 increases the energy per electron by $Z^2$, and the number of electrons is $Z$, so we pick up a factor of $Z^3$ when going from hydrogen to a heavier element like carbon. We also have 60 atoms, so the total internal energy is on the order of $60Z^3(14\ \text{eV})$, which is about $10^5$ eV. The resulting value for the $y$ factor is about $10^{13}$. The result is that for the variation in potential of the Earth as it orbits the sun, his transition probability $yx^2$ is about $10^{-6}$, which is many orders of magnitude larger than the value in his proposed experiment. This is a huge effect, which I think clearly shows that his prediction is wrong.

 

[bcrowell]

This is a longer article by Lebed: http://www.hindawi.com/journals/ahep/2014/678087/ref/ (open access, does not appear to be on arxiv).

He specifically states here that the gravitational field in the proposed experiment is to be "adiabatically switched on."

He also has this: "Note that the perturbation (29) is characterized by the following selection rule. Electron from 1S ground state of a hydrogen atom can be excited only into nS excited state." This seems consistent with my understanding that the claimed excitations are supposed to conserve spin and parity.

He says, "we propose experimental detection of electromagnetic radiation, emitted by macroscopic ensemble of hydrogen atoms (in a real experiment—molecules)." It's not clear to me why he thinks the change from atomic hydrogen to H2 is somehow no big deal.

 

[bcrowell]

I discussed this by email with Steve Carlip, who gave me permission to post the following here:

Start with the classical analog, which I discuss in section 3 of gr-qc/9909014. If you calculate the classical gravitational coupling to matter in the weak field approximation, it looks at first as if the equivalence principle is violated. It's saved by the virial theorem, which guarantees that the apparent extra "bad" term vanishes.

In classical physics, the virial theorem is a statement about the division of energy in the time-averaged behavior of a system that is at equilibrium (or at least near enough that time averaging makes sense). In a quantum system, the virial theorem still holds, but it's now a statement about expectation values in stationary states. One of the things Lebed shows -- the most interesting part, I think -- is that for a stationary state, the equivalence principle does, in fact, continue to hold, for exactly the same reason that it does in the classical case.

For a time-dependent system, things get much trickier. A time-dependent quantum state is necessarily a superposition of energy eigenstates. The "equivalence-principle-violating" term Lebed finds comes from an interference term, and is zero for any pure stationary state. The term also oscillates rapidly in time, and as in the classical case, the "bad" term goes away if one performs a time average.

But this kind of superposition of energy eigenstates also makes the definition of all kinds of "mass" -- inertial, passive gravitational, active gravitational -- problematic. For instance, Lebed considers a quantum system coupled to a classical gravitational field, and defines its active gravitational mass as the expectation value of the operator that couples to the Newtonian potential. This is the Newtonian version of a model called "semiclassical gravity." It's not unreasonable as a first step -- it's more or less equivalent to the Hartree approximation in atomic physics -- but it's known to have problems; see, for example, a recent paper by my student Jeremy Adelman, arXiv:1510.07195. If we knew how to quantize gravity, the relevant coupling would presumably be between an active gravitational mass operator and a gravitational field operator, and it's not clear whether the expectation value would be the thing that mattered.

A similar problem already exists for inertial mass. Imagine a system that's in a superposition of two mass eigenstates. Is its inertial mass just the expectation value? This ought to be answerable: act on the system with an external force, and see whether the resulting acceleration can be described as the force divided by the expectation value of the mass. This ratio will be *something*, but it's not obvious to me what. (Acceleration of some center of mass, maybe?)

There's another problem as well. As I also discuss in gr-qc/9909014, the naive definitions of active and passive gravitational mass in classical GR are gauge-dependent. To be confident of an answer, one would have to be careful to define gauge-independent versions, which I don't know how to do. For the classical, time-independent case, it's possible to trace just how the gauge dependence drops out of the final answer. For the quantum case, as far as I know, no one has looked.

Having said this, I think Lebed's actual calculation is correct (though I've certainly not checked all the details). The way I would phrase the result is to say that he's found an interesting gravitational interaction with non-stationary states, in which the gravitational field can excite or de-excite an atom in an appropriate state. This wouldn't be surprising for a nongravitational interaction: for a superposition of two mass eigenstates, for instance, one would expect an external force to accelerate the two components differently, which would excite the system. For gravity, though, one might not expect this, based on the principle of equivalence, and the fact that it *does* seem to happen is interesting. It may be significant that the effect appears as an interference term, that is, as a relative phase shift. Others have also suggested that this is the place to look for the interplay between quantum mechanics and the equivalence principle -- see, for instance, Ahluwalia, gr-qc/9711075 -- and there is probably something here worth further investigation.

Steve Carlip

 

[bcrowell]

After giving this more thought, I think I can show that Lebed's proposed effect is incompatible with previous observations. With just a little generalization, his calculations predict a similar effect due to cosmological expansion. Furthermore, they predict that the proton itself should undergo excitations and emit radiation in the form of pions, which would then decay into high-energy gammas. The calculated rate of excitation is such that a kilogram of hydrogen would emit about 10^9 gamma rays per second, which is obviously incompatible with observation. I've written up a comment on Lebed's paper, and have sent it to Steve Carlip to see if he is willing to take a look and tell me if he sees any major mistakes. I'm not ready to post it publicly yet, but if anyone here with relevant expertise is interested and wants to look it over and give comments, that would be great -- just send me an email: http://www.lightandmatter.com/area4author.html .

 

[bcrowell]

Here's a preprint of the paper I ended up writing on this: http://arxiv.org/abs/1601.01306

 

[greswd]

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.

Sorry, I was referring to this article: https://uanews.arizona.edu/story/testing-einstein-s-e-mc2-in-outer-space

I think the description given in the article is not the same as the one Lebed presents in his paper.

 

[Dr. Courtney]

Sorry, I was referring to this article: https://uanews.arizona.edu/story/testing-einstein-s-e-mc2-in-outer-space

I think the description given in the article is not the same as the one Lebed presents in his paper.

Thanks for clarifying.

 

[DrDu]

What I didn't see in your comment, but what I thought to be one of the most important points having been brought up in the discussion, is the fact that while the ground state of hydrogen + gravitational field has a formal expansion in terms of the field free eigenstates, this does not mean that hydrogen gets into instable excited states as all realistic changes of the field will be so slow that one ground state will be adiabatically transported into the other.

 

[bcrowell]

What I didn't see in your comment, but what I thought to be one of the most important points having been brought up in the discussion, is the fact that while the ground state of hydrogen + gravitational field has a formal expansion in terms of the field free eigenstates, this does not mean that hydrogen gets into instable excited states as all realistic changes of the field will be so slow that one ground state will be adiabatically transported into the other.

Lebed explicitly assumes that it's adiabatic. Yes, I think it's pretty clear that there's something wrong with his interpretation, since his predictions are contrary to the results of experiments.

I haven't been able to convince myself that there is anything trivially wrong in his arguments. His calculations show the atom changing its state adiabatically, but the locally observable properties of spacetime haven't changed, so it's no longer in the ground state. This is different from a normal case where, e.g., you adiabatically apply an electric field, so that the observable properties of the space become different.

My paper focuses on the comparison with experiment, but what I would criticize about Lebed's theoretical work in general is that his papers are silent on a lot of issues that obviously beg to be addressed. His calculations are coordinate-dependent, but the reader is left to guess what coordinates are required. He doesn't address what happens to a system when it undergoes a collision, and this makes it hard to believe that his experiment, as originally proposed, would have worked, even if his calculations and interpretation had been correct. He never seems to have considered the effect from solar gravity, which is trivial to calculate and nearly the same size as the effect he proposes for a space-based mission. He describes the calculation of probabilities of excitation, but not radiation rates; the only reasonable thing to do in order to calculate a rate seems to be to take the time derivative of the excitation probability, and presumably there is no radiation when this derivative has the wrong sign. When you calculate this rate, it depends on the dot product $\textbf{g}\cdot\textbf{v}$, which clearly violates the equivalence principle (OK, he claims that anyway) but also seems likely to violate Lorentz invariance.

Some of the things that seem to go wrong in his work, such as likely difficulties with conservation of energy-momentum, are not really difficulties that are specific to his idea. They are present more generally in semiclassical gravity. There are a lot of problems with semiclassical gravity:

http://arxiv.org/abs/1304.0471
http://motls.blogspot.com/2012/01/why-semiclassical-gravity-isnt-self.html
http://backreaction.blogspot.com/2012/01/real-thought-experiment-that-shows.html
http://relativity.livingreviews.org/open?pubNo=lrr-2008-3&page=articlesu4.html

See Lubos Motl's blog post for a nice discussion of energy nonconservation.

 

[DrDu]

Ok, but what I still don't understand: According to Lebed, the eigenstates of the hamiltonian in the field are superpositions of mass eigenstates. But to observe transitions one would have to measure mass so as to prepare a superposition of mass eigenstates and watch how they decay back into energy eigenstates, wouldn't one?

 

[bcrowell]

Ok, but what I still don't understand: According to Lebed, the eigenstates of the hamiltonian in the field are superpositions of mass eigenstates. But to observe transitions one would have to measure mass so as to prepare a superposition of mass eigenstates and watch how they decay back into energy eigenstates, wouldn't one?

Sorry, I don't understand what you mean by the second sentence. Could you explain in more detail?

 

[bcrowell]

I exchanged emails with Lebed. His initial reaction to my preprint was that he agrees that there should be nuclear excitations, but he says there shouldn't be any effect for a free-falling object. He says it matters that the system be transported at constant velocity.