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Neutron spectroscopy constrains axions, chameleons

Tobias Jenke of Vienna and 11 co-authors from Austria, Germany, and France have performed an interesting experiment with neutrons in the gravitational field (although they have done similar experiments in the past) and their new preprint was just published in the prestigious PRL (Physical Review Letters):

Gravity Resonance Spectroscopy Constrains Dark Energy and Dark Matter Scenarios (arXiv, PRL)

Semi-popular: APS, ArsTechnica, Huff. Post
Recall that neutrons' wave functions in the Earth's gravitational field have previously been mentioned on this blog as a way to debunk the "gravity as an entropic force": LM, Archil Kobakhidze.



Click to zoom in: outline and results.

What have they done?




Well, they have prepared some very cold neutrons and sent them in between two horizontal mirrors which were separated by \(\Delta z = 30\,\mu{\rm m}\) in altitude. As you know, this is a nice and simple system in undergraduate non-relativistic quantum mechanics, a potential well.




If the walls were infinitely tall and there were no gravity, the energy eigenstates would be\[

\psi_n(z) = C_n \sin \zav{ \frac{\pi n z}{\Delta z} }, \quad n=1,2,3,\dots

\] The spectrum is discrete. If the gravitational field is added, the wave functions are no longer simple sines. Instead, they are combinations of the Airy functions \({\rm Ai}(z)\) of a sort – with the right coefficients and the right boundary conditions to make everything work. It means that the \(n\)-th wave function is more likely to be found near the bottom wall (mirror) and the wave function is more quickly oscillating over there. Note that the unrestricted linear potential has a continuous energy spectrum (just shifting the wave function in the \(z\)-direction adds some energy) while the mirrors make the spectrum discrete.

These states are discrete but they also apply some frequency – in a way that you know from Rabi spectroscopy – I think that they finally tickled the mirrors in some way although they had wanted to use some variable magnetic gradients, too. In fact, it means that the height of the walls (from the mirrors) isn't infinite but a finite and oscillating as \(\cos \omega t \) with some frequency between 50 and 800 Hertz that they may adjust. This extra periodic, time-dependent disturbance may be treated as a perturbation of the original quantum mechanical system that allows the transitions between the energy levels and they measure their probabilities. For example, the transition \(\ket{2}\leftrightarrow \ket{4}\) has been measured for the first time.

Everything agrees with quantum mechanics supplemented with Newton's potential.

It follows that they may eliminate at the 95% confidence level some (previously viable) models for dark matter and dark energy, namely "chameleon fields" (a species of quintessence) and axions with masses between \(10\,\mu{\rm eV}\) and \(1\eV\) – which would add a Yukawa potential with the Yukawa length between \(2\,{\rm cm}\) and \(0.2\,\mu{\rm m}\) as long as the coupling constant is greater than something like \(g_s g_p \geq 4\times 10^{-16}\).



Some people have proposed that these animals are in between the mirrors everywhere around us and they are responsible for the accelerated expansion of the Universe.

Note that the axions would mediate new Yukawa-like spin-dependent forces between the neutron inside the mirrors and nucleons in between the walls. The Yukawa wavelength is directly linked to the distance between the mirrors. I find it plausible that such axions may exist but the "unnaturally" tiny interaction constants that are required by the experiments make them less likely. The chameleon scenario would produce some additional potential as well and it is excluded for certain ranges of parameters, too.

This GRS (gravity resonance spectroscopy) approach is a powerful way to test models of very light and weakly interacting fields and particles and extra contributions to Newton's gravitational force. There is some overlap with the experiments that have tested old large dimensions (via modifications of Newton's inverse-square law: I think that if BICEP2 is right, old large dimensions are wrong and no corrections to Newton's law will ever be found in this way) but they are not really the same. GRS discussed here uses the quantum wave functions so it may feel certain things more finely than the very fine, but still classical mechanical experiments that have measured gravity beneath one millimeter.

GRS much like other precision experiments rely on resonances and exact frequencies – experimenters get very far with frequency measurements, indeed.

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reader kashyap vasavada said...

Well! As a practicing Hindu from India and a retired physics professor, I completely disagree with you! Yes. Hinduism did not come from a single prophet and there are a variety of interpretations of scriptures with lot of common ground. BTW east and west may have different definitions of what constitutes religion! Rather than continuing these discussions of eastern religions, which Lubos may not like anyway, I would just recommend that you may want to study these religions with an open mind.If you do not, that is also OK with me! We will be still friends on this blog!


reader JonnyDamnnox said...

So it remains true. lol


reader TheDOC said...

As a Hindu from India and an unemployed man, I stand by what I say. :D


reader Paul in Boston said...

It's not true at all. I was a grad student in experimental HEP when the J/Psi was discovered in November of 1974. "Quark theory" was already dominant at the time because of the SLAC deep-inelastic scattering experiments, but J/Psi killed off the other contending theories for good. Good physicists change their minds in the face of evidence all the time. Go to webofstories.com and look through the interviews with Murray Gell'man. He mentions physicists changing their mind on the spot when proved wrong. Murray of course was never wrong ;-)


reader Luboš Motl said...

Gentlemen, I am somewhere in between the two of you. Scientists do change their minds and they are often forced to - it's their business-as-usual - but there are also big enough questions where the natural selection and recycling of the biological material has to help to get the progress, too.


reader Luboš Motl said...

Kashyap, I used to admire India-like old religions, kind of, and maybe I still do to a lesser extent. ;-)


reader kashyap vasavada said...

Hi Lubos: This is a very interesting experiment since it
relies on just gravitational interaction of dark matter (axions?). My understanding is that most other experiments need at least some weak interaction of dark matter, annihilation or some low probability scattering. BTW I suppose it is very difficult for LHC to look at low mass stable particles. Few ev mass must be out altogether. Is that right? Is there any program to look at axions at LHC? Sorry, if you mentioned this before, I must have missed it.


reader Luboš Motl said...

Nope, Kashyap! This experiment is explicitly looking for - and, by imposing an upper bound, excluding - non-gravitational interactions caused by the new fields! Gravitational interaction of dark matter is virtually non-existent relatively to the Earth's gravity.


reader kashyap vasavada said...

Well, thanks Lubos. One of the strong points of Hinduism is tolerance or (better) acceptance of other points of views. As far as I am concerned, both science and religion have limitations.Science cannot answer certain questions, for which it is ok with me to look at ancient scriptures. If some one else is happy with scientific answers to all questions, that is also his/her prerogative and ok with me.


reader kashyap vasavada said...

Thanks. I understand.


reader Gene Day said...

What a lovely experiment. I continue to be impressed by the ingenuity of our experimentalists. Those who think that particle physics is at an impasse (because we can’t afford ever bigger machines) are so wrong!


reader Tom said...

Paul, well, yeah, good physicists change their mind in the face of evidence, that’s sort of a definition. I just like Planck’s statement (given he actually said it) as it states a general truth about a “conservatism” that people embedded in professions often display. Maybe you and, for sure, Lubos have only rubbed shoulders with “good” physicists, but down in the bowels of the military-industrial complex I can promise you there are gobs of physicists who aren’t so “good”.


reader Bill Bogus said...

This reading thingy sucks. I can achieve much better comprehension speed(that is the amount of things I actually understand per minute) by simply skipping seemingly uninteresting paragraphs or sentences when I think I know where they are going.


reader W.A. Zajc said...

Lubos, you correctly put "reluctant revolutionary" in quotes. I note that the Wikipedia page on Planck attributes it to a December 2000 PhysicsWorld.com article on Planck with that phrase as part of the title. However, that article does not seem to acknowledge the true origin of the description, which AFAIK was coined by Abraham Pais in his Reviews of Modern Physics article Einstein and the Quantum Theory ( http://inspirehep.net/record/7978?ln=en ). There Pais writes "It (Planck's quantum reasoning) cast him, conservative by inclination, into the role of a reluctant revolutionary." I assume the "conservative by inclination" is part of the appeal of Planck to our TRF host.

The Rev. Mod. Phys. article might be behind a paywall; for those readers interested enough to pay for it I would recommend instead buying a copy of Pais's wonderful Einstein scientific biography Subtle Is the Lord, where the Rev. Mod. Phys. article is incorporated as a chapter in the book.

Pais's article was published while I was working on my thesis on Bose-Einstein interferometry. It helped me enormously in understanding the connection between "wave noise" and Bose-Einstein statistics. By sheer good fortune, Pais was visiting Berkeley at that time, and was kind enough to take time out to speak to a young graduate student (as did Purcell, as did Glauber; truly impressive people as well as scientists). TRF readers may also be interested in Pais's harrowing experience in wartime Holland: http://www.humboldt.edu/rescuers/book/Strobos/BramPais/BramPaisStory1.html .


reader Tom said...

Gene, yeah, they are fakes undeserving of their title, for sure. It does, however, rankle very much that US taxpayers pay such fakes so well.


reader mesocyclone said...

As I said, look up "rational ignorance." There are a huge number of people in the world who look at other aspects of their existence and are not interested in something as far removed from their experience as the big bang. This may be hard for a physicist to understand, but it's a fact of human behavior, and it doesn't mean these people are uncultural. In fact, it means that they are normal - probably more normal than many physicists. Furthermore, it is not *dumb as a doorknob" to ignore the Big Bang theory - it is simply putting a different priority on where attention is directed.

As for the word "believe" - it's not nitpicking if it biases survey results.


reader Uncle Al said...

Theory fears nothing more than experiment. There must be a prohibition against unambiguous outputs. Proper reality is politically mutable.


reader Eclectikus said...

I'm comfortable in the range 300-400. Two problems, the render of some formulas and codes, as mentioned above, and also that it does not read comments, a very substantial part in many blogs such as this one. Anyway I think this can be useful for other sites more, say, soft... I do not see myself using this in technical sites.


reader Toon Pepermans said...

Can you explain how Ganesh or Hanuman aren't in conflict with modern science? Or is my conception of Hinduism wrong?


reader lukelea said...

I read all the time but have never paid the slightest attention to how fast I read. But since I was quite old -- a sophomore in college -- before I "discovered" books, and had a very small vocabulary at the time, I always assumed I read very slowly. In fact I am sure I did -- if I am really interested I read slowly and carefully even today. And if it is written by a really good writer -- a prose stylist like John Updike or Ellen Gillchrist, say -- I not only read slowly, but I reread sentences, the very best ones, several times to savor them. That said, I was surprised to see I could read comfortably at the 540 to 560 speed on that do-hicky. Of course like everybody else when I am just looking for information or am humming through somebody's prose whose opinion I don't really value, I skim. I would would guess I "read" well over 1000 words a minute that way, maybe even 2000.

BTW, when I was in high school our English teacher required that we read Moby Dick. I locked myself into the basement of our house and "sped read" it in about an hour. By the end the only thing I could say for sure was that it was about a whale! When the teacher asked me about the symbolism all I could do was laugh. I was the outdoor type.


reader kashyap vasavada said...

Well well! I will have to write an article on Hinduism!!! Briefly the scriptures start with formless, shapeless,ultimate super consciousness in the form of Brahman. If one cannot understand that, then it is ok to worship symbolic representations of Brahman (remember matrix representations of operators!!!) as whatever deity you choose to worship. BTW, concept of Brahman is not like a king emperor watching and ruling the world from outside. It is very much present in each particle and is synonymous with laws of nature. These viewpoints depend on how far you are advanced.It is similar to a teacher explaining electricity-magnetism to students at various levels e.g primary school, high school, undergraduate physics class, graduate physics class and post doctoral seminar. You may be talking about the same thing, but you do not use the same words! There is perhaps a reality beyond our senses. Quantum mechanics and relativity are already hinting at that. We are on a measly little planet bound to an average star in the boondocks of an average galaxy which is one of the billions of galaxies in our universe. There may be infinite number of such universes. It is utterly arrogant and perhaps stupid to believe that what we can see with our eyes and understand with our mind is all there is to it in the universe. Our mind evolved in a specific way on earth during the evolution. It has definite limits. If you study eastern religions with open mind, you will realize the immense intellectual wealth in them.


reader Eclectikus said...

I am sympathetic with this view of religion, I think it's much more harmless than the monotheistic religions (and more compatible with science)... however, in terms of scientific production it seems that historical results are skewed on behalf of the latter... I don't see any obvious explanation for this paradox: the higher the irrationality of religion, better scientific results. (No offense intended, of course, just my impression)


reader kashyap vasavada said...

You raised an interesting point. I do not know the real answer. But,one reason why there is no conflict between religion and science in India is that the ancient sages who formulated religious principles were themselves some kind of scientists (astronomers) and mathematicians. Their ideas were based on thoughts and meditation only, no equipment! Correct idea of age of universe and evolution of human beings from animals are examples.Currently I see that there is a steady decline of support for basic scientific research in west (especially in U.S.) while there is a big upswing in research support in China and India. So who knows what will the next 100 years bring? Also it is not completely unlikely that the currently accepted scientific method may hit a brick wall for some fundamental questions.Science has no idea about consciousness and 90 years old debate about interpretation of quantum mechanics also may be saying something!


reader TheDOC said...

Kashyap is absolutely correct. I would like to add to what he has said. Of course, I like to think that what I say is specific to some philosophies of Hinduism, but rather specific to all people.

In ordinary people the

'higher' senses are shut. So as a result we are blind to the many cosmic wonders of this universe. Curiosity is encouraged. But the conclusions drawn from modern science are considered a tiny fraction of the truth since they are incomplete.


Indeed Lubos, you should be glad, because the world is considered 'many-dimensional' in most notions of Hinduism, so perhaps if you train your senses in your living body, you will be able to actually 'see' the most fundamental pieces of matter (strings) and not just probe it with your mind. The possibilities are unlimited for the scientifically curious individual. :D


reader Luboš Motl said...

Fine, so they're normal. Being "normal" is what I call "uncultural" or "dumb as a doorknob" and I am not one of those who will adopt this politically correct terminology of yours just in order to lick the asses of the majority.


reader Luboš Motl said...

Dear Kashyap, wouldn't you like to write a guest blog on this topic How Eastern religions got [partly] indicated by the scientific progress? ;-)


reader mesocyclone said...

Lubos, if a non-physicist "knows" that the universe started with a big bang, then doesn't he "know it because he was told so" - something you just objected to above?

It would appear that a non-physicist is in a no win position. Accept something that they cannot verify, and be looked down on by you, or not accept it, and be compared to monkeys.

Or are they to accept, against without being able to evaluate the evidence, that modern physicists are authorities they should automatically listen to? If so, does that mean they should likewise accept the pronouncements of the "97% of scientists" who proclaim catastrophic global warming?

In other words, most people are not in a position to use scientific evidence. I would wager that you accept a lot of results of, say, microbiology, without having studied the evidence. I would argue that you don't have the education to evaluate the evidence (unless you have a sideline I'm not aware of).

And once again, I raise the theory of Rational Ignorance: http://en.wikipedia.org/wiki/Rational_ignorance .

Is one a monkey for not taking an irrational amount of time to learn about something of no import to that person?

My arguments illustrate why I'm not too distressed at a lot of these and similar poll results. A lot of Americans don't believe in evolution. Fine... as long as they're not working in the areas of biology where the theory is really important.

Sure, I wish people had the interest in science that I do. But they don't.

Why do we keep having hysterics about this stuff?


reader Luboš Motl said...

Dear mesocyclone, sorry but no. The non-physicist must not only accept the results he was told by someone else; he should *understand* the actual evidence - he should know why it is true, by himself - and I told you what the evidence is in the article.


At the end, a person - whether he is a physicist or not - is or should be doing qualitatively the same thing when he is deciding whether there was the Big Bang. A non-physicist is just expected to use a simpler, approximate, more classical or old-fashioned set of arguments.


But even a non-physicist, if he is a cultural person, must be thinking about these fundamental things in some kind of a primitive physics way, just like a cultural human who listens to music perceive the music in a similar way to the musician even if he is not familiar with the details and can't compose it!


reader TheDOC said...

I will add to the profoundly true statements Kashyap has made.



Sanskrit is a deep language and cryptic myths and scriptures speak on many different levels. They are often analogies for more esoteric things. After the many wars and destruction in the past, the exact meaning and context of a lot of the scripture is now hard to find. So nowadays, even between Hindus there is disagreement on some matters of the scriptures, but there is also some consensus. So I will present my viewpoints.



Basically deities exist on two levels: they are the enlightened agents that regulate phenomena, karma and causality. Since the reside in planes presently inaccessible to our senses, we are not totally aware of the influence they exert on us.


The second level deals with the the relevant aspects of the body (specifically parts of the nervous system), mind and soul that they influence.


It is essentially this Hindu notion of a conscious universe (which I believe) which is the only source of conflict with the modern theories of physics. After all, which scientific theory says that matter fields are conscious? Their unity is not presently apparent and highly-nontrivial, contrary to what some (not all) 'new-age' pundits might have you believe.


reader mesocyclone said...

First, I hope you understand that I accept Big Bang (and evolution), but not so much CAGW, and that I have a decent math and physics background, but not an expert one. Oh, and I'm a big fan of TBBT, as is my wife, who has Penny's level of scientific knowledge.

But I think you are still missing my point. You are looking at it from the point of view of a physicist. To the physicist, the Big Bang is important. To Sheldon, this importance is self evident.

But to assert that it is even important enough for a normal member of society to dig up the simple explanation you give, is different. Did you look at the link I provided on rational ignorance?

I would much rather that a citizen would devote that time to understanding the dangers of collectivism, or other ideas that can actually affect their behavior and their life, rather than to study the evidence for the BBT (or evolution).

And this is why I get tired of people complaining about the results of these polls on scientific illiteracy.


reader Eclectikus said...

I've been thinking about it for a while, I think an answer that seems plausible is that it can be easier to keep Science (Reason) apart from the spiritual (Faith) if they are perfectly incompatible with each other. The impossibility (of temptation) to mix methods between dimensions allows sustained progress along the centuries. That would explain why so many tops of human reason as Francis Bacon, Kepler, Newton, Georg Cantor, Planck or Heisenberg, could develop their work without spiritual interference, or at least the minimum interference. Probably Hinduism can be considered a religion compatible with sciences, but in the end is just as indissoluble with them as any other.


reader Smoking Frog said...

OK. Above 860 I'm not getting sentences but I can still read words. (I can read words up to 1000 - maybe higher, but I haven't tried it.) At 860, I'm getting many sentences but not all.


reader Luboš Motl said...

Cool. Maybe I would also like to know the maximum rate at which you're actually getting the content.


reader kashyap vasavada said...

Dear Lubos: Thanks. Yes. I would like to write a guest blog about no conflict of eastern religions with science. I may have to work hard though, because most of the readership would be either atheist or belonging to Judeo-Christian faith!


reader Luboš Motl said...

Yes, Kashap, it's definitely right that a vast majority of the TRF readers are either atheist or Judeo-Christians.


You might still be surprised by the not quite negligible number of Indian readers, however.


reader kashyap vasavada said...

OK. Thanks. Do I take this as an invitation to write such a guest blog? We will work out the mechanics when I am ready. You know my e-mail address.


reader Smoking Frog said...

I'm getting most of the content at 700. (This says nothing about retention.) Above 700, I get some content, but less. I'm not being precise about this; I try a few speeds and then interpolate.


I see you're not getting many responses.


Why are you asking people for this?


reader Luboš Motl said...

Thanks for answering.


Hi, just for fun, it is not excessively important. I wanted to see how quick readers other people are etc.


I wanted to include a joke that TRF would be reformatting to this blinking-single-word format but then I decided it would be lame. ;-)


reader Smoking Frog said...

Hi. I took a speed-reading course in high school around 1960. They used a curtain that moved down the page at a rate set by the teacher. She was middle-aged and was always barking, "READY? LET'S READ!"


reader Lino said...

Lubos, you wrote that Planck 'was even able to derive the resulting formula from a funny assumption that the energy of an electromagnetic wave is NOT quantized but rather a multiple of E=hf." I'm sure you wanted to say "not continuous" instead.


reader Luboš Motl said...

Absolutely, thanks.