Saturday, March 6, 2010

PHONONIC GRAVITY (Thermodynamic Verlindic Phonons in Quantum Einstein Gravity)

"Gravitons do not exist when gravity is emergent. Gravitons are like phonons. In fact, to make that analogy clear consider two pistons that close of a gas container at opposite ends. Not that the force on the pistons due to the pressure is also an example of an entropic force. We keep the pistons in place by an external force. When we gradually move one of the pistons inwards by increasing the force, the pressure will become larger. Therefore the other piston will also experience a larger force. We can also do this in an abrupt way. We then cause a sound wave to go from one piston to the other. The quantization of this sound wave leads to phonons. We know that phonons are quite useful concepts, which even themselves are often used to understand other emergent phenomena.

"Similarly, gravitons can be useful, and in that sense exist as effective "quasi" particles. But they do not exist as fundamental particles."

... Erik Verlinde, Jan 15,2010

One of the more interesting aspects about former string theorist* Erik Verlinde's latest work is his contention that the "graviton" should not be treated as a "particle", as it is in String Theory, but rather as a "phonon", as in acoustics. The reader can read all about phonons here at Wikipedia. I wish to call attention to the last section of that entry, which is this:

 

Thermodynamics


The thermodynamic properties of a solid are directly related to its phonon structure. The entire set of all possible phonons that are described by the above phonon dispersion relations combine in what is known as the phonon density of states which determines the heat capacity of a crystal.
At absolute zero temperature, a crystal lattice lies in its ground state, and contains no phonons. A lattice at a non-zero temperature has an energy that is not constant, but fluctuates randomly about some mean value. These energy fluctuations are caused by random lattice vibrations, which can be viewed as a gas of phonons.[notes 1] Because these phonons are generated by the temperature of the lattice, they are sometimes referred to as thermal phonons.
Unlike the atoms which make up an ordinary gas, thermal phonons can be created and destroyed by random energy fluctuations. In the language of statistical mechanics this means that the chemical potential for adding a phonon is zero. This behavior is an extension of the harmonic potential, mentioned earlier, into the anharmonic regime. The behavior of thermal phonons is similar to the photon gas produced by an electromagnetic cavity, wherein photons may be emitted or absorbed by the cavity walls. This similarity is not coincidental, for it turns out that the electromagnetic field behaves like a set of harmonic oscillators; see Black-body radiation. Both gases obey the Bose-Einstein statistics: in thermal equilibrium and within the harmonic regime, the probability of finding phonons (or photons) in a given state with a given angular frequency is:
n(\omega_{k,s}) = \frac{1}{\exp(\hbar\omega_{k,s}/k_BT) - 1}
where \,\omega_{k,s} is the frequency of the phonons (or photons) in the state, \, k_B is Boltzmann's constant, and \, T is the temperature.

Steve here. Regarding the above, why is that important? I feel it's important because phonons require a large number of "particles" (wave crests?) in order to exist. A single particle does not a phonon make. Neither does a single particle have Entropy, nor Temperature. These are all collective things, requiring many particles to have meaning. In regards to how many are required is where I feel future work will focus. On a recent trip to Bell Labs Pure Physics Research Division** in Murray Hill, NJ, 2009 Nobel Prize in Physics co-winner and former Bell Labs Scientist George E. Smith was shown certain state-of-the art experiments going on using the Quantum Hall effect that may at some future time be helpful in this regard. More information will be made available in the future regarding this particular avenue following publication.

Why are phonons important in the quantum realm of the very small? I feel they're important because of the notorious weakness of gravity at that scale.  If as Verlinde speculates the phononic effect goes away with few particles, and if gravity is ruled by such effects, then the weakness of gravity is explained.

Next up we ask the question: Is there a current theory, in General Relativity-based Quantum Gravity, that might explain and explore the possibility that gravity "drops away" in the realm of the small. As it turns out there is such a theory, based on an idea by Steven Weinberg in the 1970's, and developed by Martin Reuter, a physicist at the University of Mainz in Germany. New Scientist magazine has a nice synopsis of the field, Quantum Einstein Gravity, from this article, the relevant bit repeated here:

Martin Reuter, a physicist at the University of Mainz in Germany, has other ideas. He has been developing a different theory he calls "quantum Einstein gravity", which begins where the earliest approaches to quantum gravity left off.
After physicists successfully merged the classical theory of electromagnetism with quantum theory to create quantum electrodynamics in the 1940s, and later extended their methods to work with the strong and weak nuclear forces, they had hoped that they could likewise "quantise" gravity. The idea failed miserably, because of the way gravity behaves at small scales. As you zoom in on smaller distances, the strength of gravity increases, but gravity also acts on itself, creating a feedback loop that sends the gravitational force skyrocketing. Eventually the ability of general relativity to describe the fabric of the universe breaks down.
So most physicists went off in other directions, mainly towards string theory. Reuter, however, feels they were too quick to abandon the methods that had worked when applied to every other force in nature. He had been thinking about an idea proposed by physicist Steven Weinberg in the 1970s: that at extremely small scales, there might be a "fixed point" at which the strength of gravity no longer increases, no matter how much you zoom in. There is reason to think this might work. Quantum chromodynamics, the theory of how the strong nuclear force acts on quarks and gluons, says that the strong force decreases at smaller scales until it reaches a fixed point, where it goes to zero. If a similar point exists for gravity, it would mean that physics would be able to describe gravity down to the quantum realm.
When Weinberg proposed the idea, physicists didn't have the mathematical tools to calculate this fixed point in the four-dimensional space-time of general relativity. Then in the late 1990s Reuter developed such a method. His calculations were approximate, but they suggested that a fixed point for gravity might indeed lurk in the equations. "Personally, I am completely convinced that it exists," he says.
Intriguingly, in quantum Einstein gravity, space-time at the smallest scales is fractal and the number of dimensions shrinks from the familiar four to two. This is reminiscent of CDT, which leads some to wonder if they are two descriptions of the same theory. "Ultimately the two approaches could turn out to be equivalent," Reuter says.

Hello, Steve here again. My only contribution was to unite Verlinde's idea of gravitons as phonons with Weinberg/Reuter's view of Gravity falling off at small distances. I think this may be significant. I was never comfortable with the idea of a "graviton" as a "particle." I do believe Albert Einstein explained Gravity as geometrical consequence of reality in 1915. String Theorists promote "gravitons" since among the many Rube Goldberg bits their theory depends on, one bit is that a spin-2 massless particle "falls out" of their equations. Presto change-o and abracadabra, that MUST be a graviton, so they say. Yeah well, maybe, but maybe not too. I consider it a weak argument of opinion stated as fact, which is bad science.
Verlinde's recent Gravity as an Entropic Force has gotten considerable attention, both Pro and Con. If t'Hooft likes it, that's good enough for me, up to a point. Much more interesting is the criticism against it. At Sabine Hossenfelder's fair and balanced take on the subject, here, you can see how my thought process on this developed.

Perhaps most key in getting my brain to tie all this together was Dr. Andrew Thomas' take on the whole "Verlinde" situation as being not only a refreshing new way to look at an old problem (quite correct), but the "obviousness" of Entropy, a subject few Physicists have concerned themselves with since their younger undergraduate days, but a subject near and dear (and bread and butter) to Engineers such as Dr. Thomas (Ph.D., EE, Edinburgh) and myself.

Verlinde has been trivialized to some extent in the community for using "high-school physics." Not true. Third-year Undergraduate Thermodynamics II Mechanical Engineering Physics, is more like it.

One needn't get all tied up in Strings to make sense of the world. It may be explained in simpler terms than those who work at the cutting edge of Mathematics would prefer, but if so, then so be it.

When all else fails, ask an Engineer.

Ciao. 

Steven Colyer
Pi Tau Sigma, BSME
NJ

Well, that's it for today. I have to get myself into NYC to one of its wonderful art museums today with my 2 daughters for a required college art project for my oldest. It's always nice to get out with the girls and visit Manhattan, except that it will cost an obscene amount of money (as NYC always does) that I do not have (Hello, Loan Department!) and I'd rather be here exploring this new and exciting subject in more detail, but you can't have everything. Eh, the mental break will probably do me good. March 6, 2010.

* - worked in string theory.... Who hasn't?
** - Bell Labs Pure Physics Research Division - Yes, it still exists.


George E. Smith accepts the 2009 Nobel Prize in Physics

4 comments:

Vafeta said...

http://vafeta.livejournal.com/288.html

Wes said...

Erik Verlinde has put forth a theory (based on other work) that explains where gravity comes from . Using Bekenstein holographic screens and entropy he derives the formula for gravity (both Newton and Einstein).
Better yet, by assuming a holographic screen around the entire universe, Smoot et al. have derived the source of Dark Energy.
http://arxiv4.library.cornell.edu/abs/1002.4278

Steven Colyer said...

UPDATE: I have added the Verlinde quote at the beginning of this blog article, and clicking on his name following the quote will bring you to his blog.

Vafeta, congrats on your mastery of the English language for one whom it is not your primary language. I understand the great majority of what you say. you're well on your way to mastering it.

However, there is one problem I have with this statement by you:

What if the space is not only expanding, but also the materials themselves?

What would happen then is we would not notice it. The same goes with time were it to slow, then speed up, then slow, etc., globally. We simply wouldn't notice it, nor could we measure it, unless we "stood outside the universe", an unlikely scenario. However, Cosmology is a new and raw Science, and nobody ever claimed this stuff was easy.

Wes, thanks for your reference, I look forward to reading it if my theory has legs and then seek to test it against prevailing theories of Dark Matter and Dark Energy. For the moment however I am just getting started and will confine my study to the world of the very small.

Steven Colyer said...

I'll close this blog on the day I die and not before, thanks. But since I don't know when that is (and don't wish to) stay tuned! :-)