## Wednesday, March 03, 2010

### Gravity is Entropy is Gravity is...

I've been thinking recently about Erik Verlinde's paper "On the Origin of Gravity and the Laws of Newton" (arXiv:1001.0785v1 [hep-th]). Some of you will have noticed it's been discussed in the blogosphere before. In a post on "Expanding Crackpottery," Peter Woit found it to be a "sad example of “unconventional physics”" and expresses his concern about "prominent string theorists taking up dubious lines of research." Luboš Motl finds some links to "octopi swimming in the spin foam,", Robert Helling writes bluntly "If it were not for the author, I would have rated it as pure crackpottery," and of course New Scientist reports.

Now the idea that gravity has a relation to thermodynamics is not new. It's been around since decades and has maybe most clearly been pointed out by Ted Jacobsen. I thus fail to see what's so particularly offensive about Verlinde's recent contribution. Jacobson's paper however is 15 years old, and not much seems to have come out of it, at least not that I know of. So I'll admit that I read Verlinde's paper feeling obliged to follow what's going on in my research area, thinking it's either wrong or meaningless or both.

In the course of my reading it became clearer to me what was the actual content of the paper. And what not. If you are interested, I have written up my notes and uploaded them here:

Here is a short summary: With a suitable definition of quantities, describing gravity by a Newtonian potential or describing it as an entropic force in terms of an "entropy," "temperature" and "holographic screens" is equivalent. One can do it back and forth. The direction Verlinde has shown in his paper is the more difficult and more surprising one. That it works both ways relies on the particularly nice properties that harmonic functions have. Formally, one can also do this identification for electrostatics. In this case however one finds that the "temperature" can be negative and that the "entropy" can decrease without having to do work.

Some assumptions made in the paper are actually not necessary. For example, the equipartition theorem for "bits on the screen," and the explanation for why the change in entropy is proportional to the distance the particle is shifted. One doesn't actually need that. The equivalence works pretty well for the case of Newtonian gravity, but when it comes to General Relativity things are getting somewhat murky.

The biggest problem is that Verlinde's argument to show that gravity can be derived from a thermodynamical description already makes use of quantities that belong on the gravity side. To really show that gravity can be obtained from thermodynamics, one would have to express the gravitational quantities in terms of thermodynamical ones. Unfortunately, Verlinde does it the other way 'round. He also has to use a lot of previous knowledge from General Relativity. It does not seem entirely impossible to actually do this derivation, but there are some gaps in his argument.

In any case, let us consider for a moment these gaps can be filled in. Then the interesting aspect clearly is not the equivalence. The interesting aspect is to consider the thermodynamical description of gravity would continue to hold where we cannot use classical gravity, that it might provide a bridge to a statistical mechanics description of a possibly underlying more fundamental theory. The thermodynamical description might then be advantageous for example in regimes where effects of quantum gravity become strong. Maybe more banally, you might ask what's the gravitational field of a superposition state, a state that is neither "here" nor "there." It can't have a gravitational field in the classical sense. But the thermodynamical description might still work. However, the treatment Verlinde offers is purely classical. It's not even quantum particles in a classical background, it's classical particles in a classical background. So there's way to go.

Taken together, I can see the appeal. However, at the present level it is very unclear to me what the physical meaning of the used quantities is. I would like to add that Erik Verlinde has kindly replied to my queries and patiently clarified several points in his argument.

Update March 04: The notes are now on the arxiv:1003.1015v1 [gr-qc]

Steven Colyer said...

Indian Cosmologist and Theoretical Physicist Thanu Padmanabhan claims to have been doing this stuff for 15 years. However and what I can tell, Padmanabhan has been taking an Integral Calculus approach rather than a Differential Equations approach, as Verlinde has. Is this why Verlinde's approach is harder?

Don't mind me, I'm referring to Hammock Physicist Johannes Kooelman's excellent blog articles on the subject, beginning here. I don't know.

Bee said...

Hi Steven,
Yes, I recall starting to read one of Padmanabhan's papers at some point, but didn't get very far. It was kind of unclear to me what he was trying to say. I should probably give it another look sometime. Best,

B.

Bee said...

Steven: About the link you posted. If you read my notes you'll find that you actually need neither the equipartition theorem nor holography nor the Unruh effect. Formally, this is all entirely irrelevant, though it very likely played a role in coming up with the idea. Best,

B.

Zephir said...

/*..the treatment Verlinde offers is purely classical...it's classical particles in a classical background...*/
I don't see nothing new in this approach to gravity description with compare to very classical Duillier-LeSage gravity, which derives the inverse square law in transparent and illustrative one and it can be generalized to higher number of extradimensions easily.

http://www.aetherwavetheory.info/images/physics/gravity/FatioLeSage.gif

The physics of the last century does nothing else, then just reducting various aspects of energy spreading in dense particle systems to formal models, thus replacing Aether concept by bunch of mutually inconsistent theories.

Steven Colyer said...

Thnk you Bee, I'll go readf it after this. I read Motl's critique, and he definitely didn't like bringing Unruh effect in. He likes String Theorists going GR even less. I can see a ST liking Holographic though.

Zephir said...

/*...he likes String Theorists going GR even less..*/

Because LQG + SR = ST + GR

Zephir said...

/*..I can see a ST liking Holographic though....*/

ST would accept entropy in description of expansion of space and dark energy/cosmological constant a much easier, simply because it's a dual perspective to gravity and LQG is dual to ST. When particle object collapses, the space-time formed by its material expands and vice-versa.

The stance of Motl is easily predictable in this context.

Steven Colyer said...

The stance of Motl is easily predictable in this context.

I have found it thus for all extremists.

Arun said...

Hi Bee, I don't understand T. Padmanabhan (btw, he taught me calculus of variations when I was a high school student and he was finishing his bachelor's - he and some of his friends had organized an after-hours physics club :), but I remember an equation of his, that supposedly instead of the full Einstein's equation (G_ab - T_ab) = 0, entropic considerations need it to be (G_ab - T_ab)n_a n_b = 0 where n_a are null vectors, or something like that.

----

Anyway, wanted to ask you - we have Newton's laws in their original formulation, then Lagrangian and Hamiltonian formulations, and now the Entropic formulation. Is the Entropic formulation as "fundamental" as the others?

Best,
-Arun

Peter said...

Hi Bee,
Your account looks to me a nice stepping back from strong ontological claims, and I think you do the equivalence between Newtonian gravity and elementary thermodynamics nicely. Since GR is a generalization of NG, I take it that we need a generalization of elementary thermodynamics to be able to construct an equivalence between GR and thermodynamics+. If we don't allow ourselves the mathematics of tensors and differential geometry on the thermodynamics+ side, however, I don't currently see how that might look.

In particular, I can't see that it can be elementary. I take it the introduction of statistical mechanics models instead of thermodynamics moves us away from the relatively empiricist approach you have taken in your uploaded paper, even though I agree the move to stat. mech. is probably needed to make Verlinde more interesting.

I've always found rather curious a very incomplete two page account given by Zahid Zakir in gr-qc/9906079, which takes Nelson trajectories as a starting point to construct GR, claiming that "gravitation is inhomogeneous Nelson’s diffusion, i.e. a consequence of the quantum
fluctuations". This paper is little known, to my knowledge, but it seems to me to be a possible starting point for a stat. mech. approach, in contrast to a thermodynamics approach, particularly because it puts quantum mechanics into the mix in a moderately principled way.

Thanks.

Bee said...

Dear Arun,

Well, I'm relieved you don't understand him either :-) Regarding the question what is more fundamental, it's somewhat pointless to ask if the descriptions are equivalent. Anyway, I think the idea Verlinde is trying to push is that gravity is not fundamental because it is "just" a thermodynamical (aggregate) effect. If you buy this, there ought to be a fundamental theory for the microscopic degrees of freedom giving rise to the macroscopic gravitational effect. One should then probably more correctly say Newtonian gravity is equally not fundamental as the enthropic formulation. It is hard to say if the Lagrangian and/or Hamilton formalism will turn out to be more fundamental (i.e. if the to-be-found microscopic theory has one.) Best,

B.

Bee said...

Hi Peter,

Thanks for the reference, I'll give that a look.

I had a very similar thought to what you point out: how do we get the indices on the thermodynamical quantities? It's why I'm still not entirely sure the equivalence will actually hold for the GR case without using prior knowledge, ie that there is a conserved stress-energy, that there is a killing vector, that the potential can be expressed in that vector, that we can go into a local Minkowski frame etc. Basically, I'm concerned that with all these assumptions you have everything together you need to derive GR anyway, thermodynamics or not. In any case, note that a space-time with a timelike killing vector (that is "static" in a certain sense) has additional nice properties, so it doesn't seem entirely implausible to me it might be possible to generalize the Newtonian case. I suspect though you'll still have to smuggle in the equivalence principle somewhere. Best,

B.

Neil B said...

This proposal may be suspect and I admit I haven't looked over it, I don't have the time. But in general: can the idea of an entropic force be any "worse" than e.g. Sean Carroll's ideas about entropy and the arrow of time, or some theories taking "entropy" to be fundamental (Ilya Prigogine IIUK), instead of the other laws that normally are presumed to lead to it by consequence? However I don't like the idea of what we know to be a direct interaction (?) being tied up in what the universe tends to do (and how should local variations in evolution of entropy affect something like gravity?)

There are also some issues with energy conservation, another big thermo law, in GR (see Carroll again, admitting U isn't conserved in some sense with gravity involved.) I once thought of a paradox about that: Have either an infinite or closed hyperspherical, now-expanding universe. Let's say it is filled with a bunch of test objects (acting like "galaxies" in cosmology) in say a closed Cartesian array (ie like integers in x, y, x.) Have them (as "given") connected together with elastic bands. Since the elastic forces on each object cancel out, the universe and these objects can retreat from each other without being "held back." It's as if no bands, just gravity, right? But as this universe expands for awhile, the bands can accumulate whatever amount of elastic energy they can hold from w = (1/2)ks^2 (for some duration.) That makes a problem about energy conservation.

Bee said...

Neil,

I just said that at a recent post, it is true that the total energy is not a conserved quantity in general relativity, but the stress-energy-tensor is covariantly conserved. Besides this, there are special cases in which you can define a conserved mass/energy, see here.

I don't see any relation between Verlinde's paper and Sean's elaborations on the arrow of time, except that both use the word entropy.
Best,

B.

Uncle Al said...

Grant funding is professional management - business plan, budget, PERT chart, DCF/ROI, risk assessment. Theory (process) is zero-risk fundable. As math it need only be self-consistent to publish. Experiment (product) funding is excluded for the risk of failure. Experiments are then configured to trivial outcome or ambiguity ("more studies are needed") re the LHC.

If GR arises from thermodynamics it is already quantized. But it isn't! Spacetime geometrization through curvature must be wrong. The only remaining descriptive theory is teleparallel gravitation without the EP (arXiv:0812.0034v2) describing massed body effects. Gravitation is analogous to electrodynamics’ Lorentz force via spacetime torsion. Geodesic paths are absent, quantization may not be excluded.

Opposite shoes violate the EP given teleparallel gravitation with torsion in Weitzenböck spacetime. A parity Etovos experiment opposing solid single crystal test masses of left- versus right-handed quartz is the trivial experiment. The worst it can do is succeed.

An experiment that could discredit the past 40 years of grant funding is unfundable.

tytung said...

Hi
I'm not sure if my view is right.. His analogy would imply that gravity is a kind of emergent probabilistic tendency and not really a force?

Bee said...

An attentive reader pointed out to me that there was a typo in Eq(3) of my notes. There was also a factor missing in the definition B. I've corrected these both points now.

Bee said...

tytung:

Yes, that's right. Basically the claim is that the reason gravitational masses attract each other is that it increases the entropy of the system. Best,

B.

Ervin Goldfain said...

Hi Bee,

You say

"It is true that the total energy is not a conserved quantity in general relativity, but the stress-energy-tensor is covariantly conserved"

Is this statement true in general, even for non-stationary metrics and strong-field gravity?

In GR one needs to construct a gravitational energy-momentum pseudo-tensor such that the total energy momentum tensor of matter plus gravitation is conserved. To my knowledge, the conservation law written in this form assumes that the metric is time independent. This fails to be a universal case because a general gravitational field cannot be stationary in any frame of reference.

Regards,

Ervin Goldfain

Bee said...

Ervin:

That the total energy is not conserved is not true in general. As I remarked to Neil, there are cases when you can sensibly define an energy and it is conserved.

That the stress-energy-tensor is covariantly conserved is true in general. It is in fact an ingredient to derive the field equations; it is the matter-side equivalent of the (contracted) Bianchi-identities. This stress-energy-tensor is not, in general, conserved with respect to ordinary partial derivatives, which I believe is what you have in mind. Best,

B.

Neil B said...

Ervin - see if you think my GR "paradox" affects your insights into the conservation issue. Also, the elastic bands can be replaced by cords that pull on rotors inside the distributed bodies, so the energy doesn't have to consist of "elastic energy" FWIW. I also wonder if gravity as entropic force is related to the least action principle, and if the LAP can be a case of seeking entropy increase. tx.

Bee said...

Neil: It's thermodynamics, there's no action. There's quantities like entropy, total energy, temperature, pressure, chemical potential, and/or if you like various thermodynamical potentials depending on what system you aim to describe and the relations between those. Best,

B.

Ervin Goldfain said...

Bee,

"That the total energy is not conserved is not true in general. As I remarked to Neil, there are cases when you can sensibly define an energy and it is conserved".

That, in general, no conserved energy can be defined in GR is a point that often times gets overlooked and leads to misinterpretation. Since energy is strictly conserved in isolated dynamical systems, there appears to be tension between GR defined in non-stationary metric potentials and Verlinde's model taken in the Newtonian approximation.

Regards,

Ervin

Zephir said...

/*..Newtonian gravity is equally not fundamental as the enthropic formulation...*/

Newtonian gravity is indeed ad-hoced, but derivation of inverse square law by Le-Sage theory is based on pure geometry, so it could be considered a more fundamental. We cannot have entropy concept without concept of Boltzmann gas on background in the same way, like we cannot have Le-Sage model of gravity without particle flux.

Which means, both these concepts are aether model dependent, as they're representing some reduction of infinitelly complex behavior of infinitelly hot and dense particle gas or scalar field of space-time curvatures or number set in topological space or whatever else stuff, you're able to imagine behind Aether concept.

Zephir said...

/*..the claim is that the reason gravitational masses attract each other is that it increases the entropy of the system...*/

In LeSage model gravity is shielding, i.e. dispersive effect of tachyon flux from extradimension, a reverse process of evaporation of object into smaller particles, recursivelly. It means, gravity is negentropic stuff instead from this perspective.

In AWT all objects smaller then the wavelength of CMB noise undergo gradual dispersion, i.e. evaporation while larger ones gradually condense due the shielding effects analogous to mechanism of Casimir force. It's a geometrical perspective, simmilar to observation of Alexander's dark band in heavy rain - the portion of energy is focused into small ring, whereas the another one is dispersed into larger area.

Bee said...

Ervin,

The case Verlinde considers is the case where the notion of conserved energy is well-defined. But yes, this is one of the reasons why one might wonder whether it is possible to extend it to GR in all generality. I'll admit that I haven't thought about the GR case in depth because even without the point you mention I was having some conceptual difficulties there (see post or notes). Maybe I'll think about it more closely I might have something more useful to say. Best,

B.

Zephir said...

The result of further discussion would depend on where you put zero of entropy or space-time or energy density scale. Without it we could speculate, whether entropy of Universe increases or decreases whole hours without relevant result.

I'd propose to use CMB wavelength scale, in which photons are gaining zero rest mass. It's the middle of dimensional scale of observable Universe.

Anonymous Snowboarder said...

Bee - apologies for being off topic but I've been behind in my reading of your blog. Now I know why we suddenly got so much snow - you came back! From Jan 1 - Feb 24.. 24" From Feb 24-36, 48"!

Clearly the ski resorts should hire you :)

Exl Blogger said...

Verlinde's theory reminds me of Kaluza and Klein's work on extending GR with a fifth dimension to account for electric charge. Kaluza produced his version in 1921, and KK was refined in 1926, but it wasn't until the Standard Model was pulled to together in the 70s that physicists starting working with additional dimensions in earnest. One article I read said, "No one who has worked through the mathematics of Kaluza and Klein's construction can ever forget its haunting beauty ...." Its descendants in string theory haven't quite proven their worth, but it was that "haunting beauty" that kept the idea alive.

I sense something similar with Verlinde's ideas. He, and others who have been exploring entropy as a key to the link between gravitation and the quantum world are working with a beautiful idea. Others sense this or we wouldn't be talking about the entropy of black holes or discussing the limits of our understanding of entropy in gravitational fields and quantum environments.

If we are lucky, it might take less than another 50 years before the pieces fall into place and we can see where these ideas lead.

tytung said...

Bee,

Then it seems at smaller scales (but not too small that gravity loses the meaning) fluctuation will occur where the entropy might decrease for a short time, which means gravity pushes?

Bee said...

tyung,

The entropy that enters here is not the entropy that is associated to other thermodynamical properties, so it isn't entirely clear to me where they would become important. But yes, that's why Verlinde writes (last section of paper)

"The statistical average should give the usual laws, hence one has to study the fluctuations in the gravitational force. Their size depends on the eff ective temperature, which may not be universal and depends on the e ffective value of \hbar. An interesting thought is that fluctuations may turn out to be more pronounced for weak gravitational fi elds between small bodies of matter. But
clearly, we need a better understanding of the theory to turn this in to a prediction."

"For sufficiently high sound frequency or intensity one knows that the local equilibrium condition breaks down, entropy increases, and sound no longer propagates in a time reversal invariant manner. Similarly, one might expect that sufficiently high frequency or large amplitude disturbances of the gravitational field would no longer be described by the Einstein equation, not because some quantum operator nature of the metric would become relevant, but because the local equilibrium condition would fail. It is my hope that, by following this line of inquiry, we shall eventually reach an understanding of the nature of “non-equilibrium spacetime”.

That this hope was expressed 15 years ago is the reason why I said not much seems to have come out of it. (It's not that there were no follow-up papers, but not really what one might have hoped for.) Best,

B.

Bee said...

Hi Snowboarder,

Yes, Phil already made a similar observation. You follow that logic you'll finally be lead to conclude that there's no such thing as climate change. It's just all those people like me who are travelling around with their personal weather environment ;-) Best,

B.

Steven Colyer said...

Exl, I'm not sure analogizing KK theory with Jacobson/Verlinde is appropriate, as we are talking about 2 completely different areas of Relativistic Physics. But I do like analogies, and I love discussing KK (especially that Kaluza may have been right and Klein wrong), so I'll think about it, so thanks.

Also and as a reminder, two big reasons that KK was put on the backburner were 1) its timing (it came out in the same decade as the brand new "Quantum Mechanical" theory ... which attracted the top minds of the time far more), and 2) Bohr did not approve.

tytung, are you in China? The Chinese seemed to have jumped all over Verlinde theory right after his publishing. Why is that, do you think?

I was going to comment on your "entropy decreasing" comment, but I do seem to remember that under certain conditions (very rare) it can (other than crank theories that a human being is a decrease in entropy, which is wrong and a case of pop philosophers thinking they know Physics).

I simply forget where I read that and whether or not the author himself was purely speculating (for example, a cosmologist), or had evidence to back it up (for example, an astronomer).

Can you cure my ignorance, Ty? I've been reading too much lately. I should start keeping notes.

Bee, good points. Yes, "entropy" gets thrown about quite a bit, but there are 2 different uses of the word. leading to much confusion. Reading Seth Lloyd's book "Programming the Universe" helps greatly in understanding the more recent Physics-related definition rather than the Engineering-based one. But both must follow the 2nd Law of Thermo.

Bee said...

Hi Exl,

It is an interesting comparison you're drawing there. Especially since, even after all these years, KK's idea still beautiful... but still we don't know whether it's real. (One should be so fair to mention though that Norström was 10 years earlier with adding extra-dimensions, but he didn't use GR then. I wrote a blogpost on KK here.)

There's three things to be mentioned there. One is that when people came to better understand Yang-Mills theory it became clear why KK works. (You add an additonal dimension with U(1) symmetry, which is exactly what you need.) Second, one should keep in mind the reasons why it didn't work (most obviously KK's original formulation is source-free, it doesn't contain fermions, and then I believe Einstein already was worried about the stability of the extra dimension's size, see above mentioned post). Third, and most importantly, KK might be oh-so-beautiful and elegant etc, but if you look at the standard model it simply isn't. You need fermions, and you need them in different generations, and you need them to have masses, and you need them to be chiral and so on and so forth.

This "messiness of reality" is one of the reasons why the question keeps coming back to me how useful really our sense of "beauty" might be to understand Nature, or whether we're just fooling ourselves looking for something that the human brain will find intuitively appealing. I recently wrote about that here. I believe that Peter Woit might have similar concerns when he wrote (in the comments to the post I mentioned above):

I’m not critical of the Verlinde paper because it is “totally novel” (which it isn’t), but because I read it and don’t believe you can get a serious scientific theory of the gravitational force from what he starts with (thermodynamics + vague ideas about holography + high school mathematics).

Otoh, if you're with Garrett Lisi, then we just haven't looked at groups that are large enough to really figure out the Standard Model. Though this still leaves you with the "ugly" issue of symmetry breaking. Best,

B.

Bee said...

Steven:

I haven't read Seth's book. I've meet him a few times though and he seems to have a good sense of humor, so maybe I'll put it on my reading list.

Anyway, yes, entropy can decrease, there isn't actually anything problematic with that as long as you're careful stating what you mean. The point is that it can't decrease "by itself" in isolated system, unless (and I believe that's what tytung was referring to) in form of a statistical fluctuation (also: note that "can't decrease" isn't the same as "has to increase.") You can of course decrease the entropy of a non-isolated system by doing work (is what your fridge does.) Btw, didn't you mention you're reading Sean Carroll's book? You're supposed to know all that now ;-p Best,

B.

Phil Warnell said...

Hi Bee,

Gravity as an Entropic force is an intriguing notion and one I will admit to having myself for a while, yet rather the other way around, where entropy is a consequence rather than the reason for gravity. That in the way I look at it between the minimizing compressive effect of gravity and the dispersive action of the cosmological constant it is for lack of a better way to put it the strategies that a homogenous and infinitely continuance substance would have to minimize the disturbance to its symmetry (breaking) when invaded by one being it’s opposites, with that representing matter.

That’s to recognize at the extremes gravity attempts tp manifest singularities as to have matter occupy minimum space, while in dispersion as realized with the action of a positive cosmological constant the average value of its content in respect to any one (effected) place is minimized. So if we consider (real unaffected) space as homogeneously inseparable and infinite both singularities and expansion are the resultant yet fruitless attempt to have something to become nothing as from a Lagranian perspective. So here for the first time I’ve proposed an outrageous and preposterous theory :-)

Best,

Phil

Steven Colyer said...

I am reading Carroll's book. I am also being very careful as to whether to believe what he's saying is true, or not. He seems to be far more controversial than most Scientists.

Just as Verlinde theory seems to have united that which was formerly ununifiable - Woit and Motl (both gives a thumbs down), so has Carroll's book, with the thumbs in the same direction regarding some of his conlcusions.

In Sean's case however I think it's his later stuff, the last chapters, where the Pros seem to disagree. WhatEVer. Carroll remains an excellent teacher and as long as he's talking/expositating the "known" stuff, he rocks. I like the guy well enough. He looks like my brother.

Ah, here it is, the cause of the confusion: Classical vs Statistical Thermodynamics. Every teacher of Entropy (Mechanical Engineering (Classical) or Physics (Statistical)) should read this, which is the Wiki entry for "Entropy (energy dispersal)" especially "1. Entropy as disorder is hard to teach."

Neil B said...

Thermo is a weak subject for me, so I gingerly ask: isn't "information entropy" separable from thermodynamic entropy (to some extent), and isn't it true that the entropy of subsystems can decrease? (Like, the Earth itself because it gets radiation from the Sun.) Any relevance? I would think, IE would have some role in connecting to QM. Also, I was hoping someone had thoughts about my cute little perpetual (or almost) motion machine driven by expansion of the universe.

Bee said...

B.

Bee said...

Hi Phil,

I'm sorry to say but I don't understand a single word of your outrageous theory. Best,

B.

Steven Colyer said...

"Entropy as information" is precisely the point of Seth Lloyd's book. I'll stop just short of saying that's a THIRD way of looking at Thermo, because my memory of having read the book is that it is a different interpretation of Boltzmanian Statistical Thermo (as opposed to Clausius' Classical version), rather than a specific 3rd different way. It's way cool, though. It gets into hellabits, which are hella big, right? :-)

(Almost) Perpetual Motion, Neil? No, I haven't looked at it, is it on your blog? I am glad you had the word "almost" in there, though. It occurred to me that if there's one way to get labeled a crackpot faster than saying "LeSage gravity," "hydrino," "anti-gravity" or "vectons," it's "perpetual motion." :-)

Neil B said...

Steven: this possibly valid PMM is not at my blog yet, it's in my comment here at 10:56 AM, March 03. When Bee says doesn't want to repeat answers, I think she means about already saying, energy is not always conserved in GR. I'd heard that, but we still hear about CoE is a Law and so we can't get "free energy" etc. OK, but I do want comments from others too and about specifics - is this an example of that, would it create the extra energy in the manner proposed, etc? I think it does relate to entropy because "entropy" has been defined considering total energy to be constant, so what if total energy changes?

Bee said...

Neil: Please discuss your ideas on your own blog on in a forum. You know that this is not the place to do it, so why are you stretching my patience? I was asking you to read previous comments because I already commented on the possible decrease of entropy via statistical fluctuations. Best,

B.

tytung said...

Hi previous commenters,
Yes entropy for a single closed system can decrease. But in general the probability decreases with system's size and also time period of decrease.
Second law that says entropy increases (for isolated system) has only a satistical validity.
So with smaller system size we can expect to see fluctuation of entropy very often, eg. in mesoscopic systems.

Steven Colyer said...

tytung, nice response, but to clarify and if you'll pardon me being a weenie on the subject, the second law says that entropy increases or remains constant.

That stuff in italics is important, and gives more information than "entropy never decreases", for that is NOT what the second laws. What the second law says, is ... what I said.

It's obvious to me there is great confusion on this topic. I confess to being confused myself, but the confusion is not nearly as important as the source of the confusion, which as I have stated is the confusion of what Clausius was saying and what what Boltzman was saying and mixing terms. I will not repeat myself in that regard.

But it's not JUST Clausius/Boltzman, it's also LANGUAGE, i.e., the use of words, semantics, or more to the point the MISuse of words, that being the failure of the explainer to convey them properly (and I guess I'm guilty as charged of that!).

But here comes a language we can all agree on, the most base language of them all: Mathematics!

Or is it? There is actually a baser one, one that uses less words, less notation than Math, and Phil Warnell and Plato (the blogger) know what I'm talking about:

Logic.

Case in point, this following post reply by Phil Warnell:

Gravity as an Entropic force is an intriguing notion and one I will admit to having myself for a while, yet rather the other way around, where entropy is a consequence rather than the reason for gravity.

IMO that is the most honest statement on this thread so far (from one who truly wishes to learn rather than tries to push their own agenda), because Phil, and from what what I can gather, that is PRECISEly Verlinde's point! That what you see as real is what we all have been TAUGHT to think as real, but that maybe, just maybe, we should be looking at it from the other way around. That Gravity (whatever the hell THAT is) is a consequence of Entropy (whatever the hell THAT is), rather than the other way around.

When all else fails and you seek honesty above all else ... ask a Philosopher, a ... Logicist, a ... REAL Philosopher, not a "Pop" one. And Phil is real.

(But Bee's right and your idea was outrageous Phil ... it had to be if the assumptions were wrong, yes?)

Kay zum Felde said...

Hi Bee,

how would the description of a superposition of two thermodynamic states might work ?

Best Kay

Bee said...

Don't know. I'm thinking about it. If I come to any conclusions, I'll let you know.

Agno said...

Well and clearly written article (also for a layman). I've enjoyed reading it :-)

You reverse Verlinde's argument and show that Newton's laws can be logically expressed in thermodynamical terms.

But, assuming Verlinde is right as well and gravity is induced by an entropic force, then the question arises what feeds this force so that it can do work at distance? There must be some heat (dQ) transferred to transform this potential entropic force (difference between a lower and higher state of entropy) into real work + some extra entropy (which makes the force irreversable, but not necessarily "ir-repeatable". Just like you can stretch a rubber band multiple times by using another force).

Since the overall temperature of the universe ("heat bath") is declining, if makes one wonder that when the total available 'fuel' for the entropic forces to 'act' is declining, the associated gravity should be reducing at the same rate as well. If the compressive effect of gravity decreases this way, you would expect the dispersive power of the cosmological constant (maybe also entropic per Smoot et al...) to gain in dominance and thereby accelerate the expansion of the universe.

How sure are we that gravity (esp. the G that is difficult to measure exactly) is constant throughout space/time? Could the 'constant' G be temperature dependent and decline during the evolution of the universe?

Bee said...

Agno: There's lots of contraints on space- and time-variation of G, most notably from knowing that other galaxies/stars look pretty much like ours and from baryogenesis if I recall correctly. Roughly, the interaction frequency depends on the value of G. It's not too precise (I think 10%) or so, but you can't have changes by orders of magnitude. I don't understand the rest of your comment. I don't know what the difference is between irreversible and irrepeatable. In any case, there's nothing irreversible about Verlinde's description. I also already said several times above that the entropy Verlinde is talking about has a priori nothing to do with the entropy of "stuff" in that spacetime. (Just look at my notes. The entropy has something to do with the value of the potential and the surface area of the screen, not with the equation of state of matter inside the screen.) You're making several leaps there. Best,

B.

Neil B said...

Sure, Bee, sorry I have to keep fighting that impulse. Even though conservation laws may relate to entropy issues, such complete proposals belong elsewhere. So, all: just hit my link and see a new Post about how to increase energy in an expanding universe - and pls. no more about that specific here.

I do note per the topic: it is possible to see and formulate things in different ways. Hence even if the same results are predicted, the Verlinde theory might well be a valid way to "interpret" gravity and inertia etc. He did mention it could predict some results different from standard theory. I note he mentions hot topic AdS/CFT; no comments here yet re.

I did get around to skimming Bee's linked comments. It seems to me indeed, that something about the way gravity and EM interact or relate could force a difference due to the inherently different way charges act, and re space-time curvature. Black hole radiation? I wouldn't know - will keep quiet for awhile.

Arun said...

So mathematically there are two equivalent ways to describe harmonic functions in Euclidean R3 - the usual way, φ(x) or through the T, S functions and a family of surfaces.

Does this kind of thing extend into harmonic functions on general manifolds?

Andrew Thomas said...

I think Verlinde's theory is fascinating as I think it promises to bring an end to the endless chain of "Why?" questions. To explain, if we ask "Why does the metal ball move?" we might answer with "Because it is near a magnet", but then you might drop down to a more fundamental level and say "Why does the the magnet do that?" to which you might answer "Because of the magnetic field", and then you might drop down a further deeper level and say "Why does the magnetic field have that effect?" And so on. And basically if you want to explain why something moves in physics then you just end up travelling further and further down the chain of "Why?" questions, and you can never get to the end. Not in physics, anyway.

And I just think Verlinde's theory has the potential to end the tower of "Why?" questions. This is because any eventual end to the tower of "Why?" must surely come from mathematics, not physics, as the laws of physics are rather arbitrary (why should there be such a thing as a magnetic field at all?) whereas the laws of mathematics can be "obviously correct" in a Platonic sense. In other words, there's no need to ask "Why?" to a Platonic mathematical law - it's just obvious that it has to be the way it is. And one of these obvious Platonic mathematical laws is that "Disorder will tend to increase" - to my mind, that is an obvious mathematical law which needs no further explanation - there is no point asking "Why?" to that, it is just obviously true.

So at the bottom of the chain of "Why?"s I would expect to find the 2nd law of thermodynamics and the rule of increasing entropy, because it needs no further explanation. It ends the tower of "Why?" questions as to why something moves. So it all rings true to me. In fact, I've been expecting something like this for a while. We find increasing entropy behind effects such as quantum decoherence. It just seems to underlie all change.

Neil B said...

Andrew, you have a point - although so much can then "exist" once you allow all Platonic schemes to exist as per MUH etc. It sure doesn't explain our world in particular, or why the weird features like relativistic space-time and QM (the problems of which, BTW, are not resolved by that certain process ;-)

Here's some of what bothers me about entropic gravity: there is no need for gravity (i.e., for a non-zero "G") per logical consistency with anything else, including entropy. We can "imagine everything the same" but with no gravitational attraction. The rest of physics goes on as before with little change - a logically self-consistent physical and mathematical regime.

Or, we could imagine G to be 1/10 or 100x what we have. Some say "but you can't imagine what if c was different, since constants with dimensions are relative." Well, G is different in that it has dimensions, but is logically detached from other standards of measurement. All the other properties could be the same - we can conceptualize the same values of e, h, c, etc. and not worry about G at all. Atoms would be the same to within tiny ranges, alpha the same, and so on.

So no intrinsic way to get "G" seems possible from a generality like entropy. And what's the point of saying why there ought to be gravity, when you can't say why it has the strength we find?

Plato said...

Bee,

Just wondering how the Neutron interferometer might fit into Verlinde's scenario .

If no relevance, might you comment on it some day?

Best,

Bee said...

Dear Arun:

"So mathematically there are two equivalent ways to describe harmonic functions in Euclidean R3 - the usual way, φ(x) or through the T, S functions and a family of surfaces."

Yes.

"Does this kind of thing extend into harmonic functions on general manifolds?"

Depends on how general you want them to be. What you need is Gauss's law and Green's identities. I think the manifold needs to be differentiable and I would guess it should be simply connected, but I can't really recall the assumptions to the theorems. Best,

B.

Arun said...

Hi Bee,

Second question - this is purely gravitational-static. In your example, (equations 10, 11) if we have a pair of objects in a highly eccentric object around their center of mass the area of an equipotential surface will periodically increase and decrease as they pass through periapsis and apoapsis. Hard to think of it in entropic terms. Yes/no?

-Arun

Bee said...

Yes.

If Verlinde's idea should have an extension to the time-dependent situation clearly one needs to do more.

Arun said...

Hi Bee, thanks for your patience! Some real ramble now.

QFT is able to able to give me the temperature of a horizon but not its entropy. (I think so, because if QFT could give its entropy also, string theory's entropy of blackhole would be no big deal).

Presumably, if I cut out of space any equipotential surface of a harmonic potential, and do QFT on the residual space, I will get a similar temperature result????

Steven Colyer said...
This comment has been removed by the author.
Steven Colyer said...

Peter Woit seems to be losing what hairs he has left over the use (overuse in his opinion) of the word "Entropy", which he calls the new buzz-word of this decade, as opposed to last decade's buzzword: Holographic.

I don't think Mathematicians like "high school math" as some put it.

Well fear not Mathematicians (and Computer Scientists as well), here comes John Baez and Mike Stay to the rescue:

Algorithmic Entropy
dE=TdS−PdV+μdN

All aboard the Entropy train!

Computers. You can't live with them. You can't shoot them. (But given enough time, they'll disperse.)

Andrew Thomas said...

Hi Neil, "It sure doesn't explain our world in particular". No indeed, I'm not suggesting that. I'm just suggesting in general terms that some sort of "increasing entropy" theory seems likely to lie at the base level of these theories of "Why things change". It's really quite vague, and I think Verlinde admits he is just making quite a vague suggestion - nothing too concrete yet. But it's a very interesting idea.

Just because a theory doesn't provide all the answers straight away does not mean we should immediately discard it. These things take time.

Neil B said...

Andrew - OK, again you have a point. However (and to all): I repeat, there is no apparent way here to derive "G" or even that it should be non-zero (ie, to have gravity!) Hence it is hard to see that a Verlinde type theory can make its point. If G could logically be 1/10 of current value, then why not zero? But the alternative seems to be, to be able to explain the magnitude of G. I don't think either this or any theory ever, has come close to that, true?

Bee said...

Andrew:

Sorry, I disagree with you. Verlinde's proposal is not an end to the why questions. On the contrary, it opens more questions than it answers. See, if you believe gravity is fundamental (in some quantized to-be-found version) than that's the end of the why. If you say gravity is emergent, then you have to explain what it emerges from. Or in other words, if you're talking about thermodynamics you want to know that the microscopic degrees of freedom are that give rise to the aggregate effects. Best,

B.

Andrew Thomas said...

Hi Bee, yes, I agree it's not in itself going to give clues on the actual nature of gravity. I'm not really thinking about "What is gravity?" at all. I'm not suggesting what the degrees of freedom are at all. I'm not suggesting any solutions along those lines at all. Instead, I'm considering the fundamental question "Why do things change?". This question applies to anything which changes with time, and is not specific to gravity at all. And the only way I can ever think of finding a truly fundamental answer to the question of "Why things change?" is this idea of entropy increasing, as it seems so commonsense. If you any group of objects, and it changes in an undetermined random manner, the only measure which emerges - which describes the change - is the measure of increasing entropy. It's the only thing which describes the change. Even in the absence of any physical laws at all, the entropy will increase. So change of entropy seems more fundamental than physical laws.

The approach of physics seems to be to find the "design" of the universe (for want of a better word). It's to find the fundamental structure. As you say, for the case of gravity we would want to find the degrees of freedom. So we try to find the structure and design. And that design could - potentially - have taken a completely different form (in a different universe, maybe). But this principle of increasing entropy requires no design - it is just "obvious". The form of that law would always be the same - even in a different universe.

So no, no solutions as to the nature of gravity at all. Just considering the very fundamental question of why things change.

Steven Colyer said...

"Why do things change?"

Because if they didn't we wouldn't be here to pose or ponder that question.

Sorry. Don't mind me. I just had a crazy anthropic moment there. I'll get better.

As a fellow Engineer, I fully understood your post Andrew, well done. I have come to the conclusion after some thought that even though Physiucsts and engineers have similar interests (Maths and Physics), our brains are constructed quite differently. The next step would be to define precisely how. However, I shall pass on that for the time being.

I've yet to see a simpler concept cause such consternation in the Scientific community other than Religion. It's definitely enjoyable to follow, though.

New business. Verlinde posits that the hypothetical "graviton" should be thought of in terms of being a "phonon". If that's true then you would need large multiples of particles in order for there to BE such a thing as gravity. Not enough particles? No gravity then. How's that for logic, Phil W.?

Bee said...

Andrew:

Verlinde's proposal is time independent. It does, at least so far, not tell you anything about why things change. I think you'd be better off with Sean Carroll's book on the arrow of time if that's what you're looking for. Best,

B.

Steven Colyer said...

Darn it! I just saved the Standard Model and thus saved the world from Susskind making bets against it, when lo and behold and sure enough, EVerytime I think I have an original idea, I dig and find someone else had it first. Curses, foiled again:

Stephen Weinberg's 70's idea of Quantum Einstein Gravity and Martin Reuter's mathematical framework of same.

NPP to Weinberg, Reuter and Verlinde! :-)

Steven Colyer said...

And the Wolf Prize to Frank Saueressig (who co-authored Reuter's paper here, Andrew Thomas, and myself, because The Swedish Academy is a bit "picky" about there being more than 3 recipients for any one award.

Woo-hoo! Gentlemen! We solved the riddle of Quantum Gravity! Time for a drink! Here's to Darth Motl! Cheers!

Congrats Dr. Weinberg on your 2nd NPP! May you get a 3rd for technicolor! That'll show Bardeen. :-)

Andrew Thomas said...

Hi Bee: "It does, at least so far, not tell you anything about why things change." ? I mean a change in the state of the universe - that's change. So an object moving under the force of gravity - that's change. I mean any dynamic change. And not just the usual "glass falls off a table and breaks into a lot of pieces" arror-of-time increase of entropy type of change. I mean any change - force, decay, quantum evolution, movement of particles, absolutely anything. I'm really referring to change at the most fundamental level, and I firmly believe it all has increase of entropy (in a way which is yet beyond our understanding) at its core.

Andrew Thomas said...

I know this is not the generally-held belief, but when I had a fairly extensive look at the arrow of time, I was really surprised how so many apparently unrelated effects such as the radiative arrow of time, and the psychological arrow of time, could all be traced back to the quantum mechanical arrow of time - which in turn can quite possibly be traced back to increasing entropy via quantum decoherence. And it just seemed to me that increasing entropy seemed to be behind so many phenomena, maybe it's behind all change? And, like I said earlier, the 2nd law of thermodynamics seems more "fundamental" (would be the same in all possible universes) than the other physical laws which seem rather arbitrary in comparison. So maybe increasing entropy is the engine driving everything which changes in the universe?

Anyway, that was my little thought, and I was unaware of the earlier work connecting gravity with increase of entropy, but when I heard about Verlinde's half-idea I just thought - yes! It just sounded as if it was on the right track. I know you and many others don't agree, but it just sounded right to me. Anyway, I'll leave it there, but I'll admit I'm quite excited by Verlinde's work.

Steven Colyer said...

With all due respect, Bee, I'd listen to Andrew Thomas on the Entropy, the Second Law, and the Arrow of Time before I'd listen to Sean Carroll, as these subjects are bread and butter to Engineers to the point of "obviousness" to us, whereas to Physicists it seems to be a subject you learned in undergrad days and filed away in your "1800's Physics" drawer, as you then launched into the more recent and field-specific subjects of GR, QM, QFT, QED & QCD, and GT.

Which is not to say Carroll's work is irrelevant, or even wrong. I'm curious as to where Andrew's views, which reflect Penrose's views to a great extent, conflict with Carroll's, for I would venture they have much more in common, than not. Click here for a handy page reflecting Andrew's/Penrose's views at Andrew's website.

Andrew, I've attempted to tie together my thoughts on these developments as well as your outstanding contribution here.

When all else fails, ask an Engineer. ;-p

And please don't get mad at me Bee as I did start this blog comment out with "with all due respect." :-)

Phil Warnell said...

Hi Steven,

I’m flattered that you would deem me to be what you cite as a ‘real Philosopher’, although I wish I could say I share your confidence. However at the very least I can boast to being a Phil which in ancient Greek is the word for love as to have it preceding osopher to mean lover of knowledge, which I surely am. That reminds me as to why I go by simply Phil, rather then it correctly being Philip as that has my love being of horses for which I will certainly deny in having any emotional attachment to:-) For the most part I will admit to be honest with myself as Socrates did say first and foremost “to know thyself” and to have it further reasoned "the unexamined life is not worth living". However as I have contested before I find Carl Sagan to express the best reason of all when he said :

“For we are the local embodiment of a Cosmos grown to self-awareness. We have begun to contemplate our origins; starstuff pondering the stars; organizing assemblages of ten billion billion billion atoms considering the evolution of atoms; tracing the long journey by which, here at least, consciousness arose. Our loyalties are to the species and the planet. We speak for earth. Our obligation to survive is owed not just to ourselves but also to that Cosmos, ancient and vast, from which we sprang.”

So the way I’ve always considered things, is it’s not so important if any one of our wonderings might be demonstrated as to be true, rather it is more important how marvellous that we be able to wonder at all and how grateful we should be that we can.

Best,

Phil

Bee said...

Andrew:

Well, how can I express that clearer? The fields Verlinde considers are static. They don't "change." Then there's the trajectories of particles in that background. These are time-dependent in the sense that the particle is at different locations at different times. But there's nothing irreversible about that. Do the orbits of the planets "change" in any meaningful way?

Regarding your other comment, I think we might be using the word "fundamental" in a different way. I would not call something fundamental that can be derived from another theory that contains more information. (Roughly, for details see here.) You can derive the laws of thermodynamics via statistical mechanics from the underlying theory, thus I wouldn't call these laws fundamental. You seem to use the word instead to mean that it's a very common law. Best,

B.

Andrew Thomas said...

Hi Bee, I totally bow to your superior knowledge of this subject - I'm sorry I haven't had the time to read up on it more.

You make a good point that the trajectory of a single particle is not irreversible. So how can change of entropy play a role? Good point. I would suggest that maybe a single particle moving at constant velocity is described by an unchanging amount of information, so it could be said that the entropy remains constant. Hence it is reversible.

Anyway, it's just my crazy theory! Thanks.

Bee said...

Andrew: You might find it interesting to read what Verlinde had to say about the issue of reversibility, see here. Best,

B.

Andrew Thomas said...

Just to end, the "change" I am referring to is the motion of the objects under gravity, or any motion. I'm not referring to change of the field - I'm simply talking about something moving! No, the orbits of the planets do not change, but the the planets move - that's the "change". Surely that is what Verlinde is referring to? As the masses move together under gravity, the information content changes in a way that is "most likely", i.e., the entropy increases. It's that "change" I am referring to.

About the use of the word "fundamental", you say the laws of thermodynamics can be derived from the underlying theory. I would say it is independent of any particular theory - the principle that a state which changes randomly will move to a "more likely" state, ie., entropy increase. It doesn't matter which theory you have, that principle will always remain, so it is not derived from any particular theory.

Andrew Thomas said...

Thanks for that link. So Verlinde thinks an entropic force can be reversible? Oh well, I'm rather relieved about that, but I have not idea how he came to that conlusion. I really must read his paper sometime ... :)

Andrew Thomas said...

So my crazy theory is not totally stone dead. I'll be famous in 10,000 years time.

Bee said...

Andrew: I already said that somewhere above, the second law doesn't say entropy has to increase. It says it can't decrease. That's not the same. Besides that, as I've explained in my notes since both formulations, the entropic one and the usual Newtonian-gravity one with a potential, are actually equivalent, the "entropic force" interpretation necessarily is as reversible as the usual gravitational force. Best,

B.

Steven Colyer said...

As I've said as well. Entropy can remain constant.

Phil, your problem is you're too modest. I used to have that problem as well, still do to a large extent. We must of course blame the English for this. :-)

Ted Jacobson's abstract from his famous 1995 paper, linked in the main article by Bee:

The Einstein equation is derived from the proportionality of entropy and horizon area together with the fundamental relation $\delta Q=TdS$ connecting heat, entropy, and temperature. The key idea is to demand that this relation hold for all the local Rindler causal horizons through each spacetime point, with $\delta Q$ and $T$ interpreted as the energy flux and Unruh temperature seen by an accelerated observer just inside the horizon. This requires that gravitational lensing by matter energy distorts the causal structure of spacetime in just such a way that the Einstein equation holds. Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

Repeat last line:

This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.

Sound in air. Phonons.

Verlinde's abstract:

Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.

Neil B said...

I think the point Verlinde is making, which I should have picked up on better (as I too carelessly skim through pages and papers etc.): not to explain gravity per se, but to say that, given gravity at all, the Newtonian form in reduction is the only one consistent with the entropy considerations. And it makes sense to move causally or "argumentatively" from entropy to the form of gravity. Entropy kind of is what it has to be for fundamental reasons, so gravity must follow and not lead. Hence the value of G is a separate problem and nothing to gripe about here, if I get the point.

BTW I found a relevant and alternate way to show that the electrostatic force law in N space dimensions has to be E = qr^1-N. It uses universality and consistency of energy density u = bE^2, where b depends on dimension. I figure the analogous generalization for gravity may need to follow for similar reasons of consistency, but energy density in gravity is a tricky subject ;-)!

BTW Woit isn't very commenter friendly, is he? He closed up before a month was over, and is as tight a screener as LuMo.

Steven Colyer said...

BTW Woit isn't very commenter friendly, is he? He closed up before a month was over, and is as tight a screener as LuMo.

He likes Bee well enough. Look at it this way: the more you know what toy model BRST cohomology is, the more likely he's let your stuff through. And please don't compare him to Lubos. Woit's a left-winger and Motl's a right winger. Woit works at a snobby Ivy League (redundant?) school, as did Motl once before leaving because of said snobbery. Woit works in the Mathematics Dept. of Columbia, indeed that's who owns his blog if you read Not Even Wrong's address, so he won't put anything up on that blog that would upset his Department Head. The same with Motl and Rupert Murdoch.

Neil B said...

OK, and to wrap up this OT digression (but it referenced his post on this issue): Woit has screened some of my comments which I thought were appropriate, and he's no Bee or Chad Orzel etc. about letting in comments. But to be fair, one I just sent got "up" at least, so far so good (about possible evidence for the multiverse, check it out.)

Do you think I'm right about Verlinde and the implication basically just supporting inverse square for gravity, since how could it explain the need for gravity per se (and in terms of justifying a value for G.)

Andrew Thomas said...

I think Woit is just plain rude the way he deletes perfectly reasonable comments. I'd never comment there.

eskesthai said...

Hi Bee,

I know this top part is off topic.

I have been encountering difficulties with ISP provider telus to access my own Dialogos of Eide, so have created a wordpress blog until problem corrected.

I understand that others can still see it so keep links. I can as long as I use the libraries internet access or hotels while travelling

Verlinde's example of the screen is one that I recognized very early when referring to Thomas Banchoff fifth dimensional views using the computer screen for abstract. I think this is applicable to his posturing in that article.

Best,

Plato said...

THOMAS BANCHOFF has been a professor of mathematics at Brown University in Providence, Rhode Island, since 1967. He has written two books and fifty articles on geometric topics, frequently incorporating interactive computer graphics techniques in the study of phenomena in the fourth and higher dimensions

I learn to recognize this contribution using Lee Smolin's description of "the Thing."

The screen then becomes a description "from the boundary" and then depicts the internal dynamics of blackhole?

Best,

Bee said...

Dear Arun,

Regarding your above question, I'm not sure I understand. QFT does also give you a black hole entropy with the temperature. That's not a big deal, you just integrate dS=dM/T. What it doesn't give you is a microscopic explanation for what this black hole entropy means, that's what you need ST for. (I probably don't have to tell you that historically it was the other way round, it was first argued black holes have an entropy proportional to the surface area, and then the qft calculation showing particle emission followed.) Best,

B.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Steven,

Those are indeed an interesting correlated couple of quotes you have noted here of Jacobson and Verlinde. However for me it still comes down to ask whether the math as with the information it relates is the essence of things or rather does the math as manifest as information simply quantify the quality(s) of what one is attempting to understand as to have known for what it is . That’s like when someone asks isn’t it curious we have all these squared relationships in physics, with responding what’s so mysterious about squared when it comes to describing actions found within what takes place within a three dimensional space. That’s what I mean as to what the difference being between the consequences of something as compared to the reason(s) for it, as the consequences are expressed most often quantitatively, while qualities dictate the reason for actions as observed. So from my own platonian perspective this information relates merely to the shadows, which can only be reasoned by way of its quality(s).

So for it is then to ask are things like conservation, symmetry, invariance and covariance manifested consequence or rather aspects of quality? Then to ask is entropy an aspect of quality(s) or rather a consequence of them. Further to ask can one imagine the action of entropy at all without first having either space or time to enable its action? I would argue that although Plato said nature could be recognized though it’s aspects of truth and beauty, what these ultimately stand as being are what we can have measured as to quantify the quality that has them to be, which he called the good and I find as simply as reason. As a crude analogy would be to question for instance, is a low coefficient of friction the reason for something being slippery or rather a consequence as to it being so?

Best,

Phil

Plato said...

A screen, is a 2d version of a fifth dimensional space.

Today, however, we do have the opportunity not only to observe phenomena in four and higher dimensions, but we can also interact with them. The medium for such interaction is computer graphics. Computer graphic devices produce images on two-dimensional screens. Each point on the screen has two real numbers as coordinates, and the computer stores the locations of points and lists of pairs of points which are to be connected by line segments or more complicated curves. In this way a diagram of great complexity can be developed on the screen and saved for later viewing or further manipulation Banchoff above.

The "configuration space," is where...?

Spacetime in String Theory.

Soup is?

Best,

Plato said...

Strominger: That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

This is 2005 information.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Plato,

The "configuration space," is where...?

I would say it is found in the potential of what has it considered to be, as aspects of the qualities innately true of their nature. So my observance is that we have as fundamental holism and discreteness, both of which I find hard to imagine to be resultant of an action in denial of corresponding physically real entities of mitigation. That’s to say the screen only reveals rather than holds the truth of what has them be known. It is interesting to note that the root of mathematics is to be found in counting, yet by and of itself entirely void of meaning without first something to count.

“Some physicists, among them myself, cannot believe that we must abandon, actually and forever, the idea of direct representation of physical reality in time and space; or that we must accept the view that events in nature are analogous to a game of chance. It is open to every man to choose the direction of his striving: and also every man may draw from Lessing’s fine saying, that the search for truth is more precious than its possession. “

-Albert Einstein- The Fundamentals of Theoretical Physics” in the journal [Science- May 24, 1940]

That’s to note that when it comes to what be the reason(s) for the world I still find the physical responsible for what we find, rather then what I consider the quantified actions that result as the consequences of their being.

Best,

Phil

Plato said...

Hi Phil,

Sorry for taking so long to get back to you.

Logic is often divided into two parts, inductive reasoning and deductive reasoning.

For me you are clearly defining the context of "ones approach," but in the full context of the logic, it would appear you see it as "one sided" in my description.

It is not an easy thing for me to define that "configuration space" since there is "no geometry that we know of" that can describe the interior of the black hole, yet, we have a "microscopic description" of that interior that includes gravity.

So, the configuration space while thinking of the screen, allows one the freedom to know that what we are describing from that screen "is actually describing a fifth dimensional attribute" of the space "we have created" to allow us too, "see movement" within the confines of that space.

Now, as to define this configuration space, it may mean one thing to our science advisers, yet, I would go so far as to say "that the parameters around this model" would have to be "coordinated" much as you would record the results of let's say using "the calorimeter or the scintillator." These measures are a direct result of "cosmological initiated time sequences" which we choose to measure, or, in the LHC collision processes.

When does the actual "measure" begin?

Best,

Plato said...

....cont/

If man thinks of the totality as constituted of independent fragments, then that is how his mind will tend to operate, but if he can include everything coherently and harmoniously in an overall whole that is undivided, unbroken, and without a border then his mind will tend to move in a similar way, and from this will flow an orderly action within the whole. (David Bohm, Wholeness and the Implicate Order, 1980)

I do not disregard the context of "measure" to help us along, as we move deeper into the nature of the black hole, as a configuration space, with which we might help theoretical dogma make in roads.

The Value of Time

Lee Smolin:

I suspect this reflects the expectation many people have that time is not fundamental, but rather emerges only at a semiclassical approximation in quantum cosmology. If you believe this then you believe that the fundamental quantities a quantum cosmology should compute are timeless. This in turn reflects a very old and ultimately religious prejudice that deeper truths are timeless. This has been traced by scholars to the theology of Newton and contemporaries who saw space as “the sensorium” of an eternal and all seeing god. Perhaps the BB paradox is telling us it is time to give up the search for timeless probability distributions, and recognize that since Darwin the deep truths about nature cannot be divorced from time.

The alternative is to disbelieve the arguments that time is emergent-which were never very convincing- and instead formulate quantum cosmology in such a way that time is always real. I would suggest that the Boltzman Brain’s paradox is the reducto ad absurdum of the notion that time is emergent and that rather than play with little fixes to it we should try to take seriously the opposite idea: that time is real.

So you see, I get it.:) It is a challenge between "discreetness and continuity of expression.

Yet, I would go so far as to say that defining a "configuration space for gravity" in color, was a way in which to define gravity in those points "with differentiation" so as to chart the differences within the context of that space.

This is what Verlinde "to me" was trying to do.

Part of my assumption is the photometric expression of gravity as a discriminant of those coordinated points. Again, for me clarification "as to the science" with points from advisers is to set straight, is always appreciated.

Best,

Plato said...

Calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets-Dorigo Tommaso

A bit of Canadian pride here?:)

One might understand to this point, about the necessity of understanding the limits to which such measures have been "applicable to our understanding of gravity" as is the case in the neutron example.

Plato said...

Last comment.

The Emergent Age, by Robert Laughlin

The natural world is regulated both by fundamental laws and by powerful principles of organization that flow out of them which are also transcendent, in that they would continue to hold even if the fundamentals were changed slightly. This is, of course, an ancient idea, but one that has now been experimentally demonstrated by the stupendously accurate reproducibility of certain measurements - in extreme cases parts in a trillion. This accuracy, which cannot be deduced from underlying microscopics, proves that matter acting collectively can generate physical law spontaneously.

Physicists have always argued about which kind of law is more important - fundamental or emergent - but they should stop. The evidence is mounting that ALL physical law is emergent, notably and especially behavior associated with the quantum mechanics of the vacuum. This observation has profound implications for those of us concerned about the future of science. We live not at the end of discovery but at the end of Reductionism, a time in which the false ideology of the human mastery of all things through microscopics is being swept away by events and reason. This is not to say that microscopic law is wrong or has no purpose, but only that it is rendered irrelevant in many circumstances by its children and its children's children, the higher organizational laws of the world."

In Lauglin's case, he has reached what we call a "self evidentary moment," so we might assign his logic as to a "perceptual plateau" with which he now deals with the world.

This to me is closely related to how Dirac saw in terms of notation in algebraic terms, and his visionary capabilities. The logic complete.

fhblogger said...

We continue to attribute gravity and other non-contact attractive forces to strange things like exchange particles, strings and now thermodynamics.

We continue to totally ignore the most obvious mechanism for gravity which is simply the electrostatic force - a force we all know an love, but refuse to think is related to gravity - eventhough it has nearly all the same properties of gravity. Now I know all the paper-napkin calculations will tell you that things will fall differently in an electrostatic field and that it doesn't generate a 1/r^2 force that could hold in planets - but have these experiments really been done? I have found almost no experimental research regarding the attractive effect of a charged sphere on a neutrally charged object (which is how I think gravity may act). It is always a charged object measured against another charged object. As Einstein once said - if you don't believe me, then do the experiment, you will find it to be true. I have outlined what gravity could be and how the electrostatic force works at:
http://franklinhu.com/whatisgravity.html
This is part of an integrated theory of everything at:
http://franklinhu.com/theory.html
This theory bases everything off of positrons/electrons and the electrostatic force.

Steven Colyer said...

We continue to totally ignore the most obvious mechanism for gravity which is simply the electrostatic force - a force we all know an love, but refuse to think is related to gravity - eventhough it has nearly all the same properties of gravity.

Except it doesn't have nearly close to the same features. Electomagnetism or "Electroweak" had you studied harder has attractive and repulsive properties, and Gravitation only attractive.

I couldn't read beyond that when I noted you got that wrong.

Study more.

Steven Colyer said...

Bee, you're mentioned at the end of this article by Tryggth's Blog, here.

PROCRASTINATION. Hard work often pays off after time, but laziness pays off now.

lol

fhblogger said...

Concerning the objection that electrostatic force is attractive/repuslive while the force of gravity is all attractive: The force of gravity appears to be only attractive, only because neutrally charged bodies are unconditionally attracted to any point charge regardless of the polarity. It is the attraction of "neutrally" charged matter to a point charge source, which would appear to be completely attractive. You would never see a repelling gravity because all astronomical objects all have a residual positive charge which behaves as if it were all concentrated at a point in the center. This point charge attracts the mostly neutrally charged matter of say the moon. And yes, two net positive charged objects attract if the attraction of the neutrally charaged matter (making up 99.99999...% of the earth/moon overcomes the slight repulsion of the charged part (10^-32 %).

Also fundamentally, if all you had was a postively charged ball and a negatively charged ball, you would observe only an attractive force. Would you then conclude that the force cannot be electrostatic because it is only attractive? I think not.

This is a great example of these 'paper-napkin' calculations that people use to toss out this idea, but never get beyond the napkin. I'm sure that there are minds far greater than mine that have tried to make this work, but I've thrown in a few new ideas that you might find interesting. It's one of the few theories I've heard of that can genuinely define the nature of gravity and shows how "charge" actually works as a phased wave interaction.

Arun said...

Hi Bee,

For a brief brain-fart period, I had thought that temperature is purely geometric, harmonic functions in terms of equipotentials and harmonic functions that are part of QFT modes. In that mistaken picture, G does not enter, except when you ask how mass/energy ties in with the geometry.

-Arun

Steven Colyer said...

It's more than attractive/repusive vs attractive, fhblogger, it's also about a continuous effect vs a quantum one.

The closest thing we have from mainstream science is Einstein's explanation of gravity. This always has to do something with rolling a bowling ball on a sheet of rubber. The main problem with this analogy is that it relies on the force of gravity to explain gravity. This analogy assumes the presence of a gravitational downward force to cause the ball to warp the rubber sheet. If you put this ball and sheet on the space shuttle with no gravity - suddenly this doesn't work any more. The logic is pretty circular. But it is just supposed to be an analogy - and a bad one at that.

That's a classic.

fhblogger said...

Steve, of course gravity is a lot more then attraction/repusion which is why I try to get people to go beyond the obvious and try to solve the real problems of an electrostatic gravity.

You merely comment on some of the background statements I make about gravity, but nothing about the substance of my proposals. Why couldn't the Earth simply be a big positively charged ball and we're stuck on it like bits of paper attracted to a charged comb? At first blush this should be readily plausible. A large enough charge below our feet would most definitely create a downward force which acts like the force we call gravity. None of this quantum/thermodynamic/messenger stuff is required.

It is a scientific fact that we live in a divergent electromagnetic field with a field value of about 120 v/m. Between the ground and the stratosphere is a voltage potential difference of at least 300,000 volts. Where does that come from and wouldn't that create an attractive force on us even if the electrstatic force isn't gravity? At the very least, it would add to the downward gravity force.

Get beyond the obvious objections, because if gravity = electrostatic force that would be the best type of unification there could be. That is why it is so attractive and still worth pursing - even if everyone else has given up on it.

fhblogger said...

Another interesting aspect of gravity is that experiments appear to show that gravity has no effect on electrons. Isn't this a massive violation of the equivalence principle? If you put an electron and a neutron side be side and the neutron falls while the electron does nothing, that greatly violates the equivalence of gravitational and inertial mass.

If it is true, it would indcate that only matter consisting of mixed dipole charges are affected by gravity. Why should this be? This might be true if gravity is just a divergent electric field which only acts on the dipoles.

Bee said...

fhblogger: Please read our comment rules. This is *not* a place to discuss your own work. The topic of this thread is Verlinde's paper. I will delete further off-topic comments. Thanks,

B.

Plato said...

Just throwing it out there.

Gravitomagnetism

--------------------------------

I mean it is difficult for us layman to understand, so it may be a brain fart for some , but we all reserve the right to change our minds:)

Two-dimensional conformal field theory

Planck scale Geometry? Who ever heard of such a thing?:)

Applied Conformal Field Theory

--------------------------

Is there no progressiveness in geometries that move to higher dimensions?

They are just total abstractions then, while we seek to find it's comparisons in the real world

Planck scale is not real?

Best,

Steven Colyer said...

Back to Verlinde! Hi, Bee. I was cruising the arXiv recent papers last night at hep-th, and came across this interesting March 9th paper by Andrew Randono and Leonardo Modesto, here.

The reason I point that out is their very concise overview of the challenges with Verlinde's theory in section I. Introduction.

The rest of the paper is interesting too, but I pointed it out for the Intro and wonder what your thoughts on that section are.

As for the rest, near the end they somehow tie it into MOND, or at least the Tensor-Scalar-Vector relavistic portion known as TeVeS. Quite unfortunately, TeVeS has apparently been completely discredited, as you can see in another article I came across, here.

Your thoughts on that article would also be appreciated, especially: what the heck is f(R)? Is that from Moffat's MOG?

Bee said...

Steven,

Ha :-) What would I do without you? You know, I'm actually supposed to work with Leonardo (like: right now). He told me about his paper with Andrew, but I totally missed its appearance on the arxiv. (Too much traveling increases my temptation to hit "mark all as read" in my feeds.) So when I talk to him later I should congratulate on finishing the paper. In any case, I haven't read the paper, so don't ask me what it says. Best,

B.

Steven Colyer said...

Thanks, Bee. Well fortunately it's only 8 pages long and shouldn't take long to read. It's very concise and informative, and although they tie it to MOND at the end, that may not be necessary. John Moffat is still at Perimeter, yes? So I ask: can it be tied to MOG?

The paper may have legs, and my intuition says it will. No, I'm really not qualified to understand the paper beyond the abstract and the introduction to the introduction and the Introduction itself, yet, but sometime ye olde brain neurons work in ways we don't quite understand, but "feel" are right (cozy), and that's what I call: "intuition."

I'm pretty much trying to decide what to specialize in, Bee. It sucks being a generalist (my default condition) and not getting paid for my thinking. The world doesn't pay generalists well, if at all. But I'm getting closer. No worries, Bee. We'll get to the promised land, someday, if not nearly as fast as we'd like, then eventually. Speculation will lead the way, then experiment will confirm sooner or later. Takes time, alas. So be it, shrug.

Bee said...

You could try specializing in generalizing ;-)

Plato said...

.... and you've reached a perceptual plateau.? There is no going back because you have set the parameters with which you shall deal with the world?:) It's just the way it is.

And if you wanted to claim that because of this problem with the negative factor, the S-matrix for gravity in d>=4 can't exist, then I hope that everyone would agree that such a statement has already been falsified. String theory does reduce to GR in the infrared, and its calculation of the S-matrix is obviously not invalidated by the kind of problems that you describe.Wick rotation

It's all about science, not personalities?:)

Best,

Steven Colyer said...

You could try specializing in generalizing ;-)

lol, right Bee. Except I've already done that since thanks to to this yours and Stefan's blog, I've already met the two philosophers anyone need ever meet, those being Plato and Warnell.

And so with THAT behind me, I can focus on the Science, and it's best tool, what's it called? ... oh yeah, ... Mathematics.

Yum.

Phil Warnell said...
This comment has been removed by the author.
Phil Warnell said...

Hi Steven,

I would agree that generalists are not paid nearly as well as specialists, yet because of the breath of what they know as opposed to the depth. that has them generally more employable. This could also be attributed to the potential of the second law, rather than its action which is to find equilibrium as having the generalists being in compliance, while the specialists stand in defiance,-)

Best,

Phil