The Myth of Gravity

Remember that statistical mechanics is based on time reversible mechanics, such as Boltzmann statistical thermodynamics is based on Newtonian mechanics. Newtonian mechanics is time reversal since F = ma for a = d^2r/dt^2 remains the same for t  -t. Statistical mechanics is based on adiabatic variations, which in a quantum mechanical setting means that energy levels and states are not destroyed. For quantum field theory and further with stringy black holes there are regularization procedure put in place so that an accounting of these states is possible. The entropy of a black hole is an adiabatic invariant and so the quantum states which compose the entropy S = -k*Σ_{mn}ρ_{mn}log(ρ_{mn}) are preserved. So an accounting of the degrees of freedom for a system is correctly performed. So on a fine grained level there is no loss of information. On that level Lubos is right, but there is still entropy associated with gravity or the area of black holes. Lubos is citing situations where we have a fine grained accounting of states invariant under adiabatic variations.

Where things get sticky is with the large scale and black holes. An exterior observer can't readily observe the quantum states which compose a black hole, and certainly can't enter the BH interior and bring back a report. So in effect there is a coarse graining which occurs here. Now suppose you have a spherically symmetric distribution of matter that has a black spherical "cloak" around it. This cloak is a sort of Gaussian surface we imagine that has been painted black. Birkhoff's theorem tells us the gravity field of this distribution is that of a Schwarzschild black hole, and we conclude that the entropy of states inside this black Gaussian surface is given by the Bekenstein entropy S = k*A/4L_p and A = 4π(GM/c^2)^2. Now if we peel off the black surface and look inside this has no bearing on the physics of gravity, even if we can make now an accounting of matter-states in the spherical distribution --- say it is some elliptical galaxy. This means from the perspective of gravity the entropy is the same --- which is the nature of the entropy force of gravity. Gravity is "blind" or coarse grained with respect to the particular distributions of matter-fields, which can be a star or the strings tied to the stretched horizon of a black hole.

So the area theorem of black holes dS/dt ~ dA/dt >= 0 in classical gravity or general relativity still tells us that on this coarse grained setting there is a thermodynamics to gravity. So in a curious way we can have our cake and eat it too. We have a field theory which is causal and preserves information, but which on a large scale, coarse graining or equivalently a classical treatment of black holes obeys the laws of thermodynamics and dS/dt >= 0.

Cheers LC

I'd compare Verlinde's model to epicycle model, which is incomprehensible, but formally (at numeric level) works well, although it's describing dual model (heliocentric model) in fact. So if we ignore the fact, gravity has an opposite sign regarding to entropy, we can consider Verlinde's model as it is.

But the understanding of celestial mechanics is on the dual side - in the dense aether model of vacuum itself. If we consider Universe as a interior of black hole, we are forced to consider vacuum as a very dense gas, filled by foamy density fluctuations of hyperbolic geometry simmilar to foam (you can mix watter and sugar solution to imagine it). These fluctuations manifests itself like CMB noise in vacuum. The light would spread through such foam in two dual ways, thus creating an illusion of expanding space-time above CMB wavelength scale, whereas space-time bellow CMB wavelength scale would collapse instead.

In accordance with this geometry, the noise of CMB fluctuations is gradually evaporating all objects smaller then the CMB wavelength, whereas all larger objects are condensing under omnidirectional pressure of this "ultramundane flux" in accordance to ancient Le-Sage theory. This is why every action of gravity force is followed by glowing, i.e. by radiation.

And this is what the entropic model of gravity is really about at intuitive, physical level.

You're right. It's just you who didn't understand. The points Motl raised are well known physics.

Tom

Zephir, The heat capacity of spacetime is negative. For this reason entropy increases with lower temperature and it accompanies collapse.

Equilibrium is not possible either. A black hole sitting in a background with a certain temperature and which emits Hawking radiation at the same temperature is not at eqilibirum. This is contrary to our standard expectations. The reason is that if the black hole emits a photon it get smaller and the entropy S = A/4L_p decreases. However, the temperature also increases, meaning the black hole can emit more photons. So the black hole emits more photons, gets hotter and ... . Conversely if the black hole absorbs a photon from the environment it gets colder, higher entropy and has a higher probability of absorbing more photons.

Cheers LC

I still don't see any connections of gravity to some interference. I'm particularly interested about it in connection with red shift quantization.

http://en.wikipedia.org/wiki/Redshift_quantization

http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4885v3.pdf

/* entropy increases with lower temperature and it accompanies collapse ..*/

At the case of ideal gas such dependence is exactly opposite.

we need fun ....and that is going to begin.....Mr London , I need helps....Mr Landau thanks to be near me also and Mr Feynman of course, they need a curse of thermodynamics aznd sphericality sciences ahahah

How can we do for explaining to them with my bad english, bad english but me it's true sciences.

Let's begin with phonons and rotons.....and my spherons of course .Oh my God they need curses of thermo.

ROTATING SPHERES MY FRIENDS AND THERMODYNAMICS KINETICS

THE ROTATIONS OF THE SPHERES EXPLAIN ALL ........THE SOUND AND THE ROTATIONS YOU WANT A CURSE OR WHAT .

Zephir, I don't know how to explain it better than Lubos Motl (26 April 9:04 GMT) already did. I'll make an attempt.

The equivalence principle (of inertial mass and gravitational mass) in general relativity deals with ponderable quantities of mass in relation -- the symmetry of the mutual attraction between them explains the physics of gravity in a field theory without imposing other parameters, because it is the spacetime field that is physically real.

If one tries to introduce discrete energy exchange (i.e., through massless speed of light particles, bosons) as a physically real parameter, one comes up against the fact that there is no elapsed time between these massless particles, therefore no change in the field; measure in any direction at any observer velocity, and the speed will be the same. All that we know about gravity so far is classical physics alone.

Now you know the two-slit experiment, right? This is the heart of quantum mechanics. The two slit experiment informs us that bosons communicate holistically; i.e., these massless particles make coherent wave patterns from discrete units in statistically predictable ways.

Lubos is saying that Verlinde cannot get a workable field theory that includes mass, because if one makes information a physical parameter, it is wavelike, while the deterministic interactions of classical gravity are particle-like. So we are stuck with the same problems of unification that we always had, plus--Lubos claims--an additional problem of incorporating time into the theory. Time in classical physics is a simple parameter of reversible trajectory; in non-relativistic quantum physics, time has no meaning. So when we start talking about information entropy (whose mathematical model is identical to energy entropy) as physically real, we lose time conservation--a fundamental symmetry principle.

Gravity is not physically real in classical physics. If one wants a field theory in which gravity is identical to physical information and information is dissipative, then gravity has to be physically real. There goes the spacetime field, though, because of the nonreversibility of the time parameter.

I know that Lubos Motl's objections are sound, and must be successfully countered. However, I favor Erik Verlinde's and Ted Jacobson's approach -- why? Because I see the answers in a model that exploits what Hawking & Hartle found 30 years ago -- that imaginary time preserves both time reversibility and time asymmetry in a field theory.

If you're interested, my paper "On breaking the time barrier," is here

Tom

The concern over mass is something which is important, for it is the IR part of the theory and has a correspondence with the UV scale. To illustrate something about this I outline the physics in some detail here

A sphere of area A will contains N = A/L_p^2 units of information. The equipartition theorem is E = (1/2)NkT, where E = mc^2, and T the Hawking Unruh temperature,

[math]

T~=~{1\over{2\pi}}{{\hbar g}\over{kc}}

[/math]

The work-energy theorem of mechanics E = ∫F*dr gives Newtonian gravity

[math]

g~=~{{Gm}\over{r^2}},

[/math]

and Newton's second law F = mg.

A surface area at the Bekenstein limit due to quantum black holes is a summation over all eigen-numbers of Planck units of area

[math]

A~=~c\sum_{i=1}^Nn_iL_p^2~=~c\sum_n A_nL_p^2,

[/math]

where n = n_1 n_2 ... n_N contributes energy E_n = cnħg/4πc. An accelerated surface is degenerate according to a partition function

[math]

Z(\beta)~=~\sum_{n=1}^\infty g(E_n)e^{-\beta E_n}.

[/math]

The average energy is

[math]

\langle E(\beta)\rangle~=~-{\partial\over{\partial\beta}}ln~Z(\beta),

[/math]

and the entropy

[math]

S(\beta)~=~k\Big(ln~Z(\beta)~-~\beta{\partial\over{\partial\beta}}ln~Z(\beta)\Big),

[/math]

from which the characteristic temperature for a phase transition of an accelerate surface is

[math]

T_c~=~{c\over{4\pi ln~2}}{{\hbar g}\over{kc}},

[/math]

where c = 2 ln2. The energy for N --> ∞ is ( |E| ) = 0 [here ( and ) used for bra-ket notation] for T \lt T_c. A critical point occurs as T --> T_c, with production of quantum black holes from the vacuum. For large N the result approximates E = NkT.

This theory then lends itself to phase transitions. I recently submitted a paper on this, but I can outline what happens from here. The stretched horizon is a place where strings which compose a black hole are "frozen" and have an effective mass. The string's mass is just its energy which is confined on the stretched horizon. The elementary analysis with the critical temperature indicates a possible phase transition, indeed a quantum critical point or phase transition. The analysis is done in a fairly straight forwards way with extremal black hole and the analysis of the spacetime near the stretched horizon. The physics for fields or strings that enter the horizon or quantum tunnel out is quantum physics with a V ~ |x| potential. This has Airy function solutions which satisfy Zamolodcikov's c = 1/2 CFT condition on massive fields. The masses correspond to the (8,1) irrep of the E_8 group.

Cheers LC

Entropy means that energy of the system tends to be distributed in a homogeneous way. In the universe energy of matter and energy of space tends to be distributed in a homogeneous was.

Presence of big mass creates distortion of quantum space and makes space less dens. Smaller mass have a tendency of "gravitational motion" into direction of lower density of space.

yours amrit

For once, I am happy thus hihihi

tivi

That's interesting, Lawrence. Thanks. As I mentioned elsewhere, I think we are going to the same place from opposite directions.

I think your stretched horizon where string field energies originate is the same as my four dimension horizon that I find identical to the 10 dimension limit (which means the energy on the 9 dimensional shell of S^10).

It is of interest to me that your string mass is confined on the stretched horizon, because I think the low energy of our familiar four dimensions in terms of total cosmic inertial (baryonic) mass, which I calculate from first principles to a precise 4.59% of observed cosmic composition (consistent with WMAP data) is explained by this hyperspatial fraction of length 1. Your string field masses that originate in the quantum vaccum on the event horizon -- and this tiny fraction of 10-dimension length 1 -- explains the low energy content in that as our world becomes more ordered, disorder increases in dimensions > 4 as a result of information entropy, even as entropy also increases in our own world. IOW, only our unique dimensionality can sustain open systems ("life") within a universe in which entropy can only increase.

Exta dimensions need not be compactified in this model -- we need only a sphere packing with an order normalized on 4 dimensions in which information monotonically decreases as the counting order (entropy) increases. This is consistent, I think, with Zamolodchikov's C-function extended to n dimension space > 4, if I understand correctly.

I think the problem you're going to run into is the treatment of spacetime near the horizon. I don't think you can avoid singularities, with infinite mass density. (I try to get around this by proposing a continuum of mass identical to quantum unitarity, which implies negative mass and imaginary time.)

Tom

Dear Craq...you say .Gravity is always attractive, entropy is always increasing. ....alleluia .Attractive and sorting .....

Regards

Steve

Tom,

I have to make this somewhat brief. I remembered to look here a bit late in the day. The concept of strings on a stretched horizon was first suggested by 't Hooft and developed by Susskind. A generalized version was worked out by Maldacena in supergravity, called the AdS/CFT correspondence.

The Verlinde results fit into this picture pretty well. All that I have done is to illustrate there exists a phase transition associated with this entropy force of gravity with black holes. This does go a bit further, for the Hagedorn temperature at the T ~ 1/L_s (very large) is the UV correspondence temperature at high energy to the IR temperature for the quantum critical point. So the broken symmetry phase theory at the IR domain is dual to a UV theory where the symmetries of the vacuum are those of the Lagrangian.

Cheers LC

Lawrence, you wrote, "So the broken symmetry phase theory at the IR domain is dual to a UV theory where the symmetries of the vacuum are those of the Lagrangian."

Yes, that is what I am getting at with the quantum mechanical unitariness of the mass continuum. In order to have such a continuum, however, one must define a length 1 radius on the complex plane, because the minimum measure of 2 dimensions (complex analysis) drives the real measure of the 1-dimensional metric whose range is minus infinity to plus infinity. Wherever we arbitrarily cut that line (by measurement in real analysis), is real; however, negative spacetime of 2 dimensions is the necessary generator of the physical measure function.

The price one pays to get here is negative mass and imaginary time. I find that result to be less exotic than one imagines.

I am persuaded that the simplest mathematical support for supersymmetric phase transition and resultant broken symmetry is a model in the extended complex plane.

Tom

The E_8 lattice or root space has the symmetries of the group. This is a remarkable property of E_8. This means that the lattice, which has a toroidial topology is a compactified versions of the the space of E_8. The uncompactified version can be thought of as similar to a repeated set of tiles, while the compactified version is where one of the tiles is rolled up into a torus. This is an aspect of the UV/IR correspondence. The Golden mean ratio of masses for the (8,1) portion of the irreducible representation of E_8 are the low energy IR theory, and equivalent to the high energy conformal E_8 theory.

The low energy theory describes one aspect of the string spectrum as measured on the stretched horizon. The lowering of the gravitational coupling constant, say we do this in an adiabatic manners with G --> 0 reduces the black hole to a gas of free strings with the E_8 symmetry. Similarly, if the mass of the black hole is reduced to zero the energy of the strings on the horizon approaches the Hagedorn bound. So this is the UV limit of the strings when the black hole is "evaporated."

Imaginary time is involved with the partition function for the UV limit and the Hagedorn temperature it corresponds to. I will try to spell this out in greater detail later on. Writing the TeX macros is a bit time consuming, and yesterday for some reason one of them did not work right. Oddly the file I wrote it on has no error

Cheers LC

Dear Tom,

I have also been playing with imaginary time and unusual masses. At this point, I think it is imaginary mass (or negative mass-squared - I think that mass -squared is the more appropriate relativistic quantity with which to work).

I am also approaching the problem from a different angle from you and Lawrence. And although we three might disagree on specific details, I think that our general approaches may be converging.

Have Fun!

Ray

Dear Lawrence,

I could see scale invariance and/or S-duality relating UV and IR divergences. The AdS/CFT correspondence also works well with scale invariance. But which AdS/CFT model are you using? If you are using AdS_5~CDF_4, then I think we need a minimum rank-4 transform, so that J^3 - by itself - is insufficient. In my opinion, this infers a minimum of 28 dimensions. Perhaps at some higher energy scale, this is equivalent to a G2 of Quantions and/or Pauli Matrices.

Regarding Verlinde's work, I think that "probablistic" interpretations of data are due to a smearing of phase space that is caused as extra dimensions collapse and/or decouple from Spacetime. Thus, "probabilistic" interpretations such as Quantum probablilities, and Statistical/Thermal probabilities are a property of our decoupled Spacetime. Because Spacetime Curvature and General Relativistic Gravitation are related, we should expect spacetime properties to be relevant. However, if Quantum Gravity (and Mass) originate in Hyperspace, and are transformed to Spacetime, then we should not expect to see a true and complete picture of Quantum Gravity in our decoupled Spacetime. We can only see part of the bigger picture clearly, the rest is "fuzzy" thanks to probabalistic interpretations. In a sense, you and Lobos are both correct in that Verlinde's ideas may model some features of Gravitation, but probably not all features of Quantum Gravitation.

I am trying to organize all of my "crazy" ideas on extra dimensions.

Have Fun!

Ray

Hi Steve, you're the very first case of public support of my person after five years of spreading of my ideas on the net. From some reason people are refusing to consider, we are composed of random particle stuff - the entropy is apparently more illustrative concept for them.