The Myth of Gravity

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.

One aspect of gravitation, of which there seems to be two widely diverse schools of thought, needs clarification, at least for myself. I could quote numerous authors on either side of this "argument" but, according to Einstein's GR, which is it?: Is the curved spacetime nearer a massive object "stretched", therefore "less dense", or could it be considered Lorentz contracted in the direction of the massive object (as well as time dilated)? Please pardon my ignorance and help me resolve this concept.

Sincerely,

Steve

Dear Lawrence,

Perhaps a 4-D transform operator first decomposes into a J^3 X U(1), which are then subsequently broken such that this U(1) yields the axion.

Lawrence/Ray,

I think that the only unpatchable difference between us, is your emphasis on the lattice as a physical agent. I admit I am weak in group theory; however, I can't reconcile any kind of rigid rotation with my hypothesis. My model aims at the basis for a nonperturbative field theory.

This, because my time dependent model is smoothly continuous (by analytical continuation) across the spectrum of complex plane connected spheres, infinitely self similar and scale invariant. The appearance of discontinuity in the real domain occurs on the boundary of connected sphere kissing points as random structures.

As I indicated in my ICCS 2006 paper, the exchange of a discrete point for a continuous curve is at the closest contact of kissing spheres. Because there is no way in principle to distinguish a straight vertical line from the zero boundary of kissing spheres of infinite radius, the imaginary axis is independent of dimension boundary conditions. The real axis, then, is the domain, minus infinity to plus infinity, across the equator of the complex sphere, with trivial values 1, - 1, i. IOW, the extended complex plane is sufficient to fix the origin of length 1 in any dimension > 3.

That the approach to length 1 in hyperspace (d > 3) is asymptotic and dissipative over n dimension kissing Euclidean spheres, supports time dependence. I.e., connected spheres and their external boundaries comprise the total inertial energy content of a particular sphere kissing group. When we normalize the order on S^2 = 0, the four dimensional S^3 and succeeding dimension groups, is length 1 in the asymptotic limit. The time metric is analytically continuous through the kissing group boundaries, with a correspondingly slow growth of inertia as a percentage of length 1. (This is why our low dimension reality has low inertial mass.) Inertia increases proportional to the increase in kissing number.

For this model to be coherent, however, time originates in the imaginary part of the 2 dimensional (complex) plane and space in the imaginary part of the complex (Riemann) sphere (which is the extended complex plane) -- IOW, spacetime indistinguishable from space alone; space and time self organized on the complex sphere. This is explained in detail in my "Time barrier" paper.

I hope you can see from the above, why I do not accept the physical reality of fractal shapes and lattice constructions. These are random products of inertial energy exchange, not physical causes. The n-dimensional kissing order is integral, algebraic. Symmetry is emergent, not creative. The time metric, positive and Lebesgue measurable, is continuous; because I find the 4 dimension horizon identical to the 10 dimension limit, however, we should be able to demonstrate extra dimensions using quantum computing. That it, the qubit information unit (0,1) is an absolute complex plane zero and absolute length 1, independent of dimension boundaries.

Once quantum computing is here, which shouldn't be too long now, one good thought experiment input into the program will settle the validity of quantum field theory cosmology, and its string theory extension, beyond reasonable doubt.

Tom

Steve Clark,

Remember that in general relativity, there is no preferred frame of observer reference. Every inertial frame is valid.

Tom

Hi Tom,

We almost have similarities. You are focusing on the Cardinal numbers, Steve Dufourny is focusing on the Prime numbers, and I am focussing on the Fibonacci and Lucas numbers (I know - you haven't seen my Lucas number results but this turns 'fractals' into 'integers' while admiting scale invariance, and I want integer symmetries to tie in with standard Group Theory and not have to use something as 'radical' as El Naschie's E-Infinity theory). I am certainly OK with complex numbers, but I'm not sure about the compatibility of smooth continuous functions with Quantum effects. Which is more fundamental - a discrete quantum Universe or a continuous classical Universe? Lawrence and I tend to think that the discrete quantum is more fundamental than the continuous classical. I think that smeared phase spaces caused by the collapse and decoupling of unseen extra dimensions causes discrete quantum (possibly lattice) effects to appear probabalistic and continuous. Perhaps you think that the Universe is smooth and continuous, but measurements give a discrete effect. Perhaps your studies will lead you to an interesting semi-quantum probabalistic Universe, but I don't think you are on a direct path towards the GUT or TOE.

Kissing spheres leads to lattices and a sphere (vertex) - string (strut) duality that likewise leads to particle - wave duality.

Hi Lawrence,

Are you working with an AdS_5~CDF_4 model and wouldn't it require a 4-D transform?

Have Fun!

Ray

Thanks Tom,

What I'm trying to ascertain is whether a "stationary" observer at some distance from a "stationary" gravitational field would perceive a measuring rod near the surface of the gravitational mass (but not in motion relative to the observer) to be shorter (Lorentz contracted) in the direction of the gravitational "force", as compared to a measuring rod of equal length at the observers location. I understand that for time dilation it would be so, that a clock in the gravitational field would tick slower than at some distance from the field, but would length contraction also occur?

Thanks again,

Steve

Steve,

Again, you're forgetting that there is no preferred frame. Also, what is true for clock dilation/contraction is also true for rod dilation/contraction -- they are different ways to measure the same phenomenon; spacetime is a physically real field continuum in which an observer at rest records different results than an observer in motion, yet in which we know that we share the same spacetime, by a mathematical operation called the Lorentz transformation.

For these questions, you should get a basic nontechnical book on relativity theory. I think Einstein's classic, Relativity: the special and general theories, although published long ago, is especially clear, to my memory. I make this recommendation knowing that a great deal has been written about general relativity in the last 100 years that often skips the basics and misleads by omission.

Tom

The lattice is in a way non-physical. It is entirely frame dependent, unlike a solid state physics lattice, but is something which is gauge dependent in a non-covariant way. The lattice does though define a moduli space and curvature.

Cheers LC

Hi Ray,

My hypothesis is not based on cardinal numbers, prime numbers or numerology in any form. I use cardinality to describe boundaries of dimension sets, a counting order of discrete ordered and symmetric points of n dimension Euclidean space. Though I do use a prime number structure of Sophie Germain primes, it is to define the compact, nonorientable plane of recurring singularity (equivalent to RP^2)in the evolving counting order. IOW, the underlying spacetime manifold of measure zero is the engine of change in a dynamic system; because this manifold is integral, nonorientable, compact and 2 dimensional, it is smoothly continuous with scale invariant n dimension space. This is detailed in my "time barrier" paper.

Because we know that space is mostly smooth, Euclidean, in the 4 dimension relativistic limit, if we allow 2 dimension analysis in the quantum limit then we get a unitary result for 4 dimensions and measure zero in 3 dimensions. Here's how:

In my kissing number model, the 4 dimension kissing number (24) is normal 1. The kissing number in 3 dimensions (12) is zero, and in two dimensions (6) is - 1. So in a colloquial manner of speaking, we get "4 for 2" dimensions by introducing complex analysis and consequently, system dynamics.

You ask, "Which is more fundamental - a discrete quantum Universe or a continuous classical Universe?" I answer, a contiuous scale invariant universe of discrete self similar quanta. There is thus no quantum-classical boundary -- there is coherence and decoherence at all scales, based on continuous subsystem cooperation and decoupling.

You say, "Perhaps you think that the Universe is smooth and continuous, but measurements give a discrete effect." Certainly so. It could not be otherwise in a relativistic quantum model, because we must convert continuous functions to discrete measures.

And, "Perhaps your studies will lead you to an interesting semi-quantum probabalistic Universe, but I don't think you are on a direct path towards the GUT or TOE." On the contrary, I expect my model to rehabilitate classical determinism in a supersymmetric quantum field theory. We just have to get used to manipulating calculations of negative mass and imaginary time. I don't have the ambition to explain nature in terms of a GUT or TOE -- I think that nonlinear evolution will always harbor potential surprises, even in a metastable universe.

"Kissing spheres leads to lattices and a sphere (vertex) - string (strut) duality that likewise leads to particle - wave duality." Yes, my "time barrier" paper also notes this result.

I don't know what you mean when you say that the lattic is "in a way" non physical. Either it is independent in its physical properties, or it is not. I know what you mean when you say the lattice defines moduli space and curvature. I hate to keep referring to "time barrier," but this result is also in there.

Tom

Lawrence, I apologize for confusing you with Ray on the lattice question.

Tom