Tom,
Clearly nonperturbative theory requires superspace considerations. This is where MWI does manage to have some possible context. With multiple cosmology (multiverse) considerations there are at least some nonlinear gravitational aspects to this. In this setting MWI might have some measurable context, as the eigen-branching might be associated with a unique metric back reaction, which is at least in principle detectable.
In fact this connects up with solitonic physics on the gravitational brane (D3 or D4 brane) with an underlying quantum physics, but a largely classical structure to spacetime. In other words gravity is not quantized, but is a semi-classical and classical physics which emerges from an underlying quantum field theory. The structure of this type of theory and has connections with 2-dimensional systems like graphene. Much of this stems from well understood physics.
The k = -1 curvature manifold in two dimensions, the Poincare disk, half-plane or hypersphere, describes by the Gauss-Codazzi a wave motion governed by the sine-Gordon equation
∂_{tt}φ – ∂_{xx}φ = sin(φ)
which is a fascinating equation. This is usually written as
∂_{uv}φ = sin(φ),
for u = (x + t)/2, v = (x – t)/2. This describes the motion of a particle with the line element
ds^2 = du^2 + dv^2 + 2cos(φ)dudv
which is the AdS_2 spacetime for the hyperbolic replacement cos(φ) – -> cosh(φ) with the sinh-Gordon equation ∂_{uv}φ = sinh(φ).
Exact quantum scattering matrix for this sine-Gordon equation was discovered by Alexander Zamolodchikov, which is S-dual to the Thirring model. This is a theory of fermions in two dimensions with the Lagrangian,
L = ψ-bar(γ^a∂_a – m)ψ – g(ψ-bar γ^aψ)(ψγ_aψ),
which is a fermionic theory of bosonization — similar to superconductivity. Zamolodchikov solved this theory and removed the UV divergence with the Bethe hypothesis. The solution is S-dual to the sine-Gordon equation. This points to very deep relationships with respect to gravitation. Gravitation has as its underlying quantum theory a fermionic quantum system with bosonization (a quantum critical point), where gravitation itself is not really quantized.
This fermion theory, which might be the underlying quantum theory of gravitation (gravitation might not need to be quantized directly beyond a few loop level) is the graded portion of the anyonic field on the two dimensional surface. This is described by a Chern-Simons Lagrangian, which in a more general setting of the 3×3 Jordan algebra describes associators with 3 octonions or E_8 groups. This is the possible connection between graphene and these M-theoretic foundations.
The above fermionic Lagrangian has a bosonization according to Bogoliubov functions. This is a bosonization similar to superfluidity or superconductivity. The interpretation with respect to the emergence of gravity is the onset of decoherent quantum fields in curved spacetime. The emergence of spacetime might then be a phase transition, where the parameter of “disorder” is the scale of quantum fluctuations. This plays the role of temperature if the iHt/ħ is wick rotated i – -> 1 and equated to the Boltzmann term E/kT so the Euclidean time t = ħ/kT serves as the “β” term. So this means the set of quantum fluctuation of the Ferm-Dirac field have a critical point or “attractor,” similar to the condition for a Fermi surface, where there is a bosonization.
Graphene exhibits structure similar to this, and suggests a sort of universality to this sort of physics. In other settings this is also apparent with the quantum phase transition in heavy metal http://arxiv.org/abs/0904.1993 and http://arxiv.org/abs/1003.1728
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It was thinking about the Bekenstein bound that, in part, led me to a complex plane analysis of the initial condition. I.e.:
We are used to thinking of the beginning as a point. We can keep that same idea with extension to the complex plane and C*, realizing that a complex point has infinite expansion as a line, a metric.
The Bekenstein bound defines its limit on the finite radius of a sphere. What I found is that if one considers two kissing spheres of infinite radius and zero thickness, the closest point of contact is _anywhere_ on the imaginary (Y) axis, and defines the C* (complex sphere) origin. Then, when we take the real (X) axis as the equator of the complex sphere, through the origin, we get flat Euclidean regions of arbitrarily finite area.
Then taking my specifically physical definition for "time" ("n-dimensional infinitely orientable metric on self-avoiding random walk") one may calculate boundary conditions as self-limiting, because time is now identical to physical information, in a dissipative system of n-dimension Euclidean kissing spheres.
I've always been puzzled at the lack of professional interest in the Hawking-Hartle imaginary time hypothesis -- which has been around since the 80s -- because I have found no reason for it in all that time, other than the simple belief that "time" is always a real metric. There is no particularly complicated mathematics in the idea of imaginary time, however, and we use Hilbert space complex calculations (absent a time metric) in quantum mechanical calculations, routinely.
Tom
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Lawrence B. Crowell replied on Oct. 15, 2010 @ 01:16 GMT
In some sense we might think of this as a case where one has QCD in spacetime, and there is an addition dimension. We then think of the additional dimension as an AdS spacetime which repels particle fields from its boundary. There is then a black hole in this AdS_5, and the CFT physics lies on the boundary in 4 dimensions. The conformal structure there is equivalent to spacetime isometries. Then the paths leave this domain of massless fields and approach the black hole. Here mass kick in and this renormalization group flow ends. There the AdS_5 breaks into AdS_3xR^2. The AdS_3 is dual to QCD in two dimensions or an SL(2, C) ~ SU(2) QCD-like theory. If we reduce dimensions further we have AdS_4 reduced to AdS_2xR^2, where AdS_2 is conformal structure on the two plane, or the C* plane.
Cheers LC
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Steve Dufourny replied on Oct. 15, 2010 @ 09:43 GMT
Well.
The ads cft link is just a false extrapolation of the string theory.
Thus of course that has no sense.Perhaps only for Princeton, Mr Witten and his team.
Well I am continuing.
This correspondance at bounderaies are just falses.
First a BH is a sphere and its mass is so important.
The gravitational effect my friends.
Yang muills no but we dream or what???
This holographic principle..........Susskind a Hooft are falses, we understand thus why some people work these stupidities at Utrecht also.
Dear scientists...it doesn't exist an equivalence between the strings and the jauge.......be rational^please.You can use maths but please use them well.
We have no proof and we shan't have proof .R 4 and yang mills supersymmetry no but we dream or what all that is false.
The referential and the gravity is in 3D .....????
A real circus all that.and they continue furthermore.
That's all for the moment
Steve
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Steve Dufourny replied on Oct. 15, 2010 @ 09:46 GMT
TIME IS NOT A DIMENSION ! A METRIC ! AN REVERSIBILITY ! .....the relativity is not that.
Think about evolution and increase of mass.
Steve
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Steve Dufourny replied on Oct. 15, 2010 @ 10:04 GMT
The holographic principle is a conjecture where the informations aren't understood really.
The gravitational system sorts these informations, as a BH for example.
Vever the system, intrinsic and its volume can be analyzed with only this boundary where furthermore the evolution is not taken seriously.
Mr Susskind and Mr Hooft continue simply a false work.
Please don't use freedom degrees without real plysical sense.
Boltzmann k and the entropy dear friends .Let's link with thermodynamic please.You know PV ....k ...nRT .....1/2mw².....the mass is a fractal of rotating spheres....vivrations,rotations.....Avogadro will understand what I say.
A and S .......and the distribution of mass and energy is proportional simply....Bekenstein ????
If A is proportional with events thus the system is analyzed in its globality not in its locality, because a BH has a rule of balance and of evolution.
Thus the proportionalities must be rationalized.
A computer and its bits of informations is more simple than our Universe !!!The volumes , finites and the rotations dear scientists.
Steve
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T H Ray replied on Oct. 15, 2010 @ 12:07 GMT
Lawrence,
It's gratifying to see that we have arrived at the same place.
Though my mathematical model is algebraic, the AdS/CFT correspondence is explained just as you describe it, on the 4-dimension boundary where negative mass and imaginary time explain cosmic binding energy and mass defect; i.e., the presence of ordinary (baryonic) matter is actually an anomaly in the n-dimension set of self organized universes, even though it comprises all the interesting phenomena we analyze in particle physics.
Details in my "time barrier" paper 2.9 through 3.7 and sidebar 3.
Tom
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Lawrence B. Crowell replied on Oct. 17, 2010 @ 22:20 GMT
I guess I missed this earlier. The AdS spacetime with a black hole has a negative mass for a range of BPS parameter. However, this is really a sort of mass gap. This probably does have something to do with the mass-gap problem in gauge theory.
Cheers LC
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Steve Dufourny replied on Oct. 18, 2010 @ 10:41 GMT
The fundamental problems of these extrapolations seem lost in the confusion of reality.
As a mist voiceless, like a gray cloud and bitter.
AdS spaces with their hyperbolic extentions, Lorentz would agree with the restriction of the referential.
We can invent, extrapolate, differentiate, overlay .. but our main field is what it is.
Take arguments and Cartesian coordinates.
If for example we stipulate that x, y and z are coordinates of the point.
how could you represent the geometry with x, y, z ,......, t?
We are in the heart of general relativity with the cosmological constant.
And therefore it is imperative to respect the gravity and proportionality.
We are in need also to include the evolution and its dynamics,specifics. Integers and thus reveal their first dance in a closed system evolving.
The 3-dimensional sphere is the best explanation of course.
The time will never be a certain irreversibility with loops and speudos dimensions.
You can invent all the matrix you want, our intrinsic laws will not change.
There are no other redundant dimension, the sphere in 3D and its time constant are fundamental.
All math games remain in this universal logic.
Take a hyperboloid of one sheet, we have real and imaginary axes, but this remains purely in 3 dimensions.
If you extrapolate with the infinity inside a closed system, you shall see the generatrices and the real geometrical form.An infinity inside a system is different than an infinite system itself ???? This point is very important,even foundamental.
Think about the transition of hyperboloids and ellispoids .....x²+y²+c²=a²....your quotient are just falses imaginaries..
In fact in all paraboloid, hyperboloids, ......it's the sphere the referential.
The symmetries are in 3 dimensions.And the time is not a dimension.Even with some parameters inserted inside the system.
How can we understand the cosmological constant without the evolution and the spherization.That seems not possible.
I am surprised sometimes with some analyzes or interpretations of datas.
Steve
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T H Ray replied on Oct. 18, 2010 @ 14:35 GMT
So Steve,
You live in a 2 dimensional world? Or you just have a position in 3 dimensions of space, but no position in time?
Tom
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Steve Dufourny replied on Oct. 18, 2010 @ 14:50 GMT
I accept simply my foundamentals me.I don't imagine an irreversibility of time due to a symmetry of n dimensions.
When I study evolution, I see the increase of mass and the real complexification.
And all that is in 3D.
All what you know is in 3D ,even your n dimensions which are in fact just imaginaries are in 3D.But the reals are the referentials.
When Einstein spoke about space time, Him he understood the evolution.
If you misinterpret the gravity furthermore, wawww oh my god.If the gravity and the time aren't understood , thus there is a problem in your line of reasoning.
The time is a duration, a constant, and never it's a dimension at my knowledge and for all results or datas.
What I say is very simple,we must accept our results and we must interpret corectly our UNIVERSAL SPHER AND ITS QUANTUM SPHERES AND ITS COSMOLOGICAL SPHERES.
The cosmological constant will be better understood with this gauge.
Steve
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T H Ray replied on Oct. 18, 2010 @ 16:21 GMT
Steve,
Did you not understand the question? If you don't have a time coordinate in 3 dimensions, as you implied in your original post, do you live in a 2 dimensional world with a time coordinate (i.e., a 2 + 1 dimensional reality) or do you live in a 3 dimensional world with no time coordinate (i.e., you exist in space but not in time)?
Tom
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Steve Dufourny replied on Oct. 18, 2010 @ 17:25 GMT
TH,
Do not return this question in reverse.hihih
The time is not a metric graph.
You can not interpret the time in that way.
The time duration is a constant in its locality as in its whole or globality if you prefer.
I live in a world in 3 dimensions (x, y, z) and the time has nothing to do with geometry, I think.
Have you ever read the book by Prigogine about time?
Do you see an irreversibility of time in the thermodynamic???
Steve
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T H Ray replied on Oct. 18, 2010 @ 18:19 GMT
Steve,
Yes, I am familiar with Prigogine. More on that in a moment.
If you know Einstein and classical physics, however, you have to understand that continuous functions demand time symmetry; i.e., equations that describe motion in one direction work just as well in reverse. E.g., the laws of physics would not change if the Earth orbited the sun in the opposite direction (called mirror symmetry). Why is the conservation of time symmetry important? -- answer the question I put to you. You should see that besides having a position in space, you also occupy a position in time. Were it not true, you could live in a dimension outside of the spacetime we observe, and choose to time travel wherever and whenever you wish -- you like that idea? What prevents you from jumping timelessly all over the universe, is that the time coordinate is just another point in 4 dimension (or as we usually say, 3 + 1) spacetime. Even though reversing your trajectory doesn't take you backward in time, mirror symmetry nevertheless guarantees you a definite measure of where you are in time. Otherwise, the time coordinate would not be connected at two points and therefore wouldn't be a coordinate at all; just as each spatial metric has symmetry in opposite directions, so does time.
Prigogine's work in irreversible thermodynamics describes the behavior of energy in a thermodynamically open system in which entropy decreases with energy input and spent energy dissipates into the larger environment. Energy throughput, in other words, is continuous, as in the classical system, but time reversibility is denied because the system is time-dependent. That is, e.g., if the sun, which powers biological life on Earth, were to disappear, so would the system. But the universe goes on. Prigogine's result validate the self-organizing mechanics of the universe.
I assure you, these descriptions are rational and the mathematics is sound.
Tom
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Anonymous replied on Oct. 19, 2010 @ 09:54 GMT
TH,
It's great that you have read this book on rational time.
I think you focus on a road to no avail.
A simple way of speculation and irrationalities for me.
Your first mistake is to regard this time as a pure dimension.Thus your algebras and geometry and topology and correlations with laws aren't founded.
So I understand your confusion due to "various mirror symmetries" inserted in a system loosing its fundamentals and its fondamental equations.
It also seems that you confuse the reversibility of entropic energy (and its duration and its evolution encoded) with the "irreversible time".
This is easily explained by the fact that you use your tools and referentials awkwardly.
Your topologies and correlations with gravity aren't rationals thus in simple conclusion.
The "energy conversion" of a pure mass division is totally different from a "symmetric fractal evolutionary time".
The entropic principle has its laws where confusion does not adhere.
I think humbly that time is very misunderstood in its universality.
This constant allows the harmonic construction, with Spherization.
We can travel in space but not in time.
You confound the internal clocks....rotating spheres.....and the irreversibility of time.
Steve
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T H Ray replied on Oct. 19, 2010 @ 11:02 GMT
Steve,
I guess the better way to try and get you to understand the issues is to point in the direction of Emmy Noether's first theorem. She showed that symmtery under time translation implies energy conservation. If your theory abandons energy conservation, that would be interesting.
Tom
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Anonymous replied on Oct. 19, 2010 @ 11:52 GMT
Ahahhah I guess the best for you is to restudy your foundamentals , and perhaps you can try to encircle the real sciences.
At this momment all is pseudos sciences, it's not interesting in fact really.
The only thing I find interesting is to proove you what all is false about your line of reasoning.It's logic you confound all.
Sincerely
I will arrive for this theorem..she showed what ??? a time machine, don't misinterpret her theory !.the conservation of energy you say, well think about ROTATING SPHERES AND THEIR IRREVERSIBLE MASS ALSO AS TIME.I Guess you haven't studied evolution,if it's the case, don't hesitate to study it.
HIHIHI
Steve
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Steve Dufourny replied on Oct. 19, 2010 @ 17:18 GMT
It's interesting that.
you say "She showed that symmtery under time translation implies energy conservation"
Well that needs explainations because if the evolution isn't inserted ,thus could you develop???
THE LAWS OF CONSERVATION.......WHERE IS TIME ???
In fact you must consider that the invariance by translation in time implies a conservation of E.Ok for the motion and angular moment and thus my spheres ....but where do you interepret that time is as you say,
when Eisntein said that this concept was splendid ,that do not stipulate what you say about time.
You can use it for spaces or mass or charges or....the symmetries are ok but not for the reversibility of time as a dimension.It's purelly not possible sorry but it's as that.
Steve
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T H Ray replied on Oct. 19, 2010 @ 17:29 GMT
Steve Dufourny replied on Oct. 19, 2010 @ 17:38 GMT
You are comic, it's all your answer ?
Think by yourself dear TH really ,I insist about conservations of E ,read above and answerhihihi
Steve
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T H Ray replied on Oct. 19, 2010 @ 18:14 GMT
Steve,
You shouted at me, "THE LAWS OF CONSERVATION.......WHERE IS TIME ???"
In the link I provided, if you read the material under "Neother's first theorem" you will have your answer.
If you know it all already, then you should know that your assumptions are wrong.
Tom
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Steve Dufourny replied on Oct. 19, 2010 @ 18:23 GMT
ahahah you are a specialist of irony.
My assumptions, mine are rationals.
Yours no.
You bad interpret this theorem.And lika all people I learn all days.But not these stupidities.
The conservation of laws, equations,constants,E, motion, rotations, moment........are so importants.You confound a graphical symmetry and our evolutive symmetries of time.The relativity dear TH helps to see our past and to see the real dynamic of evolution.But never we have reversibility of time,you confound a picture of our history and the reality objective of our Universe.
The translation of time and the conservation is logic in an evolutive point of vue,but not in your reasoning.
Steve
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