Right About Time? by Sean Gryb and Flavio Mercati

Dear Sean & Flavio:

I enjoyed reading your well-written and intuitive essay describing the challenges in the fundamental understanding of time. You rightly point out to the two major problems that constitute the unexplained 96% of the universe - "....(dark energy) the accelerated expansion of the Universe, which is some 120 orders of magnitude smaller than its natural value.....and the dark matter problem..."

Then, you rightly state that - "...how can we do science on the Universe as a whole?

We will not directly answer this question but, rather, suggest that this difficult issue may require a radical answer that questions the very origin of time. "

My paper -" From Absurd to Elegant Universe" provides answers to the questions you raise and forwards a mathematical model of the universe as a "Whole" to resolve the well-known paradoxes of the modern science. Julian Barbour also concludes in his paper in this forum -

"....it may be impossible to understand key features of the universe such as its pervasive arrow of time and remarkably high degree of isotropy and homogeneity unless we study it holistically - as a true whole. A satisfactory interpretation of quantum mechanics is also likely to be profoundly holistic, involving the entire universe. The phenomenon of entanglement already hints at such a possibility.."

My paper demonstrates that following a holistic approach wherein the whole universe is considered as a continuum of mass-energy-space-time, a very simple mathematical model of the missing physics (hidden variable) of the well-known spontaneous decay/birth of particles can be developed that explains the observed quantum as well as classical behaviors. The holistic model also successfully predicts the observed data at all scales from below Planck scale to beyond cosmological scales. The proposed model not only resolves black hole singularities but also the unresolved paradoxes of physics and cosmology including the dark energy and dark matter. The holistic model also explains the inner workings of QM and eliminates its paradoxes and inconsistencies with relativity. It also vindicates that time is not a fundamental entity since the observed universe and galactic expansion can be predicted without any explicit consideration of a cosmic time.

I would greatly appreciate your comments on my paper. You can contact me at avsingh@alum.mit.edu.

Best Regards

Avtar Singh

Flavio,

Thanks for the detailed response! You might have seen on my bio that I work in algebraic geometry, and the connection to characteristic classes is very intriguing. To be honest, I had never heard of shape dynamics until I read Julian Barbour's essay a week or two ago, but I will be sure to learn more about it now that I've been introduced.

I have read Sorkin, and indeed reference him in my essay. I don't feel that I can entirely agree with the axioms of the causal sets approach, but I'm fairly new to that as well. My approach is indeed similar, however.

By the way, there was another essay here about desingularization by Abhijnan Rej that has a lot of interesting geometry in it. He proposes using cycles/motives etc. Take care,

Ben Dribus

Don't worry. Soon Brendan Foster will delete both my provocations and your absurd replies. Like Julian Barbour, you will be one of the winners.

Pentcho Valev

Pogge's propaganda for relativity is not precise and not convincing to me. Every layman knows that the accuracy of a clock cannot be given as time deviation unless one knows what timespan this value refers to. Perhaps Pogge meant 1 ns per day but he did not write that. He did not even bother to tell further details like Sagnac effect and the open secret that the corrections were made empirically. He didn't give references to the opinion of true experts.

How to judge censorship? How to judge the necessity of a task force making sure that Einstein's relativity is not seriously questioned in Wikipedia?

Shouldn't we welcome the insight that we need not focussing on Einstein if already Michelson's expectation was wrong? I consider Roger Schlafly's remarks on Einstein possibly well founded but I would like to avoid hurting the feelings of believers.

Eckard

Dear Sean,

I appreciate the response. As a matter of fact, you'll find that my own physics ideas are somewhat removed from my algebraic geometry work, but that doesn't mean I wouldn't be delighted to find out about physics applications for the math stuff I have been doing.

I think you might also be interested in the essays by Torsten Asselmeyer-Maluga and Jerzy Kroll about exotic smoothness structures, even though the approach, like mine, is quite different.

By the way, I briefly mentioned a number of prominent approaches in the first part of my essay; I certainly would not have left your approach out if I had been properly aware of it at the time. Take care,

Ben

Dear Sean/Flavio,

Do mind telling me an email address or sending me an email at bdribus@math.lsu.edu? I notice you don't have addresses listed on the paper. Thanks,

Ben Dribus

Sean and Flavio,

I found your essay to be interesting. It takes me a while to digest the more interesting and solid works here, so it has taken me a bit of time to get to your paper. You make a number of very interesting points. I can only this morning discuss a few of these. I will try to follow up later today or tomorrow.

The relationship between shape dynamics (SD) and the extended configuration space (ECS) is one of conformal symmetry. SD has no explicit reference to scale, and scale independence is one aspect of conformal symmetry. The relationship between the two, or a decomposition SD --- > ECS is one where conformal symmetry is broken. General relativity has the group structure SO(3,1) ~ SL(2,C), and the extension of general relativity to conformal spacetime is to SO(4,2).

In my essay I work with the Britto, Cachazo, Feng, Witten (BCFW) recursion relationship. This is a Feynman diagram procedure in twostor space. Twistor space is the symmetry group SU(2,2) ~ SO(4,2), and so is a quantum or prequantum description of conformal relativity. The recursion relationship is a scaling principle which is conformal. In fact it leads to Yangian symmetries, which are a form of enveloping Lie algebras for gauge theory. Yangians consist of a gauge (or gauge-like) theory plus a dual theory related by a conformal symmetry, or Mobius symmetry and T-duality.

The BCFW recursion formula is a twistor theory, which has been used in the HopHat algorithm for computing gluon amplitudes at the LHC. Gravitation is in one sense the square of QCD gauge theory. After reading Giovanni Amelino-Camelia , which has regrettably and I think wrongly fallen down the community ranking, I suggested a connection between the boosts employed in κ-Minkowski and twistor theory. This might be a connection between string theory and the more loopy or triangulated theories like LQG. The Wheeler DeWitt equation has not time variables. Physically this means there is no Gaussian surface one may arrange in spacetime to localize energy. So HΨ[g] = i∂Ψ[g]/∂t = 0. The time variables is a coordinate time, used in QFT equations, which is not a proper variable in general relativity. Hence this equation is a constraint equation, classically NH = 0 and N^iH_i = 0. String theory on the other hand requires some external background field from which gravitons as closed strings are represented. This has been a problem the LQG folks like to point out --- never mind LQG has failed to produce even a first order renormalizable calculation. I speculate that somehow the two views of quantum gravity might connect, where LQG provides the background or constraint for string theory, and the field calculations of strings makes LQG more tractable.

Gravity as a dynamic force is conservative. The force in the Newtonian limit is given by F = -∇Φ(r), which is conservative. This means the force evaluated around a closed loop, such as an orbit, is zero. Thermodynamics gives nonzero evaluations for such forces. This is related to the matter in differential geometry that a p-form ω is closed if dω = 0, but a subset of them are exact when ω = dσ, or d^2 = 0. There is some cohomology behind this. The force is determined by the coboundary operator on a 0-form and we have by Stokes law

∫F•dr = ∫∫∇xF•da. da evaluated in the region enclosed by the closed loop.

Yet we know that ∇x∇Φ(r) = 0 (curl-grad = 0 or d^2 = 0) and so the force is conservative.

Verlinde's entropic gravity does not involve the dynamics of a particle in a gravity field. It involves the dynamics of an event horizon or holographic screen. The main idea is that the force on the screen over some unit distance is equal to the work

∫F•dr =W,

and this work is equal to the increase entropy of an event horizon. This by the Bekenstein theorem is S = k A/4L_p^2, for L_p = sqrt{Għ/c^3} --- the Planck length. So the entropy is a measure of how many Planck units of area there on the horizon. So the Verlinde hypothesis is

∫F•dr =TS,

or a force that displaces the horizon some increment gives

F•δr = TδS.

As a result some input of mass-energy into a black hole increases entropy, and this force is what evolves the event horizon, or equivalently the holographic screen.

Event horizons and screens have units of area, and in naturalized units with c = ħ = 1 the gravitation constant G is an area. So this measures the amount of information entangled with the black hole, or the entanglement entropy. As a result the theory you have built up with moments of inertia most likely applies on a holographic surface.

More later & cheers,

LC

Sean and Flavio,

Beautifully written essay. I just have a comment and a question.

Comment: You claim that the problem of time stems from the different way that time and space enter into the formalism of general relativity, and that the evolution equations cannot be solved starting from nonspacelike initial data. The latter is not known to be the case. Certainly for the wave equation, one can begin with data on a nonspacelike hypersurface and evolve in the spacelike direction. (The Holmgren-John theorem guarantees uniqueness, and the work of Craig and myself shows that a solution exists if one begins with data satisfying a nonlocal constraint.) As for the problem of time, I would think that it has something more specific to do with general relativity, since it doesn't arise in the quantization of other relativistic fields.

Question: I see where coarse-graining is important for the fascinating result you get for the Shape formalism, but where does renormalization come in?

Steve

For Shape Dynamics theory to fit my proposal about one analogy between geometry and physics

See http://www.fqxi.org/community/forum/topic/946

Sean & Flavio,

I think many will agree with me, that there are more prize winning essays in this contest than there are prizes ... yours is among the top. So good luck! -- and I hope you get a chance to vist my essay ("The Pefect First Question") that soundly agrees with your statement, "The truth is that quantum mechanics requires some additional structure, which can be thought of as the observer, in order for it to make sense. In other words, quantum mechanics can never be a theory of the whole Universe."

Tom

Verlinde's Entropic gravity and AdS/CFT Beyond the Standard

Model discussion is just a superstrings extrapolations.In fact,they confound the theory of informations witrh a real quantization.

In fact the works are not bad, but they are weak and not sufficient. The strings theories were just a faschion. Several convergence are relevant but it is time to be rational. The entropy is proportional with my rotating 3D spheres. Me I have explaine the gravity, him no !!! them , no !!!

The conformal group in 3+1 spacetime would then be SO(4,2) ~ SU(2,2). The connection to twisters of course is through this conformal symmetry. One can of course see this according to Desargues' theorem; Two triangles are axially perspective if and only if they are in perspective centrally. The projective rays in spacetime have a similar correspondence ω_a = ω(0)_a + ε_{aa'}π^{a'}, π^a = π(0)^a, which in the null construction is a projective Lorentz spacetime.

Your paper on 2+1 Chern-Simons SD has much the same structure as some work I just completed and will be sending to publication soon. The AdS_3 spacetime (2 space +1 time) has the CFT_2 on its boundary S^1xR. This CFT is SL(2,R)^2/Z_2, which with

1 --- > Z_2 --- > SL(2,C) --- > SL(2,R)^2 --- > 1

constructs spacetime symmetries in 4-dim. The S^1xR is the string world sheet or tube, and the CFT constructs the gravitons states. The holography here is with the boundary of the AdS_3. However, there is an additional symmetries on the string corresponding to four dimensions

There was some interesting discussion last week about commuting and anticommuting operators with SD and with causal set theory. I think this might have some interesting implications. It might provide some category theory of functors between spacetime and supersymmetry.

Cheers LC

"Moreover, the toy model may shed light on the nature of the Plank length. In this model, the Plank length is the emergent length arising ....

This dimensionful quantity, however, is not observable in this model. What is physical, instead, it the dimensionless ratio r=R. This illustrates how a dimensionful quantity can emerge from a scale independent framework. Size doesn't matter but a ratio of sizes does. The proof could be gravity."

Dear Sean

Be careful with Planck length and read Wilczek doubts about it

Wilczek:"we must extract roots",

"can be taken outside the square roots",

"In the strong system of units no square roots

at all appear in [M], [L], [T ]."

Read Wilczek http://arxiv.org/abs/0708.4361

Flavio

You said on Sept 12 "I'm reading your essay with interest...". I hope you have, or do, as I think it may be very important in context, and am looking forward to your comments.

Best wishes

Peter