Tryggth’s Blog

Things have been hectic the last few weeks. So the detour into the Reggae calculus and associated Causal Dynamic Triangulation offshoot I am working on in preparation for the deeper dive into ‘Gravity as Entropic Force’ is still in the offing. In the meantime checkout:

Gravity Emerges from Quantum Information, Say Physicists from the fine folks at Technology Review, an MIT shop. Seems the number of pre-prints appearing has drawn their attention. Also,

Johannes Koelman has a nice suggestive write up about how statistical behavior can appear, in the large, to be a force. Would be nice if some enterprising person implemented the mikado universe with StarLogo.

Have been incredibly busy with work and prepping for leading a multi-day training class. So this is just going to be a brief update on what has been going on with respect to Verlinde’s paper.

First of all, the paper continues to generate interest at a healthy rate as indicated by the SPIRES citation index. The index is not complete since the indexing relies on the format of citations, but the rate continues to be about one paper a day.

Two of the pre-prints (here and here) argue that Verlinde’s entropic derivation of gravity is logically flawed. I haven’t had a chance to look closely at these papers and have no opinion yet.

Also, Nobel laureate George Smoot (et al) have put up a pre-print with a very Verlinde-ish flavor. The abstract reads:

To accommodate the observed accelerated expansion of the universe, one popular idea is to invoke a driving term in the Friedmann-Lema\^{i}tre equation of dark energy which must then comprise 70% of the present cosmological energy density. We propose an alternative interpretation which takes into account the temperature intrinsic to the information holographically stored on the screen which is the surface of the universe. Dark energy is thereby obviated and the acceleration is due to an entropic force naturally arising from the information storage on a surface screen. We consider an additional quantitative approach based upon the entropy and surface terms usually neglected in General Relativity and show that this leads to the entropic accelerating universe.

They aren’t the first to suggest that dark energy (sorry, no reference for this statement) has an “entropic” origin. And though I suspect in the end the ontology will change, the whole approach of considering dark energy as the “Hawking radiation of the cosmic horizon” has some truth to it.
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DARPA Mathematical Challenge Twenty-two:

Settle the Smooth Poincare Conjecture in Dimension 4

• What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?

OK, where was I?

Wile E. Coyote

You know how this is going to end. The coyote is not going to catch the roadrunner. But what if the coyote’s rocket were to travel at the speed of light? And what if the roadrunner constantly accelerates but never attains the speed of light?

It turns out that if  roadrunner has a sufficient head-start (and we know coyote isn’t going to light the fuse until after roadrunner swooshes by) and roadrunner has ‘constant proper acceleration’ (though the bird will never reach the speed of light!) coyote can never catch roadrunner.  Which is a little surprising. After all, its a scenario where the coyote is always traveling at a velocity greater (namely c)  than the roadrunner.

The phenomenon is known as the “rindler horizon” and a great description of this Zeno-like ‘paradox’ is provided by the technically adept science (and science fiction) writer Greg Egan here.
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Working on a post about Rindler horizons and about how the holographic principle isn’t as weird as you might think. But in the interim some stuff I found entertaining:

Woit has some thoughts about recent ‘trends’ in physics, including Verlinde’s contribution.

A reminder that there is a well-established standard for crackpottery.

And finally…

“They laughed at Newton. They laughed at Galileo. But they also laughed at Bozo the Clown.”
– Carl Sagan

Ignore the diagram to the left.

In the previous post I compared Verlinde’s ‘revelation‘ to the hyped proposal of Garret Lisi. I also tried to lay some of the historical groundwork which is context for Verlinde’s paper. Lee Smolin, in his paper building on Verlinde’s result, provides a more concise recounting of the historical context. Check it out.

Erik Verlinde

Verlinde is not a crackpot. A postdoctoral student  and then long term research member of the Institute of Advanced Study, Verlinde has regularly published in the area of string theory. He currently teaches at the Institute for Theoretical Physics at the University of Amsterdam. But his paper has not generated a universal ‘a-ha’ among physicists. One of my favorite reactions is Robert Helling’s:

The latest paper by Eric Verlinde on gravity as an entropic force makes me wonder whether I am getting old: Let me admit it: I just don’t get it.

Helling then goes on to write that Verlinde’s paper reminds him of the following proof:

girls = time * money [obvious, a priori]

time = money [experimentally determined]

girls = money ^ 2 [substitution into line #1]

money = sqrt(evil) [biblical]

money ^ 2 = evil [square of previous line]

girls = evil [transitive property]

I have no problem with that. But I would have thought Helling more sympathetic to Verlinde’s paper. After all, Verlinde’s use of polymer elasticity as an example of ‘entropic force‘ surely would have resonated with Helling’s own investigations into the thermodynamics of protein folding. And Helling, who won a ‘Schlössmann Award’ for describing gravity as an emergent property, can’t possibly be thrown by the dethroning of gravity from the big-4 of forces. Maybe, as he says, he is just ‘getting old’.

I suspect at this stage the uncertainty about Verlinde’s paper has to do with the following:

• The derivation of Einstein’s equations has been done before using roughly the same set of assumptions (see earlier post reference to Jacobson).
• There is an incredible muddle regarding the particulars and degree of gravity emergence. For one thing, the holographic principle in its usual forms has tons of implicit assumptions about the geometry (including dimensionality) of ‘space’.
• The Unruh effect/temperature buries within itself a multitude of sins, especially relativistic quantum field theory.
• Most importantly, the paper messes with people’s usual ontology. The pre-geometric physical entities which provide the semantics to an unstated, but implied (since gravity is emergent) reformulation of the holographic principle as well as the dynamics of those essentially information-theoretic entities is pretty alien.

And yet… and yet…

It seems – at this point in time – what Verlinde has done is pointed to a reaxiomization  of some basic physics. Similar to there being several different equally adequate axiomizations (given a set of basic symbols) of propositional logic, Verlinde will focus attention on perhaps redundant underlying assumptions of quantum mechanics, general relativity and thermodynamics.

To be continued…

As mentioned on  Slashdot, on December 8th at the Dutch Spinoza-instituut,  Erik Velinde gave a talk  describing an approach to the theory of gravity wherein gravity is an emergent property. It was followed by a preprint he posted to the arxiv server on Jan. 6th. The most controversial aspect of his position and paper is the claim that gravity is an epiphenomenon and not a “fundamental” force of nature. In his paper he derives Einstein’s field equations from what he believes are more fundamental assumptions.

It’s been two and half years since Garret Lisi achieved his 70 column-inches of fame with his “Exceptionally Simple Theory of Everything“[PDF]. Also a trained theoretical physicist, Lisi made headlines around the world [here, here and here for example]. The story was made-for-tv material. Bohemian surfer/snowboarder dude unwinds the Rubik’s cube of the universe.  The theory came complete with a pretty picture. But in the end his theory suffered a wipeout:

Distler had demonstrated in his blog that this is a mathematical impossibility.

The Scientific American post-mortem on Lisi’s theory concludes with this graf (my emphasis):

Today the theory is being largely but not entirely ignored. Lisi, naturally, continues to work on it, as does Smolin. Lisi says that even if what Distler claims is true, it would only be true for the variant of E8 (“real E8”) originally used in his paper and that another variant (“complex E8”) would certainly work. Smolin argues that the press coverage gave the false impression that Lisi’s proposal was a finished work. “In reality,” he says, “almost every new theoretical proposal is first presented in a way that is flawed and incomplete, with open issues that need to be filled in…. While Lisi’s proposal has exciting aspects, this is the case with it as well.”

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