Sunday, April 18, 2010 ... //

Dark energy, the holographic principle, and IPMU

By Paul Frampton, Professor of Physics and Astronomy at Chapel Hill, NC
A Spanish translation of this text is available.

It is a high honor to be invited, by Luboš, to write about dark energy. I first met Luboš, when he was an assistant professor, at Harvard University, and found him extremely intelligent and charming in person, quite different from the aggressively strident blogger. I confess to joking that Luboš is afflicted by "blog-rage", when he sits at his keyboard, by analogy with the road-rage suffered by drivers in California when they shoot dead the other driver, after a minor fender-bender.

I take this opportunity to write, so as not to keep repeating the same thing in e-mails. I will not respond to e-mails about only dark energy, more likely to e-mails about cyclic cosmology. Also, I accept, because this is, in a real sense, outreach.

The dark energy solution, which many people including myself, had hoped to lead to new laws of physics, just as did the aether, with relativity, and eventually quantum mechanics, in the twentieth century, leads, instead, to an interesting reinterpretation, of the known laws of physics, especially of Newton's and Einstein's work on gravity.

The central theme of my work in cosmology, going back five years, and in some sense, forty-five years, is entropy. Some of the world's deepest thinkers claim, that they do not understand entropy, which can be a polite way of saying they think the concept, of the entropy of the visible universe, is rubbish. I disagree, and instead claim that the entropy of the visible universe is useful. My present thinking, based on work done since February 6 and which I do not write about, is that the work of Boltzmann in 1872 is so incredibly important, that this name should rightly be placed alongside Newton and Einstein as the best ever in physics. Boltzmann's idea was that entropy (disorder) first defined by Clausius in 1865, and a statistical concept, generally remains the same or increases. This is the second law of thermodynamics. Because this "law" can be violated, it was not immediately accepted 1872-1906 either by physicists (Maxwell) or mathematicians (Poincaré) and led to the tragic death of Boltzmann by suicide.

My solution of dark energy came as a result of Hirosi Ooguri, a Caltech professor, telling me on February 4 about some lectures by Dam Son in Tokyo February 6. Son's lectures, about the holographic principle, applied not to cosmology but to heavy ion collisions and the Navier-Stokes equation were at a new high level and so inspiring, that I realized that the visible universe is a black hole, then used a well known equation, called the PBH temperature. I believe the three papers in the order PBH are all equally important, and thence this accomplishment is more acronymous, than eponymous. The second, and final, step was to use the equally well known acronymous FDU acceleration. Actually, I was working on cyclic cosmology, as I still am, and by studying the visible universe, as a well-defined sphere of radius 48 billion light years, realized that the accelerated expansion rate of the universe is a direct result of the visible universe being a black hole.

The fact that we live inside a black hole need not cause panic, as for the "The War of the Worlds" radio broadcast, in 1938, which sounded like news, of a Martian invasion. Funnily enough, the bigger a black hole is, the less frightening it becomes. The one we live in is really big, 48 billion light years, in radius. That is over a hundred-thousand-million-trillion miles. It is an extremely nice, and friendly, black hole.

I do not know who reads this blog. I assume they are high-school students, and educated non-scientists. I do occasionally read The Reference Frame, as Luboš' blog-rage is, always, at least mildly titillating.

The holographic principle, which was my basic assumption, in solving the dark energy problem, implies that the three-dimensional world we perceive is merely an illusion and that really it is at most two-dimensional. Here, it is not only outreach to the general public which is a problem. It is also so close, to the boundary of human knowledge, that even professional physicists do not fully understand this emergence, of one or more space dimensions, and it is one major source of our present intellectual excitement.

A more important problem than the dark energy is the construction of a cyclic universe. This we started with Baum in 2007 (Physical Review Letters). The cyclicity issue is threatened by the second law of thermodynamics head on, and the new insight seems to be crucial. Again this is post February 6 and I believe Luboš wanted a description about the dark energy solution.

In my discussion of string theory, I need to mention two of its finest ever practitioners, the late great Joel Scherk (1946-1980, picture) and John Schwarz, the theoretician solely responsible for the survival of string theory as a research direction. (The Japanese theoretician, Tamiaki Yoneya, made a related important analysis.) It is fascinating how my solution of the dark energy problem, relates to string theory and, in particular, the profound and influential 1974 suggestion by Scherk and Schwarz that string theory be reinterpreted, not as a theory of hadronic collisions as originally suggested by Veneziano in 1968, but as a theory of gravity.

Writing that name, Joel Scherk, brings tears to my eyes because I knew him quite well as CERN Fellows together, and he was both exceedingly brilliant intellectually and a gentle, profound, kind person. On SPIRES one can see his work, by age thirty-four has accrued ten thousand citations. I last met Scherk, in Tokyo, in 1978 and he seemed totally normal. In 1979, I received frantic calls from mutual friends, and I will not comment further, except to say, his loss was of, potentially, a truly great theoretician of my generation.

It is worth a paragraph about general relativity. This remains as valid as ever, including the three classic tests proposed by Einstein: the perihelion of Mercury, the bending of light around the Sun, and the Pound-Rebka frequency shift, of falling light, confirmed at Harvard, in the "Pound Tower" of Jefferson Laboratory. My colleague Robert Pound died, last week. The prediction of gravitational waves from the Einstein equations remains as a classical phenomenon, already indirectly confirmed by the Taylor-Hulse pulsar binary and now awaiting direct experimental detection.

It just occurs to me that since my dark energy solution does not use string theory, Luboš must say it is rubbish because anything which is not string theory is, for Luboš?

One crucial and subtle point is about the role, of the graviton, about which I believe my work says something. In fact, I dare to say that a graviton is unnecessary, although it may be there. Without becoming too professorial, I must go back to realize that Maxwell in 1865 predicted EM waves, which were detected, by Hertz, in 1887. That was classical. The photon was first identified by Einstein in 1905, queried as late as 1922 by Bohr in a weird part of his Nobel lecture, then proven to exist by Compton in 1923. The fact of gravity waves does not, in my opinion, imply the existence of a graviton.

I have discussed dark energy, and the holographic principle. Now a paragraph, on IPMU, which is the Institute for the Physics and Mathematics of the Universe, University of Tokyo, which started Oct.'07 and, after only thirty months, is one of the most exciting places in the world to pursue research in physics, or mathematics, or their interrelationship. This minor miracle is due to three Japanese men. The first is Nakagawa san, the Vice Minister. The second is Hamada san, president of the University of Tokyo, and receptive to IPMU. The third is the IPMU director, Murayama san, with a combination of intellectual vision, and political eptitude.

So Luboš, that was my guest blog. I have never visited the Czech Republic. Sheldon Glashow once described Prague, to me, very favorably. I remind you that, one time back at Harvard, you promised a Pilsner Urquell in an original glass?

snail feedback (6) :

What exactly is the definition of a black hole in the context of this article? If our visible universe is a black hole in which matter is maximally compressed, how can it contain other black holes in which matter is compressed even more?

If the visible universe is a black hole, then wouldn't it already possess maximal entropy per unit mass?

I thought a bit more about what it might mean if the entropy is always the maximal amount. This might be pure crackpottery, but I'm just running with the notion...

Start with the assumption that the entropy of the visible universe is always S = A/(4 \ell_p^2) = 4\pi E^2/E_p^2, which is equivalent to the entropy of a black hole of equal mass. This calculation for S seems to imply that the black hole consists of n = E/E_p Planck particles.

Since the visible universe consists of a much greater number of particles than n, all of which have a mass less than the Planck mass (e.g., electrons, quarks), then there will be a lesser amount of entropy per particle than what occurs in the black hole configuration. That is, the universal entropy will still be 4\pi E^2/E_p^2, which is much less than 4\pi E^2/E_{electron}^2.

From these things it seems that in low energy density environments, there are a greater number of particles (e.g., electrons, quarks), and the per-particle entropy is low (e.g., a block of salt of many Na Cl ions). Increasing the energy density will cause the particle count to reduce, and so the entropy per-particle increases (a black hole of a few Plank particles).

I guess the main question would be: 1) Are black holes really made of Planck particles? Does a bunch of matter change from a large number of lighter particles to a small number of heavier particles somewhat gradually as the matter collapses from a star into a black hole?

The main problem I have with what I said here about a bunch of matter always having maximal entropy is that even when the matter is in a low energy density configuration, the total entropy will still be proportional to M^2. As far as I know from here and elsewhere, in the low energy density configuration the entropy should be proportional to M^1 -- so no matter how one plays around with the number of particles, the exponent will be incorrect for everything but black holes, and surely a cube of salt is not a black hole.

So, it's at this point that I need to stop talking and start reading Dr. Frampton's work to see what the solution might be. :)

We have

S = k log Ω

and it doesn't matter what the system is; for a "black hole" the accessible states Ω might be a larger set than other observable possibilities (and a lot of them degenerate, too).

The nice thing about S is that it is independent of the motion of any observer, and I guess it follows that for a black hole, S is independent of the speed of light too, somewhat surprisingly