Patrick Hayden points me to hep-th/0410036. If I understand this paper correctly and the paper is correct, this seems to me to be a BIG deal. In this paper, the author take the Hilbert-Palatini action for GR and adds two terms, both of a topological nature. These terms don’t change the fact that the classical theory derived from this action is classical GR. However, the author shows that these terms make this action the same as the action for an so(4,1) [or so(3,2) depending on whether the cosmological constant is positive or negative] Donaldson-Witten topological quantum field theory. The Donaldson-Witten TQFT is an “exactly solvable” quantum theory. What does this mean? Can anyone say a theory of quantum gravity? I knew you could. As the author puts it, “this proves that exact, non-perturbative calculations can be preformed in 3+1 dimensional quantum gravity.”
[Update 10/13/04: Well that was the quick fall. As Nathan Lundblad notes, the paper has been withdrawn!]
Nobel Closed Timelike Curve
I will have you note, that one of today’s Nobel prize winners in physics, David Politzer, has written articles on closed timelike curves (a.k.a. time travel). Does my paper on closed timelike curves look crazy now? Huh? Oh yes, it does.
Hot Enough To Melt…Err I Mean Unmelt…
From an IOP news article:
Law-breaking liquid defies the rules
Monday 27 September 2004
Physicists in France have discovered a liquid that “freezes” when it is heated. Marie Plazanet and colleagues at the Université Joseph Fourier and the Institut Laue-Langevin, both in Grenoble, found that a simple solution composed of two organic compounds becomes a solid when it is heated to temperatures between 45 and 75°C, and becomes a liquid when cooled again. The team says that hydrogen bonds are responsible for this novel behaviour (M Plazanet et al. 2004 J. Chem. Phys 121 5031).
It's Four!
When physicists say “3+1″they are not talking about the number “4”, but usually they are talking about spacetime: three spatial dimensions and one temporal dimension. One question which plagues theoretical physicists’ poor little minds is the question of why we see a macroscopic world of 3+1 dimensions. Mostly this is because physicists believe that at small enough length or time scales (large enough energies) the geometry of spacetime itself can exist in nontrivial states of connectivity. Thus we think of spacetimes at small enough scale as existing in all sorts of strange configurations (in some poor little region the spacetime may look like a 10 dimensional manifold, for instance.) “Spacetime foam” is what we call this strange state of affairs. How do we get from this spacetime foam up to where our experiments live and we seem to see a four dimensional universe?
Concerning this problem, I just today read the paper “Emergence of a 4D World from Causal Quantum Gravity,” by J. Ambjorn, J. Jurkiewicz, and R. Loll which was published in Physical Review Letters, (Volume 93, page 131301, 2004.) This paper attempts the following. Construct spacetime by glueing together a bunch of little four dimensional simplical spacetimes. Like I said earlier, if we glue a bunch of these four dimensional simplical spacetimes together, we get something which is not necessarily four dimensional. Now when we do this glueing we should insist on maintain causality (i.e. no closed time like curves and such.) So we can construct these crazy spacetimes, but what do they mean. Well now we associate with each of these spacetimes an amplitude. So there is some notion of an action S for the given simpical spacetime we have created and we assign to this an amplitude, Exp[iS]. Now what one would love to do is to sample over all of these crazy spacetimes and hence calculate the propogators for different such spacetimes. But this is hard. This is hard because of the fact that we have to sample over this crazy oscillating Exp[iS]. But sometimes it is not so hard. Sometimes it is possible to perform a “Wick” rotation and change Exp[iS] into Exp[-S]. This means the problem of calculating the total amplitude looks like adding up a bunch of different spacetimes with weights Exp[-S]: this looks just like classical statistical mechanics! What the authors of the above paper do is they insist that it is possible to perform such a rotation. They then perform Monte Carlo simulations of the resulting statistical mechanical system. And what do they find? They argue that what they find is that the resulting spacetime is indeed dominated by a spacetime of dimension “3+1!”
So starting out from something which had only a totally local sense of dimension (the original building blocks are “3+1”) you glue them together in pseudo-arbitrary (preserve causality, able to Wick rotate) ways (this is what is called “background independence”) and yet, you find, at the end of the day, that you have effectively a global “3+1” spacetime! Amazing, no?
Fate
One of the reasons I got interested in physics was because I have always been interested in the “question of free will.” Physicists don’t like to talk about free will much, especially since learning what quantum theory has to say about free will seems to put you smack dab in the middle of the measurement problem in quantum theory. In many ways, what I’m most interested in is not the question of free will, which I find too often to be an overly anthropocentric enterprise, but more the question of the determinism / indeterminism of physics. But the “free will question” has played a major role in shaping why I choose to do physics.
As so the question becomes: why was I interested in free will? Most of it is surely due to my older sister Cathy. You see Cathy is a little person. No one knows exactly what syndrome she has, but it causes her to be lopsided (one arm and leg shorter than the other), she has very poor vision and hearing, and has some mental difficulties. This makes it all sound really bad: which it is definitely not because Cathy is an amazing light in our family. She works at the local library in Yreka, loves to listen to her John Denver tapes, she loves to watch Jeopardy, and is, in general, a very happy person who brightens the lives of her many many friends.
But if you grow up with a sister like Cathy you can not avoid thinking about why you ended up the way you are and why she ended up the way she is? Was it fate and totally out of the hands of human choice? Science, and physics in particular, is the path one is reduced to in order to possibly find any answer to such a question. While we can argue forever whether reductionism to fundamental physics is central to answering this question, there can be no doubt that understanding the role of determinism and indeterminism in physics will have a profound impact on our view of this question.
On the other hand, Richard Feynman said: “Do not ask yourself… ‘how can it be like that?’ because you will lead yourself down a blind alley in which no one has ever escaped.” I don’t think Feynman was talking about science here: scientists spend much of their time answering how it can be like that. I think Feynman was talking about asking for reasons which somehow satisfy us as humans: answers that will give us short sentences explaining why. There are simple important questions which might have simple concise explanations, but finding these explanations seems impossibly difficult. And this is how I find myself coming full circle. Because this point of view, that there are simple questions for which there aren’t answers which can be found in a short time (and once we find them, we’ll know we’ve answered the question) is basically the complexity class NP. Which is computer science. The field, besides physics, which I most deeply admire.
So fate not only made me a physicist, but it also made me a computer scientist.
And the only question left remaining is whether or not it was destiny that I was born at a time when I could participate in the unfolding of the field of quantum computing, which merges physics and computer science like never before?
Time is Change
Random thoughts at 2 a.m.: I have been playing poker all night and it’s 2 a.m., so this post may make no sense when I wake up in the morning…
If we take a single spin 1/2 particle, and put it in a magnetic field, the spin precesses. We can use this to form a sort of clock by preparing the spin in a particular state and then measuring the spin along a particular direction. Of course this clock only has two value 0 or 1. So a universe with a single spin has a single bit clock. But this clearly doesn’t approximate our univerese. What do we need? More spins! So add more spins. Now we get clocks that count in some binary fashion. So we can more accurately measure a time with more spins. Look: if we add more spins we gain accuracy in keeping track of time.
Now look at relativity. If our clock has a very small mass, and it is all that exists in the universe, we will read a time which is nearly that of clocks which are infinitely distant. But add more clocks and the mass increases. Now we have a clock with a larger mass. And the larger mass will cause the clock to run slow compared to a clock at infinity. But this means that such a clock can be used to measure the time at infinity much more accurately.
Are these two effects really one and the same?
**Update** Yep, it’s morning and this makes no sense. Although the two effects scale similarly in the non-relativistic regime.
What Light Through Yonder Nite Sky Breaks
Last night we went to the boondocks (or as close an approximation as we could get to the boondocks, living in L.A.) to watch the Perseid meteor shower.
“For my part, I know nothing with any certainty, but the sight of the stars makes me dream.” – Vincent van Gogh
Driving back, I was thinking about how amazing it is that we can even do cosmology! What an amazing setup that we can look back in time by collecting light from more and more distance objects. Our universe didn’t have to be this way: it could have been action at a distance, instantaneous transformer of information, etc. And then how would we do cosmology?
Baez Decrypts
John Baez’s description of Hawking’s talk at GR17 is the best scientific commentary on the talk I’ve come across. It’s a notch above all of these descriptions I’ve read which are of the form: I don’t like Euclidean quantum gravity, but I do know [insert other theory of quantum gravity here], and we already knew [insert claim here]. Which is fine for learning about [insert claim here] but doesn’t really tell me anything about what Hawking was trying to say!
The Entropy of Lost Bets
Reading John Preskill’s description of his bet with Stephen Hawking on the black hole information paradox, I began to wonder what my requirements for thinking the paradox had been solved would be. The bet Preskill and Hawking and Thorne made was
When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.
Well at first I thought, surely a quantum theory of gravity which showed such a preservation of purity would be sufficient? Wouldn’t it? Well, a single quantum theory of gravity might be evidence, but even if we find that theory, what makes us think it is the correct theory describing our universe? Yeah, yeah, string theorists mutter something about “the only way.” So do Taoists.
This, I guess, is the funny thing about bets made by theorists. Their criteria for satisfying the bet may have nothing to do with reality. We may resolve the paradox, say in the Euclidean theory of quantum gravity, but what if the Euclidean theory of quantum gravity doesn’t correctly describe our universe. What if Twistor theory ends up giving a valid theory of quantum gravity and entails a total overhall of quantum theory such that the paradox is resolved in the opposite direction? What if the theory of quantum gravity makes it apparent that the question doesn’t even make sense?
The only way I’ll be happy is if we go out and create a black hole. Let it evaporate. And track the information flow. Admitting this, I believe, has just caused my theoretical physicists i.d. card to spontaneously combust. Excuse me while I put out the fire in my wallet.
Schurly You're Joking Dr. Bacon
A new paper, a new paper! If you love the theory of the addition of angular momentum, and don’t we all just love the theory of the addition of angular momentum, then you will really love the new paper we (Isaac Chuang and Aram Harrow) just put on the arXiv. Unfortunately my spell check changed the title to Clench-Gordon and I didn’t notice. So I expect a lot of nasy emails complaining about the title. Doh. Well that’s what the replace button is for, I guess. Here is the paper:
quant-ph/0407082
Efficient Quantum Circuits for Schur and Clebsch-Gordon Transforms
Authors: Dave Bacon, Isaac Chuang, Aram Harrow
Comments: 4 pages, 3 figures
The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/epsilon)) for accuracy epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordon transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.
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