Category: Physics

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Snarky Mode On

Robert Laughlin, Nobel prize winner for the theory behind the fractional quantum Hall effect, has a new book out, “A Different Universe.” The book is interesting, but it also has its problems. As you might guess from previous posts I’ve made, Professor Laughlin has a amazing view of quantum computers:

There is a great deal of interest lately in the quantum computer, a fundamentally new kind of computational hardware that would exploit the entanglement of the quantum wave function to perform calculations presently impossible with conventional computers. The most important of these is the generation of enormous primes numbers and the quick factorization of other enormous numbers. The impossibility of factoring a number that is the product of two large primes in reasonable time with conventional computers is the basis of modern cryptography. However, quantum computation has a terrible Achilles heel that becomes clear when one confronts the problem of reading out the answer: the effects that distinguish quantum computers from conventional ones also cause quantum indeterminism. Quantum-mechanical wave functions do indeed evolve deterministically, but the process of turning them into signals people can read generates errors. Computers that make mistakes are not very useful, so the design issue in quantum computation that counts is overcoming mistakes by measurement. A textbook method for doing this is to place a million copies of the same experiment in a small box and measure something they do collectively-generating oscillating magnetic fields, for example, as occurs in a quantum computer built with electron spins. The damage inflicted by the measurement process then affects only a few copies, leaving the rest intact. This trick is so powerful that variations of it enable you to read out the entire wave function of any quantum computer, at least in principle. However a logical implication is that you have created not a fabulous new kind of digital computer but a conventional analogue computer-a type of machine we do not use in the modern era because it is so easily disrupted by noise. Thus the frenzy over quantum computing misses the key point that the physical basis of computational reliability is emergent Newtonianness. One can imagine doing a computation without exploiting these principles, just as one can imagine proving by brute force that broken symmetry occurs, but a much more likely outcome is that eliminating computational mistakes will prove to be fundamentally impossible because its physical basis is absent. The view that this problem is trivial is a fantasy spun out of reductionist beliefs. Naturally, I hope I am wrong, and I wish those who invest in quantum computing the best of luck. I also ask that anyone anxious to invest in a bridge in lower Manhattan contact me right away, for there will be discounts for a limited time only.

Wow. Can I really read this and not respond? I just can’t resist. And especially I just can’t resist snarking. I should apologize for what I’m about to write, but my feeble mind just can’t take it. I just can’t take it anymore! So here are my suggestions for Laureate Laughlin:

1. Please read J. von Neumann’s, “Probabilistic Logics and the Synthesis of Reliable Organism from Unreliable Components.” (1956) The basis of computer reliability has absolutely nothing to do with “Newtonianness”. The basis of conventional computer reliability has to do with redudancy, and more physically with the thermodynamics of many condensed matter systems.
2. After you’ve mastered the most fundamental ideas of fault tolerance, it might be useful to understand the ideas behind error correction. Please read C. Shannon’s “A Mathematical Theory of Communication” (1948). Sure we are going backwards in time, but I think it’s important for you to realize that redundancy (“place a million copies”) is not the only way to encode information. Indeed this fact will become very important as we move on to step 3.
3. Now you’re ready for the big stuff. I know you know quantum theory like the back of your hand, so this step will be easier for you than for many others. Please read John Preskill’s “Fault-tolerant Quantum Computation.” See how the previous two ideas, when slightly modified for the quantum world, lead to a theory of fault-tolerant quantum computers. Isn’t that amazing? I consider it to be one of the most important results in physics in the last thirty years, but you’re older and wiser, so you may feel free to downgrade it. But please don’t desecrate what you haven’t had the time to understand. Quantum error correcting degrees of freedom are most distinctively not the simplistic collective degrees of freedom which you insinuate (“oscillating magnetic fields.”) The idea is more subtle, and thus, I believe more beautiful. While beauty is in the eye of the beholder, you must surely admit that your solution to the fractional quantum Hall effect is only beautiful when you have the background to understand the theory, and so too, quantum fault-tolerance is beautiful, but only once you’ve sat down and understood the theory.
Oh, and by the way, the generation of large prime numbers is easy, not hard, for conventional computers (but you did better than the string theorist Michio Kaku, who I once saw on T.V. claim that quantum computers were amazing because they could efficiently multiply large numbers.)

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My Electron is a Black Hole

There are certain coincidences which, we you first hear about them, you sit up all night thinking wild and crazy thoughts. I think my favorite example of this comes from the Kerr-Newman black hole. The Kerr-Newman solution to the Einstein-Maxwell equations describes black holes with charge and angular momentum. What is strange about the Kerr-Newman black holes? Suppose we examine the gyromagnetic ratio for these objects. The gyromagnetic ratio is 2Mm/QJ where M is the mass of the black hole, m is the magnetic moment of the black hole, Q is the charge of the black hole and J is the angular momentum of the black hole. For a Kerr-Newman black hole (and for many other charged solutions in general relativity) the gyromagnetic ratio is exactly 2. Sound familiar? Well it should, because this is the value of the gyromagnetic ratio for a Dirac electron (there are some claims that this value of 2 is a triumph of relativistic quantum field theory, but it must be said that there are nonrelativistic arguments for a value of 2 as well.) Talk about a strange and wonderful coincidence. Or more than a coincidence? So now you can spend the rest of the day worrying about whether the electron is nothing more(!) than a charge spinning black hole!

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Wormholes

A wormhole is a topological feature of spacetime which essentially links two locales in the universe. Perhaps the most famous (and one of the first examples) considered by physicists is the so-called “Einstein-Rosen bridge.” This is a solution to the vacuum Einstein equations in which one pastes two Schwarzschild solutions together in such a way that there is a link between one part of the universe and another part of the universe. Here is a nice picture:
Most people, when they think about wormholes, think about science fiction stories where wormholes are used for traveling between distant locales. Go in one throat of the wormhole and come out on the other side of the universe. Sounds like fun!
Wormhole solutions in general relativity are, however, pretty nasty. In particular they require “negative energy densities.” There is also the interesting problem that wormholes lead to time travel. Consider creating a wormhole where the wormhole connects two neighboring regions. Now take one of the wormhole throats, on a trip over to Alpha Centari and back. Then there will be a twin paradox between the throats: one of the throats will be older than the other. Thus we can use the throat to travel back in time.
Today I was reading Einstein and Rosen’s original paper [Phys. Rev. 48, 73–77 (1935)]. What was interesting to me was not so much the solution but the reason Einstein and Rosen were interested in their solution.

In spite of its great success in various fields, the present theoretical physics is still far from being able to provide a unified foundation on which the theoretical treatment of all phenomena could be based. We have a general relativistic theory of macroscopic phenomena, which however hirtherto been unable to account for the atomic structure of matter and for quantum effects, and we have a quantum theory, which is able to account satisfactorily for a large number of atomic and quantum phenomena but which by its very nature is unsuited to the principle of relativity. Under these circumstances it does not seem superfluous to raise the question as to what extend the method of general relativity provides the possibility of accounting for atomic phenomena. It is to such a possibility that we wish to call attention in the present paper in spite of the fact that we are not yet able to decide whether this theory can account for quantum phenomena.

Here we see Einstein and Rosen proposing that quantum theory is a consequence of general relativity! In particular what Einstein and Rosen were most interested in for their solution was that one could have solutions to the vacuum Einstein equations which had no singularities but which had some resemblence to (two) particles with mass. In fact Einsten and Rosen even conjecture that the throats of the Einstein-Rosen bridge could be neutral particles like a neutron or a neutrino!
One of the most interesting questions to ponder is what would Einstein’s reaction have been to Bell inequality violations by quantum theory. John Bell was able to show that correlations produced between spacelike separated quantum systems cannot in general be explained by local degrees of freedom carried with these systems. Reading the Einstein-Rosen paper, in which nontrivial topology is introducted without blinking, I’m inclined to think that Einstein would have thought of Bell’s result not as invalidating “classical” reasoning about quantum theory, but instead as a validation of the point of view advocated in this paper: that quantum theory is a consequence of a topological extension of general relativity.

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Time Machine

For sale on ebay, a time machine:
A Time Machine
The bidding, unfortunately, for this wonderful device is over. Well, uh, unless the time machine actually works in which case, words like “over” seem to have distinct problems.

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A Messy Room Encodes One Bit

How do we store information? One way is to use a magnetic media, like as is done in our hard drive, where the information is encoded into the total magnetization of a group of spins. Another way is to use a capacitor and transistor to store information into the charge on the capacitor.
Now researchers at Philips Research Laboratories in Eindhoven, the Netherlands ( Lankhorst M. H. R., Ketelaars B. W. S. M. M. & Walkters R. A. M. Nature Materials published online, doi: 10.1038/nmat1350 (1968)) have created a storage medium in which the information is stored in a very strange way. Instead of the information being encoded into the total charge or the magnetization, their information is encoded into the degree of freedom describing whether the media they have is ordered or disordered. The idea of storing information in the ordered versus disordered phase has been around for a long time (such devices are called “Ovonic”) but apparently this new research is the first really viable realization of such a device.
The researchers use antimony telluride, which is naturally in an amorphus state with many of the atoms of the material all jumbled around. A small electral pulse however, will turn this state into an ordered states with the atoms lined up in a crystaline structure. A larger electral pulse (more voltage), however, will melt this crystaline structure and return the system into the disordered jumble of atoms. The state of the system can be read out by measuring the resistance across the material (the ordered phase will have a much lower resistance.) Thus we can store our binary 0 in the ordered phase and our binary 1 in the disordered phase, read out this information, and also write this information.
Which makes me wonder which other order parameters in statistical physics can be used to store information? Can we store information in the two phases of a metal being superconducting and just regularly conducting? How about in fluid-superfluid transition? OK, both of these are totally not practical, but maybe there is an interesting order parameter which we are missing but which would make an amazingly robust and fast storage device?

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Stringing Us Along

Via Not Even Wrong, comes an article from the San Francisco Chronicle which is pretty critical of string theory. Philip Anderson, as always, comes away with an interesting quote,

“…we from outside the (string) field are disturbed by our colleagues’ insistence that every new semi-adolescent who has done something in string theory is the greatest genius since Einstein and therefore must occupy yet another tenure track. … Our sciences are becoming increasingly infected with quasi-theology, a tendency which needs to be openly debated.”

but it’s Robert Laughlin who gets in perhaps the harshest one liner about string theory I’ve heard in quite a while

But skeptics suggest it’s the latest sign of how string theorists, sometimes called “superstringers,” try to colorfully camouflage the theory’s flaws, like “a 50-year-old woman wearing way too much lipstick,” jokes Robert B. Laughlin, a Nobel Prize-winning physicist at Stanford. “People have been changing string theory in wild ways because it has never worked.”

Of course this is the same Robert Laughlin who once said (rumor mode on) that if the Stanford physics department hired anyone in quantum computing he would resign (rumor mode off).

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QCSS05

The dealine (March 15, 2005) for the Summer School on Principles and Applications of Control in Quantum Systems to be held at Caltech on August 7-14, 2005 is fast approaching. If you’ve ever wanted to learn how to apply control theory to quantum systems, this looks like an amazing opportunity. The potential agenda includes:

  1. Experiments and applications for control in quantum systems – phenomenology and motivations for control
    • Applications of optimal, relaxation-optimized , and ensemble control in magnetic resonance
    • Quantum feedback control in atomic systems: applications to precision measurement
    • Quantum control applications in quantum information science
    • Quantum dynamics of superconducting circuits and circuit quantum electrodynamics
    • Quantum measurement and feedback with nano-electromechanical systems
  2. Quantum-physical modeling
    • Quantum mechanics in the Schrödinger, Heisenberg and Interaction pictures
    • Perturbation theory and master equations
    • Quantum probability and filtering
  3. Control theory: from classical to quantum
    • State-space modeling; introduction to optimal and robust control
    • Geometric control: overview and highlights
    • Stochastic control: overview and highlights
    • Control-theoretic model reduction
  4. Frontiers in quantum control
    • Presentations on latest research by leading practitioners in the field
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Hans Bethe 1906-2005

Yesterday the great theoretical physicist Hans Bethe passed away at the age of 98. Details can be found here.
Whenever I’m traveling and I’m trying to work on a plane, I think about Bethe. Because in 1947, Hans Bethe, on the trainride back to Schenectady, made the first rough calculation of the Lamb shift. And today, when we rush around the world, jetsetting our way from conference to conference, I often wonder if we slowed down, and took the train, whether physics wouldn’t be better off.
Then, of course, there is the famous Physical Review 73, 803 (1948), “The Origin of Chemical Elements” by R. A. Alpher, H. Bethe, and G. Gamow. I’ve always dreamed of finding a coauthor with a suitable last name to go with my food item last name “Bacon.”
Finally, there is this amusing story of a conversation between Bethe and Leo Szilard:

The physicist Leo Szilard once announced to his friend Hans Bethe that he was thinking of keeping a diary: “I don’t intend to publish. I am merely going to record the facts for the information of God.”
“Don’t you think God knows the facts?” Bethe asked.
“Yes,” said Szilard. “He knows the facts, but He does not know this version of the facts.”

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Stop Blaming the Bugs

I just got through watching the movie “The Butterfly Effect.” (decent movie, I could probably form a religion from its basic plot.) The name of the movie comes from a statement you sometimes hear from those who work in chaos theory:

The flapping of a single butterfly’s wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month’s time, a tornado that would have devastated the Indonesian coast doesn’t happen. Or maybe one that wasn’t going to happen, does. (Ian Stewart, “Does God Play Dice? The Mathematics of Chaos”)

And I have to say that I’ve never understood what I’m supposed to take from this statement. Sure many systems are chaotic and we can have large differences in behavior from seemingly small changes in the initial conditions. But I sometimes get the feeling that a causal relationship is being made in this statement: if it weren’t for the butterfly, the people in the path of the tornado would be fine, i.e. the butterfly caused the tornado. But this clearly isn’t true. There are plenty of other effects which are also casually necessary for the tornado. Do I get to blame the butterfly if an even smaller change in the wavefunction of single proton somewhere in the upper atmosphere changes the initial conditions by even a smaller amount than the butterfly and this in turn changes the entire outcome of whether there is a tornado? In fact, I would argue that we can only blame the butterfly if other changes in initial conditions of comparable size do not change the outcome of whether there is a tornado or not. Chaos may be ubiquitous, but I wish we’d all stop blaming the butterfly.

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What I Do

The life of a theorist (“Good Benito” by Alan Lightman, highly recommended):

He stands up from the boxes and looks out the window. To the east, in the distance, rises the steeple of a chapel, fragile and faint. The light changes. A cloud drifts over the sun. Then the sun is uncovered again, the little room fills up with light.
He lets down the blinds but keeps the slats open. Strips of light slide from the wall to the floor. He returns to his boxes, unpacks. A set of keys. A faded photograph of a young woman with auburn hair. Two old letters from John. These last things he puts carefully in a drawer. Most of the boxes are books. He stack them against the wall, the muscles flexing in his arms. The room darkens as another cloud passes over the sun, lightens, darkens again.
Now he lies on the upholstered couch in the corner. He beings writing. He writes on a white pad of paper, wavy lines and strange signs, mathematical symbols. He closes his eyes for a while, begins writing again. Someone knocks on the door, but he doesn’t hear. He imagines corrugated surfaces, magnified again and again. He calculates and imagines, while the room glows and dims and the sun slides slowly across the floor.

The best days of a theorist are lonely periods of intense concentration mixed with a sort of day dreaming creativity. And it’s one of the reasons I find it nearly impossible to complain about what I do.