Charles Bloom : Physics Section

Well, since I do physics, I figured I might-as-well say a little something. I'm a graduate student at Caltech , doing either particle theory (including String Theory) or quantum information theory

Here are a couple of things to talk about:

• Teasers for some new things I've done that I haven't time to write up :
  
  
  • Bosonization provides insight into nonperturbative structure (also: every 2-d theory is supersymmetric (in disguise))
    
  • Fluid dynamics is a 3-d gravity theory
    
  • There's a non-perturbative diagrammatic way to do topological QFT ; I can get HOMFLY from Chern-Simons, Conway from BF, and Vassiliev from 2-d graphs.
    
  • Feynman amplitudes can be generalized to allow non-asymmetric time flow with only minor (mathematical) changes.
    
  • There's a measure tighter than Holevo Information in quantum computing which seems to be the correct bound on accessible information.
    
  • more.. ?

• Charles Bloom / cb at my domain
  send me email if you have a comment on anything here.

• The 2d Dirac Equation via light-cone lattice. Corners are a (-i) amplitude. This is new work, so far as I know. (4-1-98)

  Also, for reference, the old style The Dirac RQM equation , derived using "matrix composition" (modified 8-2-97), a formalism of my own invention (ok, so its basically trivial, but few people have actually written down the formalism, which is quite useful).

• My info-theory news articles contain more and more physics.

  One of them is An Adaptive Quantum Coder.

• Some posts from sci.phys.research on susy and sugrav, and sustr (that's supersymmetry, supergravity, and superstrings, and takes a super-long time to say).

• geometry and duality is amazing stuff.

• The Feynman Amplitude Postulate is more powerful than you think. (more to add here)

• The Kaluza-Klein and other topological aspects of Yang-Mills + Gravity

• Don't be afraid of more than four dimensions

• Some thoughts on statistical mechanics

• Some thoughts on quantum mechanical measurement

• Generalization of the relativity postulate

• Proof of Heisenberg's Uncertainty Principle directly from the [p,q] commutator. Very simple and nice.

• Take a look at my news section for an artictle on time-asymmetry, entanglement, and complexity.

• Hi, maybe some people with more astronomy knowledge could fill me in on the details of the "dark matter" question (and what's known).

  My problem with the issue is exactly the opposite of the astronomer's : why isn't there more dark matter?

  From a field-theory viewpoint, physics is all about "what consistent theory can I write down", then the question becomes "why did nature choose NOT to use such and such a theory?". A question I've always pondered is : why aren't there an infinite number of other types of matter that decouple from our own?

  That is, if I can write the L for QED, I can just as well duplicate it for "2-electrons and 2-photons" then for 3,4,.. ; I could have several copies of the standard model, or just lots of free scalars particles, etc. They all decouple (and hence, this question is usually blown off by field theory textbooks), except via gravity - in which case we would see them as something like dark matter (or perhaps a cosmological constant). (perhaps a measurement of a negative cosmo. constant means there is a preponderence of "shadow world" fermions)

• There seems to be some hypocracy in the current physics consensus towards renormalization. As Weinberg so incitefully emphasizes : we would need renormalization regardless of whether or not there are divergences, because the "base" quantities (mass, charge,etc.) are corrected by dynamical effects (recall the classical self-resistance of the electron which corrects its mass) so not equal to the "real" experimental quantities. The renormalization flow (I refuse to say "group") only emphasizes the fact that this is important. Thus, the infinities of QFT are invisible to the predictions of the theory. From an outside observer (an alien), the mechanics of our theories is irrelevant, perhaps primitive or crude; only the predictions of the theory are physical, the the divergences are nowhere in them. In this sense the divergences in our machinery are just a coincidence caused by the modality in which human beings do mathematics. Nothing I have said here is very new or shocking; what I find strange is that physicists who are aware of this find the exactly finite theories (supersymmetric QFT, and susy-strings) so appealling; after renormalization (which is necessary in either case) they are aesthetically invisible to divergences. (I do not deny that the finite theories are so unusual as to consitute an amusing mathematical construct).

  Two addenda : an assymptotically free theory, or a non-renormalized theory, might be "final" - that is, small scale/high energy effects are not dominant, so we can imagine that string theory, gravity, or whatever, cannot be large corrections. Next, I find supersymmetry particularly annoying, because the lack of a Beta function actually makes it harder to get non-perturbative information. Similarly, when you have divergences, it's a good thing, because then all finite terms are small in comparison, making computations very simple.

• I have most recently done (productive :^> ) research on the hydraulic jump in fluid mechanics. While working on the computational simulation of the jump, I wrote plot (25k,zip) an interactive plotter for Win95 (zoom,scroll,etc. on 2-d data or 2-d vector field data).

• Here's something cool I noticed the other day : The Cigarette Boundary Layer. Take a burning cigarette, carefully rub it across a vertical wall; you must apply pressure, pushing the "cherry" against the wall, but not putting out the cigarette; now pull it away. The result : a trail of smoke is left "stuck" to the wall in the path of the cigarette. Now, of course this is true, but most of the cigarette smoke blows away after it leaves the cigarette; the smoke which you have "spread" on the wall sticks there! This is a demonstration of the fact that air is a fluid, and that fluids have boundary layers on rigid surfaces, where the flow is very slow. You introduce the smoke (a flow marker) into the boundary layer, and it sticks there for a time scale much longer than it sticks in open air.

  I'm told by my cohort Ed Burns that this is even more dramatic if you use a straw to blow the smoke onto a flat surface, like a table. I encourage you to try this home experiment, especially if you are under 18.

• why self-resistance of induced fields is proportional to gravitational attraction (in non-physics lingo, why is mass heavy, given that we know why it's slow?) Perhaps this is one of the things addressed by string theory. Hmm, if there were a self-resistance to gravity, that would make things complicated : does gravity work on the "rest" mass or the "resisting" mass? (actually masses would be self-attracting, not self-resisting).

  The answer is simple. All objects in a relativistic theory naturally move at the speed of light. If they move at less than the speed of light, they are "slow". A "slow" (aka massive) object must be slow because some force is acting on it (ie the self-resistance above). A force means that space is full of gaugons mediating that force. Gaugons carry energy. Gravitons couple to gaugons (energy). Hence : gravitons couple to the "slowness", aka mass. This is why mass is heavy, given that it's slow.

• why the eigenvalue of the particle-exchange operator is equal to the eigenvalue of the rotate-360-on-particle-center operator ( aha! this one is simple topology. apparently a few other people wondered about this one too (such as Feynman) - why didn't anyone tell me!) There are several web sites on this, and the 1986 Dirac Memorial by Feynman has an even better discussion. See:

  Candle Dances & Atoms

  John Baez' outline of the Spin-Statistics proof

  JB's harmonic oscillator, spin, and groups

  Read Joshua W. Burton's summary of Feynman's Candle Dance argument

  I'll put up my notes on this some day. Feynman also shows that T^2 (time reversal squared) is the same as rotation by 360. This makes sense because T^2 is just like E^2 (exchange) or P^2 (parity). However, the T result is amusing because we can derive it a few different ways (Feynman's intuitive spin-states method, and Heine's group-theoretical method) and it has various effects, like on antiparticles, and quickly leads to bose/fermi statistics.

• Transform theory. This is a very general and powerful tool in Physics, and it is useful to think of it in terms of the image-compression paradigm : to work with a complex,large data set most easily, you must first transform the data into it's "natural" basis; i.e. the basis in which data items are un-correlated, where only their absolute magnitude has "information". For example, I think of Statistical Mechanics as a functional transform from all the coordinates & momenta of particles to the partition function. There is then a further transform which takes the partition function to the functions T,V,E, etc. You can think of the many body problem in the same way; transform all the coordinates & momenta into a base state with excitations.

• Black Hole Information theory. The big deal now-a-days is : do black holes consume information? However, it seems to me that something important is forgotten here : conservation of information is not a law of physics! Claude Shannon came up with it in 1948 because it was a useful tool in writing the theory of coding. In fact, the formal form of "Information" was simply derived so as to be "reasonable" (i.e. you demand certain properties and look for the right mathematical form. See my copy of Shannon's Entropy. I do agree that Boltzmann Entropy and Shannon Entropy are related, but the Boltzmann Stat-Mech "laws" are not something we should cling to firmly. (see my notes on stat-mech)

• Monopoles : here's the resolution to my previous qualms. Maxwell says d_i B_i = 0 , ok, that's fine and true (it must be), **except** where B is singular, at which point all bets are off. Thus monopoles can arise because of a singular string (Dirac string) in the vector potential. They also arise (more pleasingly) as topological "twists" of the field due to the way the "sheet" of field is "tied down" at infinity.

  Actually, this illustration begs the question : how can the physics of singular bundles of field be predictive? It seems whatever field equations we write down can be violated by singular points in the field. Is this true? Fortunately, it appears nature does not often take advantage of her ability to create singularities. (one might say singularities cannot be created from finite fields by any process, but of course the singularties could be left over from the big bang, or could be produced by black holes which are singularities themselves (maybe)).

  The resolution is that there need not be a singular string (though it is a nice picture, especially for duality). We can instead do it by asuming that the connection A cannot cover the sphere surrounding the monopole - we must use multiple coordinate patches. Even though A is trivial on each patch, (D*B=0) the transition function between patches contains a "kink" (winding) so that A has global structure. Integrated over the sphere, this kink provides a net flux equal to that of the monopole. Dirac's string put all the flux on a single point on the sphere - here it is on a loop (an equator) of the sphere. Dirac's theory had a special underlying invariance of the motion of the string (which was actually gauge invariance, but this was not manifest). In the connection-patch theory, gauge invariance is that we can choose the "weld equator" to be anywhere on the sphere, so that the relation of this invariance and gauge invariance is manifest. The kink in coordinate patches is a "large" gauge - it can be continuously reached by infinitesimal gauges starting at zero, so it cannot be transformed away.

  There is a very real sense in which a "large" (not connected to the identity) gauge transform is a particle (usually called a pseudoparticle, but the word pseudo is only quasi-meta-meaningful). For example, instantons are also arived at in this way - as a kink in the fiber over a 4-manifold instead of over a 2-manifold as was the case with the monopole. Though I understand this as well as anyone I've ever met, this is still a bit mysterious to me. It's quite clear how things like the "theta angle" come about in the action, but the "dynamics" of these large-gauge-kinks is a little odd. In the original Dirac string picture, duality is quite obvious:
  F <-> *F and e <-> 1/e
  
  E&M charges + Monopole Strings <-> Monopole charges + E&M Strings
  
  But it's not so obvious with the gauge-configurations.

• Group Theory. All this business with representations and lemmas and whatnot is not group theory, it's silly formalism. You can write group theory in terms of QM Operators, where each operator in the group is a Dirac-Ket-Bra (a = Sum(i,j) a(ij)|i}{j| ) and now all the eigen-ket theorems fall out easily; representations just become your choice of basis for the kets. I'll put up a short course on this style of group theory some day.

• how to derive operators for raising and lowering, given the operator you wish to raise/lower (I think this may be a provably unsolvable problem) (hmm. the inverse problem is quite easy -> I should be able to show that some matrix in the linear algorithm is not invertable..) The inverse problem is properties of the ladder operators.

• Perturbation. There are interesting things to say about perturbation : a general form for Nth order perturbation , and the idea that a perturbation expansion is somehow fundamental. I'll add these notes at some time.

• For my senior Solid State Physics class (PHY 375S at the University of Texas, taught by Robert Martinez), I wrote a thesis on the SuperFluid state of the boson Helium 4.

  I took a somewhat unique view-point, studying the low-energy states of He II as a form of condensed matter, with many of the properties of crystals. For example, the atoms act as though they were oscillating in a space confined by the lattice spacing distance (this is due to the invariance under permutations). Similarly, the scattering form factor has peaks at the reciprocal lattice lengths. Since He II is a liquid, the peaks are spread out, and the lattice oscillations are much larger than those in solids. Of course, phonons are found to be the basic excitation in He II, just as they are in crystal lattices.

  The paper is available for download here in MS Word 7.0 format helium.zip (50k)

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