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Entries categorized as ‘Astrophysics’

Philosophia Naturalis #8

March 30, 2007 · 3 Comments

This post was delayed by a number of ridiculous technical mishaps, but issue number eight of Philosophia Naturalis - the physics blogosphere’s very own blog carnival - is finally here. There were a number of very interesting submissions spanning pretty much everything that is involved in physics and the practice of it, and so I’ve split them up accordingly. Enjoy!

Cool Experiments
Motivated by some recent quantum optics work recording the birth and death of microwave photons in a superconducting resonant cavity by a French group, Chad Orzel has proclaimed this to be “the golden age of experimental quantum optics”. And indeed, it seems to be: two other such experiments include this study of the Hanbury-Brown-Twiss effect, and this more recent realization of the delayed-choice experiment first proposed by John Wheeler in 1978. A closely related experiment is that of the ‘quantum eraser’ proposed by Scully and Drühl in 1981, and this post does an excellent job of summarizing the general principles.

On the opposite end of the size spectrum, Cosmic Variance recently hosted a very interesting discussion on some analysis of cosmic microwave background radiation data from WMAP (NASA’s much-publicized effort to very accurately measure the temperature of the CMB).

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Interesting Theory
As tends to be the case, most posts were of a more theoretical bent. The mapping of the E8 Lie group recently received a good deal of press, including a rather vague article in the New York Times (the gist of which was something along the lines of “a bunch of mathematicians did something really complicated involving a pretty picture, and apparently it has profound implications but we’re not exactly sure what.”) Mark Chu-Carroll and John Baez have taken a different approach, recently posting about the actual math involved and the whole point of the project. And speaking of recent math-y work that has received a good deal of press, these two posts report on this paper by Peter Lu and Paul Steinhardt (who used to be at Penn!) on signatures of quasicrystalline Penrose tilings in medieval Islamic architecture.

Penrose is an excellent segway into two posts by Scott Aaronson. The first poses the question: “what’s the connection between a black hole having an event horizon and its having a singularity? In other words, once you’ve clumped enough stuff together that light can’t escape, why have you also clumped enough together to create a singularity?” (This is related to the Penrose-Hawking theorems of general relativity). The second (or rather, the subsequent comments) deals with possible connections between the brain and quantum computers, something Roger Penrose has discussed in a good deal of depth. (Matt Leifer has a similar post, asking the question: “if quantum computers are more efficient than classical ones then why didn’t our brains evolve to take advantage of quantum information processing?“)

There’s more out there, too: see, for example, this post discussing the much-storied Bayesian theorem and connections to Bell’s inequalities, or this post on ‘biophysical economics’, an economic theory rooted in biological and physical realities first put forth in the 20’s. Something that struck me as being particularly interesting was this post on the use of evolutionary algorithms in lattice QCD simulations. Meanwhile, Ponder Stibbons has been plowing through Huw Price’s book (Time’s Arrow and Archimedes’ Point) on some of the more philosophical questions of physics, with posts on Price’s objection to dynamical explanations of entropy increase (”they can never account for the asymmetry in our observations unless they themselves have asymmetric assumptions”) and a modern-day version of Olbers’ paradox.

And of course, a good deal of very interesting physics (albeit of a different sort) goes into fields of inquiry that some would consider unconventional, like geophysics. These two posts dealing with earthquakes and volcanoes touch on this to a certain extent. The latter is particularly interesting, looking into the various possible triggers for volcanoes (and drawing connections between large earthquakes and volcanic eruptions, motivated by a fictional account of Charles Darwin’s journey on The Beagle).

The Culture of Physics
Speaking of geophysics, Jennifer Oullette has written about a talk at the recent APS March Meeting on large-scale pattern formation in geological systems, citing some work by Meredith Betterton (who gave a talk here at Penn on an unrelated subject recently) on the creation of artificial spiky ice formations. (March Meeting is an event when thousands of physicists get together and tell each other about what they’re working on - held, incidentally enough, in March.) A number of people have posted about various events at March Meeting; see, for example, this other post by Jennifer Oullette, this post by Travis Hime, and this one by Doug Natelson - or see the PhysicsWeb blog.

Having huge meetings and partying like rock stars isn’t everything, though. Among other things, the physics community (just like any other) has its share of scandals, politics, marketplace tactics, things of that sort. Sabine Hossenfelder, for example, has recently blogged about the problems of treating the scientific community as a marketplace, while Julianne Dalcanton’s post on physics’ “cult of genius” definitely touched a nerve among readers. Meanwhile, Clifford Johnson has shared his views on recent events regarding an imprisoned theoretical physics grad student. (And of course, there’s the media aspect of things: John Conway recently picked up on his two previous posts on the search for the Higgs boson to blog about the unexpected media response.)

Communicating Physics
Tommaso Dorigo recently posted about some of the problems associated with the way physicists communicate things to laypeople, dealing specifically with an example from high energy physics (what is a lower limit at 95% confidence level, anyway?). At the end of the day, the physics blogosphere’s rather good with this kind of thing. For example, ‘basic concepts’ posts (like the ones mentioned in this excellent post, or this one - part of a series - on special relativity) do an excellent job. And hey, communicating physics is kind of the whole point of this blog carnival, in a sense. I think that’s where I’ll end things - hopefully it’s been interesting. Thanks to everyone who submitted either their posts or someone else’s.

Categories: Academia · Astrophysics · Biophysics · Education · Interdisciplinary · Mathematics · Media · People · Physics · Quantum Mechanics · Science · Sociology · Technology · Websites

Quantum Information, et cetera

March 14, 2007 · 1 Comment

Today’s been a pretty exciting day. Among other things, we finally used all these abstract concepts relating to modules that we’ve been developing in my algebra class to derive some really neat results: in particular, rational canonical form and Jordan canonical form for matrices that can’t be diagonalized. There’s just something about taking all this seemingly useless theory and deriving something nice (and not so obvious) that you can actually use from it that’s very satisfying. Hey, I may even blog about it at some point. Another interesting math idea today was the subject of a colloquium that I wasn’t able to attend (but found out a good deal about from those who did): can we hear the shape of a drum? (Among other things, the question ties in with work done by our Dean, NASA’s WMAP project/this PRL, and the general notion of inverse problems such as those people deal with in things like MRI). And of course, my abstract algebra recitation session turned into me arguing with my TA (an algebraic geometer) and a computer scientist about why statistical mechanics is The Coolest Thing ever. What can I say? Never get me started on statistical mechanics - it’s just such a gorgeous subject, and I can’t get enough of it.

Anyway, while the math colloquium was going on, I was off at today’s physics colloquium by Prof. Charles Marcus of Harvard University, something I’ve been looking forward to for a good deal of time now. And what a talk it was: although I would have preferred more technical details, the talk catered to a pretty general audience, and it was perhaps the clearest physics talk I’ve been to in a long time. He started off by reviewing the history of computation (from the Antikythera mechanism of 150 BC to the first integrated circuit, 50-ish years ago), noting that quantum information processing is really a new paradigm in this history (to paraphrase, the parallelism in computation implied by the multiplicity of states inherent in quantum mechanics is something that hasn’t really been possible till now) and surveying recent developments in solid-state implementations of controllable qubits from his lab. Most of the relevant papers are on his lab webpage (linked above), and a lot of the technical details are presented in this talk he gave at KITP in 2006, although he did present some very recent data pertaining to this paper. All in all, a very cool talk - I especially like the terminology in this field, what with the ‘Zamboni’ effect and ‘bucket brigades’.

I can’t wait for next month’s colloquium - David Nelson will be speaking!

Categories: Abstract Algebra · Academia · Astrophysics · Biophysics · Classes · Condensed Matter Physics · Interdisciplinary · Mathematics · Papers · People · Physics · Quantum Mechanics · Science

Magneto-what?

February 17, 2007 · 1 Comment

Today’s post is a quick one, since quantum mechanics and abstract algebra (in particular) and classes (in general) have kind of taken over my life. The subject is something that I got interested in about a year ago, in an advanced applied math class of all things: Magnetohydrodynamics, or MHD for short.

sun2.jpg

The basic idea behind MHD is relatively straightforward. One of the basic principles of electromagnetism is that electric and magnetic fields are intimately linked in a manner that is encapsulated quite elegantly in Maxwell’s equations; for example, a changing magnetic field can give rise to an electric field and induce a current in a conductor. One of the basic principles of fluid dynamics is that, well, fluids move in an interesting way, and the starting point for understanding this is the Navier-Stokes equations; for example, turbulence manifests itself in myriad ways, from smoke rising to ocean currents to the atmospheres of stars, and is still not very well understood.

Very well then: what happens when you have a charge (e.g. ionized) fluid whose dynamics are describable by the Navier-Stokes equations in the presence of a time-varying magnetic field? For example, the field affects the overall macroscopic motion of the fluid, which in turn gives rise to further electromagnetic effects since it is charged. How does one understand this kind of system? This question is the heart of MHD, a subject initiated by Hannes Alfven - for which he received the Nobel Prize in 1970 - and one that has been the subject of research in many, many fields, including applied mathematics, plasma physics, astrophysics, and geophysics.

The sun is an excellent example of a rich MHD system (the image above is from here, by the way): everything from sunspots to the solar wind to the Parker spiral involves magnetohydrodynamical effects. (That last one is particularly fascinating: did you know that the spiral shape of the Sun’s magnetic field “as it extends through the solar system… is similar to the pattern produced by a spinning lawn sprinkler, for similar reasons”? I didn’t before I came across MHD.) Another system that seems to be under quite intensive study at the moment is the magnetorotational insability (MRI), which is apparently a means of explaining anomalous viscosity in accretion discs.

Anyway, the mathematical details (which I had to work out for said applied math class and were surprisingly fun) get slightly complicated, but the key principles of ‘ideal’ MHD are that:

  • the charged fluids are continuous, so one can ignore mean free path effects
  • the charged fluids are perfect conductors and flow without drag
  • thermal effects don’t matter
  • the speeds under consideration are small enough to ignore relativistic effects

Now clearly these assumptions are whopping ones, and do indeed break down in many circumstances - but that’s ok. A good deal of hard work by a number of people has led to immense progress in understanding ‘non-ideal’ MHD, but it’s surprising how far you can get with these simplifying assumptions. One could, for example, start with the Navier-Stokes continuity (basically a way of saying that mass is conserved) and force (a way of saying that momentum is conserved) equations, plugging in expressions for electric and magnetic fields, and throwing in the energy equation (the first law of thermodynamics, which is a way of saying that energy is conserved) and the induction equation (one of Maxwell’s equations, which specifies how the magnetic field changes with time). But wait, we’re not done: to ‘close’ this system of equations, one can throw in two more equations: another of Maxwell’s equations (the divergence-free condition for the magnetic field to make sure you have no magnetic monopoles floating around) and the ideal gas equation of state. Turn the crank, and out pops a new field of study - MHD. So there you have it.

As an aside, I want to briefly point out that one of the reasons why this and other things of a fluid dynamics nature are of interest to applied mathematicians is because most of the time, one can’t solve these equations exactly and the analysis can be very tough (in math-speak, these equations constitute a nonlinear hyperbolic system, which means that finite-difference schemes tend to give solutions that blow up, among other things). Mathematicians can be quite good at coming up with ways of coping with this - for example, coming with means of simulating them numerically (such as Godunov’s scheme).

Categories: Academia · Astrophysics · Classes · Condensed Matter Physics · Education · Interdisciplinary · Mathematics · Physics · Science