Tuesday, August 24, 2010

The wisdom of combining complementary techniques





Thursday, August 19, 2010

Deep thoughts....

Pondering introductory mechanics has made me think again about some foundational issues that I've wondered about in the past.  Mach's Principle is the idea, put forward by Ernst Mach, that the inertial properties of matter depend somehow on the distribution of matter at far away points in the universe.  The classic thought experiment toted out to highlight this idea is "Newton's bucket".  Imagine a bucket filled with water.  Start rotating the bucket (relative to the "fixed stars") about it's central axis of symmetry.  After transients damp away due to viscosity of the water, the water's surface will have assumed a parabolic shape.  In a (non-inertial) frame of reference that co-rotates with the bucket, an observer would say that the surface of the liquid is always locally normal to the vector sum of the gravitational force (which wants to pull the liquid down relative to the bucket) and the (fictitious, and present because we're working in a rotating frame) centrifugal force (which is directed radially outward from the rotation axis).  [In an inertial frame of reference, the water has arranged itself so that the gradient in hydrostatic forces provides the centripetal force needed to keep the water rotating about the axis at a constant radius.]  This rotating bucket business, by the way, is a great way to make parabolic mirrors for telescopes.

Mach was worried about what rotation really means here.  What if there were no "fixed stars"?  What if there were no other matter in the universe than the bucket and liquid?  Moreover, what if the bucket were "still", and we rotated the whole rest of the universe about the bucket?  Would that somehow pull the liquid into the parabolic shape?  This kind of thinking has been difficult to discuss mathematically, but was on Einstein's mind when he was coming up with general relativity.  What does acceleration mean in an otherwise empty universe?  There seems to be reason to think that what we see as inertial effects (e.g., the appearance of fictitious forces in rotating reference frames) has some deep connection with the distribution of matter in the far away universe.  This is very weird, because a central tenet of modern physics that physics is local (except in certain very well defined quantum mechanical problems).    

The thing that's been knawing away at the back of my mind when thinking about this is the following.  There is a big overall dipole moment in the cosmic microwave background.  That means, roughly speaking, that we are moving relative to the center-of-mass frame of reference of the matter of the universe.  We could imagine boosting our velocity just so as to null out the dipole contribution to the CMB; then we'd be in an inertial frame co-moving with the overall mass distribution of the universe.  If inertial properties are tied somehow to the overall mass distribution in the universe, then shouldn't the center-of-mass frame of reference of the universe somehow be special?  Some high energy theorist may tell me this is all trivial, but I'd like to have that conversation.   Ahh well.  It's fun that basic undergrad physics can still raise profound (at least to me) issues. 

Friday, August 13, 2010

Memories and The Mechanical Universe

As I get ready to teach honors mechanics to first-year undergrads, I have been scouting the web for various resources.  I ran across the complete series run of The Mechanical Universe (streaming for residents of the US and Canada), a great show that I remember watching on PBS occasionally when I was in high school.  It's based on first-year physics at Cal Tech, and each episode opens and closes with David Goodstein lecturing to a class in an auditorium.  It's very well done, and the computer animation was exceptionally good and informative, considering it was produced in the mid-1980s.  Thanks, Annenberg Foundation, for making this show available!  (Funny sequel of sorts:  I actually had the pleasure of meeting Prof. Goodstein in 2003, and for some irrational reason I was surprised that he didn't look exactly the same as he had in 1984....)

Wednesday, August 11, 2010

What I missed, plus book recommendations

I'm finally back from travel, just in time to immerse myself in prep for the upcoming semester. It's hard to believe that classes start in 10 days.

While I was away from blogging, it looks like I missed some fun posts. For example, the Japanese group that made the first major discovery of the iron pnictide superconductors has found that sake (or something in sake) boosts superconductivity in a related compound.  Chad Orzel did a pretty nice job posting about superconductivity as well, though I might do a different post later about this.  He also had a post prompted by a reader demanding to know why all statistical physics courses are lame.  (The answer is, of course, that the reader had never taking stat mech from me :-).  Ahem.  Perhaps not.)  Along related lines, Charles Day at Physics Today has started a blog, which I will add to the blogroll at right.  Glad to see that he leaps into discussing why he likes condensed matter physics.  I also missed the excitement about the proposed proof that P != NP.  The discussion online about the would-be proof is very impressive - it's always nice to see Fields medalists blogging, especially when they write as well as Terence Tao. 

One final remark for now.  I strongly recommend reading The Alchemy of Air and The Demon Under the Microscope.  These are terrific, interesting books, and they really do a great job of making science (in this case chemistry) as exciting as any novel.  Many thanks to Paul Chirik for recommending them to me.