Copasetic Flow

Here's today's special relativistic EM question.  Can the Thomas precession be shown to be a special case of the perihelion advance of relativistic elliptical orbits?  Any ideas?  Here's what's going on: We've been deriving the special relativistic  orbit of a charged particles around another fixed charged particle.  At the end of the day, you wind up with a perihelion advance which is a fancy way to say that major axis of the elliptical orbit won't stay put.  It swivels around, (orbits), the charged particle as well.  The advance angle of the major axis winds up being\\ $\delta\phi = 2\pi\left[\left(1 - \dfrac{\kappa^2}{l^2}\right)^{-1/2} - 1\right]$ Which is very, very, similar to the Thomas angle for the spin precession, or gyroscopic precession along a circular orbit at special relativistic speeds:\\ $\delta\phi = 2\pi\left[cosh\left(w\right) - 1\right]$ $= 2\pi\left[\left(1 - \dfrac{v^2}{c^2}\right)^{-1/2} - 1\right]$ In the expression...

This is kind of cool from yesterday's EM notes.  Our professor pointed out that if you calculate the field from a relativistically moving electric charge, you'll always find that it's pointed straight at the point of observation.  Anyone have any idea why?  The argument could certainly be made that if you measure the field from a static charge that it will also be pointing straight at you.  Then, there's also the realization that the Lorentz transformation only affects the E and B fields in a frame that are perpendicular to the frame's tangential velocity.  I'm not sure that's either here or there since the point of observation can be anywhere.  Here's the associated diagram for the curious.

The lab book today was a bit sparse and a bit dry.  This is a bit odd considering I got to play lab yesterday...  You'll see. First, here's an archival video of the presentation I did last Sunday for the TX APS section meeting here in College Station.  I fumble a few times, but the content is all there.  If you have any questions, they are very, very welcome! The second video has some kind of cool stuff in it.  Not stuff that went the way I had hoped mind you, but cool nonetheless.  Here's the deal; we'd hoped to make a spiffy little superconductor visibly quenching video.  The idea was to suspend a superconductor as a pendulum in a magnetic field.  It was hoped that as the field increased, the superconductor would swing away from the pole of the magnet, (it did), and that as the field increased more, the superconductor would quench and fall from it's suspended state, (it didn't).  Our melt-texture growth superconductor from CAN just wo...

 As always, look to the bottom of the post for background on what's going on. Finally, enough of theory and presentations!  I got back to the lab today!  Here’s the apparatus I built/used. NOTE:   As always, look to the bottom of the post for background on what's going on. No, the oscilloscope is not sticking its tongue out, that’s a floppy disc.  Remember those?   The small solenoid is what’s deemed a pickup coil.  It’s the first prototype, of the coil that will be used to measure the actual currents and magnetic fields produced by the can crusher magnet.  It’s exactly what it looks like, six complete turns made from a jumper wire.  The Styrofoam cup is to avoid abusing the small magnet block too much when it’s dropped.   The ‘scope pictured can capture a single waveform.  Here, it’s slowed way down to make a sweep over the course of several seconds.  It’s being used to look at the...

Summary :  Working more on using the superconductor to detect its own quenching field.  The initial setup is shown below.  The quenching test is described in the following.  A YBCO superconductor is placed between the poles of a very uniform magnet and then cooled into its superconducting state.  The field frozen into the sample at the state transition opposes the fringing fields on the magnet.  However, had the magnetic field been strong enough to quench the superconductor, the results would have been the pendulum swinging freely beyond the pole pieces' diameter until it encountered a field less than its critical field at which point, it would have re-entered the superconducting state and frozen in those field lines, suspending itself.  There's another realization of this process that will be tested today.  The pendulum is again suspended in a uniform field and the field is slowly increased.  It is suspected the sample will be deflected u...

I'm playing around with tracking metrics on my writing activities today.  Clearly I need to enhance my charting presentation skills, but the information here is kind of interesting to me.  It's about me, so of course it is, but it's interesting to think about in terms of why a writing log is useful as well.  Here's what I learned  As the semester has ramped up, I've been doing more writing on EM homework and less on EM notes in preparation for class.  That's not a sustainable model.  Work on the hray presentation an proposal has been ramping up nicely.  I need more detail on what aspects of each project I'm working on and more tracking towards defined goals.

Summary:  It looks like I'll finally get a good understanding of the gamma notation for moving proper velocities to lab velocities and back.  It'll be nice to know it inside and out, but a little irksome given all that can be done with the hyperbolic notation we're not using.  I want to maintain my fluency in both. There may be a subtle second notation for inverted Lorentz transforms.  As it turns out, the subtle notation difference of moving around indices in the top and the bottom with spaces is meant to keep track of which index comes first when you go back to side by side notation. First, we cover Lorentz transforms, (which are not in fact tensors), and contractions and arrive at the interesting result in equation 1.99: $\Lambda^\mu_\rho \Lambda^\sigma_\mu T^\rho_\sigma = \delta^\sigma_\rho T^\rho_\sigma$ Which indicates the transpose of the Lorentz transform times itself follows a sort of orthogonality rule making use of contravariant indices. Q: ...