Einstein's relativity in metaphor and mathematics by Enders A. Robinson

Apologies for the long hibernation.  I was getting a paper ready to submit and pushed just about everything else off to the side.  Hopefully, I'll get to write here more frequently as time progresses.  Today, if you're looking for a book on special relativity and you'd like to know more about Gudermannians, then Dr. Robinson's book just might be the one for you.

If you're a Landau and Lifshitz fan like me, it will take you awhile to get used to the style of this book. However, once I got my head wrapped around Dr. Robinson's metaphorical style, I really enjoyed his explanations of special relativity. There are no universes cluttered with rigid rods and ideal clocks at every coordinate point! In one chapter the author manages to introduce the hyperbolic nature of space time, Lorentz contraction, and Larmor time dilation all using the metaphor of ants living on a rope hung over a heater with laser holographic communication devices. The example comes off amazingly simply, but still manages to be entertainingly absurd.
The only two downsides are that the book is very, very linear. By the end of the ant chapter the author still hadn't fessed up that the chapter was about anything other than ants. Also, he makes some allusions that are historically inaccurate. In one chapter, Gudermann's space time is referred to. While this makes sense mathematically, and is a cool moniker for the concept, Gudermann died before Minkowski coined the phrase space time.

What about Dr. Robinson himself you ask?  He's also a very interesting guy who appears to have made it big in oil exploration!

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr.

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…