Skip to main content

Alcubierre Derivations in Open Access

I was able to play with the Alcubierre warp drive derivations for a bit today!  I'm still trying to absorb all the niceties, but here's what I understand so far.  I'm just getting started on all of this and everything is very shaky.  So, please, anyone who happens to be familiar with oh, I don't know, the 3+1 formalism of GR say, please feel free to jump in.  Actually the more involvement the merrier, whether it be with suggestions, corrections, or questions.

Which brings up the Alcubierre github repository[1].  I went ahead and made an open access github project that for the moment holds only a mathematica file with the derivation details I've been able to compile so far, a wiki, and one open issue, (the space curvature graph looks a little too jaggy).  Here's the graph by the way, king of the 'Hello World' moment for Alcubierre work I suppose, (picture 1):

I'd hoped to have more to say about this tonight, but hopefully I can check in again tomorrow when I have a firmer grip on all of this and a bit more coherent one at that, (late night last night).

//Scraggly notes for tomorrow.....
Alcubierre uses a 3+1 formalism.  This means that space is assumed to exist in constant time slices, one slice for each instant of time.  He furthermore makes space flat.  In doing this, he shows that the line element, (the Pythagorean formula for spacetime), indicates that the space will be 'globally hyperbolic' and therefore can't violate causality, in other words, you can't go back in time and prevent your own birth.  the way I'm interpreting this is that if I have to move along a hyperbolic path, (picture 2 the red curves are the hyperbolas), in my coordinate system, then I can't execute a close curve, and I can't get back to where I started, (time-wise).

1.  github repository


Popular posts from this blog

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…