Recent content by Paul Colby

I don’t follow your question. [deleted synchronous gauge]

As I recall transverse refers to ##\partial^\mu h_{\mu\nu} =0## which is the case. EM waves are transverse in that E and H are orthogonal to the wave vector.

There should be one (and only one) def per state. onStarting, onOpen, onClosed, onOpening, and, onClosing. Anyway, a working solution is a working solution.

Cool project. State machines can be very effective. I find the design pattern used here kinda ugly. For certain, it works, but an alternative I've found useful is to encapsulate States as functions. In a recent project I needed to parse bytes from a USB device in realtime. In c++ states were...

If I recall correctly, a plane wave in the TT gauge propagating along z is, $$ h_{\mu\nu} = H_+ f(t-z) + H_\times g(t-z) $$ where ##f## and ##g## are arbitrary functions. The constant polarization matrices are, $$ H_+ = \left(\begin{array}{cccc} 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & -1 & 0...

At this point I find it instructive to consider some numbers. A round trip time for light in a 4km long interferometer is, $$ \frac{8\times 10 ^3}{3\times 10^8} = 27 us $$ Gravitational events detected are in 500ms to 1s duration range. Of course the number of light transversals for LIGO is much...

The spin states are completely degenerate since your Hamiltonian doesn't depend on spin. You've chosen an orthogonal set of spin states so you're diagonal already. I can't think of a reason why this wouldn't generally be the case. Nice work.

I mean proper distance changes with ##s##, the proper time. These are frame independent quantities. In the TT coordinates, ##s=t##. The actual measurement occurs at the point where the beams from each arm are combined. What’s measured is the time variation of the light intensity caused by the...

Yes. The ##\Gamma^\mu_{\nu\alpha}## terms in the geodesic equation only sprout space components in the TT gauge. Basically, ##\Gamma^x_{tt}=\Gamma^y_{tt}=\Gamma^z_{tt} = 0##. A point particle at rest in this frame remains at rest as the wave passes because all the ##\frac{dx^\mu}{ds}## terms...

In the TT gauge (coordinates), the metric stain, ##h_{ab}##, only has spatial components, ##h_{xx}, h_{xy},\cdots##, are non-zero and are time dependent. One way to view LIGO is in terms of the proper lengths of the interferometer arms. These lengths are time dependent as the wave passes. “At...

Is it clear Clifford algebra should be able too? Are symmetric matrices even in the algebra?

So, been back for a while. I left kinda disappointed with the noise performance of these tests. Syncing two radios with a common clock is work and it takes special hardware to boot. This got me thinking about trying to do things a different way. In the interim I've been reworking software for...

Yeah, starting from scratch with enough competence to actually do the design work is definitely the way to go. Also, cooling everything or most things is the way to go. There are definitely better ways than using cheap devices intended as general purpose radios for Hams. None of these are in...

This is a good question. I’ve done some experimenting separating the radios and shortening the cables from the clock generator. I’ve succeeded in reducing the common noise to the point that it can’t be used for syncing them. Every port is a two way street, noise comes in and noise definitely...

The total Johnson noise per Hz is ##4k_BTR##. For a perfectly matched network, only ##k_BTR## of it gets into the receiver. In this case it is ##1.38\times 10^{-23}\; 290\times 50 = -187 dBW/Hz## Did I miss something? Often not a vacuous question for me