Paul Colby's latest activity

Metrics are symmetrical. TT gauge can only be obtained outside the sources. The 8 conditions are$$\partial^\mu h_{\mu\nu} =0 \quad...

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...

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

Cool project. State machines can be very effective. I find the design pattern used here kinda ugly. For certain, it works, but an...

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##...

At this point I find it instructive to consider some numbers. A round trip time for light in a 4km long interferometer is, $$...

The spin states are completely degenerate since your Hamiltonian doesn't depend on spin. You've chosen an orthogonal set of spin states...

I mean proper distance changes with ##s##, the proper time. These are frame independent quantities. In the TT coordinates, ##s=t##...

Yes. The ##\Gamma^\mu_{\nu\alpha}## terms in the geodesic equation only sprout space components in the TT gauge. Basically...

In the TT gauge (coordinates), the metric stain, ##h_{ab}##, only has spatial components, ##h_{xx}, h_{xy},\cdots##, are non-zero and...

I noticed the following question generated quite a lot of interest on the Internet. Which is larger ##e^{\pi}## or ##\pi^e##? Most (if...

Upon further reflection, I think that my previous answer is correct except in some particular case. Let us consider the case where : $$...

It actually isn’t different if you are close to the center of one of the plates. And it is a good example to show that the “vertical”...

I think it similar to the proof that pi=4 in the video below at 1:39. The explanation at 15:09 points out the fallacy @PeroK mentions above.