Recent content by Paul Colby

Strange? All my Hilbert spaces look like a corridor lined with doorways leading to death.

The PDP-8 I used to collect photon counting data had a bunch to display registers.

Or the advanced civilization they stumble upon can't imagine taking the risks or making the personal sacrifices needed to make such a voyage, even with their current technology.

I would think so, right? Shine a frosted and unfrosted LED on a white sheet of paper. You’ll note the paper isn’t uniformly illuminated and that the illumination pattern isn’t the same between diodes. A lux meter at a fixed position will sample just one set of angles which corresponds to some...

Isn’t detecting a saddle point straightforward?

Are there known examples of unstable solutions that yield stationary numerical configurations?

Never let best be the enemy of good enough. You have closed-form expressions for both methods. You could do an error analysis using the closed-form expressions. Several ways come to mind. One is to do a Monte Carlo simulation and add random errors to the model parameters. Another is to take...

To a good approximation when light interacts with transparent plastic it’s either scattered or absorbed. Frosting is a roughening of the surface which shouldn’t change the material's absorption. One way to measure the total light output by a source is to use an integrating sphere. This is a...

While this is true, my understanding is that representation theory yields just a solution of the reps field equations. The corresponding ladder operators require more work.

My fluency hovers somewhere between 0.5 and 0.75 Copenhagen Interpretations.

Typically people use feedback to solve such problems. This doesn’t require an accurate model of motion. All that’s needed is a measurement of the error and a response function.

There is a coordinate system, referred to as the TT gauge, that I find makes visualization of bar detectors easier. Think of an isolated atom, a point mass. As the GW passes, the atom follows a geodesic. In the TT gauge, an atom at rest stays at rest. It’s X, Y and Z TT-coordinates don’t change...

Also, for Ohms law, current flowing through a resistor dissipates energy in the form of heat. For Newton, force goes into kinetic energy. This process is reversible. A closer mechanical analogy would be a loss term ##F=-\alpha \frac{dx}{dt}##.

This is an excellent question which is why I have the best free will money can buy.

In physics, all theories are quantitative and formulated in terms of mathematics.