Recent content by Paul Colby

Visualize as a manifold seems to be all you consider. There’s the algebraic aspect of ##SO(3)## as well.

Given your original question concerning photons and the double slit experiment, how have your views changed? The experiment showed that the interference pattern persists even with a significant path length change in one of the two paths.

Interference patterns happen for multiple “it”s, right? From post #5 “it” was water waves, sound waves or EM waves. “It” could also be particle beams of various flavors. Each of these physical systems are quite different yet exhibit similar wave phenomena. In post #1, two expressions, one from...

What is “it” in terms of currently accepted theory?

Except, this sounds to me like you're infering one event, photon emition, from the photon detection. That's not how thermal sources work, at least by the mathematics. Photon numbers are neither certain nor conserved in the interaction between the source/field or the field/detector. When or...

More specific? I was discussing just the quoted statement I quoted in post #15. Hard to get more specific. What is really called for is being more complete. That would require a discussion of the mathematics used to describe the EM field. I did supply an established fact; the interference...

Actually, I would say your statement is filled with notions that are incorrect. A double slit interference pattern happens independent of the number of photons. It can be realized one photon event at a time. Photons are quanta of energy and momentum exchanged between the EM field and the...

My training is in experiment side of physics. If I turn on this "forced physical" interaction, I would have to get up from my stool and adjust the experimental apparatus. I'd block a slit, actually change some EM boundary condition, thus changing the interference pattern in some way. In fact...

A double slit interference pattern can be produced using sound or water waves. So interference is a wave phenomena in each of these cases. The “awe and mystery” of the optical example comes about because of the quantum mechanical nature of photons, not the interference pattern.

The issue I have with this is the equation of motion, ##m\frac{d^2x}{dt^2} + k(t)^2x = 0##, Is quite different than this one, ##m\frac{d^2x}{dt^2} + k(x)^2x = 0##. [edit] Just to add some clarification, the first equation corresponds (less a dampening term) to that found in the WIKI. The...

The notion that just a nonlinear component, like a non-linear spring, leads to parametric amplification left me wondering. This wiki article https://en.wikipedia.org/wiki/Parametric_oscillator actually gives a simple harmonic oscillator model for a parametric amplifier that paints a very...

For parametric amplification, doesn’t one need to change a parameter? In your case it would be changing the spring constant with time. For electronic examples, one uses a voltage dependent capacitance. A reversed biased diode has a junction capacitance that depends on the bias voltage, for example.

Cool. For an analytic function, ##f##, in two complex variables one may solve ##f(z_1,z_2)=0## for ##z_2## as a function of ##z_1##. Zeros, as you pointed out, are not isolated points. For analytic functions of a single variable, the zeros are isolated if the function is not identically 0.

Why is this any different than very large fluctuations being observed in local gas pressure in statistical mechanics? All micro-states are possible. We just don’t observe ones like these because they are just too rare.

I was slowly tumbling to this fact. ##z_1## and ##z_2## correspond to analytically continued polar coordinate angles. In my problem, each zero corresponds to a new vector in a separable Hilbert space. Non-isolated zeros are problematic. Fortunately, the sphere is conformally mapped to the...