Recent content by Paul Colby

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...

Ah, problem solved. In the form asked, one simply solves ##f(z_1,z_2)=0## for ##z_2## in terms of ##z_1##. The real problem that was troubling me is addressed by realizing real polar coordinates, ##(\theta,\phi)##, are in fact just a single complex coordinate. The functions, ##f##, are really...

This question crops up in solving electromagnetic boundary value problems. For problems with rotational symmetry, if ##f## has a node at ##(\theta,\phi)## then ##(\theta,\phi')=0## for all other ##\phi'##. This (I think) implies that, $$f(\theta,\phi)=F(\theta)G(\phi)$$ which, for the problems...

These kind of discussions always add a bunch of stuff that’s just not there, IMO. There is no part of this interferometer experiment that isn’t described by classical EM wave, beyond the quantization of the field wave amplitude being a QM operator. This wave exists everywhere in the experiment...

By this view, why isn’t QM more understandable to you than classical physics? It’s clearly a better theory. All the things known about nature that bother you will remain true in any new theory. So why hope a new more complete theory will ease you? At best you can only expect to maintain a status...

It may well happen that this deeper understanding will be even less understandable in the sense that people find QM at the moment. I see no reason a more inclusive theory would improve the current situation. In fact, I expect the opposite.

One comment, $$dS = \frac{\delta Q}{T} $$ was know from thermodynamics. Unclear that atoms were even a thing when this form of entropy was coined.

Inequality with QM is by far the more interesting question. People definitely get benefits from reformulating a problem in different way. It potentially opens up new solutions and new ways of thinking about problems. As to this paper rendering QM more satisfactory to those perplexed by the...

If it is a new theory, the authors clearly don't know either.

It's beyond my depth but I saw a recent paper Strings from almost nothing that sounds interesting to me. If this has been discussed previously on this forum I apologize.

I agree. In philosophy any statement X may be argued as well as any statement not X with no acceptable means of determining which, if any[1], is to be preferred. [1] don’t leave out any middles.

Clearly, I can’t. Which is also my point. Neither has anyone else. I’m also not the one employing such a term.

So, dressing the same physics up in a different mathematical framework definitely can have value. However, how is this mathematical formalism more realistic than what one started with? QM things still do QM things.