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Paul Colby replied to the thread Graduate Zeros of functions analytic in 2 variables.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##... -
Paul Colby reacted to mathwonk's post in the thread Graduate Zeros of functions analytic in 2 variables with
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I don't know if the argument for my statement is of interest, but it is nice and fairly short; namely, Riemann showed for analytic... -
Paul Colby replied to the thread Undergrad "The wavefunction never collapses".Why is this any different than very large fluctuations being observed in local gas pressure in statistical mechanics? All micro-states... -
Paul Colby reacted to mathwonk's post in the thread Graduate Zeros of functions analytic in 2 variables with
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are z1, z2 complex variables? if so, the zeroes of an analytic function of 2 complex variables are never isolated. -
Paul Colby replied to the thread Graduate Zeros of functions analytic in 2 variables.I was slowly tumbling to this fact. ##z_1## and ##z_2## correspond to analytically continued polar coordinate angles. In my problem... -
Paul Colby replied to the thread Graduate Zeros of functions analytic in 2 variables.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... -
Paul Colby posted the thread Graduate Zeros of functions analytic in 2 variables in Topology and Analysis.This question crops up in solving electromagnetic boundary value problems. For problems with rotational symmetry, if ##f## has a node at... -
Paul Colby reacted to bhobba's post in the thread Graduate How valid is the indivisible interpretation of quantum mechanics? with
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I have been investigating Barandes's approach further, and indeed, it is quite general and can be applied to QFT. As an overview of the... -
Paul Colby replied to the thread Undergrad Entanglement might be the result of an underlying law?.These kind of discussions always add a bunch of stuff that’s just not there, IMO. There is no part of this interferometer experiment... -
Paul Colby replied to the thread A question about quantum entanglement.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... -
Paul Colby replied to the thread A question about quantum entanglement.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... -
Paul Colby replied to the thread Graduate Musing on the Foundations of Statistical Mechanics.One comment, $$dS = \frac{\delta Q}{T} $$ was know from thermodynamics. Unclear that atoms were even a thing when this form of... -
Paul Colby replied to the thread Graduate How valid is the indivisible interpretation of quantum mechanics?.Inequality with QM is by far the more interesting question. People definitely get benefits from reformulating a problem in different... -
Paul Colby replied to the thread Graduate How valid is the indivisible interpretation of quantum mechanics?.If it is a new theory, the authors clearly don't know either. -
Paul Colby reacted to PeterDonis's post in the thread Graduate Strings from almost nothing with
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A search on the arxiv number of the paper didn't turn up any other threads here on PF. So I think we're good.