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Mathematician


Apr
1
comment Sensor Temperature with time constant
Migrating per OP request.
Feb
19
comment Does the 1-D poisson's equation have monotonic potentials if $\rho=\rho(\phi(z))$?
@Anode: no. You evaluated at $\phi = 0$, which is nonsense. Integrating a derivative in $z$ you should evaluate at $z = z_0$ and $z = 0$. Incidentally it also makes your choice of upper bound of integration "$\phi'$" look very bizarre. (Also, at this level it is a problem with calculus, and has relatively little to do with physics.)
Feb
19
comment Does the 1-D poisson's equation have monotonic potentials if $\rho=\rho(\phi(z))$?
Let me expand on Qmechanic's comment: $$\int_0^{z_0} \frac{d}{dz}\left( \frac{d\phi}{dz}\right)^2 dz \neq \left(\frac{d\phi}{dz}\right)^2$$ Instead $$\int_0^{z_0} \frac{d}{dz}\left( \frac{d\phi}{dz}\right)^2 dz = \left(\frac{d\phi}{dz}\right)^2 \Big|_0^{z_0}$$The "wrong" expression looks "manifestly positive". The correct one doesn't.
Dec
5
comment How is it possible for astronomers to see something 13B light years away?
let us continue this discussion in chat
Dec
5
comment How is it possible for astronomers to see something 13B light years away?
@Alfe: you should really ask a new question :-). But the answer to your questions are, in order: (1) Yes. (2) The problem with explaining ly is that in GR, while there is a notion of absolute time difference (by maximal proper time) between two causally related events, there is no notion of "absolute spatial distance". Spatial distance is only defined relative to fixing what it means by "now" (remember, time is not absolute!) That things are simpler in special relativity is really a happy accident. (3) No problem. (4) No. (5) What about it?
Dec
5
comment How is it possible for astronomers to see something 13B light years away?
@Alfe: the "contradiction" is only in your understanding of general relativity. General covariance does not mean what you think it means, and in particular it does not mean that by attaching a local coordinate system you can pretend you live in Minkowski space and do computations as if you live in Minkowski space.
Dec
5
comment How is it possible for astronomers to see something 13B light years away?
@Alfe: you assumed that the universe is static. Going back to basic noneuclidean geometry in two dimensions, let us consider the following scenario: start with two points, draw a straight (geodesic) line between them. Start the two points moving with the same speed in the direction perpendicular to the line. In the flat Euclidean geometry the distance between the two points remain forever the same. In a hyperbolic (negatively curved) geometry, the distance between the two points get larger and larger. The latter is basically what happens in an expanding universe.
Aug
20
comment Trapping a lightray
@John: in addition, I find it rather surreal to have a professor of physics tell me that it is worthless to consider an idealised system that is impossible/impractical to realise in our physical world, and that older and approximate theories should be immediately discarded in their entirety just because they weakly violate a more newly described physical principle. But since I don't gain anything from defending this gedankenexperiment, I shan't argue further on this issue.
Aug
20
comment Trapping a lightray
@John: geometric optics works well enough for us (and our ancestors) to build working eye glasses and telescopes, in spite of the fact that the thin lens approximation may not always be valid. Newton's original laws of motion runs counter to the "physical intuition" of Aristotles because in the real world there is friction and a ball doesn't go on rolling forever. Idealisation and abstraction are powerful aids to problem solving, and have long traditions in physics.
Aug
19
comment Trapping a lightray
@john: the user did say "photon" and "perfectly reflecting". The former (particle assumption) validates the lack of diffraction, the latter validates the lack of absorption.
May
26
comment Strain and stress tensor
This is more of a physics question (see Tharsis' answer below). I am migrating accordingly.
Apr
12
comment Interaction potential in standard $\phi^4$ theory
@QFT: you may want to post that as a more fleshed out separate follow up question. I don't have Srednicki, and I don't understand what you are asking in your edit.
Apr
11
comment Are Mathematical Physics and Occam's Razor compatible?
I migrated this from Meta, but I wonder why this question is asked at MSE and not at, say, Physics.Stackexchange...
Apr
11
comment What is the physical meaning of charges at light-like infinity in asymptotically flat space-times?
Consider an observer in Minkowski space applying a constant acceleration....
Mar
8
comment Einstein +Maxwell 's tensor
Also, this question belongs better on physics, so I am migrating it over. Please register on that site so you can edit the question into better form.
Mar
8
comment Einstein +Maxwell 's tensor
What do you mean by "Without knowing EM"? In nonlinear theories of electromagnetism your expression is manifestly false. See for example equation (7) on page 7 of arxiv.org/abs/1012.1400. If you assume you are working with Maxwell's linear theory, you have a Lagrangian formulation to which you add the Hilbert-action and assume minimal coupling to get the form above.
Feb
28
comment Cylindrical wave
One can justify this by using a little bit of differential geometry. The Laplacian term in the wave equation, using the curvilinear coordinate expression of the Laplace-Beltrami operator can be written in spherical/cylindrical symmetry in the form $r^{-\beta} \partial_r(r^{\beta} \partial_r u))$, which contains a term that looks like the logarithmic derivative $D \log f = f^{-1} Df$, and differs from the LHS of the identity I wrote down in where the "inner" $\partial_r$ sits.
Feb
28
comment Cylindrical wave
Didn't an extremely similar question get migrated to Maths last month?
Jan
31
comment Interaction potential in standard $\phi^4$ theory
@Qmechanic: yes yes, I welcome suggestions on other colloquial names for "change of coordinate system on the target manifold".
Jan
31
comment Interaction potential in standard $\phi^4$ theory
It is just a standard gauge transformation / change of variables. I really don't see what there is to elaborate (honest!). You graph the potential $U$, you graph the standard $\phi^4$ potential, you notice that the two potentials are exactly the same except for translations. You note that translations do not change the kinetic energy part, and voila!