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Mathematician


Apr
8
awarded  Nice Answer
Apr
1
comment Sensor Temperature with time constant
Migrating per OP request.
Mar
31
awarded  Nice Answer
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
19
reviewed Reject suggested edit on What software programs are used to draw physics diagrams, and what are their relative merits?
Dec
13
awarded  Yearling
Dec
11
awarded  Enlightened
Dec
11
awarded  Nice Answer
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.
Oct
23
awarded  Announcer
Oct
15
awarded  general-relativity
Oct
9
revised The inner workings of the Olbers paradox
edited tags
Sep
30
awarded  Nice Answer
Sep
24
awarded  Nice Answer
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.