Recent content by dnquark

You've missed one outcome: 2 people share a b/day and another 2 people share a b/day on the same day. The case you quoted "2 people share same b/day" implicitly assumes that the other people have different birthdays. See this for the explicit formula which should give you the missing...

This thread keeps coming back because nobody gave an entirely satisfactory explanation that motivates v^2 proportionality. (I can't give one either, I came here in search of one). What puzzles me is all the explanations that involve work-energy theorem. They make sense mathematically, but...

Let me make my question more concrete: why does \omega > 0 refer to the future light cone?.. What is the relationship between this cone (a dispresion relation, really) in frequency-momentum space and the time dynamics?

We might have different editions; are you talking about the Fourier representation of Klein-Gordon field? This I don't quite understand -- referring to k^\nu k_\nu = 0 as "light cone". To me, this is a relation between frequency and wavenumber, or energy and momentum. A "light cone" is an...

Yes, and that's what bugs me about this... I can't figure out whether this is something trivial not worth thinking about, or has some depth behind it. The discussion of positive/negative frequencies/energies is reminiscent of this discussion (courtesy of John Baez)...

The following formula is taken from a book by Rubakov: A_\mu = \int_{k_0 \ge 0} [e^{ikx}a_\mu(k) + {\rm c.c.}] d^4k I am trying to understand why it makes sense to integrate only over the positive values of the frequency k0. (Pretty much any time I write down Fourier integrals, I...

I don't understand why Lagrange multipliers are necessary. Why not take OP's first line and plug into Euler-Lagrange equations? You will end up getting a nonlinear 2nd order ODE that I don't know how to solve off the top of my head, but you can easily confirm that catenary is a solution.

It looks like you Rayleigh range is much larger than the focal length of the lens. In this case, your focused spot size will be given by f \lambda/(\pi w_i), where w_i is the initial waist size. You should find the derivation in any book on lasers (e.g. Yariv or Siegman)

I figured it out. The problem was sloppy conversion between index and matrix notation (to this day I haven't seen a good reference that explains the best way to perform it). In any case, if you do this carefully and introduce distinction between upper and lower indices, defining contraction...

My problem is that I've heard all these statements before -- but can anyone point me to a concrete, preferably numerical, example of when something is or is not a tensor?..

From the list of very fundamental things I am confused about: Let's say I have two bases and a transformation matrix T that allows me to convert between them, like so: A'_i = T_{ik} A_k, where A and A' express the same vector in the two bases. If I have a second rank tensor, it will...

Hi all. I need to take the following integral by contour integration (it's actually a simplified version of another integral that I'm working on): \int_{-\pi}^\pi \frac{e^{i\omega}}{\sqrt{e^{i\omega}-1/2}\sqrt{e^{i\omega}-3}}. I am transforming it using z=e^{i\omega} into \frac{1}{i}\int...

Reiterating what people said: \nabla \cdot B = 0, just like all of Maxwell's equations, is an empirical fact and cannot be proven from first principles. It does, however, follow from some more fundamental expressions. Namely, B = \nabla \times A. Since \nabla \cdot \nabla \times {\rm...