Recent content by Manicwhale

In math, differential forms are alternating: dx^dy=-dy^dx. But in physics, we seem to exchange the order freely: dxdy=dydx. What's going on? I am comfortable with an answer that involves tensors, differential geometry, physics, volume forms, etc. In fact, this is really something I should...

Thanks! I think that all sounds right. I'm reassured now.

I'm reading an article (http://arxiv.org/abs/gr-qc/0403075) which proves that a certain spacetime is geodesically complete. It does this by proving that the first derivatives fo all coordinates have finite bounds. My question is why this is enough. Is it just a simple ODE result? We know...

Thanks! Turns out that's the least of my difficulties in this book, but it's quite interesting.

I'm reading Hawking and Ellis, and on p.16 they say that "The subspace of T_p defined by \langle \omega,x \rangle=(constant) for a given one-form \omega, is linear." But in what sense is this true? For if the constant is non-zero, the 0 of T_p is not in the subspace, nor does it satisfy...

Thanks. Also, in terms of why we'd notice it at any scale, would it be right to say that while space expands, certain forces (e.g. EM, or gravity on larger scales) keep objects (e.g. the earth, or galaxies on larger scales) together, so that the distances (as measured by the length of a...

I can think of two reasons: 1. Expansion is very small, and therefore not noticeable. That is, space expands by 0.00005% in a year (which does not rule out the universe expanding by say, a million light years in a year), so we don't feel it. 2. Everything expands, so we don't notice it. But...

I got the same question, except it's worded slightly differently. It wants us to show that a relativistic electron of velocity v=hk/m (h is hbar) with dispertion relation w^2/c^2 = k^2 + m^2c^2/h^2 (slightly different from the one from the previous question) satisfies group velocity x...

How many people out of the original number entering as a physics or physics/math undergrad (overall, not at any specific university) will: 1. Get their B.Sc.? 2. Get their Ph.D.? 3. Become a PostDoc, or stay in the academic stream in some way? 4. Become a professor? 5. Become a tenure...