Recent content by physlosopher

So, two points: (1) I think that what others are trying to say is that even if the "exact solution" for t is a number with infinitely many digits, the problem you seem to be worried about holds for any such number. For example, maybe I know the answer is 1/3 (a rational number). If I have to...

I will read your reply to the other post and think a bit, but this is very helpful. Thank you!

Sorry to post again, but does anyone know whether it would be better to ask this question in a different forum?Maybe it's awkward because it's sort of a QFT question about a condensed matter system?

Thank you for the response! However, my question pertains more to quantum mechanics than to which Legendre transform of the energy is being minimized.

Hi all, thanks in advance for your help! For context, I'm generally new to condensed matter and many-body QM and am working through Altland and Simons' Condensed Matter Field Theory. I'm thinking in general about magnetic ordering. I've seen a Heisenberg-like spin Hamiltonian derived by...

Thanks in advance for any insight! Following Pathria's discussion of phase transitions, I'm getting tripped up on the discussion of Landau's theory. Pathria begins with a zero-field free energy ##\psi = A/NkT## where ##A## is the Helmholtz free energy. He proceeds to characterize the...

I'm in a first-year grad course on statistical mechanics and something about multivariable functions that has confused me since undergrad keeps popping up, mostly in the context of thermodynamics. Any insight would be much appreciated! This is a general question, but as an example imagine...

I hope this is the right place to ask a question like this! I've seen two different versions of problem 1.14 in the third edition of Jackson's Classical Electrodynamics. Has anyone else noticed this? My friend has two PDF copies of the book, each of which has a different problem 1.14. We...

Thank you. That's what I thought. It was starting to drive me insane.

How would you all propose interpreting a claim like "we know that in Schwarzschild spacetime, coordinate time ##t## is the same as proper time ##\tau## as measured by a distant stationary observer."? This is stated shortly after the other quote I mentioned above. It's the sort of claim that's...

Fantastic, this is what I was looking for as a sanity check - thank you. As I suggested in my last post, I may very possibly just be misreading the text, but regardless I'm glad I'm not totally off base about my (possibly mistaken) interpretation of it being problematic.

Right, and that would have nothing to do with that observer assigning physical meaning to the difference in coordinate time between the light being emitted and the light being received, right? I think this is the crux of the question I'm trying to ask. You could use the coordinate time...

I understand that, my apologies if I wrote something that was unclear. This is why I was confused when the text I'm reading seemed to imply that the coordinate time difference I described, between events that are spatially separated, could be understood to correspond to some proper time...

Surely there are at least cases in which coordinate time can inform us about physical reality, or else it wouldn't be useful to talk about it? Can we think about something like a map between it and proper time? If so, the question I posed is about a specific case of that: the text I'm reading...

Edit: I'm leaving the original post as is, but after discussion I'm not confused over coordinate time having a physical meaning. I was confused over a particular use of a coordinate time difference to solve a problem, in which a particular coordinate time interval for a particular choice of...