Recent content by homology

Folks, A friend and I are interested in finding a forum to discuss the philosophy of the foundations of mathematics. He's a mathematician and I'm a mathematical physicist. Some of the topics we're interested in are understanding intuitionism and understanding Wittgenstein's lectures on the...

There are a couple answers you might be looking for, so let me know which one you're after: (1) How to compute with the Legendre Transform (like you might have to in Thermo). (2) What is the meaning (usually) of the Legendre Transform (3) The geometrical meaning of the Legendre Transform...

Damn I think I figured out my problem. I was going off Carroll's definition/discussion of (anti-) symmetry (Spacetime and Geometry) which implies that an exchange of a pair of indices in a totally antisymmetric tensor yields a sign change. This is fine I realize now, what is not fine is the...

Simple question I am confused on. If I have a tensor M^{\alpha\beta\gamma} that is totally antisymmetric in its indices then is it the case that M changes sign under the exchange of any two indices? And as a followup, a totally symmetric tensor has no sign changes on any pair exchange of...

Fair enough, I have been a bit sloppy with my meaning. Though would you agree that Tg can be thought of as a linear transformation on V? Let me try to explain, I'm going to use roman indices to make the texing easier. Let e_i be a basis for V and a^i the corresponding dual basis in V*...

Oh, I totally agree. It seems motivated from a matrix multiplication standpoint and a composition of functions standpoint, but I lost points on this one. And he's stubborn. So it almost doesn't matter if I'm right. Its pretty frustrating.

That's sort of the point of the post. He's out of practice and I'm trying to respectfully debate the point with him. I feel like its quite obvious but wanted to get other folks perspective. Maybe I should have put this in SR/GR forum? Thanks

Elfmotat, That is what I'm asking. So you agree that 'matrix wise' you need to 'operate' on different sides to lower different indices? Do you have a reference. The instructor is somewhat out of date and responds better to references.

it looks like you're multiplying by 'g' first each time, but the sum doesn't make it look like matrix multiplication.

But that's just the thing. In SR when we talk about observer's we are actually talking about frames. Inertial frames are equivalence classes of observers. Just because you 'see' a supernova in the sky tomorrow night doesn't mean you'd actually say it happened in January 2012. As a physicist...

this is sort of my point. If they are all in the same reference frame they can determine (and agree) on the distances (spatial) from themselves to the objects and figure out the 'actual' time each event occurred and they will agree because all of their clocks run the same. however, if you...

@256bits Naturally I disagree. That interpretation requires absolutely no relativity. The loss of a universal simultaneity is a hallmark of special relativity. The instructor's interpretation make the exercise irrelevant to any of the physics of the text. The word "see" clearly (to me)...

Please read the following carefully. The point of the following is to distinguish between T^{\mu}_{\mbox{ } \nu} and T_{\mbox{ }\mu}^{\nu} which clearly involves a metric tensor. But when you want to go from component manipulation to matrix operations you have to be careful. Components are...

The use of the word "see" in relativity Homework Statement From Spacetime and Geometry by Carroll: problem 1.3) Three events A, B, and C are seen by observer O to occur in the order ABC. Another observer O' sees events to occur in the order CBA. Is it possible that a third observer...

We probably need to be careful to understand the times in which these folks worked. Things like group theory, operators, manifolds etc are common in physics now you'll see most of them at the undergrad level. But even the topic of matrices was not common among physicists at one time let alone...