- #1
DavidL070949
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Hi! Apologies in advance for a somewhat long post.
First, by some background: Long ago in what seems like a galaxy far away, I got a Ph.D. in physics (statistical physics) before switching gears and going into law. The nature of my grad school was such that there wasn't any coursework - you got an office, and advisor and were expected to produce a thesis in a reasonable number of years. Great for learning to be independent but it did result in a number of holes in my education. Fast forward a number of decades, post-retirement, my interest in physics got rekindled and I began to work my way through the MIT open course on general relativity on my own. Great course! But it can at times be a bit tough to do this solo and I've gotten stuck on Problem set 3, #3(b). There's a set of worked out solutions that I found online. Unfortunately, it contains errors, including (I think) one in the work on this problem, which deals with electromagnetic fields as seen by an observer with 4-velocity U. I've attached the page with the problem in question. It seems like one way to address this is to plug in the formulas for E and B into the formula given for the generating field tensor and show that the rhs reduces to the lhs, which is what I did. From the problem, it seems like one is supposed to get to the place where the Levi-Civita symbol identity given with the problem should come into play. But the expression I got to only has one index in that part to sum over and the identity needs two. The other way to do this would be to contract the non-field tensor portions of the E and B 4-field formulas with both sides and show that the rhs reduces to the target field. That hasn't gotten me very far either. So, I'm stuck and would appreciate any help/insight anyone can add.
First, by some background: Long ago in what seems like a galaxy far away, I got a Ph.D. in physics (statistical physics) before switching gears and going into law. The nature of my grad school was such that there wasn't any coursework - you got an office, and advisor and were expected to produce a thesis in a reasonable number of years. Great for learning to be independent but it did result in a number of holes in my education. Fast forward a number of decades, post-retirement, my interest in physics got rekindled and I began to work my way through the MIT open course on general relativity on my own. Great course! But it can at times be a bit tough to do this solo and I've gotten stuck on Problem set 3, #3(b). There's a set of worked out solutions that I found online. Unfortunately, it contains errors, including (I think) one in the work on this problem, which deals with electromagnetic fields as seen by an observer with 4-velocity U. I've attached the page with the problem in question. It seems like one way to address this is to plug in the formulas for E and B into the formula given for the generating field tensor and show that the rhs reduces to the lhs, which is what I did. From the problem, it seems like one is supposed to get to the place where the Levi-Civita symbol identity given with the problem should come into play. But the expression I got to only has one index in that part to sum over and the identity needs two. The other way to do this would be to contract the non-field tensor portions of the E and B 4-field formulas with both sides and show that the rhs reduces to the target field. That hasn't gotten me very far either. So, I'm stuck and would appreciate any help/insight anyone can add.