Recent content by FreeThinking

FYI & FWIW: I just found what I think is an excellent series of Youtube videos on Quantum Entanglement by Dr. Eddie Boyes for those of us who have never quite understood it. I'm only about half-way through, but I have already found it valuable. Just wanted to share my "discovery". I tried...

o_O Ok, thanks. This is way, way, way over my head, but I get your drift. There's more than one way to look at this, and one can get very abstract about it. For now, I'm going to have to stick to a more concrete view until I get more experience with it all. I've been reading Hobson and I find...

@fresh_42: Thanks for your reply. The first part of your first paragraph sounds to me like you are saying the exact opposite of what I said: Me: Dir deriv is a case of the more general covar deriv. You: Covar deriv is a case of the more general dir deriv. The last part of your first...

I have a question. MTW says that the covariant derivative is a machine with slots that accepts inputs and produces an output. Looking specifically on page 255, Box 10.3, part A, sub-parts 3 through 5, here's how I interpret what they're saying there: ## \boldsymbol \nabla ## is a machine...

Peter: My apologies. I was trying to be brief and may have pulled an MTW on you. Just ignore it for now and don't spend any more time on it. I'm working on a longer version that will hopefully explain things more clearly. I've got things going on so it may be a few days before I can post it. I...

Ok, I've stared it a while longer, and here's what I'm seeing: Based on how MTW defines things, as described above, I get ## \boldsymbol \nabla_\gamma T^\beta_\alpha = \Lambda^\mu_\gamma T^\beta_{\alpha,\mu} ##, using ## \boldsymbol e_\gamma = \Lambda^\sigma_\gamma \boldsymbol \xi_\sigma ##...

***** WARNING: LONG POST ***** NOTE: The questions I ask in this post are rhetorical. It was just an easy way to describe what I was thinking at the time. Please don't waste your time trying to answer them. Today I have answers to most of them anyway. I want to be clear that, despite how it...

Ok. That's why I asked the question, rather than assuming they were wrong. That's the kind of thing I meant when I asked, "What am I missing?" So the two rules are connected in this way. I just never spotted that in all my Googling. I will say that the connection seems a bit obscure to me...

Thank you for that invitation, I'll take you up on it, but it will take me awhile to compose that post. Now that I have finally figured out at least one way to derive Carroll's equation 3.71 on page 77 of his lecture notes, I'm going back and reviewing both Carroll & MTW to see if I understand...

I agree that the main thing is to understand the maths, not the verbiage. This discussion is helping me on both counts. MTW and every other book & article on the subject are what they are and we're stuck with them. My problem was, being such a novice especially with the non-coordinate symbols...

@PeterDonis: P.S. Sorry, I forgot to mention that Carroll's lecture notes are practically burned on my screen, I've been studying them so long. And a lot of other printed & online resources. They've helped, but it has still be very difficult for a dummy like me. Good night, and thanks again.

@PeterDonis: Thanks. That makes me feel better about my confusion. It's well after midnight here & I'm losing coherence, so I'll be brief. I think for someone like me who is studying on their own as a hobby with only the internet to ask questions of, the text becomes more important than it...

@fresh_42: Ok, now I understand you. I've never known the word "spleen" to mean that, but apparently it is used, at least in the U.S, I don't know about anywhere else, to mean "complain" or "rant". So, thanks for your guess. It was certainly better than anything I was coming up with.

@strangerep: Thanks for the additional references. I'll check them out. I can believe different authors wrote different parts. In fact, I would suspect that more than a few graduate students got thrown into the mix as well. My problem is that MTW is my first exposure to a lot of the math with...

@fresh_42: Thank you for response. Unfortunately, I have no idea what you said. I looked up the word "spleen" but could find no definition that fit the current context. And I have no idea what "(co-)chain complexes" are. Whatever they are, I hope that's not what MTW meant or I might as well give...