Caution: I'm new at this stuff.
On page 573 of Gravitation (Misner, Thorne, Wheeler), they write down what I think is the electromagnetic wave equation for a discussion on Optics, "Next insert the vector potential (22.25) into the source-free wave equation (22.19d):"
I am wondering if the...
malarchy
Ok, I'm full of malarchy, my apologies. Ill nevertheless try to explain the above question and then cut to the chase.
So, 2 things, first to explain the above:
1. In the 474 page area they are talking about the linearized gravity field equations an earlier form of which they...
wave equation? maybe not..
Here are 2 links to show the equation. Maybe I need to read more, but here they are:
In the first link page 141 looks like the EM wave equation if I think about the d'Alembertian operator being split into time and spatial derivatives.
(Darn this isn't working now...
wave equation? maybe not..
Here are 2 links to show the equation. Maybe I need to read more, but here they are:
In the first link page 141 looks like the EM wave equation if I think about the d'Alembertian operator being split into time and spatial derivatives...
1. wave eqn vs. particle motion; 2. curl curl in 5-D
I've got 2 questions now.
1. It seems that the GR book I'm reading comes up with a "wave equation" to describe the motion of a charged particle. This equation reminds me of the EM wave equation that you get when you take the curl of both...
Thank you!
Hi, Mentz114,
My heartfelt thanks for your reply.
I had to think about it to see if I was going to run into another question - I still might. But I was summing (as you aptly suggested) when I shouldn't have been, and you writing those out (and the link to the curl) helped out...
here's a link to the page in the book
here's a link to the page in the book from google books (amazon also has a link to it). Don't worry this link is legal it's from google books as their way of advertising the book to sell it. Only if you have time... it's page 71. This link allows you to...
by the way
by the way, it sounds like I should not sum; that I should leave them as a tensor (antisymmetric). If so I'm not sure how I would write the terms out if I wanted to write them equation style.
you are right and...
Firstly, Thank you for your response.
Yes, I'm getting 9 components just like that. You are right I am summing them and it sounds like I should not be. Also, yes, this is supposed to be a generalized curl and I'm trying to see if it works out to the curl I know in 3-D...
Can anyone explain to me how to expand this expression for curl which I find in the GR book I'm reading (by Hobson, Efstathiou and Lasenby, page 71)? In a section entitled Vector Operators in Component Form they state the curl as a "rank-2 antisymmetric tensor with components":
(curl)ab =...
Thanks, haushofer,
Looks like a great book; I think I'm going to get it. Also... what about the Helmholtz equation that you get from the Maxwell's equations; any idea where to read about that in higher spatial dimensions? I may post that as a separate question but am very interested in an...
Dear Vid,
Thank you so much! Can't wait to read this, and very cool that he was your high school physics teacher! Meanwhile I hope this doesn't discourage others from posting a response but... this response does look excellent! My heartfelt thanks for your help.
Anyone know what topic, branch of math, book, or subject I should look up in order to find a formulation for Maxwell's equations in higher spatial dimensions? I don't mean having time as a 4rth dimension. I mean a 4rth (and more) spatial dimension. This would require the maxwell exquations...