Talk:Formulation of Maxwell's equations in special relativity

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Contents 1 Suggestions 2 Four-vector notation 3 Question 4 Opinion re tidy up

[edit] Suggestions

I think this needs to be completely reorganized and rewritten with better notation. Time permitting I'll be more specific, but for now let me just say that there are many missed opportunities to explain logical relations between the various expressions which are stated. For example, instead of just writing out the stress-energy tensor, explain how it arises from a well-known machinery which applies in other situations. This can be linked to articles on Noether's theorem in differential equations. It would also be valuable to explain how the Killing vectors of Minkowski spacetime are related to electromagnetic fields, and to seque into discussion of null and non-null fields. ---CH 19:22, 14 April 2006 (UTC)

Yip, totally agree with that; just added the cleanup tag. MP (talk) 16:17, 21 April 2006 (UTC)

[edit] Four-vector notation

I was trying to figure out the notation, like for starters, what are the superscripts a and b? So I went to four-vector, where it is explained "for a = 0, 1, 2, 3". Now what the heck does that mean? Do these four small integers have some special significance that someone could just tell us please? Dicklyon 20:39, 12 July 2006 (UTC)

The superscripts are a shorthand labelling convention. So, for example, U^a (a=0,1,2,3) means that if you put a=0, you get U⁰, a=1, you get U¹ etc.... In more detail:

(U^a) = (U⁰,U¹,U²,U³)

The 'four-vector' business, just means, roughly, that the U^a thingy is a vector with 4 components - U⁰ is the 0th component, U¹ is the 1st component etc.... Hope that helps. MP (talk) 20:44, 12 July 2006 (UTC)

OK, but then the symbol with superscript can be either a whole 4-vector, or a component, depending on context or what? Seems awkward. Dicklyon 06:09, 13 July 2006 (UTC)

U^a for (a=0,1,2,3) is a 4-vector, and U⁰,U¹,U²,U³ are it's components. Each component has a single scalar value while the vector contains all four scalar values (see Einstein notation). In relativity, (0,1,2,3) are typically taken to be (t,x,y,z). Because time and space as we know them from day-to-day experience are only a special case in relativity, numerical indices are used for generality. Also, "for (a=t,x,y,z)" just looks rediculous.

[edit] Question

If time speeds up, would we even be able to make that observation?

[edit] Opinion re tidy up

This page contains some important information not captured elsewhere on Wikipedia. For example, it is the only page I could find which mentions the contravariant and covariant electromagnetic tensor being equal, owing to the form of the Minowski metric. It's also the most compact page describing some other underlying features of the electromagnetic tensor, and has the most explicit description of the relationship between wave equations and Maxwell's equations. I agree that the page is a bit of a mess, but it is useful for teaching purposes, despite its messiness, so certainly shouldn't be deleted or massively reformed without finding more appropriate places for its information.