I'm going to be completely unambiguous on this: the problem I am about to ask is an assigned homework problem so please, do NOT simply just reply with the answer. I have no intention to cheat.(adsbygoogle = window.adsbygoogle || []).push({});

That said, the question I have is with regards to problem 12.55 in Griffith's Intro to Electrodynamics. I'm pretty sure not everyone has the book so I'll sum up the basic points of the question:

Griffiths states that the four-dimension gradient operator d/dx^u (pretend the d's are partials, and pretend the u is superscripted-- sorry, I don't know how some of you manage to get the symbols all nice) functions like a covariant 4-vector, so often times it's written d_u for short. He then states that the corresponding contravarient gradient vector would be d^u = d/dx_u. Now, we're supposed toprove that d^u(phi), that is, the contravarient gradient acting on some scalar function phi is a contravarient 4-vector.

I have no clue as to how to do this. My professor has provided us with the hint of considering the direct Lorentz transformation and how the transformation relates to dx'^u/dx^v, as well as the inverse transformation. We're supposed to use the chain rule somehow to get back to the proof but after laboring on this problem for several hours I'm convinced that I am stuck. Something tells me that this problem shouldn't take more than 10 minutes but all this tensor stuff is all fairly new to me (ie, I didn't learn of any of this stuff till earlier this week!).

Can anyone here provide me with any hints or perhaps a better insight of the problem? From a superficial standpoint, I see that contravarient and covariant vectors differ only in terms of the signs on certain components such as to make their dot product invariant. Is there more to this?

What the heck is going on? :yuck:

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# Contravariant gradient?

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