Relativistic Electromagnetism (Undergrad Level)

[Arman777]

I have looked several special relativity books but in each of them the metric is defined as ##\eta_{\nu\mu} = (+1, -1, -1, -1)##.

Is there a book where the metric is defined as ##\eta_{\nu\mu} = (-1, +1, +1, +1)## ?

 

[PeroK]

What difference does it make?

Griffiths introduction to EM uses the latter.

 

[Arman777]

What difference does it make?

Griffiths introduction to EM uses the latter.

I am not sure..I guess it changes the signs "-" becomes "+" etc. which is confusing.

 

[Arman777]

Other then Griffith ? I am looking for something like Gauge transformations and electromagnetic tensor etc.

 

[vanhees71]

Hm, isn't the east- and west-coast convention pretty much uniformly distributed over textbooks and papers? In the beginning it's of course very useful to find a textbook suiting ones needs and stick with it for a while just to get a feeling for it. On the other hand it's also good to be able to switch from one to the other convention.

When I started the work for my diploma thesis my adviser told me: "I don't dictate anything, but we all use the west-coast convention." ;-)). That's why I use the west-coast convention since then. It's simply because the majority in my scientific community (high-energy heavy-ion physics) uses this convention (but even within this community there are also people using the other convention).

 

[BvU]

On a side note: I was breastfed with the Minkovski spacetime ##\, (x,y,z,ict) \, ##, and later had (still have) difficulty absorbing the ##g_{\mu\nu}## stuff and co- and contravariance.

It must have been deemed didactically advantageous at the time (early seventies), but I don't see it popping up very often anymore. It's not even mentioned under sign convention or metric tensor
(the latter might even be sensible: it's not needed , ##g## = identity?)

Anyone know the history (and perhaps the outcome) of this fascinating field of confusion and disagreement ?

 

[vanhees71]

The ##\mathrm{i}c t## formalism I'd strictly avoid. It's very confusing, cannot be extended to general relativity. There is no disagreement. It's simply unnatural and nowadays only very rarely used. That said, my favorite textbook about classical physics, Sommerfeld's Lectures on Theoretical Physics (6 vols.) uses this convention. It's not per se bad, but it's doing more harm than good in practical calculations.

 

[Vanadium 50]

I disagree with the notion that it is easier to keep track of factors of i than of minus signs: factors of -1.
I disagree with the notion that people learning E&M are incapable of keeping track of minus signs.
I disagree with the notion that students are the people best equipped to decide what sign convention their textbooks should use.

 

[robphy]

I have looked several special relativity books but in each of them the metric is defined as ##\eta_{\nu\mu} = (+1, -1, -1, -1)##.

Is there a book where the metric is defined as ##\eta_{\nu\mu} = (-1, +1, +1, +1)## ?

Quoting myself from
https://physics.stackexchange.com/questions/607885/relativistic-electromagnetism-undergrad-level-book-with-metric-eta-nu-mu

Are you looking for a text primarily on electrodynamics that uses the negative-timelike convention? Or a special relativity text that uses the negative-timelike convention which treats electrodynamics as merely one of several topics ? Possibly helpful: https://en.wikipedia.org/wiki/Sign_convention#Relativity

 

[dextercioby]

Other then Griffith ? I am looking for something like Gauge transformations and electromagnetic tensor etc.

Brian Felsager, Geometry, Particles and Fields (1983) is all you need.

 

[italicus]

I remember a box in “Gravitation” by MTW, where a farewell is celebrated to the old use of “ ict” . The authors underline in particular that using ict hides the physical difference between time component and space components of the metric , which brings to hyperbolic geometry of Minkowski spacetime.
There are a lot of authors that use the signature (-,+,+,+) for the metric, f.i. the same MTW uses it, as well as Shutz. But Landau and Lifshitz use (+,-,-,-) , if I remember well. It’s a matter of convention, so one has to be careful when reading a new book on relativity, especially when using metric to lower or raise indexes.

 

[vanhees71]

Landau Lifshitz changed the convention from one edition to another. In Misner, Thorne, Wheeler there's a table listing the conventions used in various textbooks (available at their time of course).