# Tensor expression

1. May 17, 2007

### Norman Albers

How do we express the Minkowski field tensor for circular currents?

2. May 18, 2007

### AlphaNumeric

Albers, though you're now banned, I'll take this opportunity to explain to you why your question doesn't even make sense.

The Minkowski 'field tensor' (which in itself of dubious terminology) is the flat space-time metric. While you can pick various coordinates to express this in, such as the diag(-1,1,1,1) cartesian form or the spherical form (or infinitely many others), they are all the same thing, flat space-time.

If you then introduce charge carrying objects (and thus some notion of energy) to the system, the space-time will become curved in some way. As such, the space-time metric will no longer be Minkowski but something else. Now if someone were wondering what the space-time metric was, they'd ask "What is the space-time metric for such a system?", or to more closely resemble your question, "What is the Lorentzian space-time metric?" Minkowski is, by it's very name, flat and empty (if you're working in GR).Anything in the space-time will disturb this.

This is why your question isn't particularly well phrased and as pointed out to you in a previous thread, it's somewhat of a sign you are attempting to jump in head first to a subject you know little about. As I told you many weeks ago, it's no skin off my nose if you don't bother to learn any kind of relativity or applied differential geometry, but it would VASTLY aid your understanding and abilities in doing whatever it is you're attempting to do if you did learn some.

Besides, if you're so confident about your amazing ability in relativity, why can't you solve the Einstein Field Equations for a circular current of some kind in the energy-momentum tensor? Or are you not sure how to write a metric in cylindrical coordinates ;)

3. May 18, 2007

### pmb_phy

Why? Wouldn't it be better just to ignore him rather than give him the feeling that he'll get a response from someone whenever he posts non-sensical questions?

Pete

4. May 19, 2007

### AlphaNumeric

I'm a hopeless care for hoping he'll see the light and realise he'd advance so much faster if he actually opened a book and learnt rather than trying to reinvent the wheel.

5. May 22, 2007

### mathwonk

don quixote, the patron saint of teachers.