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Re: unit 4-vectors



On 11/30/2003 11:00 AM, Joe Heafner wrote:

What if the metric carries the +--- signature? I've seen both
conventions.

Six of one, half a dozen of the other.

The physics is the same, obviously.

Advantages of the -+++ signature:
-- nonrelativistic three-space is a subspace in a way
that is super-easy to interpret. This is a big
attraction for me.
-- Seems to be in fashion among experts in the field,
and has been for quite a while.
-- You can have unit vectors in spacelike directions
(but not in timelike directions).

Advantages of the +--- signature:
-- Some useful things like (p dot p) and (u dot u) turn
out positive, where u := (d/d tau)x is the four-velocity,
and p := (m u) is the energy/momentum four-vector.
-- You can have unit vectors in timelike directions
(but not in spacelike directions).

Since unitoid vectors are good for all practical purposes,
worrying about where to find unit vectors per se is not a
significant consideration in the choice of signature.