Minkowski Metric: Timelike vs Spacelike

[jaljon]

hello

Whic one of these to metric are Minkowski metric
ds^2 =-(cdt)^2+(dX)^2

ds^2 =(cdt)^2-(dX)^2

and what about timelike (ds^2<0) and spacelike (ds^2>0) for each metric?

With my appreciation to those who answer

 

[bcrowell]

Welcome to PF!

These are both ways of writing the Minkowski metric. People refer to this as (-+++) and (+---) signatures. It doesn't matter which one you use as long as you're consistent. It can be confusing reading the literature, because different people use different signatures.

 

[Dale]

Both are considered the same metric, just with a different sign convention. My personal preference is the first one, but both are well accepted.

When I want to use a metric with positive timelike intervals squared I tend to use $c^2d\tau^2=c^2dt^2-dX^2$. It is just a convention, but that is my preference.

 

[Fredrik]

The first convention seems to be more popular in texts about classical SR and GR. The second convention seems to be more popular in books on quantum field theory.

 

[robphy]

http://en.wikipedia.org/wiki/Sign_convention
"East Coast" vs "West Coast"

 

[jaljon]

bcrowell, DalesPam, robphy Thank you very much

my queastion is

if I use first one

ds^2 =-(cdt)^2+(dX)^2

spacelike: (ds^2>0) then -(cdt)^2+(dX)^2>0 then (dX/dt)>c



if I use second one

ds^2 =(cdt)^2-(dX)^2

spacelike: (ds^2>0) then (cdt)^2-(dX)^2>0 then (dX/dt)<c


we know in light cone spacelike out of cone that mean (dX/dt)>c but why second one (dX/dt)<c

 

[George Jones]

if I use second one

ds^2 =(cdt)^2-(dX)^2

spacelike: (ds^2>0)

No, for this convention for the metric, spacelike means ds^2 < 0.

 

[robphy]

spacelike: outside the lightcone... so "faster than light"
(dx/dt)^2 > c^2 (i.e. either (dx/dt) > c or (dx/dt) < -c).

Thus, spacelike means dx^2 > c^2 dt^2
("larger square-of-the-magnitude of the spatial-part than that of c-times-the-temporal-part")

So, spacelike is dx^2 - c^2 dt^2 > 0.

Now on to the conventions...
If ds^2 = -c^2 dt^2 + dx^2 (-+++), then spacelike is ds^2 > 0 (in -+++... that is, "+ for space").

If ds^2 = c^2 dt^2 - dx^2 (+---), then spacelike is ds^2 < 0 (in +---... that is "- for space").

 

[jaljon]

thanks