Re: What is the Minkowski metric?

Hello!

The "metric" is a way of describing the four dimensions of our universe (3 
space, 1 time) in a mathematical way. Let's kind of sneak up on it: 
suppose that, in two-dimensional plane geometry, I want to go from some 
point to some other point (like on the screen here). Let's call the 
horizontal direction x and the vertical direction y. To get from where I 
am to where I want to go, I can go some horizontal distance x and then 
some vertical distance y. Or I can take a shortcut and go there in a 
straight (but diagonal) line, the length of which I'll call r. The 
Pythagorean theorem tells me that r^2 = x^2 + y^2. (I'm using the ^ sign 
to indicate a superscript here - r, x, and y are all squared). So this is 
kind of a recipe for figuring out distances between points. (I can do this 
in three dimensions by adding z^2 as well).

OK, so what does this have to do with time? Well, when we start figuring 
out the distance between two events in both space and time, we have to do 
it a little differently. If I travel some distance in space x and 
some "distance" in time t, the square of the "straight line" connecting 
them is given by s^2 = x^2 - c^t^2. So there's a minus sign; the metric is 
just a fancy way of telling you to put it there. There's also a factor of 
c, the speed of light; we often set that equal to one so we don't have to 
worry about it). We can write the metric as (1,1,1,-1): this tells us that 
we add the squares of the three space lengths and subtract the square of 
the time "length". Sometimes it's written as (-1,-1,-1,1); this doesn't 
really matter. The crucial point is that the space and time parts have 
opposite signs.

Here's a short article explaining the metric:
 http://www.theory.caltech.edu/people/patricia/minkc.html

Here's a long article that explains the metric, tensors, vectors, and many 
other things. Some of it may be too advanced for you right now, but parts 
of it should make sense:
 http://www.geocities.com/CapeCanaveral/Lab/4059/tensors.html


I hope this helps!