Time, a brief history

One anti-intuitive aspect to nature we've learned from General Relativity is that time and space are entirely relative.What one observer calls space, another will call time and vice-versa.
What some would call before, others will call after, e.t.c.
Time is simply a path in spacetime.However near the Big Bang classical spacetime itself starts to give over to something else entirely. Concepts like before and after break down entirely.

Introduction.The equations, as nwr said, worked regardless of whether spacetime is considered real or not. Einstein himself didn't use the idea of spacetime, instead using ideas functions of velocity for empirical results. Later however it was found that relativity is more naturally (in a mathematical sense) a theory of a four-dimensional geometry called Minkowski geometry.
The four dimensional space described by this geometry is called Minkowski space, or as it is more commonly called by the public "spacetime".However one might ask, what does a physicist mean when they say space and time are unified into one entity?2-D basics.Let's start with a two dimensional geometry, of the kind most people are familiar with.
This is a 2-D plane labelled by the x axis and the y axis.
Any point can be labelled by any two numbers x and y.
(Like the point (1,2) or (2,3), e.t.c.) Now let us say we have two points on this plane: How far away are they from each other?
Well we can draw a triangle from point one to point two as such: And we find that the distance between the two points is (using Pythagoras' theorem):
ds^2 = dx^2 + dy^2.
Where dy is the difference in the y values (y2 - y1) of the two points, dx is the difference in the x values (x2 - x1) of the two points and ds is the distance between the two points.



Now let's jump to four dimensions.This is a 4-D plane with not just a x axis and y axis, but also a z axis and a w axis.
So any point can be labelled by four numbers x,y,z,w.
(Such as (1,3,4,2), e.t.c.)
What the distance between two points in four dimensional space then?
Well it's:
ds^2 = dx^2 + dy^2 + dz^2 + dw^2Where,
dx is the difference in the x values,
dy is the difference in the y values,
dz is the difference in the z values,
dw is the difference in the w values,
and ds is the difference between the points.(As an example the points (1,3,1,2) and (9,7,5,4) are a distance of 10 apart.dx = 8, dy = 4, dz = 4, dw =2.
So,
ds^2 = dx^2 + dy^2 + dz^2 + dw^2 = 100.If ds^2 = 100, ds=10.)




Time for a change.However this is just 4-D space. Every dimension is a space dimension.
Lets change one of them to a time dimension.Now we have a 4-D plane with a x axis, y axis, z- axis and a t-axis.
Any point can be labelled with four numbers (x,y,z,t)
So far this is the same as when every dimension is a spatial one.
Now what is the distance between two points in this plane.
It turns out to be:
ds^2 = dx^2 + dy^2 + dz^2 - dt^2.
Where dt is the difference in the time values.
Compare this with the distance formula for four spatial dimensions above:
ds^2 = dx^2 + dy^2 + dz^2 + dw^2.So time is just like a spatial dimension except you take away the square of difference in time values of two points, instead of adding it, when you are trying to find out the total distance between them.Nearly all of special relativity falls out if we just assume the distance between points in the universe is governed by:
ds^2 = dx^2 + dy^2 + dz^2 - dt^2.So we say the universe is "A 4-D plane with the above formula as the rule for distances".Formally, we call "A 4-D plane with the above formula as the rule for distances" a Minkowski space or sometimes spacetime, because you use both space and time in the formula for distance.This message has been edited by Son Goku, 03-26-2006 06:15 PMThis message has been edited by Son Goku, 03-26-2006 06:45 PM

If we measure time with a different set of units than space (as humans naturally do, although we don't sometimes in cosmology) we need to know how much meters is a second worth.It turns out (using Foucault's method basically, but there are more developed ones) that a second is equivalent to 300,000,000 meters.So in essence if I had a ball located in the middle of a room at twelve o' clock its coordinates in spacetime are (0 0 0 0) let us say.
The clock one second into the future has the coordinates:
(0 0 0 300,000,000).A second is 300,000,000 meters in the temproal direction.(It's actually 299,792,458 meters, but you get the idea.)

That is exactly correct.Now lets look at light. Light travels 300,000,000 meters in one second.So the starting point and ending point of a light beam after a one second journey are one second and 300,000,000 meters apart and so, as you concluded, they would have zero distance between them even though they are in different points in Minkowski space.This is why light doesn't experience time and distance, because even though it can occupy many points, there is no distance between them.

Yeah, pretty much. They aren't actually slowed down. They're just continuously absorbed and emitted by the material in the glass.