Well, let me try and say something useful rather than just grumbling.
I would call a "road" a curve, which is a path through space-time. Cuves can be specified in many ways, one of the standard ways is via four functions:
t(lambda), x(lambda), y(lambda), z(lambda)
which give the coordinates (location on the curve) of a moving object/observer as a function of some parameter lambda.
The parameter "lambda" may be (but is not required to be) the "proper time" of the traveling observer, i.e. what the observer reads on his "wristwatch".
We draw a distinction between "coordinate time" and "proper time" here. Coordinate time is the time coordinate 't', assigned to an event, while "proper time", tau, is what the traveling observer reads on his wristwatch (i.e a clock that he carries along with him on his journey).
What SR basically says is that the quantity
<br />
c^2dt^2 - dx^2 - dy^2 - dz^2<br />
called the Lorentz interval, is a universal invariant for any observer in an inertial frame.
Hopefully the idea of "inertial frames" can be directly imported from Newtonian physics.
As a consequence of this, the manner in which one transforms coordiantes between different inertial frames is not the familiar "Gallilean transformation", but rather the "Lorentz transformation".
The Gallilean transformation is
x' = x - vt
t' = t
and is valid for Newtonian physics.
The Lorentz transformation is
x' = \gamma(x - v \, t)
t' = \gamma(t - v \, x/c^2)
where \gamma = 1/\sqrt{1-(v/c)^2}
and replaces the Gallilean transformation when special relativity (rather than Newtonian physics) is used.
More on the transformations can be read at
http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/ltrans.html
[total re-write for clarity]
Consider two events (in a 2-d space-time, for simplicity)
Event 1 is at (x1,t1)
Event 2 is at (x2,t2)
Consider the SAME two events in a different 'frame'of reference;, the "primed" frame, (which must be an inertial frame of reference)
Event 1 is at (x1', t1')
Event 2 is at (x2', t2')
According to to the Gallilean transformation, the time between the two events will be invariant, i.e. the same for all observers in inertial frames.
This is because t2' - t1' = t2 - t1
This is no longer true in SR. In SR, what is invariant is the Lorentz interval, which is
c^2(t2' - t1')^2 - (x2' - x1')^2 = c^2(t2-t1)^2 - (x2-x1)^2.
This can be seen by direct substitution of the defintion of the Lorentz transform, and a lot of mathematical substitution
i.e x2' is defined by the Lorent transform in terms of (x2,t) by the equation
x2' = \gamma (x2 - v t2)
use the similar defintions to replace x1', t2', and t1' with unprimed variables, and simplify the resulting expression.
