Special Relativity's space-time circus is based on
the 'transformation' equations by which it is believed
one can relate a nominally 'stationary' system's space
and time coordinates to those of an inertially (not
accelerating) moving other observer. 

That moving observer's own physical body and coordinate 
system might have been identical in size to those of the 
stationary observer before the traveller began moving, 
but are 'seen' as very different by the stationary observer 
when the relative velocity of the two is great enough, a 
high percentage of the velocity of light.

Concerning ourselves - as is customary - with just
the spatial coordinate axis that lies parallel to
the direction of motion, and with time, Einstein
arrived at these formulas that relate the moving
system measures or coordinates (x' and t') to the
stationary system coordinates (x and t):

      x' = (x - vt)/sqrt(1-vv/cc)      (Eq 1x)
      t' = (t - vx/cc)/sqrt(1-vv/cc)   (Eq 1t)

The v is for the two systems' relative velocity as seen 
by the stationary observer, and is positive if the dir-
ection is toward higher values of x.  By concensus,
the moving system x'-axis higher values also lie in
that direction, and all axes parallel the other system's
corresponding axis.

We used vv to mean the square of v but might use v^2
for that purpose below. Similarly for c.

Because it is believed that no physical object can
reach or exceed c, the square-root term in both
denominators is presumed always less than one, which 
means that the formulas say both x' and t' will tend to
be greater than x and t, respectively.  However,
SRians call the x' result 'contraction' - which means
shortening - and the t' result 'dilation' - which
means increasing.