Would you like to make this site your homepage? It's fast and easy...
Yes, Please make this my home page!
BACK TO SITE PLAN :
LENGTH CONTRACTION AND TIME DILATION
NOTE: The upper case "SPACE" denotes the abstract mathematical
construct, in order to distinguish it from the "space" of
Let X,Y lighttimeSpace referentials of coordinates x(i),y(i),
moving relativly at the speed V along x(2),y(2), chosen as
For simplicity's sake we shall disregard the trivial space
dimensions x3,y3,x4,y4 and consider X,Y in 2D Minkowski
SPACE with Lighttime coordinates x1=ctx, y1=cty, space
coordinates x2,y2 and signature: [-1 0,0 1].
Let beta=V/C, gamma=1/sqrt(1-beta^2)
Lorentz Transformations may be written:
Let's call observed and observing Referentials respectively
"home" (H) and "not-home" (N) and the coordinates of their
systems "h" and "n".
We may rewrite ,:
Let's consider space sub-SPACE and chose coordinates so
[1a] becomes: h2=gamma*n2 or n2=h2/gamma [1b]
We see that dn2 < dh2
[1c] is Lorentz Space Contraction.
Let's consider Lighttime sub-SPACE and chose coordinates
so that n2=0.
h1=gamma*n1 or n1=h1/gamma [2b]
implying differentials or "elementary covering Rods".
(see Einstein's Covering Principle in "NATURAL MODEL")
dh1 > dn1
Lighttime distance corresponding to the elementary period
between two clock ticks, is measured. as any distance, with
Rods, which contract in the N (not-home, relatively moving)
Referential. Thus, the elementary period of N takes
more Rods, or is longer than that of H (home Referential).
The N-clock ticks slower than H-clock. Calling elementary
periods of H and N respectively dth and dtn, we get:
dtn > dth 
Whatever may be the metaphysical vision of time, we consider
in Physics time as that what is measured by intervals between
clock ticks, dismissing hypothesis of its nature. We say
that time "dilates" when the clock ticks slower and that
time dilates in the N (relatively moving) Referential with
respect to the relatively stationary H.
This effect of clocks relatively slowing down in relatively
moving Referentials is known as Lorentz Time Dilation.