Twin Paradox
One twin stays at home, whose reference frame is given in green.
The other twin heads out in a fast rocket(light blue).
After a while the second twin starts back for home(dark blue).
The time experienced by the traveling twin headed out, plus the
time experienced coming home, is less than the time experienced by
the stay at home twin.
How the graphics work
The above picture is based on the technique of Brehme diagrams.
I have made adaptations to allow for more than two reference frames.
(The only good reference I have to these diagrams uses a restricted
form to simplify derivation of the algebraic Lorentz transform)
When drawing this diagram there were a couple of factors to be
considered for it to adhere to Special Relitivity:
- The speed of light is a constant for all frames. This is met
by drawing the space and time axis such that the angle between
them is bisected by the primary light axis
(red, pointing up and right).
- An object has a constant spacial coordinate in its own rest
frame. Here I took care to draw the space axis at a right angle
to the objects path through space-time.
We can measure the time and space of an event in a coordinate system
by ploting an index line perpindicular to the axis in question and
through the event. The interval between two events is given by the
distance between the indices.
For a more complete tutorial see
Guide to Einstein's Relativity
Here we have an example of this technique applied to a tachionic
situation. (Admitably a reach beyond the certain.) The diagram
shows a starship heading out using a "tachion jump", and then
returning with the same technique. (Or equivilent, a tachion based
data exchange.) When you look at the time axis you will notice
that both legs of the trip have a time flow in the same direction
as home, but at different rates. But the two legs have time flow
opposed to each other. This implies that "improper" use of the
tachion jump drive (engaging "foreward" it while at tachion speed)
would enable our starship to travel backwards in time. Home is
at tachion speed relitive to a tachion. I.E., The state of being a
tachion is relitive.
How did I extripolate to tachion speed?
As an object is accelerated toward light speed, its space and time
axis become more parallel (or anti-parallel), until at light speed
its local coordinate system becomes degenerate. Pushing beyond light
speed (this is math after all) we find the angle between the axis
is still bisected by the principle light axis, but on the "wrong"
quadrant. Notice how I have divided space time into 2 portions
with the borders being "lightlike". Relitive to home, the time axis
of a tachion is "spacelike" and the space axis is "timelike".
home
Questions may be e-mailed(see home) or addressed to
sci.physics.relitivity