Introduction
For this experiment, unlike Experiment 1, you don't need Javascript, but you need:- a twin brother or sister (depending on your gender),
- a spaceship (min. warp 0.95 required),
- some common knowledge about Relativity Theory.
The journey
After saying good-bye to your twin, you go onboard of your ship, program the speed for 284407km/s, direction "just ahead" and keep that course for 30 days (according to your wrist watch).To pass the time, you can do (without using a calculator!)
the following calculation:
According to Albert Einstein's article 'Zur Elektrodynamik bewegter
Körper', published 1905 in the Annalen der Physik, a frame with
a uniform movement of speed v relatively to an inertial observer
frame, will suffer a time-dilation
relatively to the observer by (1-v2/c2).
In your case, your twin as attentive observer will have noted that
for your travel, the time-factor is 0.1, and so what you thought
was 30 days, were 300 days on earth!
Just to check this out, you decide to go back home,
same speed, opposite direction.
During the second part of the travel, you could do another reflection,
just to past time and to awake your curiosity of what will happen
when you are back:
we know now the thoughts of your twin; for him you will have traveled
for 60 days while on earth 600 days were gone, so he expects that
you will return younger than him.
But you could also claim that in your refering frame
-the spaceship-, it seems that the earth made a travel away and back
to you; thus the journey lasted 600 spaceship-days, that would be
60 earth-days from your point of view.
So you may expect that, when your twin returns with the earth to
your spaceship, he must be younger than you.
| Will you be older or younger than your twin when you are back? |
Settlement
In the classical litterature, this situation is known as the "clock paradox".The 'Special Theory of Relativity' only applies for an observer which is an inertial frame. The contradiction is solved by saying that the earth may be considered as an inertial frame, but the spaceship, because it has to stop and accelerate in the opposite direction in the middle of its travel, is during this period subject to other (acceleration) forces and cannot be considered as an inertial frame, and it cannot use itself the formulas of Special Relativity to apply them to the earth.
We could imagine a sequel (Back to the Future III) where the spaceship does a uniform circular mouvement starting and ending at the earth. This time again, because of its mouvement, the spaceship is subject to a centrifugal force and again is not an inertial frame having the right to use Special Relativity.