This is the story of a pair of twins, Heckle and Jeckle.
Heckle was very competitive and always wanted to prove himself to others.
While Jeckle just wanted to watch TV. Jeckle learned from the TV
(pbs) that nothing could go faster than the speed of light due to special
relativity. Heckle insisted otherwise and vowed to show that he
could go faster than the speed of light. Heckle argued that he could
accelerate at 9.8 m/s2 for 800 days. Then slow down for
800 days and still be well ahead of a beam of light that left at the same
time.Heckle built a spacecraft that would accelerate him, and enough life
support, at 9.8 m/s2, so he would feel as if he were on earth.
One day he and a blast of light would leave earth. For 800 days he
would accelerate away from the earth. Then as he said, slow down for 800
days. He would wait for a while, then att the right moment he would hold
up a mirror to reflect the beam back towards earth, then race and beat
that beam home. Of course for the final 800 days, Heckle would have
to slow down again so he didn't crash into the earth at more than twice
the speed of light.
Upon arrival All those who doubted him would have to admit their error.
Problem
Statement
Heckle was so sure he was right that on the day
of departure, he took his time getting his spacecraft off after the flash
of light had left.
And after he left Jeckle wrote an idl program to
predict how far he would actually go. idl
code
Jeckle realized that after the first 1600 days of
accelerating and decelerating, Heckle would not have caught up with the
light, or even attained it's speed. Being ever stubborn, at day 1600
Heckle would cheat and send another false beam of light back towards earth
and try to catch that. Again he would fail. Jeckle saw that
although only 3200 days (~9 years) had passed for Heckle, Fully 6665 (~18
years) days would have passed for Jeckle and everyone else on earth.
During this time Jeckle would see his brother travel only 7.4 light years
out and 7.4 ly back. A distance covered by light in less than 15
years.
And here's the space time diagram Jeckle made of Heckle's journey.
The units of space are light years.
The units of time are days.
The curved line is the path of Heckle. The diagonal lines are those
of light. The vertical line is the earth. And the one horizontal
line is idl assuming that Jeckle wanted to connect all the points.
Notice that Heckle's speed approaches but never attains that of light.
When Heckle finally did return, he admitted defeat. That blow
was softened by the fact that Heckle's stocks had quadrupled in value and
the little girl that had had a crush on him had grown into an attractive
woman. After 9 years in solitude, Heckle had adjusted his attitude.
He and the woman married and settled in Virginia.
The end.