Game Development Reference
In-Depth Information
Δt' = γΔt
where:
1
1 - v 2
c 2
γ =
is called the Lorentz factor .
For velocities approaching the speed of light, the effect of time dilation is dramatic.
Imagine if you had a twin sister. She boards a spaceship and is accelerated to three-
fourths the speed of light relative to you on Earth. Upon her return, according to her
clock, 20 years have elapsed since she left. However, due to time dilation you will have
aged 30 years. While this seems paradoxical given that you both will have observed each
other's time as running slowly compared to your own, the paradox is resolved by the
fact that special relativity claims only that inertial frames of reference are identical. For
the spaceship to return to Earth, it must accelerate by changing directions or, in other
words, become a noninertial frame of reference. Once the ship is no longer an inertial
frame of reference, there will appear to be a jump in the stay-at-home twin's age. Strange
but true!
In addition to time dilation due to relative velocity, time also slows down in the presence
of strong gravitational fields as a result of Einstein's theory of general relativity. This sort
of time dilation is not relative in the sense that if I were closer to a black hole than you,
we'd both agree that my clock is ticking less often than yours. However, given that all
physical processes would be slower, there is no way to establish which clock is “faster”
and which is “slower.” It is all relative!
As some games require a way to speed up or slow down time, the applications of time
dilation allow for a physical phenomenon to enable time manipulation. Imagine your
character needing to be sent to the future to complete some task. That character could
be put into a centrifuge and accelerated near the speed of light. Upon exiting the cen‐
trifuge, he would essentially have time-traveled into the future. However, if you plan to
stay within the limits of physics, then it is a one-way trip: there is no way to reverse time
in relativity! Additionally, if you would like to send a character to a nearby star, you can
do so within the limits of physics as well. By accelerating a spaceship, a human being
would be able to travel a great distance in a lifetime. In fact, with a constant acceleration
of 9.8 m/s 2 , which would make the astronauts feel like they were on Earth, you could
travel the entire visible galaxy. However, you would have essentially time-traveled bil‐
lions of years into the future. We are sure that you can imagine any number of scenarios
where such a mechanism might make your game more interesting while always re‐
maining in the realm of the physically possible!