Answer 2:
This is a great and fascinating question! The
answer might deceive you! Letβs start by a
definition of light year. A light year is the
distance that light travels in vacuum in one
year, about 6 trillion miles or 10 trillion
kilometers. One might therefore conclude that in
order to travel one light year at one tenth the
speed of light, this trip would take 10 years.
This is correct, but is only half the answer!
The
second half of the answer lies in the field of
special relativity. The most relevant
concept is called time dilation, and
considers the frame of reference when we measure
time. A simple idea is to think of two identical
twins holding identical clocks, one on Earth and
one traveling in a highspeed spaceship. The twin
who travels and comes back will actually observe a
shorter passage of time than the (now older) twin
on Earth! This comes from the fundamental
assumption that the speed of light must remain
constant no matter which frame of reference is
observed. In real life, satellites up in orbit
have clocks that run slightly slower than the ones
on the surface of the Earth.
So back to the puzzle: An observer on Earth sees a
space traveler take 10 years to travel 1 light
year at 1/10 the speed of light. But how much time
passes for this space traveler? There is an
equation for calculating time dilation given the
relative velocity of an object:
Ξπ‘β²=
Ξπ‘_{0} / β1β π£^{2} /
π^{2}
Where Ξπ‘_{0} is the travelerβs time frame
(called
proper time), Ξπ‘β² is Earthβs time frame,
π£ is
the speed of the traveler (referenced by Earth),
and π is the speed of light. For everyday
velocities (such as airplane speed), π£ βͺ
π so the
effects of time dilation are negligible. But
greater than 1/10 the speed of light, we start to
see noticeable effects.
If we plug the numbers
into this equation, we see that the traveler
actually observes a time span of Ξπ‘_{0} =
9.95 years,
or 18.3 days short of 10 years to complete the
trip! In fact, if the traveler was going at 99%
the speed of light (a supposed trip of just over a
year), according to him, his trip would only take
52 days to complete!
These concepts of time dilation and special
relativity are especially interesting to
ponder. For instance, if one day we develop
nearlightspeed travel, we may be able to travel
βforwardβ in time relative to Earth. A traveler
could travel for a few years in her spaceship, and
come back to Earth to find that everyone else has
aged decades or centuries! Another possibility is
that for those bold travelers that explore the
deep reaches of space, they can travel great
distances away without having aged much, all
thanks to time dilation.
One last thing to consider, it is often
confusing to figure out who is the observer in
which reference. Just remember that
Ξπ‘_{0} is always the observer (can be
person on Earth, space traveler, or anybody). From
this, we know that π£ must be the πππππ‘ππ£π
velocity of the person or object being observed,
whose time span is Ξπ‘β². This means that for two
twins who are on Earth and traveling in space,
each twin measures the otherβs time to be going
slower, because of the relative velocity between
each other! A confusing idea indeed, but if we
think about two twins observing each other from
far away, each will observe the other as being
physically smaller, but we know that both twins
are of course the same size.
You may check out this page talking
about time dilation and space travel:
relativity
