the
important thing to understand about relativity is right in the name: it is
relative. That is,
for a massive object there is no such thing as having an objective, absolute
speed that is agreed upon by all observers. A massive
object cannot actually reach the speed of light, which will become apparent
later on in this answer. But to roll with the question, let’s imagine a
velocity that is just below the speed of light. So, if a
spaceship is traveling past an observer (let’s say it’s moving past us on
Earth) at nearly the speed of light, we see it moving by very fast. From the
spaceship’s perspective, however, the ship is stationary. From the ship’s
perspective, the Earth and the surrounding planets and stars are passing by the
ship’s window at nearly the speed of light. That’s easy
enough to visualize, but the following section is where things get weird, and
you’ll see why it matters in a bit. The
velocity of massive objects is relative to every observer, but the speed
of light is always constant.

From Earth,
we see the high-beams shining from the spaceship moving at light speed, a
number we refer to as c, as in E=mc^2, which happens to be
299,792,458 meters per second. Since the ship is moving at close to c relative
to Earth, the high beams seem to us to be barely inching away from the ship—the
ship is right on the light’s tail, so to speak. From the
spaceship, they also understand that the light is beaming off into space ahead
of them at the speed of light. Now here’s the counter-intuitive thing about the
speed of light: remember that from the perspective of those on the ship, they
are stationary and it is the surrounding universe that is passing by them
through their window. So when they measure the speed of the light in their
high-beams, the light isn’t barely inching away; it is also zooming off into
the distance at c. They measure c in all directions as if they
were stationary. In
relativity, c stands for constant, because all observers witness
it to be the same constant speed, no matter their own motion. No object with
mass can reach or exceed c; light always seems to be moving towards you or
away from you at c, in all directions.

Next Lorenz
contraction and time dilation, the nature
of relativity was actually discovered based on this exact finding about the
speed of light. Because the Earth is moving through space, scientists believed
that light would seem to travel slower if they measured a beam pointed in the
direction of the Earth’s movement (since Earth is chasing behind the light) as
opposed to a beam shined perpendicular to the Earth’s movement. They ran an
experiment and were amazed to find that light seemed to be going at exactly
the same speed relative to their instruments, regardless of whether it was
travelling along the Earth’s path or perpendicular to it. This was the
famous inferometer experiment of 1897, and it was the finding
that Albert Einstein eventually based his 1905 theory of special relativity on,

Now here’s
where it applies to our question, because of
this finding, in order for the wonky observations of various observers to be
reconciled, two things must take place as the ship travels. One is Lorentz
contraction: the ship seems squished, lengthwise, to the observer on Earth. If
the people on the ship think the ship is 100 meters long, and the ship is
moving about 99.5 percent of the speed of light, well, those of us on Earth see
the ship as about 10 meters long (you can run the calculation for Lorentz
contraction here).
So the person on the ship thinks they’re running at 5 meters per second, but we
on Earth would perceive them to be running at 0.5 meters per second—not
accounting for time dilation, so of
course the other component is time dilation. In addition to the discrepancy in
distance, there is also a discrepancy in time. That is, the person on the ship
runs from back to front in what they think is 20 seconds. To those of us on
Earth, the people on the ship are moving in slow-motion, so we see the jogger
taking 200 seconds to get from the back to the front of the ship (you can run
the calculation for time dilation here),
which compounds with the fact that the ship is only 10 meters long from our
perspective. That means we on Earth see the runner travelling only 0.05
meters per second faster than the ship is traveling—not fast enough to close
the gap and reach the speed of light. The effect of time dilation and Lorentz
contraction increase as you go faster, approaching infinity at c, so they
always overpower any attempt to reach c.

The
observations are relative. Another
really counter-intuitive aspect about relativity is that the observer on the
ship has the exact same observations of us on Earth as we do about the person
on the ship. Since the people on the ship think they’re stationary, they look
at a Lorentz-contracted oval-shaped Earth that appears squished as it flies by
them. The rest of the local universe is squished as well, with all the planets
in oval-shaped orbits, and the stars in front of them seeming to be only 10
percent as distant (the stars on their left and right appear to be the same
distance as they do to us on Earth). They also observe Earthlings moving in
slow-motion.

An object
with mass can never reach light speed. With all
this in mind, it’s easier to see how reaching the speed of light is impossible.
The more the people on the ship power their rockets and accelerate, the more
they do accelerate—in the sense that the surrounding universe seems
to contract more and more, making distances shorter and their progress through
those distances increase dramatically. From the Earth, though, the ship appears
to approach light speed (or c) more and more, but the closer they get
to c, the more the ship’s length contacts and the less of a difference it
makes when they try to accelerate. They will inevitably run out of fuel before
they get to c. (The thrust of their rockets also appears to slow down as
time slows. That’s not to be confused with their forward motion, which is still
approaching c.),

so if the ship
were to actually reach light speed, three things would have to have happened:
the surrounding universe would have had to become completely two-dimensional from
the ship while the ship seems completely two-dimensional from Earth
(impossible), the people on the ship would observe time for the surrounding
universe to have completely stopped while people on Earth would observe time to
have completely stopped on the ship (impossible), and the ship would have to
have used an infinite amount of energy to get to c (impossible). The ship
would also be said to have infinite mass, because anything that they hit would
experience an infinite amount of energy on impact (impossible). Even a single
atom they impact would cause an explosion of infinite energy that would destroy
both the ship and the entire universe.

It would
also violate the finding that c is constant; an observer travelling
at c would stop observing light travelling at c, since they would be
travelling at the same speed as the light. Light going in their direction would
seemingly be frozen, which brings with it a host of other conceptual problems. Only things
without mass can travel at c: light, gravity, electromagnetism and the
strong nuclear force. These things can only travel through a
vacuum at exactly the speed of light, never any slower, well I did say it was a long answer! and many thanks to Matt Pizzuti for answering it!

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