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Ever since Albert Einstein published
his Special Theory of Relativity in 1905,
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one equation has been the bane of humans
hoping to explore the stars:
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In addition to informing our understanding
of gravity, space, and time,
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this formula implies that traveling
at or beyond light speed is impossible.
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And given how expansive the universe is,
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this speed limit severely restricts
our ability to zip around the cosmos.
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But while most physics textbooks
describe this speed limit,
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their explanations don’t always
tell the whole story.
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In Einstein’s equation,
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E stands for energy, m for mass,
and c for a constant—
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specifically, the speed of light
in a vacuum.
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C squared is a huge number,
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which means it requires enormous amounts
of energy
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to move even small amounts of mass
close to the speed of light.
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This relationship is why the only
particles that can travel at light speed
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are those with no mass at all,
such as photons.
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That’s the short answer for why
objects with mass
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can’t reach or exceed light speed.
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But to make full use
of Einstein's equation,
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physicists often include
one more variable.
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This gamma represents the Lorentz Factor,
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which models how an object’s velocity
changes the way that object
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experiences time, length,
and other physical properties.
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Now, when an object’s velocity is a very
small percentage of the speed of light,
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this variable resolves to 1,
so it doesn’t impact the equation.
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However, when an object is moving
fast enough,
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this denominator drops to 0.
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Since dividing by 0 is impossible,
this breaks the equation
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and makes the variables
therein mathematically impossible—
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hence the unbreakable speed limit.
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But what does it actually mean
for this math to break down?
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To answer that,
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we need to understand the physical
system its modeling: spacetime.
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After Einstein published
his theory of special relativity,
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his mentor Hermann Minkowski
realized that— if his student was right—
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it would mean space and time
were not two separate entities,
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but one connected system.
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And everything in the universe travels
through space and time simultaneously.
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However, traveling through one of these
vectors limits the speed at which
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we can travel through the other.
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To picture this, imagine
moving north at a fixed speed.
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You could turn to travel east
at the same speed,
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but moving northeast would mean you move
in both directions more slowly.
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The tradeoffs are the same when
we move through spacetime.
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Since our typical movement through space
is so much slower than the speed of light,
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we mostly perceive moving through time
at a relatively steady speed.
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But if an object managed to move
through space at the speed of light,
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it would no longer move through time.
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This is the kind of time dilation
charted by the Lorentz Factor,
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which models how time slows
down for objects moving
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at incredibly high velocities.
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This nuance is just one
of several hiding in E=mc².
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For example, the c in Einstein’s
equation refers specifically
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to the speed of light in a “vacuum,”
which outer space approximates.
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But light’s speed is actually defined
by what it’s traveling through.
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For example, when light
travels through water,
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its speed is reduced by about 25%.
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And scientists can propel low mass
particles like charged electrons
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through water at speeds
faster than these photons.
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This means that underwater, some particles
can travel faster than light;
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and doing so emits a ghostly blue glow
known as Cherenkov radiation.
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Despite these loopholes,
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the major takeaway of E=mc² remains true.
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As far as we know, we still can't
travel faster than light in a vacuum.
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But this hasn't stopped scientists from
theorizing what might happen if we did.
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If you were on a spacecraft
approaching light speed,
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your vision would likely
become kaleidoscopic.
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The direction your ship moved
would appear blue-shifted,
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while the things next to and behind you
would be red-shifted.
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And if you were somehow able
to reach or exceed light speed,
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it might even manifest
as some kind of time travel—
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potentially letting you chat
with Einstein himself
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to rewrite our fundamental
understanding of physics.