Did you know that you could
be older than your twin? Like, years older? According to Einstein's
theory of special relativity, it's possible, because time
can tick faster or slower, depending on how you're moving. Wha? Yeah. We'll get back to that. But first, we're going to learn
all of special relativity. Don't worry, there are
only two postulates. One is that the
laws of physics are the same for everyone's
perspective, or frame of reference, while
in uniform motion. So that means that
on a plane cruising at 800 kilometers per
hour, an object you drop will fall straight down,
just as it would if you're stationary on the runway. Same physics in
those two frames. Otherwise, plane rides
would get real weird. The crazy implication
of this postulate is that there's
no experiment you could do to tell that
you're moving, even at 800 kilometers per hour-- even at
a million kilometers per hour-- because you can only tell you're
moving relative to something else, like the clouds
outside your window. The second postulate is that
the vacuum speed of light is the same for all observers--
300,000 kilometers per second. Let's just pause
on that for a sec. Do you know how freaky this is? It means that if you're flying
toward me in a spaceship going close to the speed of light
and you shine a laser at me, you'll still measure
that light to be going at 300,000 kilometers
per second, and I'll measure the light
to be going at 300,000 kilometers per second as well. So those are the
only two postulates of special relativity. The speed of light
is a constant, and the laws of
physics are the same in every inertial
reference frame, "inertial" meaning not moving,
or moving at constant velocity. Basically, you're
not accelerating. And when you do accelerate, like
when you experience turbulence, or during takeoff when you're
pushed back into your seat, you can tell you're moving, and
special relativity no longer applies. So it's from just
these two postulates that we derive an
entire physical theory and get crazy things like
length contraction and time dilation, and other weird
quirks of physics that are real. One such quirk is that time
can tick at different rates depending on how you're moving. We call this time dilation. It's weird, but it's real. Why does it happen? Consider two frames. One is you stationary on Earth,
and one is your twin zooming by in a rocket. You have identical clocks. Let's look at yours first. Each time light makes
round trip in your clock, you count by one. Your twin will measure the
same rate on her own clock. Now, things get weird
when you watch her clock. Because of her
sideways motion, you see that her light has to travel
a longer distance for one tick. And since the speed of light
is the same for all observers, her round trip ticks
must take more time. So time actually ticks
slower on her moving rocket according to you,
stationary on Earth. And this is a real phenomenon--
it's not some weird mind trick. We don't usually
notice this, though, because time dilation
is quite insignificant until you're moving close
to the speed of light. So now, from your twin's
perspective, you are moving. Therefore, your clock
must be running slower according to your twin. And because the
laws of physics are the same in both of these
frames, yours and hers, each frame is equally correct
in saying the other's clock is running slower. This is where the
paradox starts. Imagine you and your
twin start off on Earth. You stay here, but
your twin zooms off in a spaceship at half
the speed of light, turns around, and comes back. The whole trip takes
30 years, but you see your twin's clock tick slower. So due to time dilation
during the journey, she only aged 26 years,
four years less than you. Now, here's the
crux of the problem. From your twin's perspective,
she was stationary, and you on Earth moved
away and came back. You're the one moving at
half the speed of light, so your twin should see
your clock going slower and should think you
are only 26 years older by the end of the trip. So yeah, that's not possible. When your twin gets back, she's
either younger or she's older. She can be in a
superposition of both. This isn't quantum. So how do we solve this paradox? Well, the answer
lies in the details. When your twin turns around,
she has to accelerate, which means she's no longer
in an inertial reference frame while she accelerates, and so
special relativity no longer applies to her. It's not as simple
as saying your twin sees you make round
trip, and you see your twin make a round trip. It's not a symmetric
problem like that, because when your
twin accelerates, we can tell the difference
between the physics that might happen in those two frames. She will feel the acceleration
during the turn around, and you will not. So when she gets back, she will
agree with you that you are 30 and she is 26. One last question. What's happening to the
clocks during the period of acceleration? We still get time
dilation, but we have to use a
different set of rules from the general relativity. General relativity
states that clocks run slower in accelerated
reference frames. So while your twin is turning
around, her clock runs slower, and she sees the same thing. She sees your clock
running faster than hers, so you're aging quicker. It's during this
period of acceleration that you become the older twin. Now, this phenomenon of time
dilation in an accelerated reference frame is
related to time dilation in a gravitational field. General relativity
says that clocks run slower in
gravitational fields, as you may have seen occur
in the movie "Interstellar." You can get time dilation
and other strange things occurring during
different forms of motion. Special relativity
and the twin paradox are just the tip of the iceberg. [MUSIC PLAYING]
It's untrue to say that special relativity breaks down in non-inertial frames. Link