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.
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