[MUSIC PLAYING]
Einstein's theory of special
relativity has shown us mass
and time are not the concrete
things we imagine them to be.
In recent episodes, we
started breaking apart
our preconceived
notions of these ideas.
In this episode, we're going
to rebuild our understanding
and explore the origin
of matter and time.
What is a thing?
No mystery there.
It's just a chunk of stuff
that's a self-contained hull.
It has boundaries and
various properties.
Maybe color, shape, size, mass.
This clock is a thing.
You're a thing.
I'm a thing.
Galaxies are things.
And of course, things
occupy a location in space.
For example, right here.
And a location in time,
typically right now.
In recent episodes,
we cast some doubt
on the typical understanding
of two of these properties.
A thing's mass, and a
thing's experience of time.
It's really important that
you're up on those episodes.
So go ahead and watch
them if you haven't yet.
Today, we're going
to bring together
these ideas to explore what
matter, time, and things really
are.
A while ago, we introduced
the space time diagram.
It's just a graph of
position in space--
just one special
dimension for simplicity--
versus position in time.
In this picture, a thing
ends up tracing a path
through time and space.
And we call that
path its world line.
In fact, thinking in four
dimensional space time, a thing
is its world line.
So we define a thing
as its complete spatial
and temporal existence.
Let's break it down.
You put something-- say this
clock-- on this diagram.
And what's it do?
If it's not moving
in space, it'll
just sit in the same
spot on the x-axis.
But it will move up at a
nice steady space in time.
There's nothing you
can do about that.
Time marches on.
But let me give it a tap.
Now, it moves both
in space and time,
because position is changing.
That diagonal line
tells you its speed
isn't changing after
the first push.
Constant speed equals
constant change in position
x with time t.
The slope tells you how
much position is changing
for each tick of the clock.
So slope represents speed.
This is a pretty steep slope.
So not too much x for every t.
It's a slow state.
OK.
Bad scientist.
I didn't define my units.
Let's make it easy and
use what physicists
call natural units, which
just means that we take
the speed of light equal to 1.
Light travels 1 x tick
for every 1 t tick.
And x and t are whatever they
need to be for that to work.
For example, we could make
the time divisions 1 second,
and the space divisions
300,000 kilometers,
because that's how far
light travels each second.
If we do that, then
light speed things
will always level a 45
degree diagonal path.
Always.
And nothing can ever go faster.
So it's possible for
something to travel
one of these steeper paths.
They're separated more
by time than space.
Sub light speed things
can travel them.
And we call them
time light paths.
These would be impossible
faster than light paths.
They're called space lag.
There's not enough
time for anything
to travel that much space.
And the 45 degree path,
that's a light like path.
But what does this look like
if we replace our regular clock
with a photon clock?
Now remember, a photon
clock marks time
with a particle of light
bouncing between two mirrors.
Each back and forth bounce
is one tick of the clock.
Now we'll get back
to why this is
a good measure of the
flow of time in a minute.
Stationary, the world
line of the photon clock
looks like this.
The clock travels smoothly
straight upward in time.
But It is unmoving in space.
However, the
internal photon still
has to travel those 45
degree light like paths,
because photons can only
travel at the speed of light.
A second photon clock
with a constant speed
with respect to the first,
travels a steeper time
light path.
This is where that whole
invariant speed of light thing
gets really interesting.
Regardless of the
speed of that clock,
the internal photons always
do those 45 degree paths
back and forth.
But check it out.
On the timeline of
the stationary clock,
the ticks of the moving
clock don't match up.
The moving clock appears
to tick at a slower rate.
This is the same result
that we saw in the episode
on time dilation.
And besides the invariance
of the speed of light,
the other fundamental
principle of Einstein's
special relativity at play
here is the Galilean relativity
of motion.
There's no preferred inertial,
or non-accelerating, reference
frame.
Now that means that in the
frame of reference of the moving
clock, it is stationary.
And from that frame, the first
clock appears to be moving.
The whole space time
diagram can be transformed
to give the second
clock's world line
a constant location in space.
Stretch these corners and
squish these ones like this,
and we're basically applying
the Lorentz transformation,
which we discussed a while ago.
Our space and time axes shift.
So the second clock is still.
But the first clock is moving.
But those 45 degree lines,
and hence the speed of light,
stay the same for everyone.
And look.
The now stationary frame
sees the now moving frame
as having a slower clock rate.
That's totally weird.
But it's the right answer.
So what this means
is that there's
no single preferred vertical
time axis, or indeed,
horizontal space axis.
We can draw that time axis along
any constant velocity time-like
path, and just Lorentz transform
to get a valid perception
of space time.
This means that the flow of
time is not a universal thing.
It's defined locally for any
observer, or indeed, thing.
But there's no global
rate of time flow
that everyone can agree on.
What defines that
local time flow?
First, let's think
more carefully
about what these clock
ticks really are.
We already covered the
fact that real matter
is comprised of massless light
speed components confined
not by mirrored walls,
but by interactions
with other particles
and force fields.
And that's an interpretation
we can take even
for the most
elementary components
of the atom, in which the
familiar electrons and quarks
are composites of massless
particles confined by the Higgs
interaction.
Or be it on time scale
shorter than the plank time.
In this analogy,
those clock ticks
become interactions between
the internal parts of our atoms
and nucleons.
At each interaction, particles
exchange energy, charge,
and other properties
that result in change.
In those particles, and in the
configuration of the ensemble--
the object itself-- the internal
machinery of the thing evolves.
And on our space time
diagram, our object
becomes an impossibly
complex ensemble
of light speed
world lines confined
in equally complex ways.
Just as with the
photon clock, it's
only the ensemble that can
travel slower than light,
or be still.
Its most elementary
parts can't do that.
They have to travel
at light speed.
Now, a note of
caution is important.
We're extrapolating the
validity of space time diagrams,
and these tiny lifelike
segments into the quantum realm.
Even the Planck scale realm.
But this picture is still
a meaningful perspective
on reality.
It's a pretty wild view take on
our understanding of our theme.
It's not just a
single world line,
but an evolving arrangement
of many light-like paths
that only taken together,
give us a sense of stillness,
a sense of thingness,
and a sense of time.
That time manifests
as the rate of change
of its internal machinery.
And the rate is governed
by the speed at which
that machinery can interact.
Now here's something that seems
to be a more concrete reality
than the flow of time.
Those interactions which
proceed by causal connections.
One of them-- a point on
the space time diagram--
can influence
another if a signal
can travel between the two.
Those causal
time-like paths can be
thought of as a series
of light-like segments.
Two infinitesimally nearby
bits of the universe
can affect each other at
exactly the speed of light.
This gives us an ordered
sequence of cause
and effect-- this, then that.
Time traces that ordered
sequence, and looks different
from different perspectives.
But the causal order looks
the same to everyone.
In this picture, time
and mass and matter
become emergent properties
of the causal propagation
of patterns of interactions
between timeless,
massless parts.
But what defines the
direction of the flow of time?
And what is the nature of
these most elementary causal
interactions?
Great questions for future
episodes of "Space Time."
For our recent episode
on when time breaks down,
you guys had some
amazing questions.
Kovacs asks, how can it be
that if an elementary particle
doesn't experience time,
that they can still decay?
So any particle that can
decay, or even oscillate
between states, like the
electron's chirality flip,
is experiencing time,
which goes hand-in-hand
with them having mass.
However, quarks and electrons
gain their intrinsic mass
by interacting with
the Higgs field.
In fact, these guys are
really composite particles.
The familiar electron
is really a composite
of the left and the
right-handed chirality electron
and anti-positron, which
on their own are massless.
So when I say that elementary
particles don't feel time,
that's what I'm talking about.
These basic vibrations of
their quantum fields-- the time
that the electron
or quark feels--
is felt by the
composite particle,
not by their components.
OK.
So a lot of you
independently realized
that the time dilation
of special relativity
seems to generate a paradox.
What happens when an
astronaut does a round
trip at a large fraction
of the speed of light,
and returns to compare her
clock to one left on Earth?
From both perspectives,
the other clock
was moving, and so should
have ticked slower.
But which clock has the time
lag when they get back together?
This is a famous problem
call the twin paradox.
You have a pair of twins.
One takes a fast trip
around the galaxy.
The other stays at home.
When they get back together,
which appears older?
So, nice work if you came
up with this independently.
The resolution is that there
is no such thing as a paradox.
If you see an
apparent paradox, it
means that you're
missing something.
In this case, it's that special
relativity doesn't fully
describe the scenario here.
In order to compare
clocks, the astronaut
has to turn around at the end
of the journey and come home.
That change in motion
is an acceleration.
And special relativity
only describes
the relative effects
on time and space
due to a constant
relative motion.
To account for the
effect of acceleration,
you need to use
general relativity.
[INAUDIBLE] tells us that
accelerating reference frame
feels a slower passage of time.
So the answer is that
the astronaut's clock,
or the traveling twin,
has experienced less time.
Ectoplasm2369 asks whether you'd
feel time dilation in a warp
drive.
That's actually
a great question.
So for the Alcubierre
warp metric,
there's actually no
time dilation either due
to motion or acceleration.
Your timeline remains
synced to the timeline
of your point of origin.
Bruno JML would like to know
in what reference frame Pink
Floyd's "Dark Side of the Moon"
syncs to when time breaks down.
So in order to fit the whole
album into the episode,
you need to slow your clock
by accelerating uniformly
from rest to 99% of the speed
of light by the end of eclipse.
The start of the
song time should
sync with the appearance
of the photon clock.
[MUSIC PLAYING]
