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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.
GR 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.
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