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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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