NARRATOR: Einstein showed us that matter, mass,

and the flow of time are intrinsically connected,

but opened the question, are they even real?

Let's find out.

In a previous episode, we talked about the speed of light--

the fastest speed there is.

And we talked about how this speed limit is really

the speed of causality.

It's the maximum speed at which two neighboring bits

of the universe can talk to each other.

Anything without mass has to travel this speed.

But what is it about mass that prevents something

from reaching the ultimate speed?

The answer to this will take us to a much deeper question--

what is the origin of matter and time?

However, it's going to take us a couple of episodes

to get there.

So today, we're going to look at the true nature of matter

and mass a little more closely.

We've already covered Einstein's famous equation,

E equals Mc squared, and showed that most of the mass of atoms

comes from the kinetic and binding energy

of the quarks that make up protons and neutrons.

But saying that mass is energy doesn't really get us very far.

It just begs the question, what is energy?

That's a huge topic that we'll build up to.

For now, let's look at this energy

in terms of what's actually happening in an object

when it exerts this property we call mass.

Let's ignore the gravitational effect of mass for the moment,

and just consider mass as the degree to which an object

resists being accelerated.

We call this inertial mass.

A good place to start is with a thought experiment

that we'll call a photon box.

Imagine a massless box with mirrored walls-- impossible,

I know, but it's an analogy for something real, as we'll see.

Now fill it with photons, also massless,

that bounce around inside the box in all directions.

All the walls of the box will feel the same pressure,

so there's no overall force on the box.

But let's give the box a little nudge-- increase its velocity.

Now the back wall of the box moves

into the incoming photons.

It feels a little more pressure from their impact than before.

In the meantime, the front of the box,

moving away from the incoming photons, feels less pressure.

There's a net backward force that feels like a resistance

to the change in speed.

The photons exert a force on the box,

the box also exerts a force on the photons-- Newton's

Third Law, which gives us the conservation of momentum.

Momentum lost by the box is transferred to the photons.

Now, if the box stops accelerating,

then everything jiggles around and momentum

gets shared out evenly between the box and the photons again.

But as long as acceleration continues,

the pressure differential persists.

Acceleration is resisted in a way

that feels exactly like mass.

In fact, it's indistinguishable from mass, because it is mass.

The photon box is massive, even though none of its components--

not the photons, not the walls-- have any mass.

Somehow, mass arises in the ensemble where

it doesn't exist in the parts.

How much mass does the box have?

It's the energy of the photons divided

by the square of the speed of those photons.

And you can derive the famous E equals Mc squared just

by looking at how momentum transfers

between the photons in the box under acceleration.

But E equals Mc squared describes

the universal relationship between mass

and confined energy, not just confined photons.

So let's look at another example of confined energy.

A compressed spring holds more energy than a relaxed spring.

It holds potential energy.

So is a compressed spring more massive than a relaxed one?

You bet it is.

Again, we can describe this in terms

of a straightforward physical effect.

An already compressed spring is harder to compress

further compared to a relaxed spring.

But that's exactly what you have to do when you try to move it.

Push the spring, and it doesn't all start moving instantly.

First, the rear compresses a bit.

And then a pressure wave communications the force

to the front until the whole spring is moving.

That initial push is harder for the compressed spring

than for the relaxed spring.

It feels like it's more massive, because it is.

These seemingly very different physical effects-- the box

of photons and the compressed spring--

both give the same translation between mass and energy,

E equals Mc squared, because the underlying cause is the same--

the confinement of interactions that themselves

travel at the speed of light.

Photons in the photon box, but even

in the spring, the density wave is ultimately

communicated by electromagnetic interactions between the atoms.

That itself is a speed of light interaction,

even if the resulting density wave isn't.

OK, so how does this stuff translate to something

like a proton?

99% of the mass of the proton is in the vibrational energy

of the quarks plus the binding energy of the gluon field.

The actual intrinsic mass of the quarks is a tiny contribution.

So the proton is a lot like a combination of our photon

box and our compressed spring-- quarks,

bouncing off the walls in the binding gluon field, which

itself acts like a compressed spring, holding

potential energy.

And as we saw recently, even those quarks, as well as

electrons, gain their tiny masses

from a type of confinement via the Higgs field.

Take away the Higgs field, and they are massless speed

of light particles.

It looks like everything with mass

is composed of a combination of intrinsically massless,

light-speed particles that are prevented from streaming freely

through the universe, as well as the fields that

confine those particles.

So is mass really not a fundamental property?

Is it just the result of massless

particles and fields bumping and sloshing around inside things

resisting acceleration?

Yeah, it kind of is.

This acceleration resisting mass, inertial mass,

seems to be an emergent property of the ensemble.

But we can't talk about mass without talking about gravity.

Massive objects exert and respond

to the force of gravity.

They have what we call gravitational mass.

But how does the inertial mass of our photon box

end up translating to gravitational mass?

Once we accept Einstein's description of space-time

as described by general relativity,

it's not so surprising that the photon box

feels the pull of gravity.

The equivalence principle tells us

that the feeling of being accelerated out in space

is fundamentally the same thing as the feeling of weight

in a gravitational field.

Holding up our photon box against Earth's surface gravity

has to be just as hard as trying to accelerate it

at 1 g in empty space.

The photon box feels heavy.

Same with the compressed spring--

it's harder to accelerate than a relaxed one,

and it also feels heavier in a gravitational field.

In fact, the equivalence principle

tells us that the gravitational mass

of an object and the inertial mass are the same thing.

But mass doesn't just respond to a gravitational field.

It generates one.

Mass curves the fabric of space.

Actually, it turns out that it's not just mass that bends space.

The presence in the flow of energy and momentum

as well as pressure all have their quite different effects

on the curvature of space-time.

Individual photons affect space-time.

And when you trap them in a box, the curvature that they produce

looks just like gravity.

So confined massless particles generate a very real

gravitational field.

OK, so mass is an emergent property of the interactions

of massless particles.

What about time?

A single photon experiences no time,

nor does any massless particle.

Their clocks are frozen.

But our photon box has mass, so it must experience time.

When and where does this time arise?

The individual photons don't have it

when they travel from one side of the box to the other.

Do they get time when they bounce off the wall?

Does the ensemble of photons somehow feel time

that individual photons do not?

We'll explore these questions when we delve deeper

into the mystery of matter and time

in the next episode of "Space Time."

In the last episode of "Space Time,"

we talked about how the Higgs field gives

elementary particles mass.

And as always, you guys had some great questions.

Caleb Limb asks, does this mean the Higgs field makes

a little friction in space?

Well, this is a bit of annoying pop-sci misinformation.

The Higgs field isn't like molasses

or like a crowd full of physicists.

It doesn't act like friction, because friction slows down

particles.

The Higgs field doesn't slow particles down.

It gives them inertia-- a resistance to acceleration.

It makes them harder to speed up or slow down.

And importantly, it prevents them

from traveling at the speed of light.

Felix Feist points out that given

that the right-handed electron doesn't have weak hypercharge,

shouldn't it be massless?

Well, yes and no.

The right-hand electron can interact with the Higgs field

by picking up some weak hypercharge.

In fact, this flipping back and forth between handedness

is probably more accurately thought

of as the electron being both right- and left-handed

at the same time, because the interchange happens

on time scales shorter than the Planck time.

There's a quantum blur surrounding the current state

of the electron.

It's really the composite particle that has mass.

The naked left- or right-handed electron is massless.

Death by PowerPoint wonders whether there

could be a point in space somewhere

where the Higgs field takes on the value of zero,

and what the ramifications would be.

Well, actually, yes-- or at least there was.

At extremely high temperatures, the Higgs field

takes on a value of 0 everywhere.

And it's believed that this was the case in the fraction

of a second after the big bang.

Then, without an infinite source and sink of weak hypercharge,

the weak nuclear force and the electromagnetic force

were all the same force.

Only when the universe cooled down did the Higgs field gain

a nonzero value in a phenomenon called spontaneous symmetry

breaking.

Then the weak force carriers gained mass

and became differentiated from the electromagnetic carrier--

the photon.

The ramifications-- we wouldn't have atoms

without a nonzero Higgs field.

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