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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