In the last episode, we saw how matter fills mass because of the energy of its internal moving parts.

You might want to watch that episode now, because today we're going to go even deeper and explore the connection between matter, motion, and the nature of time.

The watched pot never boils.

A boring college lecture lasts forever.

While weekends and summer break seem to finish even before they start.

Our perception of time depends on how much attention we pay to it.

We have internal clocks, neural processors dedicated to the counting of seconds and hours.

While our memories layer over the course of our lives, and in their ordering, we see the flow of years.

Our often flawed perception of time comes from watching patterns in our brains evolve.

But that's just perception, right?

A second is a second, a decade is a decade.

And a perfectly engineered clock will always tick at the same right.

Actually, no.

Any clock is just an arrangement of matter.

Every tick is the result of countless interactions between the tiniest subatomic elements.

The rotating gears are comprised of atoms vibrating in metal lattices, bound by electrons flickering in their orbits, themselves held in place by protons that are comprised of quarks in constant motion.

The sum total of this motion results in a smooth, consistent evolution of time.

But do the individual components of the clock feel the same flow of time?

Down to the atoms and nuclei, yes.

The most accurate clocks in the world are atomic clocks, which can drift by less than a billionth of a second each day.

All of the atoms in such a clock feel the same length of a second.

But what about the quarks, the electrons?

This is where our conception of time starts to break down.

Why?

Because of motion.

See, the flow of time depends fundamentally on motion.

The faster an object moves relative to you, the slower its clock appears to tick.

A particle moving at the speed of light experiences no time.

Its clock is frozen.

Those electrons and quarks bounce around at such high speeds inside the atom that they experience time very differently to the atom itself.

And in a sense, the most elementary particles are intrinsically timeless.

The familiar smooth flow of time only emerges as these particles are bundled into what we think of as matter.

Time happens for the atom in a way that it doesn't for the atom's parts.

Today, I want to show you why time depends on motion, which in turn will show us why light speed particles are timeless, and why having mass and experiencing time are fundamentally connected.

In the last episode, we compared the nucleons of atoms-- protons and neutrons-- to the imaginary photon box, a massless mirrored box filled with light, which despite being composed only of massless things, itself does have mass.

We're going to use a very close cousin to the photon box to explore time-- a thought experiment of Einstein's that we'll call the photon clock.

Imagine a clock made from two mirrors and a photon bouncing between them.

Every back and forth bounce of the photon results in a tick of the clock.

The tick rate depends on the speed of light and on the distance that the photon has to travel between the mirrors.

The rate of ticks is consistent, time flows smoothly, until the clock starts moving relative to me.

Now imagine moving the mirror sideways.

From my perspective, light now takes a longer, diagonal path.

But here's the weird thing.

As we saw in a previous episode, the speed of light is what we call invariant.

All observers, regardless of their own speed, will report seeing the same speed for any particle of light-- any photon.

This fact isn't intuitive, but it's extremely well tested.

OK.

So from my point of view, the photon takes longer to make the up-down journey.

It appears to travel more distance, but at the same old speed.

To me, it appears as though the ticks take longer in the moving clock compared to an identical photon clock standing still right next to me, which ticks at the normal rate.

Some other guy who is riding along with the moving clock would see it ticking at the normal rate, and quite bizarrely, will see my clock ticking slower.

After all, my clock is moving relative to them.

This effect is the time dilation of Einstein's special relativity.

And again, it's very well tested.

Now what if the clock is traveling at the speed of light?

The apparent distance that the photon needs to travel to reach that top mirror becomes larger and larger as the clock speed increases.

And that distance is infinite when the clock reaches the speed of light.

From our point of view, the photon clock could never complete a tick because the photon could never reach that mirror.

Time is frozen.

By the way, similar arguments will show us that a photon clock in an accelerating reference frame-- say on a rocket ship in empty space-- will also tick slower compared to a non accelerating clock.

The overall distance that the photon has to travel is larger in an accelerating frame.

Because that top mirror is running away from the rising photon faster than the bottom mirror catches up to the falling photon.

Ticks take longer.

But Einstein's equivalence principle tells us that a frame suspended in a gravitational field is indistinguishable from an accelerating frame.

And so clocks must also tick slower the deeper they are in their gravitational field.

This is the gravitational time dilation of general relativity.

So what does this odd example of the photon clock have to do with real time and real matter?

Well, if our photon clock behaves this way, then so does the photon box.

They're really the same thing.

In a fast moving photon box, we perceive that its internal particles have further to travel to bounce off the walls compared to an identical stationary photon box.

Note that this is not the same thing as accelerating the photon box, which gives it the feeling of mass.

Here, we're talking about something moving at a high but constant speed.

And from the last two episodes, we know that atoms and their nucleons are all kind of like photon boxes.

They're made up of things that would move at the speed of light, except that they're confined.

Quarks and electrons confined first by their coupling with the Higgs field, and then by the forces binding them into atoms.

So as an atom races past you at high speed, you would see all its internal bits ticking slower, just like the photon clock.

See, in an atom, that ticking corresponds to interactions between its component particles and fields, in which the internal parts exchange energy, momentum, and other properties-- interactions which hold the atom together.

The rate of these interactions, this ticking, represents the rate at which the atom will change from one arrangement, one state, to the next-- the rate at which an atom evolves.

In a fast moving object, the interactions driving this evolution appears to happen more slowly.

Time passes more slowly.

Move fast enough, and time barely passes at all.

So the confinement of light speed particles gives matter mass.

In fact, this confinement, this bundling of energetic moving parts, is what makes it matter.

But now it looks like this same bundling of light speed particles can also given matter time.

Atoms feel time in their internal evolution similar to our own perception of the changing patterns in our brains.

But what is it about not traveling at the speed of light that allows matter to have structure and to change?

What prohibits matter from reaching the speed of light?

Is time even a real dimension?

And what defines its direction?

We'll have time for all of this on a future episode of Space Time.

In the last episode, we talked about the true nature of matter and mass.

And you guys asked the hard questions.

Paramdeep Singh, and a few others, questioned the plausibility of massless walls in our photon box thought experiment.

And yes, massless walls are impossible.

However, the thought experiment still works if you say that the walls do have some mass.

In that case, the box's mass increases by the amount equal to the energy of the contained photons, divided by the speed of light squared.

Bernardo Sousa, and a number of others, want to know whether a compressed spring really is actually heavier than a relaxed spring, and whether that's measurable.

And yes, it really is more massive, but not by much.

Compress a car suspension spring completely, and its weight would increase by maybe a trillionth of the gram-- not measurable on your bathroom scales, but it would be measurable on very precise laboratory scales.

Joshua Hillerup raises a great point.

Shouldn't the resistance to acceleration produced by a compressed spring only take effect along the length of the spring, as opposed to the side?

Actually, no.

In the compressed spring, there's increased pressure throughout the material.

That pressure increases the resistance to further compression in all directions.

So it feels massive, regardless of the direction in which you push it.

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