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Quantum Mechanics

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Einstein showed us that matter, mass, and the flow of time are intrinsically connected. But – are they even real?

In a previous lecture we talked about the speed of light, which is really the speed of causality. It’s the maximum speed at which two neighboring parts of the universe can talk to each other.

Anything without mass [e.g., the photon and gluon] has to travel at 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, for today, we’re going to look at the true nature of matter a little more closely.

We’ve already covered Einstein’s famous E=mc² in a previous lecture and showed that most of the mass in atoms comes from the kinetic and binding energy from 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 it, but for now let’s look at what’s actually happening in an object that 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 the “photon box.”

Imagine a massless box, with mirrored walls… Now, fill it with photons,

also massless, that bounce around inside the box in all directions.

All of 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 of the box moves into the incoming photons. It (this back wall of the box) 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 backwards force that feels like a resistance to the change in speed.

The photons exert a force on the box,

but the box also exerts a force on the photons – Newton’s third law of motion, which gives us conservation of momentum. Momentum lost by the box is transferred to the photons.

Editor's note:

"Momentum can be defined as 'mass in motion.' All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion. The amount of momentum that an object has is dependent upon two variables: how much stuff is moving and how fast the stuff is moving. Momentum depends upon the variables mass and velocity.

"Momentum is a derived quantity, calculated by multiplying the mass, m (a scalar quantity), times velocity, v (a vector quantity). This means that the momentum has a direction and that direction is always the same direction as the velocity of an object's motion. The variable used to represent momentum is p."

Now, if the box stops accelerating, then everything jiggles around and momentum gets shared around evenly by 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 – has any mass.

Somehow, mass arises in the ensemble of 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.

Editor's note: solve for "m" in E=mc² by using simple algebra

And you can derive the famous E=mc² just by looking at how momentum transfers between the photons in the box under acceleration.

But E=mc² 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 all doesn’t start moving instantly.

First, the rear compresses a bit. And then a pressure wave communicates 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 effects – the box of photons and the compressed spring –

both give the same translation between mass and energy, E=mc², because the underlying cause is the same – the confinement of interactions that themselves travel at the speed of light… electromagnetic interactions between atoms.

That itself is a speed-of-light interaction – even if the resulting density wave isn’t.

Ok, so how does this stuff translate into something like a proton?

quarks and gluons in the proton 'shell' = the photons-in-a-box plus compressed springs as contained energy

99% of the mass of the proton is 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 of 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 mass just the result of massless particles bumping and sloshing around inside things, resisting acceleration?

Yeah, it sort 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 respond to and exert 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 1G 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 interactions of massless particles.

But 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 to one side of the box to the other… (to be continued)