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Quantum Mechanics

Dr. Nick Lucid: What is mass?

The classic definition says its the amount of stuff inside something. But when we go looking for the "stuff" there's nothing there but energy.

 

 

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Editor's prefatory comment:

The following is a collection of notes, largely, a transcript of a youtube video on the subject of mass by Dr. Lucid. He’s one of the best physics teachers on the net, and his zany sense of humor keeps you on guard.

 

 

According to Newton’s second law,

F = M x A (force = mass times acceleration)

mass measures an object’s ability to resist change in motion (inertia)

More mass = less acceleration.

Mass also appears is in Newton’s law of gravity.

It says that two masses exert gravity on each other over some distance.

More mass in either object = more gravity between them both.

Newtonian laws of motion (mechanics) explain pretty well most things, 99% of things, in 99% of the universe. But it’s not fundamentally correct.

But, his laws don’t really explain what mass is, just what effects it has.

The easiest, most common, definition of mass (often found in textbooks) is that mass is the amount of stuff things have inside them.

But that’s rather vague.

What “stuff”? – yeah, exactly.

This is a really deep question, and the deeper we look, the deeper the questions we ask, that 1% unaddressed by Newton, becomes more and more important.

This other “1% of 1%” is governed by two types of physics: 1) relativity and 2) quantum mechanics.

With relativity, Newton’s two equations have been modified to better represent, to more closely match, the universe.

But there’s a consequence to this correction.

Like a lot of things with Einstein's relativity, mass is relative to the observer. That means, it depends on who or what is measuring it.

 

one's position, motion, and inertial frame of reference determine what 'happens' and what is 'real' 

Everything is moving in the universe – from the smallest particle to clusters of galaxies. Therefore, in order to speak of an object’s speed, it’s important to acknowledge the “inertial frame of reference.” “Inert” literally means “without movement” (see the root word “energy” within "inert"). This frame of reference is what we pretend is standing still in order to measure something else’s movement.

For example, to say that a car is moving at 60 mph has no meaning unless we pretend that the ground is stationary; which, it is not, as it’s part of the Earth, part of solar system, part of the galaxy, all of which are moving rapidly.

In the cartoon above, we have an observer on the ground watching someone bounce a ball inside a train-car. The person in the train sees the ball go up and down, but the observer on the ground sees a parabolic arc for the ball as it moves horizontally ahead with the train.

Einstein had a few of these “train” thought-experiments which demonstrated that simultaneity of occurrence vary with motion, who’s observing, and where. For example, Einstein postulated a train moving at the speed of light with someone atop the train who would attempt to observe, with mirrors, lightning striking both ends of the train at the same time. One of these occurrences, however, would not be apparent to the rider as the train would speed away from the event at light speed, disallowing information of the event to reach the observer. However, someone on the ground would see both flashes of lightning.

 

 

Yes, “relativistic mass” is a real thing.

It isn’t always useful, and sometimes it’s unnecessarily confusing, but it’s still a valid way of looking at the world.

To understand this, we need to take a look at the most famous equation of all time:

E = mc2

The “m” here is relativistic mass.

This means that the “E” is the complete energy content (comprised potentially of all the different kinds of energy).

That “E” could be elastic, thermal, kinetic – whatever.

If the object has more energy, it’s harder to accelerate, it’s affected more by gravity, and it generates more of its own gravity – no matter what kind of energy it is.

But there’s one type of energy that usually dominates – “rest energy”!

The part of mass associated with rest energy is called “rest mass.”

So, the distribution usually looks something like this: it’s almost all rest mass.

Why do we call it “rest mass”?

It’s the amount of mass we’d measure if it were at rest, relative to us.

Let’s say an object starts to speed up.

 

Because its kinetic energy increases, so does its total mass, otherwise known as “relativistic mass.” But its rest mass stays the same.

While rest mass usually dominates, it doesn’t always.

 

If something is small enough, or moving fast enough, kinetic energy can noticeably contribute to overall mass.

There are even things that don’t have any rest mass at all.

In order for something to have rest mass, it must have a “rest frame”. There must be some frame of reference in which it is at rest or stationary.

 

Editor's note: We see parallels between "rest mass" with a "rest frame" and the "inertial frame of reference," which we pretend is stationary (discussed above in the Einstein thought-experiment).

 

Light, the photon, doesn’t have a rest mass or a rest frame. Light is always travelling at the same speed, according to all observers, everywhere.

 

It has relativistic mass, but not rest mass. All of its energy is kinetic energy.

In fact, anything without rest mass is going to behave similarly as the photon.

Gluons also have no rest mass, so they also travel at the speed of light for all observers.

Speaking of gluons, let’s look at quantum mechanics, because we still haven’t explained everything.

How is this “rest energy” stuff actually energy? What is it?

It can’t just be “existence energy” because photons and gluons exist, but they don’t have rest mass or rest energy.

It comes down to what kind of stuff objects are made of. Particles!

For example, steel is made of mostly iron and carbon atoms in a crystal solid.

 

Steel has mass, because its atoms do.

But, taking a closer look at one of the atoms, we have the same problem.

Atoms have mass because their subatomic particles do, and most of that mass is from the protons and neutrons. 

But, protons are made of three quarks.

But the mass of those quarks represents only 1% of the total mass of the proton.

The other 99% comes from the kinetic energy of those quarks and, more importantly, from the binding energy of the gluon field holding those quarks together as a proton.

On a fundamental level, 99% of the mass of you or me, what we would call our “rest mass,” is actually just other types of energy.

 

So, the breakdown looks more like this. Almost the entire chart is made up of different types of energy.

But what about this remaining 1%?

That’s just the rest mass of all these particles over here (on the left):

 

According to quantum theory, those particles have mass due to an interaction with something called the Higgs field.

 

See, most quantum fields hover around zero energy, but the Higgs field hovers a little higher than the others [and] fills all of space…

The point I’m making here is that it’s still all about energy. The Higgs field is an energy field. All quantum fields are.

So, what’s mass?

When you measure the mass of something, you’re measuring its energy content. That energy can be made up of a wide range of different types. But, in the end, it’s all just energy.

 

And, just so I make this abundantly clear, less than 1% of this is from the Higgs field. The other 99% or more is from other energy that has nothing to do with Higgs.

E = mc2

Since this famous equation says that mass is really just energy, maybe it’s time we just stopped discussing “mass” altogether.

 

 

Editor's last word:

Many thanks to Dr. Lucid for this great explanation and the great artwork.

Over the years, I would read commentary, to the effect, “Nothing can go faster than the speed of light. This is because mass increases as light-speed is approached. This means that a rocket-ship approaching the speed of light would undergo an enormous increase in its mass, requiring an infinite amount of energy.”

This never made perfect sense to me. Would the steel of the rocket-ship find its “hard little steel bee-bees” multiplying as light-speed drew near?

But now we know that it’s none of that; there are no “hard little bee-bees” as particles. Moreover, the kind of mass that’s being increased would be “relativistic mass” borne of augmented amounts of kinetic energy.