- Quote:
*Such collisions and transformations are happening continuously and stably inside protons and neutrons. They are completely benign, cause no damage, and always conserve the number of extra quarks.* - Endnote:
*It is not at all obvious that a proton could have so much inner activity and yet preserve outward stability. In fact, it is possible only because of quantum physics. Atoms have this property, too; quantum physics allows electrons both to surround a nucleus in a static manner and yet to maintain considerable motion.*

That an object can be both static in one sense and fundamentally active in another is a fundamental property of quantum physics.

A hint of this feature already turns out to be essential in understanding elementary particles. In chapter 17, we see that a stationary electron is a vibrating object; it is both inactive (in that it is stationary) and yet active (in that it is vibrating, giving it energy-of-being via ** E=fh**, and thus, via

**, rest mass.)**

*E=mc*^{2}But this is just a first step. The shape of a stationary electron is widely spread out, much broader than an atom, and nearly uniform on microscopic distances. All of its activity comes from its vibration. In atoms and protons, however, there is something additional going on, which is what this endnote really refers to.

### The Motion of an Electron in a Box

In a sequence of posts (post #1, post #2) I have explained some of the surprising features of electrons when constrained by walls, as when one is placed in a box. These posts are intermediate steps on my way to explaining how an electron behaves in an atom and how a quark behaves in a proton (post #3).

A ordinary particle placed inside a box just sits there; it doesn’t move, and shows no activity. But electrons aren’t ordinary particles. Because (in the language of chapter 16) an electron is better described as a wavicle, rather than a “particle” as we normally imagine it, its behavior inside a box reflects the same “inner activity and outward stability” that we observe in protons.

In particular, even when an electron in the box is in its lowest-energy state (the “ground state”), it vibrates as a standing wave. The frequency of that vibration depends on the size of the box. And thus, even when the electron is as static is it can be, it responds to the size of the box that it is in.

Moreover, the smaller the box, the more compact the shape of the standing wave — the more quickly the wave’s shape must vary from one side of the box to another. And this shape now leads, counter-intuively, to a form of motion.

Quantum physics implies that the more rapidly the electron’s shape varies from place to place, the more capable it is, if it collides with some other object, of causing that object to move. To make that object move, the electron must be carrying what physicists call “momentum” — which it can only have if it is moving. Indeed, a change in the shape of the electron wavicle from place to place is an indication that it has momentum.

Momentum is a sign of motion across the box. And yet, how can an electron in a box, sitting in its ground state, be moving, when it is merely a vibrating standing wave, not in any way changing its position within the box?

The point is that **its motion may be non-zero even if its average motion is zero**. In a way, this is almost the definition of activity within stasis.

### Stasis and Activity

Let’s consider the following sequence of numbers:

0, -1, 0, 1, 0, 2, 1, 0, 0, -1, -2, 0

Here’s one sense in which these numbers are static and go nowhere: if you add them up, their sum is zero, and so **their average value is zero**.

And yet these numbers are changing from one to the next, which makes them active. We don’t see this activity in their average. But we do see it in **the average of the squares of the numbers**, which are

0, 1, 0, 1, 0, 4, 1, 0, 0, 1, 4, 0

The sum of these squares is 12, and thus the average of the squares is 12/12 = 1, not zero.

So again: the average of the numbers is 0, but the average of their squares is not zero, and is instead 1. This combination of facts tells us that not all the numbers are zero, and that at least two must be well away from zero.

In a conceptually similar way, an electron in a small box may not be moving on average, but it is neverthless in motion (and carrying momentum). Even though that motion (and momentum) has a variable direction that averages out to zero, it is nevertheless present. The smaller the box, the more motion it has.

### The Motion-Energy of the Electron in a Box

This extra motion (and momentum) leads to extra energy. As I already mentioned, **the smaller the box, the faster the electron in its ground state will vibrate** — i.e., the higher frequency it will have — and because ** E=fh** for any wavicle, that means the electron has extra energy (beyond its usual

**internal energy). What is this extra energy? It is precisely the motion-energy associated with the momentum. This consistent, because the motion-energy of the electron depends on the square of the momentum, not the momentum alone — and so it averages to a non-zero value, even though the average motion is zero.**

*E=mc*^{2}In short, the electron in a box may be static, yet it has extra activity compared to the free, stationary electron. The smaller the box, the more momentum and motion energy it carries.

### A General Quantum Effect

This is a general feature of small quantum objects. A proton with quarks, anti-quarks and gluons inside it is more complicated than a box with an electron in it, but the conceptual issues are the same. In their ground states, the quarks, anti-quarks and gluons are static and yet highly active. Even though the overall internal motion within an object may average to zero, it cannot be ignored, because consequences of that motion, including but not limited to higher energy, can have profound, striking, and easily observed effects.