2
Starting here, and until Chapter 8, I will drop the adjective normal in talking about normal matter, and just say matter. We won’t revisit the dark side until then.
3
Toward the end of this book, I’ll discuss other strange ideas, for which the evidence is as yet much less convincing. I want you to appreciate the difference!
4
Both protons and neutrons are always spinning: we say they have an intrinsic, fundamental spin. We’ll have much more to say about the property of fundamental spin later. It plays a crucial role in modern ideas about the ultimate unification of forces.
6
The flavors of quarks should not be confused with their color charges. Color charge is a different, additional property. There are u quarks with a unit of red color charge, u quarks with a unit of blue color charge, and so forth. Thus with 3 flavors and 3 colors, we have 3 × 3 = 9 kinds altogether.
7
Strictly speaking, the laws of quantum mechanics are universal: they apply to macroscopic star systems just as well as to microscopic ones like atoms. For macroscopic systems, however, the quantum restrictions on orbits have no practical significance, because the spacing between allowed orbits is minuscule.
8
Actually, a very few extremely smart quantum-mechanicians, most notably James Bjorken, had even more sophisticated arguments indicating that it might work after all.
9
Thus the force falls off faster than 1 over the distance squared, as you’d have without screening.
10
When Gross and I discovered asymptotic freedom we were young and naive, and we didn’t fully appreciate the importance of naming things in catchy ways. If I had it to do over, I’d call asymptotic freedom something sexy, like “Charge Without Charge.” “Asymptotic freedom” was suggested by my good friend Sidney Coleman, whom I forgive.
11
They were much more challenging in 1973 than they are today, because technique has improved.
12
It’s not a quantum leap: quantum leaps are small.
13
Of course, “simple” is a complicated concept. See Chapter 12.
14
This is because the total momentum is conserved. It was zero at the start, because the electrons and positrons were moving at the same speed in opposite directions. So it must still be zero at the end, as is observed. Of course, in principle we might discover experimentally that momentum is not conserved, but then we’d really need to backtrack, all the way to unlearning first-year physics.
15
For this example, you’re supposed to ignore the fact that the three triangles are in different places. If that bugs you, you can imagine that they’re infinitely thin triangles stacked on top of one another.
16
There won’t be a quiz.
17
I once had a very interesting conversation about that with Feynman himself. He told me that he had originally hoped to remove vacuum processes from the theory, and was very disappointed to find that he couldn’t do it in a consistent way. I’ll tell you more about that conversation in Chapter 8.
18
Earlier I mentioned a third quark flavor, the strange quark s. There are also three more quark flavors: charm c, bottom b, and top t. These are even heavier and more unstable than s. We’ll ignore them all for now.
19
The boost symmetry of special relativity changes the energy of particles—but it also changes the behavior of the scales you’d use to weigh them, in just such a way that there’s no net detectable effect. Our local color symmetry, on the contrary, makes no change in normal scales (such as you find in grocery stores), which have zero overall color charge. So they will register the changed weight, and we’re stuck with it.
20
As we’ll discuss later.
21
In his second paper, he derived Einstein’s second law.
23
Actually, deep Queens; Feynman was from Far Rockaway.
24
No pun intended. Nope, no pun here, folks.
25
That is, to a good first approximation.
26
For experts: they decouple at low energies, as well.
27
For more details on the weak interaction, see the glossary, Chapter 17, and Appendix B.
28
That is, the ones I think are most promising—the ones we’ll be discussing in Chapters 17-21.
29
Technical point: To measure the length of a path that goes in directions other than the local north-south or east-west, you break the path into little steps, use Pythagoras’ theorem on each one, and add up the lengths. The smaller the steps, the more accurate the measurement.
30
Mathematicians and physicists usually call them x1, x2, x3—less quaint, more opaque.
31
But I’ve advertised a promising opportunity in the endnotes.
32
To avoid introducing too many complications at once, I’ve deferred discussion of another extremely interesting astronomical discovery, “dark matter.” We’ll get to it later.
33
We’ll be discussing supersymmetry in more depth later, in connection with unification. The main thing to note here is that it suggests a ridiculously large contribution to the density, just like everything else.
35
If you’re willing to take my word for it, and would rather avoid the dizzying details, you can proceed directly to the section “The Big (Number) Crunch.”
36
To avoid possible confusion: in this way of counting, north and south count as just one direction—stepping 1 mile south is the same as stepping minus 1 mile north.
38
At least, that’s a good working hypothesis, and it’s justified by its success.
39
Maybe I’m being naïve here.
40
Attentive readers will recognize this as Schrödinger’s second law.
41
Salieri’s mediocrity is debated by serious music critics. Regardless, he’s notorious for being mediocre.
42
Warning: may induce déjà vu. I quoted this before, in Chapter 8.
43
It’s not in the Olympics, of course, so it’s not an Olympic event. But as a challenge worthy of the Greek gods and goddesses, it’s Olympian.
44
More precisely, Newton’s theory describes the results of general relativity approximately. Newton’s theory works best when the bodies are slowly moving, compared to the speed of light, and are not too large or dense.
45
We’ve discussed the close connection between ultrashort distances and ultralarge energies previously. See the endnotes for pointers and some additional comments.
46
I’ll get to the exceptions shortly.
47
Whole books have been written about neutrinos and their properties. (They do interact, after all—just very rarely.) Because the subject is highly technical and somewhat tangential to our main topics, I’ve been very selective and telegraphic in this discussion. For a few more details, and further references, see the endnotes.
48
The neutrinos are a special case, as we just discussed.
49
Strictly speaking, electromagnetism is a mixture involving pieces from both SU(2) and U(1), as we just discussed. So the U(1) is not quite electromagnetism. It has its own proper name, hypercharge. But I’ll generally use the more familiar, not-quite-pedantically-correct name for it.
50
More on this later, in Chapter 21.
51
I mentioned this before, in Chapter 8.
52
Reinforced by a striking numerical success—description upcoming.
53
For more on the quantitative aspects, see the following chapter and the endnotes.
54
The kind of matter made from photons, electrons, quarks, and gluons.
55
For a deeper discussion of these matters, see Appendix B.