1.2. PHYSICAL PROLOGUE: DIMENSIONS, UNITS, CONSTANTS, AND PARTICLES 7

The equivalence of units of mass, length, and time can be restated as follows:

(1.6) 1 MeV

∼

= (6.581966 ×

10−22 second)−1

∼

= (1.973224 ×

10−11 centimeter)−1.

Again, in the subatomic world these are more than formal equivalences. The precise

constants are usually not important, but the orders of magnitude express relations

among the characteristic energies, distances, and times of elementary particle in-

teractions.

When we first discuss relativity in Chapter 2 and quantum theory in Chapter

3, we will include the factors of c and explicitly for the sake of clarity, but starting

with Chapter 4 we will always use “natural” units in which c and are both equal

to 1. We can still quote lengths in centimeters, times in seconds, and masses in

MeV, but having chosen one of these units, we must relate the other two to it by

(1.6).

Once one has made [l] = [t] =

[m−1],

the dimensions

[m1/2l3/2t−1]

of electric

charge cancel out, so that charge is dimensionless, and the unit of charge in the

Heaviside-Lorentz system is simply the number 1. The basic physical constant is

then the fundamental unit of charge, the charge of a proton or the absolute value of

the charge of an electron, which we denote here by e. The related quantity

e2/4π

(or

e2/4π

c if one does not use “natural” units) is the fine structure constant α,

which is nearly equal to 1/137 and is often quoted that way:

α =

e2

4π

= 0.0072973525 =

1

137.035

,

which gives

e = 0.30282212.

(In some parts of this book, the letter e may denote the charge of whatever particle

is in question at the time; this is always an integer multiple [

1

3

-integer in the case

of quarks] of the e here.)

One can carry the reduction of different dimensions one final step by including

gravity. Having set and c equal to one, one can set the coeﬃcient G in Newton’s

law of gravity F =

Gm1m2/r2

equal to one too. This yields an absolute scale of

length, time, and mass, called the Planck scale. Since G = 6.674×10−11 m3/kg · s2,

we have

Planck length = 1.616 ×

10−33

centimeter,

Planck time = 5.390 ×

10−44

second,

Planck mass = 2.176 ×

10−5

gram = 1.221 ×

1019

GeV.

The Planck length and time are ridiculously small, and the Planck mass ridiculously

large, on the scale of ordinary particle physics. There is much speculation about

what particle physics on the Planck scale might look like, none of which will be

discussed in this book.

Here is a quick review of the terminology concerning subatomic particles. To

begin with, there are two basic dichotomies: all particles are either Bosons, with in-

teger spin, or Fermions, with half-integer spin; and all particles are either hadrons,

which participate in the strong interaction, or non-hadrons. The fundamental

Fermions are quarks, which are hadrons, and leptons, which are not. Quarks com-

bine in triplets to make baryons, of which the most familiar are the proton and