Simple Nature - Light and Matter

All of these strange effects, however, are very small when the relative velocities are small

compared toc. This makes sense, because Newton’s laws have already been thoroughly tested

by experiments at such speeds, so a new theory like relativity must agree with the old one in

their realm of common applicability. This requirement of backwards-compatibility is known as

the correspondence principle.

Relativity has implications not just for time and space but also for the objects that inhabit

time and space. The correct relativistic equation for momentum is

p=mγv,

which is similar to the classicalp=mvat low velocities, whereγ≈1, but diverges from it

more and more at velocities that approachc. Sinceγbecomes infinite atv=c, an infinite force

would be required in order to give a material object enough momentum to move at the speed of

light. In other words, material objects can only move at speeds lower thanc. Relativistically,

mass and energy are not separately conserved. Mass and energy are two aspects of the same

phenomenon, known as mass-energy, and they can be converted to one another according to the

equation

E=mc^2.

The mass-energy of a moving object isE=mγc^2. When an object is at rest,γ= 1, and the

mass-energy is simply the energy-equivalent of its mass,mc^2. When an object is in motion, the

excess mass-energy, in addition to themc^2 , can be interpreted as its kinetic energy.

Chapter 8, Atoms and Electromagnetism, page 473

All the forces we encounter in everyday life boil down to two basic types: gravitational forces

and electrical forces. A force such as friction or a “sticky force” arises from electrical forces

between individual atoms.

Just as we use the word mass to describe how strongly an object participates in gravitational

forces, we use the wordchargefor the intensity of its electrical forces. There are two types of

charge. Two charges of the same type repel each other, but objects whose charges are different

attract each other. Charge is measured in units of coulombs (C).

Mobile charged particle model:A great many phenomena are easily understood if we imagine

matter as containing two types of charged particles, which are at least partially able to move

around.

Positive and negative charge: Ordinary objects that have not been specially prepared have

both types of charge spread evenly throughout them in equal amounts. The object will then

tend not to exert electrical forces on any other object, since any attraction due to one type of

charge will be balanced by an equal repulsion from the other. (We say “tend not to” because

bringing the object near an object with unbalanced amounts of charge could cause its charges

to separate from each other, and the force would no longer cancel due to the unequal distances.)

It therefore makes sense to describe the two types of charge using positive and negative signs,

so that an unprepared object will have zerototalcharge.

TheCoulomb force lawstates that the magnitude of the electrical force between two charged

particles is given by

|F|=

k|q 1 ||q 2 |

r^2

.

Conservation of charge: An even more fundamental reason for using positive and negative

1080 Chapter Appendix 5: Summary