bei48482_FM

their backward momentum increases. Thus this method of exchanging basketballs has

the same effect as a repulsive force between the boys. If the boys snatch the basket-

balls from each other’s hands, however, the result will be equivalent to an attractive

force acting between them.

A fundamental problem presents itself at this point. If nucleons constantly emit and

absorb pions, why are neutrons and protons never found with other than their usual

masses? The answer is based upon the uncertainty principle. The laws of physics refer

to measurable quantities only, and the uncertainty principle limits the accuracy with

which certain combinations of measurements can be made. The emission of a pion

by a nucleon which does not change in mass—a clear violation of the law of conser-

vation of energy—can take place provided that the nucleon reabsorbs it or absorbs

another pion emitted by a neighboring nucleon so soon afterward that even in principle

it is impossible to determine whether or not any mass change has actually been involved.

From the uncertainty principle in the form

E t (3.26)

an event in which an amount of energy Eis not conserved is not prohibited so long

as the duration of the event does not exceed  2 E. This condition lets us estimate

the pion mass.

Let us assume that a pion travels between nucleons at a speed of  c(actually

 c, of course); that the emission of a pion of mass mrepresents a temporary energy

discrepancy of E mc^2 (this neglects the pion’s kinetic energy); and that E t .

Nuclear forces have a maximum range rof about 1.7 fm, and the time t needed for

the pion to travel this far (Fig. 11.19) is

t

r



c

r









2

414 Chapter Eleven

t = r/c

r

π+

c

π+

c

t = 0

p n

n n

n n

n p

Figure 11.19The uncertainty principle permits the creation, transfer, and disappearance of a pion to

occur without violating conservation of energy provided that the sequence takes place fast enough.

Here a positive pion emitted by a proton is absorbed by a neutron; as a result, the proton becomes a

neutron and the neutron becomes a proton.

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