196 The Poetry of Physics and The Physics of Poetry
to gather information about the system. In order for the information to
be useful, we would like to be certain that the act of making one’s
measurement on the system does not alter it to the extent that we are
no longer dealing with the same system. Otherwise, we will collect
information of successively different systems and never be able to
describe the original system. For example, suppose I wish to know
both the position and momentum of a body at the same time. If each
measurement of the position imparts some unknown momentum to the
body I will never be able to measure both its momentum and position
simultaneously. For the measurements of macroscopic bodies this has
never been a problem. One could always arrange to measure the position
of a large body without affecting its momentum.
Let us consider the determination of the position and momentum of
an automobile, for example. If I were to determine the position of an
automobile by crashing another automobile into it then I would certainly
change the original auto’s momentum in some undetermined manner
making the precise measurement of its original momentum impossible.
But I do not have to make my measurement in such a heavy-handed
manner. For instance, I could throw a tennis ball at the car and the
change in the momentum I would produce would be almost completely
negligible. If I wish to be even more discreet about my measurement I
can make my measurement of the car’s position visually. Even in this
case, I will affect the car momentum ever so slightly since a visual
measurement involves bouncing light off the car into my eyes.
As we know, light carries momentum so even in this case we impart
some unknown momentum to the car. This effect is completely
negligible when one takes into account that the momentum of the car is
1030 times the momentum of a photon of visible light. This can also be
seen by examining the uncertainty principle mathematically for the case
of an automobile whose length, mass and velocity are approximately
3 meters, 1000 kg and 30 m/sec respectively. The uncertainty principle
states that ∆p ∆x = m ∆v ∆x = h = 6.6 × 10-34 kgm^2 /sec.
If we divide the uncertainty evenly between the momentum and the
position, the uncertainty principle prevents us from measuring the length
of the car or its velocity more accurately than one part in 10^19. Since the
accuracy for making measurements is much less than this and since the
accuracy needed to describe a system does not have to be anywhere near
one part in 10^19 the uncertainty principle has absolutely no effect of the
description of a macroscopic system like an automobile.