Page 68 - Introduction to Information Optics

1.7. Accuracy and Reliability Observation 53

However, if the radiation frequency v becomes higher, such as
AE = hv > ykT, then we have
A^ . (1.182)

We see that, as the radiant energy required for the observation increases, the
more accurate time resolution can be made. But the perturbation of the
observation is also higher. Thus, the time resolution A? obtained by the
observation may not even be correct, since AE is large.
In the classical theory of light, observation has been assumed nonperturb-
able. This assumption is generally true for many particles problems, for which
a large number of quanta is used in observation. In other words, accuracy of
observations is not expected to be too high in classical theory of light, since its
imposed condition is limited far away from the uncertainty principle; that is

AEAt »h,

or equivalently,
Ap Ax » h.

However, as quantum conditions occur, a nonperturbing system simply does
not exist. When a higher-quantum hv is used, a certain perturbation within the
system is bound to occur; hence, high-accuracy observation is limited by the
uncertainty principle.
Let us look at the problem of observing extremely small distance Ax
between two particles. One must use a light source having a wavelength / that
satisfies the condition
/<2A x (1.183)

Since Ax is assumed to be extremely small, a high-frequency light source is
required for the observation, which corresponds to a higher momentum:

(1-184)

In turn, this high-frequency source of radiation corresponds to a higher-
quantum hv, in which it interacts with the observed specimen (as well as with
the observing equipment), which causes the changes of momentum from — p
to p. Thus, we have

h
Ap = 2p» — . (1.185)
Ax