I have read that it is impossible to determine the
position and momentum of an electron at the same time. Does this mean
that our instruments are too crude, and will always be too crude, to
measure these things without disturbing the system or does it mean that
the nature of physical reality is that in principle, not in practice,
that it can never be done?
It comes out of the math. There are certain pairs of measurements that
do not commute under the operation of matrix multiplication. That is, the
order of the matrix multiplication matters. For these pairs of measurements
the theory states that we can never know both values simultaneously, no
matter how good the measurement instrumentation. Momentum and position are
one such pair. Energy and time are another pair. An interesting result of
the latter relationship is that very short pulses of laser light (time is
very well known) have a very broad emission spectrum (energy isn't well
This "uncertainty principle" is a consequence of quantum mechanics, a very
successful theory in physics. According to quantum theory, it is
impossible in principle to measure both the position and momentum of an
object to within a certain degree of precision at the same time. The more
precisely you know the position, the less precisely you con know the
momentum, and vice versa. Part of the reason is that any method you use to
measure one quantity will perturb the other.
It is possible that in the future we will find that quantum theory is
incorrect, and that, among other consequences, it is possible to know both
quantities at the same time. So far, however, the predictions of quantum
mechanics have survived every test and the theory has been around for about
a hundred years now.
Richard Barrans Jr., Ph.D.
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Update: June 2012