THE QUANTUM DESCRIPTION OF
MATTER AND ITS MOTION
In everyday life and in classical physics, we say that a system has a position, that
t is oriented in a certain direction, that it has an axis of rotation, and that
t is in a state with specific momentum. In classical physics, we can talk in this
way because the state – the situation a system ‘is’ in and the properties a system ‘has’ –
and the results of measurement coincide. They coincide because measurements can be
imagined to have a negligible effect on the system.
Because of the existence of a smallest action, the interaction necessary to perform
a measurement on a system cannot be made arbitrarily small. Therefore, the quantum
of action makes it impossible for us to continue saying that a system has momentum,
position or an axis of rotation.We are forced to use the idea of the rotating arrow and to
introduce the concept of wave function or state function. Let us see why and how.
The Stern–Gerlach experiment shows that the measured values of spin orientation
are not intrinsic, but result fromthe measurement process itself (in this case, the interaction
with the inhomogeneous field). This is in contrast to the spin magnitude, which is
intrinsic and state-independent.
Therefore, the quantum of action forces us to distinguish three entities:
— the state of the system;
— the result of the measurement.
In contrast to the classical, everyday case, the state of a quantumsystem(the properties a
system ‘has’) is not described by the outcomes ofmeasurements.The simplest illustration
of this difference is the systemmade of a single particle in the Stern–Gerlach experiment.
The experiment shows that a spin measurement on a general (oven) particle state sometimes
gives ‘up’ (say +1), and sometimes gives ‘down’ (say −1). So a general atom, in an
oven state, has no intrinsic orientation. Only after the measurement, an atom is either in
an ‘up’ state or in a ‘down’ state. It is also found that feeding ‘up’ states into the measurement
apparatus gives ‘up’ states: thus certain special states, called eigenstates, do remain
unaffected by measurement. Finally, the experiment shows that states can be rotated by
applied fields: they have a direction in space.
These details can be formulated in a straightforward way. Since measurements are
operations that take a state as input and produce as output an output state and a measurement
result, we can say:
— States are described by rotating arrows.