The Quantum Description OF Matter And Its Motion by Rmb

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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;

— theoperationofmeasurement;

— 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.


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