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There is nothing special about the transmission and absorption of photons
through a polarizing film. Exactly the same conclusions as those outlined above
are obtained by studying other simple experiments, such as the interference of photons
(see Dirac, Section I.3), and the Stern-Gerlach experiment (see Sakurai,
Chapter 1; Feynman, Chapter 5). The study of
these simple experiments leads us to formulate the following fundamental principles of
quantum mechanics:
*Dirac's Razor.* Quantum mechanics can only answer questions regarding the
outcome of possible experiments. Any other questions lie beyond the realms of
physics.

*Principle of the Superposition of States.* Any microscopic
system (i.e., an atom, molecule, or particle) in a given state can be regarded
as being partly in each of two or more other states. In other words, any state
can be regarded as a superposition of two or more other states. Such superpositions can be performed in an infinite number
of different ways.

*Principle of Indeterminacy.* An observation made on a
microscopic system causes it
to jump into one or more particular states (which are related to the type
of observation). It is impossible to predict into which final
state a particular system
will jump. However, the probability of a given system jumping into a given final
state can be predicted.

The first of these principles was formulated by quantum physicists (such as Dirac)
in the 1920's
to fend off awkward questions such as ``How can a system suddenly
jump from one state into another?'',
or ``How does a system decide which state to
jump into?''. As we shall see, the second principle is
the basis for the mathematical formulation of quantum mechanics.
The final principle is still rather vague. We need to extend it
so that we can predict which possible states a system can jump into after
a particular type of observation, as well as the probability of
the system making a particular jump.

** Next:** Ket Space
** Up:** Fundamental Concepts
** Previous:** Photon Polarization
Richard Fitzpatrick
2013-04-08