Fundamental Principles of Quantum Mechanics

There is nothing particularly unique about the transmission and absorption of photons through a polarizing film. Exactly the same conclusions as those outlined in the previous section are obtained by studying other simple experiments involving photons or microscopic particles. For instance, the interference of photons [108,32], or the Stern-Gerlach experiment [54,46,95]. An examination of these 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 Superposition of States:

Any microscopic system (e.g., 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 (that are related to the type of observation). In general, it is impossible to predict into which final state the 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 microscopic system suddenly jump from one state into another?'' or ``How does a microscopic system decide into which state to jump?'' 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 into which possible states a system can jump after a particular type of observation, as well as the probability of the system making a particular jump.