QUANTUM METAPHYSICS - E-thesis

with each other, and in consequence produced a new overall situation that could not be explained
by using particle-mechanical models. The wave function gives an amplitude for the wave that
describes the system in all possible spatial points at any given time. This wave consists of several
oscillatory modes, eigenstates, while the multiplier shows the amount by which each mode
influences the result. All possible oscillatory forms can be explained as superpositions of
eigenstates in the same way that all the possible forms of oscillation of a string can be
represented as a combination of its stationary waves, basic tones, and harmonic overtones. 463
Many of the strange features of quantum mechanics are made easier to understand by a brief
consideration of the character of waves. Typically, a wave is born when something vibrates
somewhere. Light is accepted as being a vibration of electric and magnetic fields. Quantum
waves are viewed as oscillations of possibility. In other respects they follow the same laws as all
other waves. 464 The basic measure of a wave is its amplitude, which measures the deviation of its
physical variable from the resting state. Another important variable is a wave’s intensity, which
is proportional to the square of its amplitude. For all waves except quantum waves, the intensity
is a measure of the amount of energy a wave carries at each point within it. As quantum waves
carry no energy at all, they are sometimes called “empty waves”. The intensity of a quantum
wave (i.e. its amplitude squared) is interpreted as a measure of probability.
Waves can take many forms. Oscillatory waves pass through specific cycles in space and time.
Frequency is the number of cycles completed in a certain time period and wavelength is a
measure of the space that an oscillatory wave spans as it passes through a single cycle. Each
point on a wave possesses a definite phase which is a measure of how far that point has
progressed through the wave’s basic cycle. The phase of a wave governs what happens when two
waves meet. Whenever waves come together, the amplitude at each point of the resulting wave is
simply the sum of the amplitudes of the constituent waves. This is called the superposition
principle or interference. Ordinary waves obey the superposition principle at small amplitudes,
but not when amplitudes become large. Failure of the superposition principle is called nonlinearity,
and shows up as distortion in hi-fi systems and as turbulence in water waves. Quantum
waves are simpler. Their amplitudes appear to sum in all circumstances.
As with all continuous periodic functions, waveforms resulting from the Schrödinger equation
can also be written as a unique sum of sine waves with differing spatial frequencies, amplitudes
463 Pais 1991, 282-283.
464 Herbert 1985, 72.
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