QUANTUM METAPHYSICS - E-thesis

and phases. As every waveform corresponds to a unique Fourier spectrum, sine waves can be
thought of as a universal alphabet which can be used to express any wave. Subsequently, it has
been shown that there is nothing particularly special about Fourier sine waves, since any other
waveform family such as impulse waves or spherical harmonics will do just as well, so a specific
wave can be decomposed in many different ways. This means that there is no “natural” way to
take a wave apart, and that unlike a clock, a wave has no specific intrinsic parts. 465 When
considering their adaptation to quantum systems, this means that the same shape of wave can be
represented in many different ways. The way of expression that is chosen will depend on the
measurement being attempted.
To some degree, Schrödinger's equation resembles the classical equations of motion of Hamilton
and Maxwell. In fact, the relationship between Schrödinger's wave mechanics and classical
mechanics has been compared to the relationship between wave optics and geometrical optics:
classical mechanics represents a special case within the more general wave mechanics. 468 For
example, while it is possible in certain situations to solve for the position of a particle with the
probability "one" using the classical equation, i.e. with absolute certainty, the square value of the
amplitude of the wave function at a given point is interpreted as the probability n/N, statistical
likelihood with which a particle can be observed at that point if many measurements are made.
The wave function was generally thought to be some kind of probability function and Max Born
stated his probability interpretation in 1926. This idea, which replaced causally-problematic
words concerning quantum jumps, was adopted into the developing Copenhagen
interpretation. 469
Schrödinger hoped his theory would show that the world fundamentally consisted of waves.
However, he soon encountered problems when he tried to explain the world realistically by only
using the wave explanation. In his equation, waves could not be interpreted as the waves of
three-dimensional physical space, because in order to describe several particles one needs to
operate with multi-dimensional spaces. Moreover, the waves are complex, and their form is
465 Herbert 1985, 84-88.
466 Herbert 1985, 72.
467 Herbert 1985, 84-88.
468 Petersen 1968, 90.
469 Pais 1991, 286. March 1957, 105. While the Psi-function is in general complex in the technical mathematical
sense, the square of its absolute value is real. The Psi-function is related to matters of observation by a circuitous
route. Probabilities associated with Psi enter in the calculation of various other probabilities and some of these latter
probabilities are finally coordinated by rules of correspondence with certain experimental concepts. Nagel 1961,
307-308.
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