QUANTUM METAPHYSICS - E-thesis

abstract and by itself insufficient for physical theories, since the theories must predict the
behaviour of particular objects so that they can be supported by experiments. M, being a total
abstraction from all particularities and observational conditions, is newer observed: observations
are always of particular representations of M. What we observe in experiments is characterised
by initial and boundary conditions that are expressed in coordinates, but to say that observables
are conventional does not imply that they are phantasmal. Once an observable is chosen, its
eigenstates that realize the coordinate bases are as physical as any other state, and the classical
quantities that realize its eigenvalues are concrete. Thus the conventionality of representations
does not lead to relativism. Quantum mechanics prescribes rigid transformation rules among the
various representations that leave the quantum state invariant. 510
An attempt can also be made to visualise the abstract relationship between quantum states and
observables by employing the language used for wave functions. As has already been pointed
out, in quantum theory the wave function of the system under investigation can always be
presented as an expansion of the desired wave-types. In this way, different families of waves
correspond to different physically measurable attributes. 511 A fixed spatial position is associated
with a momentum wave. Momentum is associated with spatial sine waves, and energy is
connected to temporal sine waves. Spin is connected to spherical-harmonic waveforms.
Waveforms and the connection with their attributes tells us why some attributes are quantised
and others are not. Quantised attributes are connected to restricted waveforms such as sphericalharmonic
waves whose vibrations are limited to the spherical surface. Clearly, each possible
waveform corresponds to some dynamic attribute which can, in principle, be measured. The
number of different waveforms is infinite.
This can lead to the conclusion that quantum theory does not directly describe independent
objects in space-time any more than it describes their enduring attributes. With the help of
quantum theory, a desired object can be connected to a wave function whose form incorporates
information about all the possible observable attributes of that object. Observable attributes are
not however manifested without interaction or measurement. During measurement, the wave
function is cut to the wave expansion of the desired attribute in which each term has its own
amplitude. The square of this amplitude gives the probability that the value in question will be
509 Auyang 1995, 85-86.
510 Auyang 1995, 87, 96.
511 Herbert 1985, 102. Quantum entities have two kinds of properties: static and dynamic. For example, mass,
charge, and spin are static, while position, momentum and the direction of spin are dynamic.
196