QUANTUM METAPHYSICS - E-thesis

possible states of the system, and these can be calculated to develop in a deterministic manner in
a mathematical state-space. In a measurement situation, the quantum system is however
”projected” onto normal space and the result obtained is one of the many possible presentations
of the system and a realisation of one of its possible values. For example, the system being
investigated can, if required, be localised in a single position, but measurements naturally cannot
provide knowledge about whether particles have positions other than those which result from
specific interactions.
In classical physics, the state means a system’s space-time situation, its position and its velocity
in space at a specific moment. Examination of the fundamental equations of quantum mechanics
shows that quantum theory employs a definition of state that is quite unlike that employed by
classical mechanics. 499 The state function in quantum mechanics does not bestow any specific
position or momentum on particles. 500 It cannot be thought of as describing more a particle than
a wave 501 , and the state vector’s relationship to the classical concept of an object remains
obscure. Also, the thought that an object ”owns” even its primary properties becomes a problem
when no clear and observable properties can be attached to the wave function itself, only the
possibility of different observable realisations in different interactive situations. Dirac
characterised the new situation produced by quantum mechanics by saying that ”an observable
introduces a set of basic states in which the characteristics of a state can be revealed. 502
While all observables in quantum physics are represented by self-adjoint operators on the state
space, not all self-adjoint operators represent observables. Among the infinitely many selfadjoint
operators in a Hilbert space, physicists use no more than a handful. 503 In quantum
mechanics, if the eigenvalue of an operator can be measured, it corresponds to an observable. 504
Since a state vector can be treated as a sum or organised source of different kind of observables,
quantum mechanics is often presented as indicating that the different objects and phenomena
which influence the macroscopic world are fundamentally indivisible and profoundly
interdependent.
499
Nagel 1961, 306. The state-description employed in quantum theory is extraordinarily abstract. The so-called
Psi-function does not lend itself to a intuitively-satisfactory non-technical exposition.
500
Velocity does not have a clear role at the micro level and momentum cannot be considered to be classical, but
the relations to energy are similar to those at classical level. Hodgson 1991, 258-260.
501
When introducing students to the handling of quantum physics, they are told: “We have abandoned the notion of
a wave packet as representing a particle. This notion was helpful to us in making the Schrödinger equation plausible,
but now it is Ψ(x,t) and its probabilistic interpretation that tell us where the particle is, without the particle being
thought of as 'made up out of waves'." Gasiorovits 1974, 54
502
Quoted in Auyang 1995, 20.
503
Auyang 1995, 87.
193