QUANTUM METAPHYSICS - E-thesis

esult of an experiment. 479
The characteristics of a state, represented by a unit vector, are more concretely revealed in its
relation to other states. As a vector can be represented as the linear combination of other vectors,
a state can similarly be expanded into a linear superposition of other states. This is the
superposition principle. 480 Many of the differences between quantum mechanics and classical
mechanics are caused by the existence of these superpositions. The superposition states belong to
the so-called "pure states". In addition to them, it is also possible to form so-called "mixed
states". If the system under studied consists of several particles, it is possible to calculate its
possible quantum states by bringing together the systems that describe individual particles. In
observation situations, however, individual particles are not necessarily independent of each
other due to the superpositions of these combined states. An observation concerning one particle
can therefore influence the state of another. Moreover, further complications are created if the
system consists of several identical particles: it is simply impossible to identify any specific
identical particle, even on a theoretical basis. The states in which identical particles have
exchanged places must be counted as one.
By the mid-1920s, after twenty-five years of confusion, scientists had actually produced three
operating versions of quantum mechanics. In fact, all these theories carried virtually the same
content: it could be said that they expressed the same message in different languages. A physicist
who was applying them could therefore choose which formalism worked best for his particular
task. In the late 1940s, Richard Feynman introduced yet another interesting way of approaching
quantum theory. In Feynman's path integrals, the quantum system is represented as a sum of all
possible states. It is as if the quantum system goes through all its available options. Each particle
appears to travel down all the paths available to it and everything that might happen to the
system influences the future of this particle. The wave function that remains can be concluded
from diagrams by summing over the histories. In such a case, most of the possibilities cancel one
another out. 481
479 Auyang 1995, 68.
480 Auyang 1995, 18.
481 Feynman 1991. For example, Forrest 1988, Herbert 1985 and Hodgson 1991 include a concise presentation of
quantum formalism. For a comprehensive historical account, see Schweber (1994) QED and the men who made it.
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