QUANTUM METAPHYSICS - E-thesis

description of this situation in natural language. This does not mean being satisfied with one of
the non-credible auxiliary hypotheses with which later interpreters have attempted to rescue the
basic presumptions of classical physics, but a comprehensive and exhaustive interpretation, a
world-view on the basis of which the new features of quantum theory become understandable. In
this way, mathematical language would not be used as an instrument but more as a stage in
understanding. 784 A portrayal of such a type translated into natural language will certainly be
unavoidably tentative and metaphorical. The guiding principle when postulating metaphysical
claims that are outside the dimension of direct empirical verification can only be that such claims
should be credible and compatible with experimental facts. Successful conjecture, i.e. new
hypotheses concerning reality, can at their best reveal new concretely-observable connections
and relationships, as Kant understood.
In searching for invariances, physics has not taken a clear stance concerning the fundamental
relationship between mathematical structure and reality. What is the nature of mathematical
objects and universal concepts? Are mathematical laws linked to ontology or epistemology? Is
mathematics the universal language in which The Book of Nature is written and which humans
can understand by using their intelligence, or is it nothing more than a human creation which
suits our analysis of experience? It is certainly true that in physics, natural language, suitable as it
is for the portrayal of an intuitive understanding of our everyday environment, does not work as
well as abstract mathematics. Physical laws are mathematical and the proportion of mathematics
in physical theories is ever-growing. For example, the attempt to understand particle physics has
consisted almost completely of mathematics, group theory and the geometry of abstract
spaces. 785
From a historical point of view, powerful growth in mathematics has either preceded or been
linked to each leap forward to a better understanding of reality and its more-comprehensive
portrayal. Mathematics was developed strongly in antique times, and bloomed again at the time
of the Renaissance. 786 In the 1800s, intense development occurred once again when, among other
things, imaginary numbers added a new dimension to the sequence of numbers. In some basic
way, mathematics appears to display the structure of the world it is addressing. The mathematical
theories of physics help in predicting new phenomena and point to hidden connections between
key position in quantum mechanics. Only in one case it can be thought that the state-function exists in space-time.
784
The endeavour to use visualisible ordinary concepts does not represent an attempt to reduce scientific language
to common language.
785
Omnes 1999, 272.
786
In 1687, only a handful of mathematicians were really able to understand Newton’s Principia. Toulmin, 230.
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