id: 05933515
dt: j
an: 2011d.00789
au: Quale, Andreas
ti: On the role of mathematics in physics: A constructivist epistemic
perspective.
so: Sci. Educ. (Dordrecht) 20, No. 7-8, Special issue: Ninth international,
history, philosophy and science teaching conference: select
contributions, 609-624 (2011).
py: 2011
pu: Springer Netherlands, Dordrecht
la: EN
cc: M50 E20
ut: observable physical world and mathematical models of theoretical physics;
general relativity; quantum physics; physics and mathematics;
philosophy of sciences; unphysical mathematical solutions; epistemic
dichotomy
ci:
li: doi:10.1007/s11191-010-9257-8
ab: Summary: The association between the observable physical world and the
mathematical models used in theoretical physics to describe this world
is examined. Such models will frequently exhibit solutions that are
unexpected, in the sense that they describe physical situations which
are different from that which the physicist may initially have had in
mind when the model is employed. It will then often be the case that
such an unexpected solution actually represents a physically realisable
situation. However, this solution may also, in some cases, describe a
system that is unphysical-i.e. a system that, according to our physical
intuition, simply cannot exist. It is argued that this latter fact
poses a problem for the epistemic position of realism in physics: a
mathematical theory that professes to give a correct description of
physical reality should not give rise to such unrealistic solutions.
Some concrete examples are examined, and their implications are
discussed from the relativist epistemic perspective that is implicit in
the theory of radical constructivism. It is suggested that the
occurrence of these unphysical solutions also has significance for the
teaching of physics. In conclusion, it is advocated that the students
be exposed, from the start of their physics education (mainly in
secondary school), to the relativist ontology that is advocated by
radical constructivism; here the appearance of unphysical solutions
does not pose an epistemic problem. Paper presented at the June 2009
IHPST-10 conference, held at the University of Notre Dame, in South
Bend, Indiana.
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