id: 05877758
dt: j
an: 2011b.00924
au: Quale, Andreas
ti: On the role of mathematics in physics.
so: Sci. Educ. (Dordrecht) 20, No. 3-4, 359-372 (2011).
py: 2011
pu: Springer Netherlands, Dordrecht
la: EN
cc: M50 E20
ut: mathematical models of theoretical physics; physics and mathematics;
philosophy of sciences; axiomatic approach; arithmetic; unphysical
mathematical solutions; epistemic dichotomy
ci:
li: doi:10.1007/s11191-010-9278-3
ab: Summary: I examine the association between the observable physical world
and the mathematical models of theoretical physics. These models will
exhibit many entities that have no counterpart in the physical world,
but which are still necessary for the mathematical description of
physical systems. Moreover, when the model is applied to the analysis
of a physical system, it will sometimes produce solutions that are
unphysical ‒ i.e. describe a physical system that simply cannot exist
in the real world. It is argued that this 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
contain such unrealistic objects. Some concrete examples are examined,
and their implications for physics are discussed from a relativist
epistemic perspective. I argue that the appearance of the unphysical
entities and solutions also has significance for the teaching of
physics. It is recommended that the students be exposed from the start
to a relativist ontology, as advocated by the theory of radical
constructivism; here the unphysical objects do not pose an epistemic
problem.
rv: