Chapter 11
Physics Education Research
and the Foundations of Physics: A Case
Study from Thermodynamics and Statistical
Mechanics
David Sands
Abstract The connection between mathematics and physics poses problems for
students, but even professional physicists do not always notice when mathematical
treatments fail to reflect physical processes. By way of example, I draw on the
foundations of thermodynamics, which is a highly mathematical but conceptually
challenging subject. The failure of mathematics to connect to physics concepts, in
particular energy conservation, raises a number of questions. First, how is it that
generations of professional physicists have been seduced by the elegance of mathematics into overlooking underlying difficulties with the physics? Secondly, what
can this tell us about the how of physics: how is it done, how do we justify a theory?
Thirdly, should PER encourage us to look more critically at the fundamental
foundations of physics, and if so, what does it reveal about the way we should be
teaching these subjects? Not all of these questions can be answered yet, but in this
chapter I illustrate some of the more profound mathematical difficulties in thermodynamics and briefly discuss what approach to teaching thermodynamics might
fruitfully be taken.
11.1 Introduction
At the GIREP-ICPE-EPEC conference in Dublin, 2017, I presented an argument that
the foundations of thermodynamics were flawed and asked how this should affect the
approach to the teaching of thermodynamics. This chapter is on the same topic and
inevitably draws on many of the same arguments, so some overlap is unavoidable.
However, the arguments against the concept of thermodynamic entropy as a property
of a body are numerous and in this work I shall attempt to present the case against
entropy slightly differently.
D. Sands (*)
Department of Physics and Mathematics, University of Hull, Hull, UK
e-mail: D.Sands@hull.ac.uk
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_11
117
Physics Education Research
and the Foundations of Physics: A Case
Study from Thermodynamics and Statistical
Mechanics
David Sands
Abstract The connection between mathematics and physics poses problems for
students, but even professional physicists do not always notice when mathematical
treatments fail to reflect physical processes. By way of example, I draw on the
foundations of thermodynamics, which is a highly mathematical but conceptually
challenging subject. The failure of mathematics to connect to physics concepts, in
particular energy conservation, raises a number of questions. First, how is it that
generations of professional physicists have been seduced by the elegance of mathematics into overlooking underlying difficulties with the physics? Secondly, what
can this tell us about the how of physics: how is it done, how do we justify a theory?
Thirdly, should PER encourage us to look more critically at the fundamental
foundations of physics, and if so, what does it reveal about the way we should be
teaching these subjects? Not all of these questions can be answered yet, but in this
chapter I illustrate some of the more profound mathematical difficulties in thermodynamics and briefly discuss what approach to teaching thermodynamics might
fruitfully be taken.
11.1 Introduction
At the GIREP-ICPE-EPEC conference in Dublin, 2017, I presented an argument that
the foundations of thermodynamics were flawed and asked how this should affect the
approach to the teaching of thermodynamics. This chapter is on the same topic and
inevitably draws on many of the same arguments, so some overlap is unavoidable.
However, the arguments against the concept of thermodynamic entropy as a property
of a body are numerous and in this work I shall attempt to present the case against
entropy slightly differently.
D. Sands (*)
Department of Physics and Mathematics, University of Hull, Hull, UK
e-mail: D.Sands@hull.ac.uk
© Springer Nature Switzerland AG 2021
B. G. Sidharth et al. (eds.), Fundamental Physics and Physics Education Research,
https://doi.org/10.1007/978-3-030-52923-9_11
117