Theories of Matter: Infinities and Renormalization

This paper looks at the theory underlying the science of materials from the perspectives of physics, the history of science, and the philos-ophy of science. We are particularly concerned with the development of understanding of the thermodynamic phases of matter. The question is how can matter, ordinary matter, support a di-versity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor (steam) rise from a pot of heated water. Different phases can be qualitatively different. For example, walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. The nature of the phases is brought into the sharpest focus in phase transitions: abrupt changes from one phase to another and henc