Bounds on Physics and Cosmology, Malcolm A.H. MacCallum

Bounds on physics and cosmology can arise in several ways. There are limits arising at high energies or great distances, and others from the enormous amount of data detailed models would require. These limits exist in both principle and practice. There are also interesting bounds on applicability of particular theoretical frameworks, and their overlap: for example, the quantum to classical transition and the way in which general relativity contains Newtonian gravitational theory as a limit. Considering these can throw light on some general ideas of philosophy of science, such as those of Kuhn and Popper. *** This talk was delivered during the conference “The Limits of Physics and Cosmology” organized by Copernicus Center for Interdisciplinary Studies. There exist various kinds of limits which are inherent in cosmological research and physics. The most conspicuous one is connected with scientific method itself. It manifests itself during attempts to construct (or discover) suitable mathematical structures to model the physical world. However, this limit may be even more profound. Over the past 300 years we have become accustomed to the mathematical and empirical method which has proven to be uncannily successful in describing the enclosing universe. But is there a fundamental limit to the method itself which is intrinsic to the structure of the world? Another group of limits which are more connected to ourselves – as human beings – are conceptual ones. The two monumental theories of physics of the 20th century – General Relativity and Quantum Mechanics - are incompatible and this inconsistency is not only on the mathematical level, but also on the conceptual. Usually scientists believe that the reconciliation between the relativist and quantum realms is possible. But is there a conceptual limit within ourselves as elements of the world?