On a Manifestly Covariant Classical Mechanics or Ruminations on 'The Computable Universe' and the Role of Mathematical Physics in Solving the Natural Resource Problems of the Future

摘要

We informally discuss a number of puzzling fundamental issues that illustrate one might view the laws of physics as a loosely connected patchwork of different theories, rather than a grand unified scheme, even within the realm of chemistry. One long-lasting difficulty is the merging of special relativity and quantum mechanics: the many-body Dirac equation, which is the most satisfactory description of the effects of relativity in chemistry, is not Lorentz invariant. In this article, we address the formulation of a manifestly Lorentz invariant classical mechanics in which each particle is described by individual space and time coordinates, while the system as a whole evolves according to a Hamiltonian dynamics based upon a universal evolution parameter. The physical interpretation of the theoretical framework, or its agreement with experiment, in particular when the transition would be made to a quantum theory in four dimensions, is not clear at present. Our search for an understanding of the physical concepts underlying the covariant mechanics has led to a broader view on the use of mathematical and theoretical physics: it could possibly be at the basis for a "computable physics" in which the laws of physics are redesigned such that they are optimally suited for computer simulations, rather than aim for the accurate description of physical reality. in the final section of the article, it is argued that this may be a fertile way to address some Of the natural resource problems the world is likely to face in the future. This article essentially covers much of the material presented by one of the authors (MN) at the Odyssey meeting in Edmonton, June 2008, and we hope reflects some of the stimulating discourse that can ensue when people from different disciplines are brought together to share their thoughts.