Causality, Measurement Theory and the Differentiable Structure of Space-Time

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewells measurement theory, in which the wave packet is reduced without recourse to the observers conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewells measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Spis treści:
Prologue
Part I, Introduction to Part I
1. Mathematical structures on sets of points
2. Definition of causality on a structureless set
3. The topology of ordered spaces
4. Completions of ordered spaces
5. Structures on order-complete spaces
Part II, Introduction to Part II
6. Real numbers and classical measurements
7. Special topics in quantum mechanics
8. Von Neumanns theory of measurement
9. Macroscopic observables in quantum physics
10. Sewells theory of measurement
11. Summing-up
12. Large quantum systems
Epilogue
Appendixes
References
Index.