The entire thesis can be downloaded as one postscript file here (40M). A series of publications on the topic can be found here with the central results in [1] and [2].

Quantum time

Jonathan Oppenheim (2001)

In quantum mechanics, time plays a role unlike any other observable. We find that measuring whether an event happened, and measuring when an event happened are fundamentally different - the two measurements do not correspond to compatible observables and interfere with each other. We also propose a basic limitation on measurements of the arrival time of a free particle given by 1/Ek where Ek is the particle's kinetic energy. The temporal order of events is also an ambiguous concept in quantum mechanics. It is not always possible to determine whether one event lies in the future or past of another event. One cannot measure whether one particle arrives to a particular location before or after another particle if they arrive within a time of 1/E of each other, where E is the total kinetic energy of the two particles. These new inaccuracy limitations are dynamical in nature, and fundamentally different from the Heisenberg uncertainty relations. They refer to individual measurements of a single quantity. It is hoped that by understanding the role of time in quantum mechanics, we may gain new insight into the role of time in a quantum theory of gravity.

The entire thesis can be downloaded as one postscript file here (40M).

Downloadable Sections

  1. Table of Contents
  2. Graphic Plate for Introduction
  3. The Introduction including the table of contents, acknowledgments, and dedication to my father.
  4. Graphic Plate for Chapter 2
  5. When does an event occur
  6. Graphic Plate for Chapter 3
  7. Physical clocks and time-of-arrival
  8. Graphic Plate for Chapter 4
  9. Time of arrival operators
  10. Graphic Plate for Chapter 5
  11. Traversal time
  12. Graphic Plate for Chapter 6
  13. Order of events
  14. Graphic Plate for Conclusion
  15. Conculsion
  16. Bibliography
  17. Appendices
  18. The entire thesis (40M)


The thesis contains a number of cartoons, drawn by the infamous French Situationist, Victoria Scott.
  1. Alice and Bob hanging out on a clock
  2. A dead cat in a box
  3. Alice and Bob try to measure the time of arrival
  4. Bob running in a jar
  5. Alice and Bob play marbles
  6. Who killed Schrodinger's cat?
  7. Weighing Schrodinger's poodle

[an error occurred while processing this directive]