## 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/E_{k} where E_{k} 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

- Table of Contents
- Graphic Plate for Introduction
- The Introduction including the table of contents, acknowledgments, and dedication to my father.
- Graphic Plate for Chapter 2
- When does an event occur
- Graphic Plate for Chapter 3
- Physical clocks and time-of-arrival
- Graphic Plate for Chapter 4
- Time of arrival operators
- Graphic Plate for Chapter 5
- Traversal time
- Graphic Plate for Chapter 6
- Order of events
- Graphic Plate for Conclusion
- Conculsion
- Bibliography
- Appendices
- The entire thesis (40M)

## Cartoons

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

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