The quantum theory of time: a calculus for q-numbers
- URL: http://arxiv.org/abs/2108.02771v3
- Date: Thu, 5 May 2022 17:48:56 GMT
- Title: The quantum theory of time: a calculus for q-numbers
- Authors: Samuel Kuypers
- Abstract summary: In quantum theory, physical systems are assumed to evolve relative to a c-number time.
This c-number time has turned out to be unnecessary for explaining dynamics.
In the timeless approach to quantum theory developed by Page & Wootters, subsystems of a stationary universe can evolve relative to a 'clock'
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In quantum theory, physical systems are usually assumed to evolve relative to
a c-number time. This c-number time is unphysical and has turned out to be
unnecessary for explaining dynamics: in the timeless approach to quantum theory
developed by Page & Wootters (1983), subsystems of a stationary universe can
instead evolve relative to a 'clock', which is a quantum system with a q-number
time observable. Page & Wootters formulated their construction in the
Schr\"odinger picture and left open the possibility that the c-number time
still plays an explanatory role in the Heisenberg picture. I formulate their
construction in the Heisenberg picture and demonstrate that c-number time is
completely unnecessary in that picture, too. When the Page-Wootters
construction is formulated in the Heisenberg picture, the descriptors of
physical systems are functions of the clock's q-number time, and derivatives
with respect to this q-number time can be defined in terms of the clock's
algebra of observables, resulting in a calculus for q-numbers.
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