Quantizing Time

引力与量子测量问题

Gravitation and the Problem of Quantum Measurement

本文提出放弃广义相对论量子化、转向半经典引力的可能性，并给出相应形式化框架，借此考察量子测量问题，重点分析EPR佯谬与Page-Geilker实验。

A fundamental problem in quantizing general relativity

We point out a fundamental problem that hinders the quantization of general relativity: quantum mechanics is formulated in terms of systems, typically limited in space but infinitely extended in time, while general relativity is formulated in terms of events, limited both in space and in time. Many of the problems faced while connecting the two theories stem from the difficulty in shoe-horning one formulation into the other. A solution is not presented, but a list of desiderata for a quantum theory based on events is laid out.

Quantizing the damped harmonic oscillator

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigroup governing the dynamics of the system is a logical extension of the doubling procedure, and it allows one to avoid the mathematical difficulties encountered with the previous method.

Quantizing time: Interacting clocks and systems

This article generalizes the conditional probability interpretation of time in which time evolution is realized through entanglement between a clock and a system of interest. This formalism is based upon conditioning a solution to the Wheeler-DeWitt equation on a subsystem of the Universe, serving as a clock, being in a state corresponding to a time $t$. Doing so assigns a conditional state to the rest of the Universe $|ψ_S(t)\rangle$, referred to as the system. We demonstrate that when the total Hamiltonian appearing in the Wheeler-DeWitt equation contains an interaction term coupling the clo…

On Quantizing $T^*S^1$

In this paper we continue our study of Groenewold-Van Hove obstructions to quantization. We show that there exists such an obstruction to quantizing the cylinder $T^*S^1.$ More precisely, we prove that there is no quantization of the Poisson algebra of $T^*S^1$ which is irreducible on a naturally defined $e(2) \times R$ subalgebra. Furthermore, we determine the maximal ``polynomial'' subalgebras that can be consistently quantized, and completely characterize the quantizations thereof. This example provides support for one of the conjectures in Gotay et al 1996, but disproves part of another. P…

超光速变换与不确定性

Superluminal Transformations and Indeterminism

本文通过一个与理论无关的不可能定理证明，任何允许非保序超光速变换的框架必须放弃有限信息、时间对称信息内容、过去存储记忆或时间决定因果顺序等假设，从而指出超光速变换相关的本体不确定性不能源于有限信息。