Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations
Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations
复制标题
时间算子与哈密顿量典型共轭生成平移的经验充分性
作者：
O. Stoica
要允许一个标准共轭时间算符，哈密顿算符必须是平移的产生器（就像动量算符在空间中产生平移一样），因此它的谱必须是无界的。但人们认为，支配我们世界的哈密顿函数是从下面限界的。此外，从标准模型的场和参数的数量来判断，哈密顿量似乎要复杂得多。在本文中，我将给出由汉密尔顿主义者生成翻译的例子。它们可以表示为偏导数算子，就像动量算子一样，但是当用其他可观测值的函数表示时，它们可以表现出任何程度的复杂性。这些例子包括任何实现标准理想测量的量子世界，任何包含时钟或自由无质量费米子的量子世界，任何没有时间循环的确定性时间可逆动力系统的量子表示，以及任何不能返回到过去状态的量子世界。这样的世界和我们的世界一样复杂，但它们承认有时间操作者。我证明了，尽管有无界的哈密顿量，它们不会像任何量子或经典世界一样衰减到无限负能量。由于具有相同希尔伯特空间维度的两个这样的量子系统是一元等价的，即使它们的可观测物的物理内容非常不同，它们是希尔伯特空间原教旨主义（HSF）的具体反例。考虑可观测值消除了HSF的模糊性和由page - wooters形式主义引起的时钟模糊性问题，这也是由假设HSF引起的。这些结果为恢复量子力学公式中的时空对称性和page - wooters形式主义提供了额外的动机。
To admit a canonically conjugate time operator, the Hamiltonian has to be a generator of translations (like the momentum operator generates translations in space), so its spectrum must be unbounded. But the Hamiltonian governing our world is thought to be bounded from below. Also, judging by the number of fields and parameters of the Standard Model, the Hamiltonian seems much more complicated. In this article I give examples of worlds governed by Hamiltonians generating translations. They can be expressed as a partial derivative operator just like the momentum operator, but when expressed in function of other observables they can exhibit any level of complexity. The examples include any quantum world realizing a standard ideal measurement, any quantum world containing a clock or a free massless fermion, the quantum representation of any deterministic time-reversible dynamical system without time loops, and any quantum world that cannot return to a past state. Such worlds are as sophisticated as our world, but they admit a time operator. I show that, despite having unbounded Hamiltonian, they do not decay to infinite negative energy any more than any quantum or classical world. Since two such quantum systems of the same Hilbert space dimension are unitarily equivalent even if the physical content of their observables is very different, they are concrete counterexamples to Hilbert Space Fundamentalism (HSF). Taking the observables into account removes the ambiguity of HSF and the clock ambiguity problem attributed to the Page-Wootters formalism, also caused by assuming HSF. These results provide additional motivations to restore the spacetime symmetry in the formulation of Quantum Mechanics and for the Page-Wootters formalism.
时间和量子钟：最新发展回顾
影响因子：
3.1
作者：
Altaie M
通讯作者：
Altaie M