Quantum physics and time: on time operator

Izuru Fujiwara

Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 1-17 The Time as an Observable in Quantum Mechanics Tetsuo Gotō, Shigefumi Naka and Katsuhito Yamaguchi Progress of Theoretical Physics Vol. 64 No. 1 (1980) pp. 18-27 Rational Construction and Physical Signification of the Quantal Time Operator Izuru Fujiwara Progress of Theoretical Physics Vol. 64 No. 2 (1980) pp. 363-379 Explicit Construction of Time-Energy Uncertainty Relationship in Quantum Mechanics Izuru Fujiwara, Kazuki Wakita and Hisao Yoro

Valia Allori

H. D. Zeh

Danilo Tavella

The concept of a global time is routinely employed across physics, from relativistic systems to quantum networks and distributed measurements. However, the operational conditions under which a global temporal ordering is physically meaningful are often left implicit. In this technical note, an operational criterion for the existence of a global time is provided, based on the comparability of internal temporal registers. While local time may be well defined in multiple subsystems, a global operational time exists if and only if their registers can be related through closed physical loops that allow verification of transitivity and stability. Classes of physically relevant systems are identified—such as entangled systems without classical comparison, distributed asynchronous networks, and regions separated by horizons—in which local clockability persists but global time becomes ill-posed. The result does not introduce new physics nor reinterpret existing theories, but clarifies the domain of validity of global temporal descriptions as an operational concept.

Lucien Hardy

This is a book about operational probabilistic theories. The standard approach in such theories is from a time forward perspective. In this book we mostly take a time symmetric perspective. This presents a branding problem. Is this a niche book merely about time symmetry? No. This is a comprehensive book about operational probabilistic theories, but mostly from a time symmetric perspective. In fact, this book consists of (1) a simple book about simple operations having simple causal structure (where all the inputs are before all the outputs), and (2) a complex book about complex operations that can have complicated causal structure (a complex operation is equipped with a causal diagram). For the simple case we are able to show that the time symmetric perspective is equivalent to the time forward perspective. In each book we set up (A) operational probabilistic theories (OPTs) in terms of operations, (B) Operational Quantum Theory (OQT) in terms of operator tensors which correspond to operations, and (C) the theory of Hilbert objects which can be doubled up to give operator tensors. Operations are required to be physical which guarantees that circuits built out of operations have probabilities between 0 and 1 and that certain causality conditions are met. We prove that when we wire together operations the resulting networks are also physical. We model Sorkin's impossible measurements with complex operations and show that physicality prevents anomalous signalling. We develop diagrammatic notation for Hilbert objects. This includes mirrors for doubling up and mirror theorems. We use this framework to prove time symmetric causal dilation theorems for various causal diagrams.

Kimberly R. Chapin