Quantum anarchism: the state-less formalism for quantum mechanics



Institute of Physics PAS

October 13, 2023 12:00 PM

A foundational tenet of classical theories is that dynamical physical quantities are represented by trajectories. It follows that the dynamics of a classical system can be fully characterized by the master measure, a non-negative distribution functional defined on the space of trajectories. Then, all quantitative questions concerning the system dynamics in any context---be it the influence on other coupled systems, or the measurements carried out by an observer---are answered with an appropriate restriction of the master measure.

This form of trajectory picture is generally invalid in quantum theory. Instead, in the standard formulation of quantum mechanics the measurement is bestowed with a special status that exempts it from the 'ordinary' rules that apply in all other non-measurement contexts. The quantum state and its measurement-induced collapse is then introduced to facilitate the resultant dichotomic mode of description. This inelegant solution is not without its problems, however. The measurement problem is used as an umbrella term for various unresolved issues with this formulation; they range from philosophical questions about the ontological status of quantum states, to more mundane questions about traceable physical models of state collapse. Many aspects of the measured problem have been hotly debated with no end in sight since the very conception of quantum mechanics over 100 years ago.

Here, our aim is to argue that the essential parts of the measurement problem are rooted in a misreading of the formalism of quantum theory. We show that the trajectory picture actually persists in quantum mechanics, albeit in a different form than that known from classical theories. The quantum analogue of the classical master measure is identified as a positive semi-definite bi-measure on the space of trajectory pairs. In this formulation it is evident that, in reality, the measurement does not (and never had) required a special status---analogously to classical theories, the description in terms of quantum master measure covers all contexts, including the measurement. With the special measurement status rescinded, the concepts that were postulated to facilitate it---i.e, the state and its collapse---thus become redundant.