Nona Semana Integrada do Instituto de Física de São Carlos

When clock and system interact: Page-Wootters’ mechanism

Não agendado

20m

Doutorado

Palestrante

Leandro Mendes

Descrição

Although everyone could agree that time passes when questioned about the nature of time, if it is only a parameter or an observable, mixed answers would be given. Some (or perhaps most) would state that time is nothing more than a parameter that appears in Schrodinger’s equation and it is representative of a classical clock on the wall of a lab oratory. Others would want to elevate time to an observable and put it on an equal footing to other quantities as position and momentum in a similar way that was done in special relativity.(1) What it seems is that if time really is an observable it is an inaccessible one. One solution for the seemingly inaccessibility of time was given by Page and Wootters.(2) They argued that time could not be observed because there may exist a superselection rule (SSR) for the energy, in a similar way that there is a SSR for charge.(3) This statement leads to the question: If there is an SSR for the energy how do we agree that time passes? Page and Wootters proposed that time emerges from correlations between non-interacting subsystems in a way that part or parts of the subsystem act as clocks for the rest, and in respect to which the time flows. Here we investigate the Page-Wootters’s conditional probability interpretation for time when clock and system are interacting. We introduced two types of interaction taking the form of an Ising Hamiltonian in a transverse and non-transverse field. It is seen that the interaction between clock and system do not always presents itself as disruptive, being able to improve the mechanism, specially in the regime of high interaction.

Referências

1 PAGE, D. N.; WOOTTERS, W. K. Evolution without evolution: dynamics described by stationary observables. Physical Review D, v. 27, n. 12, p. 2885-2892, 1983.
2 STRELTSOV, A.; ADESSO, G.; PLENIO, M. B. Colloquium: quantum coherence as a resource. Reviews of Modern Physics, v. 89, n. 4, p. 041003-1-041003-34, 2017.
3 WICK, G. C.; WIGHTMAN, A. S.; WIGNER, E. P. The Intrinsic parity of elementary particles. Physical Review, v. 88, n.1, p.101, 1952.