A subdynamics theory has been presented recently in which quan¬ tities characteristic of an irreversible behaviour, such as that of a collision process, appear in the generator of evolution. The original dynamics, with degrees of freedom in large number, is first widened once self-energy parts have been recognized. The redundancies are then constrained by the requirement that the evolution takes place entirely in a subdynamics associated with a vacuum defined by reference to the observational situation of interest. This scheme, resulting in no loss of physical information, is examined in detail in the simple case of potential scattering, after that incoming, outgoing and intermediate degrees of freedom are distinguished. The relation with previous approaches is analysed.
The authors have presented [1] a subdynamics theory in which quantities characteristic of irreversible behaviour - such as that of a collision process - appear in the generator of kinetic evolution. This theory is applied to the simple case of potential scattering. The original dynamics is first widened after incoming, outgoing and intermediate degrees of freedom are distinguished. An extended concept of vacuum state is introduced by reference to the observational situation of interest. The redundant degrees of freedom are then constrained by the requirement that the physi¬ cal evolution takes place entirely in the subdynamics associated with that vacuum. The relationship with previous treatments of the same system is analysed in some detail. PACS numbers : 05.30 ; 02.90 ; 11.20.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self-energy processes (already found in quantum electrodynamics), which allows for the widening of the dynamics through the introduction of specific additional variables leading to the recognition of such processes. A projection technique modeled on that introduced long ago by the Brussels group defines a subdynamics that is shown to contain the starting formulation in its entirety. (It corresponds to a restricted class of initial conditions, namely the reversible ones.) A new kinetic description is obtained in which, e.g., collision processes for privileged components arise from the original interaction. This method is applied successively to various models, and we focus in this paper on the possible presence of temporal behaviour excluded in ordinary quantum mechanics. Among the differences between this framework and that of ordinary quantum mechanics, the possibility appears for the purely exponential decay of a particle, while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
The compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics is a challenging problem. Our solution requires an extension of the latter. Such an extension of a reversible formalism is made possible by the presence of self‐energy processes (already found in quantum electrodynamics) which enables the widening of the dynamics by the introduction of specific additionnal variables leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics which is shown to contain entirely the starting formulation (it corresponds now to a restricted class of initial conditions, namely the reversible one). A new kinetic description is obtained in which e.g. collision processes for privileged components arise from the original interaction. This method is applied successively to various models and we focus in this paper on the possible presence of temporal behaviours excluded in ordinary quantum mechanics. Among those differences, the possibility appears of a purely exponential decay for a particle while ordinary quantum mechanics requires long time tails associated with the finite lower bound in the spectrum of the Hamiltonian.
In Newtonian spacetime, the canonical description of a classical
N-particle system requires
3N degrees of freedom. Not all of these are physical, however, since the conservation of the net momentum implies that only
3(N−1) accelerations are independent. Hence, three constraints can be used to eliminate the unphysical centre-of-mass variables, at the level of the Lagrangian, leaving only the subset of observable displacements and momenta, which are relational. Imposing the constraints does not change the dynamics of these variables, at the classical level, and is analogous to a gauge-fixing procedure, which removes redundancy in the description of the system. In classical physics, therefore, the number of physical degrees of freedom equals the number of independent relational degrees of freedom. Here, we show that this is not the case in quantum mechanics. While an operator-analogue of the classical net momentum exists, it cannot be used to impose constraints that restrict the degrees of freedom in the theory, without a loss of physical information. This means that all
3N canonical degrees of freedom are physical, even though only
3(N−1) of them are relational. We explore the physical consequences of the non-relational variables and show that they give rise to generalised uncertainty relations (GURs), for the relational quantities that define the quantum reference frame (QRF). Hence, it is shown that the non-relational degrees of freedom refer to the frame itself and that the non-Heisenberg terms in the GURs define its Galilean-invariant spreads, in both real space and momentum space. The implications of this result for recent work on relational models, including the ``perspective neutral'' framework for QRFs, are discussed. Its implications for the wider relational program, and, in particular, the relevance of the latter to quantum gravity research, are also critically assessed
Abstract A challenging problem facing physicists is the compatibility of irreversibility, as expressed by the second law of thermodynamics, with ordinary quantum mechanics. We present a solution through an extension of the latter. The presence of self‐energy processes (already found in quantum electrodynamics) is fully exploited to get an extension of a reversible formalism. They enable the widening of the dynamics by the introduction of specific auxiliary variables, leading to the recognition of such processes. A projection technique modeled on the one introduced long ago by the Brussels group defines a subdynamics that is shown to contain entirely the starting formulation (it corresponds to a restricted class of initial conditions, namely, the reversible one). A new kinetic description is obtained in which, for example, collision processes for privileged components arise from the original interaction. A very simple model and its generalizations are considered. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004