A basic time asymmetry is said to exist in the conventional quantum theory of measurement because the initial state, determined by the initial measurement, suffers a reduction of the wave packet when a succeeding measurement is made. It is shown, completely within the conventional framework, that the sense of this time asymmetry can be reversed and a retroductive formalism introduced which is based upon the fact that only the final state is known. Moreover, if both the initial and final states of a set of measurements are fixed, a completely time symmetric formalism can be constructed for the time interval between these given states. The selection of the predictive scheme can be made with the help of macroscopic considerations and consequently it appears that the basic time asymmetry is not a consequence of conventional quantum physics including measurement.
A basic time asymmetry is said to exist in the conventional quantum theory of measurement because the initial state, determined by the initial measurement, suffers a reduction of the wave packet when a succeeding measurement is made. It is shown, completely within the conventional framework, that the sense of this time asymmetry can be reversed and a retroductive formalism introduced which is based upon the fact that only the final state is known. Moreover, if both the initial and final states of a set of measurements are fixed, a completely time symmetric formalism can be constructed for the time interval between these given states. The selection of the predictive scheme can be made with the help of macroscopic considerations and consequently it appears that the basic time asymmetry is not a consequence of conventional quantum physics including measurement.
We examine the assertion that the "reduction of the wave packet," implicit in the quantum theory of measurement introduces into the foundations of quantum physics a time-asymmetric element, which in turn leads to irreversibility. We argue that this time assymmetry is actually related to the manner in which statistical ensembles are constructed. If we construct an ensemble time symmetrically by using both initial and final states of the system to delimit the sample, then the resulting probability distribution turns out to be time symmetric as well. The conventional expressions for prediction as well as those for "retrodiction" may be recovered from the time-symmetric expressions formally by separating the final (or the initial) selection procedure from the measurements under consideration by sequences of "coherence destroying" manipulations. We can proceed from this situation, which resembles prediction, to true prediction (which does not involve any postselection) by adding to the time-symmetric theory a postulate which asserts that ensembles with unambiguous probability distributions may be constructed on the basis of preselection only. If, as we believe, the validity of this postulate and the falsity of its time reverse result from the macroscopic irreversibility of our universe as a whole, then the basic laws of quantum physics, including those referring to measurements, are as completely time symmetric as the laws of classical physics. As a by-product of our analysis, we also find that during the time interval between two noncommuting observations, we may assign to a system the quantum state corresponding to the observation that follows with as much justification as we assign, ordinarily, the state corresponding to the preceding measurement.
We investigate the origin of the arrow of time in quantum mechanics in the context of quantum cosmology. The ``Copenhagen'' quantum mechanics of measured subsystems incorporates a fundamental arrow of time. Extending discussions of Aharonov, Bergmann and Lebovitz, Griffiths, and others we investigate a generalized quantum mechanics for cosmology that utilizes both an initial and a final density matrix to give a time-neutral formulation without a fundamental arrow of time. Time asymmetries can arise for particular universes from differences between their initial and final conditions. Theories for both would be a goal of quantum cosmology. A special initial condition and a final condition of indifference would be sufficient to explain the observed time asymmetries of the universe. In this essay we ask under what circumstances a completely time symmetric universe, with T-symmetric initial and final condition, could be consistent with the time asymmetries of the limited domain of our experience. We discuss the approach to equilibrium, the electromagnetic system, and T-violation in the weak interactions in such universes. The decoherence of alternatives that is necessary for the prediction of probabilities in the quantum mechanics of closed systems is the origin of a fundamental limitation on quantum cosmologies with initial and final conditions. The initial and final density matrices cannot both be pure; if they are there is no decoherence and no prediction.
This study proposes a time-symmetric framework for quantum measurement that restores microscopic reversibility at the level of the dynamical description while remaining compatible with causality and thermodynamic consistency. Instead of invoking a stochastic wavefunction collapse, the measurement process is modeled as a bidirectional informational update between a forward-evolving state and a backward-propagating effect, governed by a completely positive generator and its adjoint. Within this operator-based formalism, pre- and post-selected statistics are treated on an equal footing, yielding a unified description of both. The proposed scheme rigorously preserves complete positivity, normalization, and the no-signalling principle, and it is shown to satisfy Spohn's inequality for the associated quantum Markov semigroup, thereby ensuring non-negative entropy production within this setting. The framework admits a direct experimental interpretation across a range of scenarios, including weak measurements, EPR-Bell tests, homodyne detection, and photon counting. Furthermore, in the classical limit, the bidirectional update is demonstrated to reduce to the well-established Kalman filter and Rauch-Tung-Striebel (RTS) smoother used in classical estimation theory. These results support the view that the apparent temporal asymmetry of quantum measurement arises not from fundamental dynamical irreversibility, but from informational conditioning, specifically, the one-sided way in which measurement outcomes are incorporated into our description. In this sense, the arrow of time in measurement theory may be understood as an arrow of information.
More them any other topic in the foundations of physics, the problem of the arrow (or arrows!) of time seems to be characterized by a unique ‘slipperiness’: it is not only difficult to find answers to the questions once posed, but difficult to find meaningful questions to ask in the first place. Perhaps this is because an asymmetry with respect to the sense of time is built into us at an even deeper level than other ‘synthetic a priori’ conceptions about the world such as the continued existence of unknown objects. However that may be, in this situation, rather than trying to pose general questions which may turn out in the end to be ill-defined, there may be something to be said for trying to formulate much less speculative, indeed perhaps in retrospect trivial questions to which at least we have a hope of finding a definite answer. This is what I shall do in this essay: to be specific, I shall ask whether a test which is currently being designed concerning the validity of a certain ‘common-sense’ view of the macroscopic world (‘macrorealism’) would be affected if we were to relax our common-sense assumptions about the direction of causality in time. Let me start with a very brief review of established ideas concerning the formal (a)symmetry of the quantum theory with respect to the direction of time. The classic works on this subject are the paper of Aharonov et al. (‘ABL’) and the book by Belinfante. In these discussions the notion of ‘measurement’ is taken as primitive and undefined.
The operational formulations of quantum theory are drastically time oriented. However, to the best of our knowledge, microscopic physics is time-symmetric. We address this tension by showing that the asymmetry of the operational formulations does not reflect a fundamental time-orientation of physics. Instead, it stems from built-in assumptions about the users of the theory. In particular, these formalisms are designed for predicting the future based on information about the past, and the main mathematical objects contain implicit assumption about the past, but not about the future. The main asymmetry in quantum theory is the difference between knowns and unknowns.
Dynamical collapse models embody the idea of a physical collapse of the wave function in a mathematically well-defined way. They involve modifications to the standard rules of quantum theory in order to describe collapse as a physical process. This appears to introduce a time reversal asymmetry into the dynamics since the state at any given time depends on collapses in the past but not in the future. Here we challenge this conclusion by demonstrating that, subject to specified model constraints, collapse models can be given a structurally time symmetric formulation in which the collapse events are the primitive objects of the theory. Three different examples of time asymmetries associated with collapse models are then examined and in each case it is shown that the same dynamical rule determining the collapse events works in both the forward and backward in time directions. Any physically observed time asymmetries that arise in such models are due to the asymmetric imposition of initial or final time boundary conditions, rather than from an inherent asymmetry in the dynamical law. This is the standard explanation of time asymmetric behaviour resulting from time symmetric laws.