Online research in philosophy

In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting "time-symmetrized" interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics.

A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model has the advantage of yielding sensible results for energy eigenstates and does not require the use of time-dependent wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not the absolute time of transit. A comparison is given with the weak-measurement post-selection calculations of Steinberg.

A physical and mathematical framework for the analysis of probabilities in quantum theory is proposed and developed. One purpose is to surmount the problem, crucial to any reconciliation between quantum theory and space-time physics, of requiring instantaneous "wave-packet collapse" across the entire universe. The physical starting point is the idea of an observer as an entity, localized in space-time, for whom any physical system can be described at any moment, by a set of (not necessarily pure) quantum states compatible with his observations of the system at that moment. The mathematical starting point is the theory of local algebras from axiomatic relativistic quantum field theory. A function defining the a priori probability of mistaking one local state for another is analysed. This function is shown to possess a broad range of appropriate properties and to be uniquely defined by a selection of them. Through a general model for observations, it is argued that the probabilities defined here are as compatible with experiment as the probabilities of conventional interpretations of quantum mechanics but are more likely to be compatible, not only with modern developments in mathematical physics, but also with a complete and consistent theory of measurement.

We present a scenario describing how time emerges in the framework of weak quantum theory. In a process similar to the emergence of time in quantum cosmology, time arises after an epistemic split of an undivided unus mundus as a quality of the individual conscious mind. Synchronization with matter and other mental systems is achieved by entanglement correlations. In the course of its operationalization, time loses its original quality and the time of physics as measured by clocks appears. avoided/explicated.

Time flows. This oft-lamented fact of human existence seems plain enough, but is remarkably difficult to explain scientifically. Physical theory follows a greater goal—symmetry—and the directional nature of time is left adrift. The phenomenon must nevertheless be explained.Scientists since Isaac Newton have searched classical mechanics for answers, but precious little progress has been made on his mystical ideas. The discoveries of thermodynamics, though clearly relevant, have posed more problems than they have solved.Now a new solution presents itself through quantum mechanics. The intimate relation between thermodynamics and time is not in doubt, but now quantum theory is explaining how the laws of entropy arise from a stranger reality. The theory of decoherence begins to explain time as a holistic quantum concept.

The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → -q) & (q → -p) or defineable as [(p → -q) & (q → -p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and thus a matter of fact. The two types are therefore diametrically opposed. In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. ΔEΔt ≥ h is known to derive from the quantum relation E = hv plus the Fourier relation ΔvΔt ≥ 1. And the Fourier relation assigns a logical incompatibility between Δv = 0, Δt = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that ΔEΔt exists if and only if h > 0, which latter supposition is a factual truth, entailing that a ΔE = 0, Δt = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via ΔvΔt ≥ 1) on condition that E = hv is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility. To circumvent this undesirable result, I reinterpret E = hv as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = v. It is true that E = v times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering ΔvΔt ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) ΔEΔt = ΔpΔq ≥ h's.

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's version or in Bohm's version, does not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time.

Well known quantum and time paradoxes, and the difficulty to derive the second law of thermodynamics, are proposed to be the result of our historically grown paradigm for energy: it is just there, the capacity to do work, not directly related to change. When the asymmetric nature of energy is considered, as well as the involvement of energy turnover in any change, so that energy can be understood as fundamentally "dynamic", and time-oriented (new paradigm), these paradoxes and problems dissolve. The most basic consequence concerns the particle-wave dualism. For a reversible inter-conversion of a particle into a wave, subject to a dynamic energy, a self-image of information has to be generated: quantum theory has to be complemented by a theory of information. Then, quantum processes can be derived from classical ones and the second law of thermodynamics with the tendency of increasing entropy follows in a straightforward way.

Many physicists believe that time constitutes a serious problem in quantum mechanics. We show nevertheless that quantum mechanics does not involve a special problem for time, and that there is no fundamental asymmetry between space and time in quantum mechanics over and above the asymmetry that already exists in classical physics. The apparent problem of time arises when the time parameter is put on a par with dynamical position variables rather than with the coordinates of space. The commutation relations and uncertainty relations are generally considered to embody the essential content of elementary quantum mechanics, but the traditional mathematical expression of the uncertainty principle it shown to be quite unsatisfactory. It is the total energy that decrees whether or not the time variables of a system can be sharply determined.