Quantum measurement is a physical process. A system and an apparatus interact for a certain time period, and during this interaction, information about an observable is transferred from the system to the apparatus. In this study, we quantify the energy fluctuation of the quantum apparatus required for this physical process to occur autonomously. We first examine the so-called standard model of measurement, which is free from any non-trivial energy–time uncertainty relation, to find that it needs an external system that switches (...) on the interaction between the system and the apparatus. In such a sense this model is not closed. Therefore to treat a measurement process in a fully quantum manner we need to consider a “larger” quantum apparatus which works also as a timing device switching on the interaction. In this setting we prove that a trade-off relation, \, holds between the energy fluctuation \ of the quantum apparatus and the measurement time \. We use this trade-off relation to discuss the spacetime uncertainty relation concerning the operational meaning of the microscopic structure of spacetime. In addition, we derive another trade-off inequality between the measurement time and the strength of interaction between the system and the apparatus. (shrink)

Some authors, inspired by the theoretical requirements for the formulation of a quantum theory of gravity, proposed a relational reconstruction of the quantum parameter-time—the time of the unitary evolution, which would make quantum mechanics compatible with relativity. The aim of the present work is to follow the lead of those relational programs by proposing a relational reconstruction of the event-time—which orders the detection of the definite values of the system’s observables. Such a reconstruction will be based on the modal-Hamiltonian interpretation (...) of quantum mechanics, which provides a clear criterion to select which observables acquire a definite value and to specify in what situation they do so. (shrink)

In this contribution in honour of Paul Busch, we criticise the claims of many expositions that the time-energy uncertainty principle allows both a violation of energy conservation, and particle creation, provided that this happens for a sufficiently short time. But we agree that there are grains of truth in these claims: which we make precise and justify using perturbation theory.

I explore two logical possibilities for the discretization of time, termed ``instantaneous" and ``smeared". These are found by discretizing a continuous theory, and the resulting structure of configuration space and velocities are described. It is shown that results known in numerical methods for integration of dynamical systems preclude the existence of a system with fixed discrete time step which conserves fundamental charges universally, and a method of avoidance of this ``no-go" theorem is constructed. Finally the implications of discrete time upon (...) quantum cosmology are discussed. NB : At this point this paper is a draft, citations and formatting are not completed. (shrink)

Parmenides’ Poem on Nature contains a proof that the world could not have come into being in time, because no explanation could be given for why it would do so at a given time. This same proof reappears in the Leibniz-Clarke Correspondence, where it is directed against Newtonian absolute time. Newtonians, Leibniz explains, believe that time is homogeneous and absolute, but this makes it inexplicable how God could have chosen to create the world on a given day. Similarly, in his (...) correspondence with Schrödinger in the 1930s, Einstein suggests that certain quantum mechanical occurrences, such as the spontaneous decay of a radioactive atom, are absurd, because they cannot be assigned a definite location in time. In Schrödinger’s version of Einstein’s argument, we must say that the cat dies twice: first, inside the box; yet, second, when we open the box. But both accounts cannot be true. Since each of the authors discussed was aware of the approach of his predecessors, they share a structure. In this article, I develop a unified account of all three. (shrink)

The problem of the validity and interpretation of the energy-time uncertainty relation is briefly reviewed and reformulated in a systematic way. The Bohr-Einsteinphoton-box gedanken experiment is seen to illustrate the complementarity of energy andevent time. A more recent experiment with amplitude-modulated Mößbauer quanta yields evidence for the genuine quantum indeterminacy of event time. In this way, event time arises as a quantum observable.

The discussion of a particular kind of interpretation of the energy-time uncertainty relation, the “pragmatic time” version of the ETUR outlined in Part I of this work [measurement duration (pragmatic time) versus uncertainty of energy disturbance or measurement inaccuracy] is reviewed. Then the Aharonov-Bohm counter-example is reformulated within the modern quantum theory of unsharp measurements and thereby confirmed in a rigorous way.

La interpretación modal-hamiltoniana fue introducida para resolver ciertos problemas de interpretación vinculados a su ontología y a la medición cuántica. Su regla de actualización establece que todo sistema cerrado tiene su energía bien definida, y debido a la indeterminación entre la energía y el tiempo esto plantea un interrogante respecto a la situación temporal de estos sistemas. En este trabajo se analiza el problema del tiempo en sistemas cerrados y se propone la reconstrucción de un tiempo relacional compatible con la (...) perspectiva holista. (shrink)

This paper gives a philosophical assessment of the Montevideo interpretation of quantum theory, advocated by Gambini, Pullin and co-authors. This interpretation has the merit of linking its proposal about how to solve the measurement problem to the search for quantum gravity: namely by suggesting that quantum gravity makes for fundamental limitations on the accuracy of clocks, which imply a type of decoherence that “collapses the wave-packet”. I begin by sketching the topics of decoherence, and quantum clocks, on which the interpretation (...) depends. Then I expound the interpretation, from a philosopher's perspective. Finally, in Section 6, I argue that the interpretation, at least as developed so far, is best seen as a form of the Everett interpretation: namely with an effective or approximate branching, that is induced by environmental decoherence of the familiar kind, and by the Montevideans’ “temporal decoherence”. (shrink)

For an observation time equal to the universe age, the Heisenberg principle fixes the value of the smallest measurable mass at mH=1.35×10-69\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}=1.35 \times 10^{-69}$$\end{document} kg and prevents to probe the masslessness for any particle using a balance. The corresponding reduced Compton length to mH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$m_\mathrm{H}$$\end{document} is, and represents the length limit beyond which masslessness cannot be proved using a metre ruler. In turns, is (...) equated to the luminosity distance dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} which corresponds to a red shift zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. When using the Concordance-Model parameters, we get dH=8.4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H} = 8.4$$\end{document} Gpc and zH=1.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}=1.3$$\end{document}. Remarkably, dH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_\mathrm{H}$$\end{document} falls quite short to the radius of the observable universe. According to this result, tensions in cosmological parameters could be nothing else but due to comparing data inside and beyond zH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_\mathrm{H}$$\end{document}. Finally, in terms of quantum quantities, the expansion constant H0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_0$$\end{document} reveals to be one order of magnitude above the smallest measurable energy, divided by the Planck constant. (shrink)

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. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 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 Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν 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 = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν. It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 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!) Δ E Δ t = Δ p Δ q ≥ h’s. (shrink)

Time, along with concepts as space and matter, is bound to be a central concept of any physical theory. The chapter first discusses how time is treated similarly in quantum and classical theories. It then provides a few references on time‐reversal. The chapter discusses three chosen authors' (Paul Busch, Jan Hilgevoord and Jos Uffink) clarifications of uncertainty principles in general. Next, the chapter follows Busch in distinguishing three roles for time in quantum physics. They are external time, intrinsic time and (...) observable time. It also provides a brief discussion on time operators, in particular Pauli's influential proof. Finally, the chapter talks about time‐energy uncertainty principles with intrinsic times. (shrink)

The Energy-Time Uncertainty (ETU) has always been a problem-ridden relation, its problems stemming uniquely from the perplexing question of how to understand this mysterious Δ t . On the face of it (and, indeed, far deeper than that), we always know what time it is. Few theorists were ignorant of the fact that time in quantum mechanics is exogenously defined, in no ways intrinsically related to the system. Time in quantum theory is an independent parameter, which simply means independently known (...) . In the early 1960s Aharonov (1961-64) and Bohm (1961-64) mounted a spirited attack against the ETU, which sealed its fate to the present date. By emphasising that time is always “well-defined” in quantum theory, they were led to the conclusion that no ETU should exist, a view shared by many in the 1990s, if Busch (1990) is to be believed. In a similar vein, I emphasize that (a) physical systems occupy a particular energy state at a particular instant of time, if at all; (b) even in absence of all time-measuring instruments, it is still trivially warranted that one can measure a system's energy as accurately as one pleases, and simply announce “The system's energy is exactly E NOW!”, a possibility which no quantum mechanics of any sort, or any physical theory whatsoever, can afford to tamper with or change, except circularly. One never loses one's own perception of time, when one measures the energy, a fact which no measurement conceivable can interfere with or affect. Both (a) and (b) uniquely entail that energy and time are compatible, if not indeed intimately interconnected, contrary to what the relevant uncertainty seems to affirm. In response to Aharonov's and Bohm's initial problem, I reinterpret ΔEΔt ≥ h , as directly derived from authentic quantum principles, without however having to assume a direct incompatibility between its related concepts, attributing their complementarity to conditions other than ordinarily assumed. (shrink)

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page–Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.