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量子論におけるレトロディクション I

K.-I. Izawa, T. Taniguchi

Published Jan 1, 2017• 0 citations
OpenAlex

Abstract

We consider retrodictive aspects of quantum theory. As a first step, we adopt quantum mechanics of a single free particle in one-dimensional space. Under successive mearsurements of particle position and momentum as a wave packet, we derive estimation on retrodictive probability, which happens to coincide with the expression for predictive probability into the past.

Related papers

量子レトロディクションと履歴

K.-I. Izawa, T. Taniguchi

We further see the content and consistency of our claims on retrodictive aspects of quantum theory based on the previous papers, which deal with quantum mechanics of a single particle in one-dimensional space under successive mearsurements of particle position and momentum as a wave packet. The content of retrodiction can be best understood as statements on the past recorded in the present state. Conditional probabilites with the past and future states specified are consistently obtained through the ordinary predictive and/or our retrodictive probability formula in any combined way.

•Jan 1, 2018•0 citations

量子論におけるレトロディクションII

K.-I. Izawa, T. Taniguchi

We continue to investigate retrodictive aspects of quantum theory based on the previous paper numbered I. We now proceed to consider quantum mechanics of a single interacting particle in one-dimensional space. Under successive mearsurements of particle position and momentum as a wave packet, we argue that a piecewise approximation to the particle motion, when applicable, results in the classical retrodiction just as it results in the classical prediction.

•Jan 1, 2018•0 citations

Quantum Retrodiction

Stephen Mark Barnett, John Jeffers, David Thomas Pegg +2 more

Prediction, of course, is the making of statements about the likelihood of future events. retrodiction (or postdiction) is the making of statement about past events. In these lectures we shall study the rules governing retrodictive probabilities both in the quantum and classical domains. In doing so we develop a powerful tool with which to interpret physical phenomena and both analyse and interpret experiments. We use retrodictive methods to analyze a number of phenomena in quantum optics including the familiar photon antibunching, entanglement and ghost imaging and the perhaps less familiar ideas of quantum scissors, quantum computation in the past a single-particle analysis of two-particle interference. Quantum retrodiction is a quantitative theory and the familiar techniques for evolving quantum states and modelling open systems are applicable to retrodictive problems, but only with the introduction of some novel features. We conclude with a few remarks on more philosophical issues related to the arrow of time and wavefunction "collapse" in the measurement process. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Springer eBooks•Aug 29, 2005•6 citations

Quantum Pasts and the Utility of History

James B. Hartle

From data in the present we can predict the future and retrodict the past. These predictions and retrodictions are for histories – most simply time sequences of events. Quantum mechanics gives probabilities for individual histories in a decoherent set of alternative histories. This paper discusses several issues connected with the distinction between prediction and retrodiction in quantum cosmology: the difference between classical and quantum retrodiction, the permanence of the past, why we predict the future but remember the past, the nature and utility of reconstructing the past(s), and information theoretic measures of the utility of history.

arXiv:gr-qc/9712001•Physica Scripta•Jan 1, 1998•35 citations

Uniqueness of the Airy packet in quantum mechanics

K. Unnikrishnan, A. R. P. Rau

The general form of a nonspreading wave packet in one-dimensional free space is derived from first principles, employing a decomposition of the quantum mechanical evolution operator of the free particle. In agreement with the classical analysis of Berry and Balazs, the corresponding probability density is proportional to the square of an Airy function, and the packet propagates with constant acceleration.

American Journal of Physics•Aug 1, 1996•75 citations

Aspects of the Problem of Retrodiction

Bernard d’Espagnat

The problem of retrodiction is associated with basic questions, but for this very reason it is, unfortunately, quite difficult, even in classical physics. In quantum physics it is even more subtle. In quantum mechanics, a consistent definition of what is called a "system" leads to problems that do not exist in classical physics, and correspondingly the answers to the questions raised are less straightforward. This chapter discusses the conditions under which it is possible to speak of an "independent time evolution" of a system S and to study what kinds of predictions can legitimately be made when these conditions are fulfilled. It describes retroactive computation to investigate whether or not the assumed knowledge in question is really consistent with the standard quantum mechanical formalism. The concept of retrodiction is related to the notions of time reversal and of irreversibility. Both these notions play a central role in physics.

CRC Press eBooks•Mar 5, 2018•0 citations
We consider retrodictive aspects of quantum theory. As a first step, we adopt quantum mechanics of a single free particle in one-dimensional space. Under successive mearsurements of particle position and momentum as a wave packet, we derive estimation on retrodictive probability, which happens to coincide with the expression for predictive probability into the past.
We further see the content and consistency of our claims on retrodictive aspects of quantum theory based on the previous papers, which deal with quantum mechanics of a single particle in one-dimensional space under successive mearsurements of particle position and momentum as a wave packet. The content of retrodiction can be best understood as statements on the past recorded in the present state. Conditional probabilites with the past and future states specified are consistently obtained through the ordinary predictive and/or our retrodictive probability formula in any combined way.
Prediction, of course, is the making of statements about the likelihood of future events. retrodiction (or postdiction) is the making of statement about past events. In these lectures we shall study the rules governing retrodictive probabilities both in the quantum and classical domains. In doing so we develop a powerful tool with which to interpret physical phenomena and both analyse and interpret experiments. We use retrodictive methods to analyze a number of phenomena in quantum optics including the familiar photon antibunching, entanglement and ghost imaging and the perhaps less familiar ideas of quantum scissors, quantum computation in the past a single-particle analysis of two-particle interference. Quantum retrodiction is a quantitative theory and the familiar techniques for evolving quantum states and modelling open systems are applicable to retrodictive problems, but only with the introduction of some novel features. We conclude with a few remarks on more philosophical issues related to the arrow of time and wavefunction "collapse" in the measurement process. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
From data in the present we can predict the future and retrodict the past. These predictions and retrodictions are for histories – most simply time sequences of events. Quantum mechanics gives probabilities for individual histories in a decoherent set of alternative histories. This paper discusses several issues connected with the distinction between prediction and retrodiction in quantum cosmology: the difference between classical and quantum retrodiction, the permanence of the past, why we predict the future but remember the past, the nature and utility of reconstructing the past(s), and information theoretic measures of the utility of history.
The problem of retrodiction is associated with basic questions, but for this very reason it is, unfortunately, quite difficult, even in classical physics. In quantum physics it is even more subtle. In quantum mechanics, a consistent definition of what is called a "system" leads to problems that do not exist in classical physics, and correspondingly the answers to the questions raised are less straightforward. This chapter discusses the conditions under which it is possible to speak of an "independent time evolution" of a system S and to study what kinds of predictions can legitimately be made when these conditions are fulfilled. It describes retroactive computation to investigate whether or not the assumed knowledge in question is really consistent with the standard quantum mechanical formalism. The concept of retrodiction is related to the notions of time reversal and of irreversibility. Both these notions play a central role in physics.