Predicting the Quantum Past

Badis Ydri

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.

Albert Einstein, Richard C. Tolman, Boris Podolsky

It is well known that the principles of quantum mechanics limit the possibilities of exact prediction as to the future path of a particle. It has sometimes been supposed, nevertheless, that the quantum mechanics would permit an exact description of the past path of a particle. \n \nThe purpose of the present note is to discuss a simple ideal experiment which shows that the possibility of describing the past pathof one particlewould lead to the predictions as to the future behaviour of a second particle of a kind not allowed in the quantum mechanics. It will hence be concluded that the principles of quantum mechanics actually involve an uncertainty in the description of past events which is analogous to the the uncertainty in the prediction of future events. And it will be shown for the case in hand, that this uncertainty in the description of the past arises from a limitation of the knowledge that can be obtained by measurement of momentum.

Adrian Kent

Edward R. Floyd

We examine certain pasts and presents in the classically forbidden region. We show that for a given past the trajectory representation does not permit some presents while the Copenhagen predicts a finite probability for these presents to exist. This suggests another gedanken experiment to invalidate either Copenhagen or the trajectory representation.

Chris Jay Hoofnagle, Simson Garfinkel