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                       Phys. Rev. D 49, 6543–6555 (1994)

Unitarity and causality in generalized quantum mechanics for nonchronal spacetimes

James B. Hartle*
Department of Physics, University of California, Santa Barbara, California 93106-9530

Received 14 September 1993; published in the issue dated 15 June 1994

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime possesses nonchronal regions which cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives on two spacelike surfaces lying in regions of spacetime where foliating families can be defined may be nonunitary if a nonchronal region lies between them. This paper describes a sum-over-histories generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such nonunitarity. The usual notion of state on a spacelike surface is lost in this generalization. Anomalies such as nonconservation of energy or "Everett phones" that are exhibited by some generalizations of quantum mechanics are not found in this one. However, the generalization is acausal in the sense that the existence of nonchronal regions of spacetime in the future can affect the probabilities of alternatives today and signaling outside the light cone is possible. The detectability of nonunitary evolution and violations of causality in measurement situations are briefly considered.

© 1994 The American Physical Society

On Dec 26, 2011, at 1:33 PM, JACK SARFATTI wrote:


"The existence of this radio to the past" creates the possibility of new
paradoxes, now in the classical domain. In particular the
unproved theorem paradox [2] can arise. Bob reads the
proof of a theorem in a book and uses the set-up of Fig.1
(top panel) to send it back in time to Alice. Alice sub-
sequently publishes it in the book from which Bob will
read it. Where did the proof come from?"

This is precisely how new ideas are always created in the human mind.
Indeed this is the basis of Penrose's objection to "strong AI".

The evidence is there in Libet ---> Radin et-al ---> Bierman ---> Bem.

The analogy here is to Einstein's recognition of the invariance of the vacuum speed of light.
Einstein realized that simultaneity is not invariant under observer motion transformations.
Physics in 1905 fell into place with that insight. Similarly, recognizing that the above "paradox" is not a paradox, but is, in fact, how things are - the mystery of conscious creativity falls into place with a Gestalt Shift. This is all part and parcel with entanglement signal nonlocality with orthodox quantum theory as a limiting case of a more general post-quantum theory.

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