Subject: Quantum
states and spacetime causality
Date: Wed, 04 Jan 2006 10:22:38 +0200 From: Dimi Chakalov <dimi@chakalov.net> To: Dorje C Brody <d.brody@imperial.ac.uk> CC: Lane P Hughston <lane.hughston@kcl.ac.uk>, Chris Isham <c.isham@imperial.ac.uk>, Christian Beck <c.beck@qmul.ac.uk>, Larry Horwitz <larry@post.tau.ac.il>, Bernard S Kay <bsk2@york.ac.uk>, Andrei Khrennikov <Andrei.Khrennikov@vxu.se>, Andre Gsponer <Andre.Gsponer@cui.unige.ch> Dear Dorje, I've been trying, in the past five years, to understand your ideas. Regarding your latest paper [Ref. 1], may I ask two simple questions. Once we make the "collapse", can we trace back the "instant" at which the quantum beast could have entered our light cone? Please see http://www.Goddoesnotplaydice.net/Gisin.html#Ken and the discussion of QM & STR at http://www.Goddoesnotplaydice.net/Khrennikov.html#Belavkin I believe there should exist a Lorentzinvariant, reversible, bidirectional, and smooth transition from the hidden unobservable quantum reality to the normal world of tables and chairs, and back to the hidden unobservable quantum reality. If true, what could be the "back bone" of this reversible transition? The socalled global time coordinate in GR [Ref. 2] can't fit the bill, I'm afraid. More at http://www.Goddoesnotplaydice.net/Rosinger.html http://www.Goddoesnotplaydice.net/Wald.html#note I will appreciate the feedback from your colleagues, too. Please also note that I will be in London January 1523, and will be happy to discuss these issues privately, as you did five years ago. Kindest regards, Dimi
References [Ref. 1] Dorje C.
Brody, Lane P. Hughston, Quantum states and spacetime causality, quantph/0601020
v1,
Figure 1. Fuzzy spacetime. Once
the symmetry is broken, a quantum
[Ref. 2] Bernard
S. Kay, Quantum Field Theory in Curved Spacetime,
"We shall also assume, except where
otherwise stated, our spacetime to be globally hyperbolic, i.e. that
M admits a global time coordinate, by which we mean a global coordinate
t such that each constantt surface is a smooth
Cauchy surface i.e. a smooth spacelike 3surface cut exactly once
by each inextendible causal curve. (Without this default assumption, extra
problems arise for QFT which we shall briefly mention in connection with
the timemachine question in Section 6.) In view of this definition, globally
hyperbolic spacetimes are clearly timeorientable and we shall assume a
choice of timeorientation has been made so we can talk about the "future"
and "past" directions."
Note: Alan
Rendall argues that "a singularity in general relativity cannot be
a point of spacetime, since by definition the spacetime structure would
not be defined there." In the same vein,
the state of an unobserved quantum system 'out there' cannot be embedded
in spacetime due to the incompatible requirements from STR
and QM, as we know since 1931. Obviously, we have to extend the notion
of reality.
D. Chakalov
========= Subject: To the
memory of Asher Peres
Dear Daniel, I too learned a lot from Asher, as acknowledged on my web site, and had the rare privilege of exchanging numerous emails with him on the crucial issue of QM & STR. Yet he never shared with me his opinion on the generic problems of quantum information, which occur from the clash of QM with STR. He just replied with "I have no pertinent comments". Regarding the recent update of your paper [Ref. 1], Sec. VII, "The Omissions & Perspectives", may I ask a simple question: Once we make the "collapse" (or whatever you call it), can we trace back the instant at which the quantum beast could have entered our light cone? http://www.Goddoesnotplaydice.net/Brody.html You you say 'yes', you'll "discover" time operators in nonrelativistic QM. If you say 'no', you will expose a generic limitation to "quantum information": it cannot be manipulated *locally*, at the scale of tables and chairs, where STR holds. No way. http://www.Goddoesnotplaydice.net/Gisin.html Thus, "quantum information" can at best be used as an intellectual exercise. I wonder if you have some pertinent comments. Regards, Dimi
"To the memory of Asher Peres, teacher and friend" ======== Subject: Biquaternion Quantum Mechanics
Dear Dorje, Regarding your quantph/0208076, "Complex Extension of Quantum Mechanics": Do you know somebody in U.K. working on biquaternion QM? See Elio Conte (1994), "Wave Function Collapse in Biquaternion Quantum Mechanics", Physics Essays, 7, 14. I think you can't make QM more "complex", can you? Anyway, what puzzles me is that feature of biquaternion algebra: you have zerodivisors, i.e., nonzero elements which product is *zero*. I've speculated extensively on some entities which do not "collapse", simply because are "outside" the Hilbert space, http://members.aon.at/chakalov/Vecchi.html Of course, I could be wrong about biquaternion QM, but at least I'm trying to avoid any nonlinear "modifications" of QM (A. Peres (1995), "Quantum Theory: Concepts and Methods", Ch. 9.4, p. 278). Anyway, I will highly appreciate your feedback regarding biquaternion QM, as well as info from your colleagues. Best  Dimi
