Subject: Quantum states and space-time causality
Date: Wed, 04 Jan 2006 10:22:38 +0200
From: Dimi Chakalov <>
To: Dorje C Brody <>
CC: Lane P Hughston <>,
     Chris Isham <>,
     Christian Beck <>,
     Larry Horwitz <>,
     Bernard S Kay <>,
     Andrei Khrennikov <>,
     Andre Gsponer <>

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

and the discussion of QM & STR at

I believe there should exist a Lorentz-invariant, reversible, bi-directional, 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 so-called global time coordinate in GR [Ref. 2] can't fit the bill, I'm afraid. More at

I will appreciate the feedback from your colleagues, too. Please also note that I will be in London January 15-23, and will be happy to discuss these issues privately, as you did five years ago.

Kindest regards,



[Ref. 1] Dorje C. Brody, Lane P. Hughston, Quantum states and space-time causality, quant-ph/0601020 v1,


Figure 1. Fuzzy space-time. Once the symmetry is broken, a quantum
space-time event can be interpreted as a space-time-point-valued
operator, whose expectation determines a point in Minkowski space.

[Ref. 2] Bernard S. Kay, Quantum Field Theory in Curved Spacetime,
gr-qc/0601008 v1,

"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 constant-t surface is a smooth Cauchy surface i.e. a smooth spacelike 3-surface 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 time-machine question in Section 6.) In view of this definition, globally hyperbolic spacetimes are clearly time-orientable and we shall assume a choice of time-orientation 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
January 6, 2006


Subject: To the memory of Asher Peres
Date:  Sat, 07 Jan 2006 00:29:35 +0200
From: Dimi Chakalov <>
To: Daniel Terno <>

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?

You you say 'yes', you'll "discover" time operators in non-relativistic 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.

Thus, "quantum information" can at best be used as an intellectual exercise.

I wonder if you have some pertinent comments.


[Ref. 1] Daniel R. Terno, Introduction to relativistic quantum information, quant-ph/0508049 v2.

"To the memory of Asher Peres, teacher and friend"


Subject: Biquaternion Quantum Mechanics
Date: Tue, 13 Aug 2002 16:03:50 +0300
From: Dimi Chakalov <>
To: "Dorje C. Brody" <>

Dear Dorje,

Regarding your quant-ph/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 zero-divisors, i.e., non-zero elements which product is *zero*. I've speculated extensively on some entities which do not "collapse", simply because are "outside" the Hilbert space,

Of course, I could be wrong about biquaternion QM, but at least I'm trying to avoid any non-linear "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
Dimiter G. Chakalov
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.