| Subject: The Big Problem
Date: Mon, 24 Feb 2003 05:34:26 +0200 From: Dimi Chakalov <dchakalov@surfeu.at> To: bassi@ictp.trieste.it, ghirardi@ts.infn.it CC: oldstein@math.rutgers.edu, jbarbour@online.rednet.co.uk, joy.christian@wolfson.ox.ac.uk, peres@photon.technion.ac.il, sofiaw@netvision.net.il, as2@york.ac.uk, adler@ias.edu, kochen@math.princeton.edu, woit@math.columbia.edu Dear Professors Bassi and Ghirardi, It is a real pleasure to read your recent paper "Dynamical Reduction Models" [Ref. 1]. It seems to me that the Big Problem -- "finding a consistent relativistic generalization of the dynamical reduction theories" -- and the Schnitt problem (footnote 8) are intermingled with what Bell called the UNspeakable, http://members.aon.at/chakalov/Römer.html#2 Am I wrong? If not, please take a look at the conceptual solution proposed at http://members.aon.at/chakalov/faq.html http://members.aon.at/chakalov/Zurek.html Note that the dynamics of the quantum state is always non-unitary and is fully relativistic: there are no problems to keep in the Holon a superposition of a cat and a dog, http://members.aon.at/chakalov/Brukner.html#Joos BTW what I like in Barbour's hypothesis is that it is falsifiable: solve the measurement (macro-objectification) problem in line with STR, and his hypothesis will be proven wrong. Is your theory falsifiable? With best regards, Dimi Chakalov
John S. Bell
Reference [Ref. 1] Angelo Bassi, GianCarlo Ghirardi.
Dynamical Reduction Models. Fri, 21 Feb 2003 11:30:22 GMT,
"We will show that superpositions of states corresponding
to different macroscopic configurations of macro–objects cannot be avoided
within a strict quantum mechanical context. Correspondingly, the appearance
of macroscopic situations which are incompatible with our definite perceptions
about such objects is inescapable. This "empasse" can only be circumvented
either by adopting a precise and unambiguous interpretation which differs
from the orthodox one, or by modifying the theory itself.
"Without any loss of generality, we will assume that,
by resorting to appropriate procedures, one can "prepare" the system
S in any one of the three above considered states |u> , |d>
and |u + d>.
"Accordingly, after the preparation,
the system is in a precise and known state, and it can be treated as isolated
from the rest of the universe, at least until the
measurement process begins.(footnote 8) We stress that if one denies these
assumptions it is not even clear what he takes quantum theory to be about.
"However, finding a consistent relativistic generalization of the dynamical reduction theories, remains, as Bell has stressed, *the big problem* to be faced." ========== Subject: Re: The Big Problem
Dear Professors Bassi and Ghirardi, In my preceding email of Mon, 24 Feb 2003 05:34:26 +0200, I asked whether your theory is falsifiable, http://members.aon.at/chakalov/Bassi.html I hope you will agree that the Big Problem -- "finding a consistent relativistic generalization of the dynamical reduction theories" -- necessitates a covariant presentation of *the* quantum state. The latter is 'neither true nor false'. [Ref. 2] In your reply to Griffiths [Ref. 3], you elaborated, in the context of decoherent histories (DH) formalism, on this peculiar faculty of the quantum state, stressing that a statement about the quantum state is neither true nor false per se: "each of them acquires a truth value only when it is considered a member of a precise (among the infinitely many ones which are possible) decoherent family." Hence in order to talk about *the* quantum state, we need to keep in mind all infinitely many and "incompatible" decoherent families en bloc, the UNspeakable included, http://members.aon.at/chakalov/Römer.html#2 That's really tough [Ref. 4], unless we learn how to think about 'the set of all sets' which is UNspeakable too, http://members.aon.at/chakalov/Vecchi.html By making the preparation for measurement, http://members.aon.at/chakalov/Bassi.html#preparation we inevitably introduce a Schnitt dividing the world into 'measured system' and 'the rest of the universe'. We strongly (if not religiously) believe that the former is in some precise and yet-to-be-measured state, and happily write down its wave function. Then we make the measurement but -- surprise! -- we're struck by the measurement (macro-objectification) problem, http://members.aon.at/chakalov/right.html#Bassi_Ghirardi which has been introduced ab initio by the Schnitt, since we all know that the world itself is a holistic system the constituents of which do not possess *any property whatsoever*, http://members.aon.at/chakalov/Lloyd.html#2 It's sort of a magic circle, isn't it? In my opinion, the only way to break it is to work with the Holon or *the* quantum state, http://members.aon.at/chakalov/faq.html If you wish to stay confined to its wave function only, you're heading toward a dead-end, as we know since the inception of quantum mechanics, http://members.aon.at/chakalov/Corbett.html#2 I hope you will agree with Chris Isham that we need a creative leap [Ref. 4], which brings back the wild guess of Roger Penrose some ten years ago that "our brains have somehow contrived to harness the details of a physics that is yet unknown to human physicists." [Ref. 5] This is what PHI is all about. BTW two years ago Prof. GianCarlo Ghirardi agreed to review my CD ROM (Subject: Re: Free CD ROM, Tue, 26 Jun 2001 11:40:30 +0100), but I haven't heard from him ever since. You can download the basic content of my CD from http://members.aon.at/chakalov/PHI_info.zip Enjoy! Best regards, Dimi Chakalov
John S. Bell
References [Ref. 2] William Faris, Review of Roland
Omnès "The Interpretation of Quantum Mechanics", Notices of the AMS, 43(11)
1328 (November 1996),
"This says that the probabilities of a set of mutually
exclusive properties whose disjunction is sure add up to one. It is not
necessarily assumed that every property can be measured or that all these
probabilities are empirically meaningful.
"The radical view is provoked by the puzzle over whether
we understand a world in which properties on the atomic scale are typically
neither true nor false."
[Ref. 3] Angelo Bassi, GianCarlo Ghirardi.
About the Notion of Truth in the Decoherent Histories Approach: a reply
to Griffiths. Phys. Lett. A 265, 153 (2000),
"In Standard Quantum Mechanics, on the other hand, one cannot even think that systems possess physical properties prior to measurements: mathematically, this is reflected in the peculiar properties of the Hilbert space (with dimension greater than 2): the set of projection operators cannot be endowed with a Boolean structure, and it is not possible to attach consistently truth-values to them, as implied by the theorems of Gleason, Bell and Kochen and Specker. "Thus, giving a truth value to the histories of a given
decoherent family corresponds to the assertion that such histories speak
of specific physical properties that the system under study possesses objectively,
independently from our (in general) probabilistic knowledge of the system
and of any act of measurement. This, in our opinion, is the nicest feature
of the DH formalism, the one emboding all its advantages with respect to
the standard quantum formalism.
"This, in turn, means accepting that statements like "this
table is here", "the Earth is moving around the Sun", "that electron has
spin up along such a direction" are -- in general -- neither true nor false
per
se: each of them acquires a truth value only when it is considered
a member of a precise (among the infinitely many ones which are possible)
decoherent family; moreover, their truth values may change according to
the decoherent family to which they are associated. In some families it
may be true that "this table is here" or that "the Earth is moving around
the Sun", while in other families it may be false that "this table is here"
or that "the Earth is moving around the Sun". This state of affairs is
the direct consequence of denying our assumption, and it should be evident
to anyone that if one takes such a position then he is spoiling the statements
of the DH approach of any physical meaning whatsoever."
[Ref. 4] C.J. Isham, A New Approach to
Quantising Space-Time: I. Quantising on a General Category,
"In the present paper an operator-based approach to quantising
space, or space-time, structure is described.
"Finally, note that, when discussing the quantum theory of causal sets, I have assumed that the space K[c] associated with each causal set c is a standard Hilbert space, in accordance with normal quantum theory. However, in [14] it is argued that normal quantum theory is problematic in such a situation because the use of the continuum real and complex numbers assumes a priori that the background space and space-time are manifolds, which is not the case if the space-time is a causal set. This suggests that each K[c] should be replaced by something quite different: in fact, by whatever the analogue is for that specific causal set c of the Hilbert space of states in normal quantum theory. It is a task for future research to decide what this may be, but once the decision is made, the techniques described in the present paper would be a good starting point to construct a theory in which the causal sets, and the associated quantum theories, are themselves subject to 'quantum fluctuations'. "These projects are exciting, but it should be emphasised
that what is described in the present paper is only a 'tool-kit' for constructing
operator-based models of quantum space-time or space: it needs a creative
leap to use these tools to construct a physically realistic model of, for
example, quantum causal sets. The key step would be to choose a decoherence
functional for the quantum history theory. This decoherence functional
would be constructed from the operators described in this paper, but new
physical principles are needed to decide its precise form. This is an important
topic for future research." [Ref. 5] Roger Penrose, Shadows of the Mind, Oxford University Press, Oxford, 1994, Sec. 3.28, "Conclusions", p. 208; see also Sec. 1.21, "Is mathematical imagination non-computational?", p. 59. =========== Subject: The S model
I'm reading your recent paper [Ref. 1] with great interest. May I ask two questions. Is your S model irrelevant to the problems in [Ref. 2]? To what extent -- if any -- your interpretation of superposition, "to be understood in an appropriate way" [Ref. 1], differs from Joos' |cat> + |dog> , http://members.aon.at/chakalov/Adami.html#6 ? Regards, Dimi
[Ref. 1] A. Bassi, G.C. Ghirardi, Quantum
vs classical computation: a proposal opening a new perspective, Thu, 10
Apr 2003 15:43:00 GMT,
"We then formulate a new classical model of computation
(the S model) which captures some features of quantum computation, in particular
the possibility of inputting superposition (to be understood in an appropriate
way) of states: thanks to this property, we will show that some classical
problems can be solved in a surprisingly fast way.
"III. THE S MODEL OF COMPUTATION "In this section we define a new model of computation,
which we call the S model: its building blocks are just three states, |0>>,
|1>> and |s>>. The state |s>> will formally play the role of the *superposition*,
to be understood in an appropriate way, of states |0>> and |1>>.
"To summarize, we have defined a consistent computational
model which tries to capture some features of quantum computation: the
building block is the sbit which has two computational basis states plus
a third state which can be seen as the superposition of the two basis states.
Operations on sbits are defined on the computational basis and the requirement
of weak additivity (the analog of linearity within quantum computation)
defines in a unique way their action for all other states; although the
combination of two w-additive operations is not always w-additive, all
convertible classical circuits can be easily turned into the corresponding
w-additive circuits. Finally, there exists a universal set of w-additive
gates."
[Ref. 2] Subhash Kak, Three Paradoxes
of Quantum Information, April 10, 2003,
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