Subject: Gravity and QM: March 14, 2002
Date: Tue, 08 Jan 2002 17:43:02 +0200 From: "Dimiter G. Chakalov" <dchakalov@surfeu.at> To: Marco Matone <marco.matone@pd.infn.it> CC: ppearle@hamilton.edu, ghirardi@ictp.trieste.it, bal@physics.syr.edu, j.halliwell@ic.ac.uk, toller@science.unitn.it, mlr1000@cam.ac.uk, ahluwalia@phases.reduaz.mx, i.raptis@ic.ac.uk, k.savvidou@ic.ac.uk, l.smolin@ic.ac.uk, carlip@dirac.ucdavis.edu, baez@math.ucr.edu, nabhan@iucaa.ernet.in, jeeva@sc.edu, C.Anastopoulos@phys.uu.nl, Erasmo.Recami@mi.infn.it, Giovanni.AmelinoCamelia@cern.ch, Puthoff@aol.com, stuckeym@etown.edu, arminjon@hmg.inpg.fr, norbert@physik.unizh.ch BCC: [snip] Dear Professor Matone, Regarding your very interesting hypothesis that the quantum potential could be at the origin of gravitation, hence a possible quantum origin of the gravitational interaction [Ref. 1], may I request your opinion on the possible role of gravity in QM. The problem has been stated by Einstein in a letter to Born dated 29 April 1924 (cf. below), and was further explained by Pearle as the absence of a 'chooser' in QM [Ref. 2]. This problem is in the heart of QM [Refs. 3 and 4] and has been tackled by many theoretical physicists working toward quantum gravity [Ref. 5]. What can you say on the problem of the 'chooser' in QM [Ref. 2]? Do you see some possible solution with the quantum potential [Ref. 1]? It seems to me that there is a highly nontrivial *conceptual* problem here  please correct me if I'm wrong  which has to be elucidated and understood in full details. I believe it boils down to the highly deceiving notion of "point", as revealed in the following four problems: 1. The inner product problem: the problem of fixing the inner product in the Hilbert space of physical states by requiring that it is invariant under Diff(M) [Ref. 6]; 2. The problem of time: the problem of requiring that the dynamics is encoded in the action of Diff(M) on the space of states [Ref. 6]; 3. The measurement problem in QM [Ref. 7]; and 4. The measurement problem in GR: the energy of the gravitational field is not localizable, i.e. there is no uniquely defined energy density [Refs. 810], http://members.aon.at/chakalov/Anandan.html In plain English, the problem is that neither QM nor GR can describe the world we see around us, with seemingly sharp, pointlike localization of tables and chairs, *one at a time*, http://members.aon.at/chakalov/Raptis.html It is my conjecture that the 'chooser' (please see above) does exist in Nature and is provided by a 'universal time arrow', http://members.aon.at/chakalov/PHI.html#point I see it as an irreversible chain of temporal, transient "slices"  one at at time  of a nonphysical entity called 'the whole Universe', which can not be *physically* reached due to the nature of Planck scale cutoff, http://members.aon.at/chakalov/Magueijo.html It is irreversible because every next "slice" (I wish I could say 'spacetime foliation') contains totally new information (information gain) than literally emerges [Ref. 11] from 'the whole Universe' viewed as an infinite (actual infinity) pool of propensities for the joint evolution of matter and mind along the universal time arrow, http://members.aon.at/chakalov/qualia_1.html#1 Hence the nonphysical entity called 'the whole Universe' contains absolutely everything: "Time is Nature's way to keep everything from happening all at once" (J.A. Wheeler). Strangely enough, we can say nothing *specific* about It, http://members.aon.at/chakalov/chakalov.htm#1 If we look at the future, It is 'nothing', an empty set, from which brand new things can and will emerge [Ref. 11] in the potential future, http://members.aon.at/chakalov/PHI.html#summary To sum up, if we have this potential future *and* the irreversible past  our past light cone in which we *believe* there were (past perfect) "points"  then we can perhaps solve the four tasks listed above, and find the 'chooser' in the quantum realm. This is how I'm trying to assemble the jigsaw puzzle of quantum gravity. I think it will be a very nice gesture if we try to solve the problem of Einstein (14 March 1879  18 April 1955), which he painfully stated seventyeight years ago, on 29 April 1924. We all owe him a lot. I will highly appreciate your professional opinion and efforts (I'm just a psychologist), as well as those from all physicists reading these lines. Let's try to make him a birthday present, by March 14, 2002. Thank you very much in advance. Wishing you a fruitful and happy year 2002,
Dimiter G. Chakalov
A. Einstein, BornEinstein Letters, 29 April 1924
References [Ref. 1] Marco Matone. Equivalence Postulate
and Quantum Origin of Gravitation. Extended version,
references added, to appear in Found. Phys. Lett.
Mon, 7 Jan 2002 16:06:36 GMT,
"3. The existence of the classical limit implies that
the quantum potential depends, through the hidden initial conditions coming
from the QSHJE, on fundamental length scales which
in turn depend on h . It is a basic fact that
these initial conditions are missing in the Schrödinger equation.
In particular, the emergence of the Planck length,
and therefore of Newton's constant, arises from considering
the classical limit for the free particle of vanishing
energy.
"The most characteristic property of the quantum potential
is its universal nature: it is a property possessed
by all forms of matter. On the other hand, we know
that such a property is the one characterizing gravity. Therefore,
if we write down the classical equations of motion for a
pair of particles, we should always include, already
at the classical level, the gravitational interaction.
Furthermore, the quantum potential for a free particle is negative
definite. This should be compared with the attractive nature of
gravity."
[Ref. 2] P. Pearle. Collapse Models.
"In pursuing the research discussed here I have made some
bets as to the nature of an eventually satisfactory
physical theory. One of them is that there is such
an object, a statevector in a suitable Hilbert space plus something
*more*. I shall argue that *more* must be added because standard
quantum theory (SQT) is a theory of choices without a chooser:
*more* is a chooser.
"There is a big difference between a conditional statement and an absolute statement: "if" you win the lottery "then" you will get ten million dollars" can't compare with "you have won the lottery and you get ten milliondollars." "The statements of SQT are conditional. Faced with
the statevector c_{1}a_{1}>+c_{2}a_{2}>, SQT says
"if" this is the description of a completed measurement
"then" the physical state is a_{1}> or a_{2}>." But actually,
what the "if" is conditioned upon, what the words "a completed measurement"
mean, lies outside the theory's ken. SQT is not a complete
description of nature because it fails to predict a physical
phenomenon, namely that an event does  or does not
 occur."
[Ref. 3] A. Peres. Interpreting the Quantum
World.
"In classical mechanics, a dynamical variable indeed has
a definite value at each point of phase space. Specifying
a point in phase space is the standard way of indicating
the state of a physical system. However, in quantum mechanics,
a dynamical variable is represented by a Hermitian matrix (or, more
generally, by a selfadjoint operator). It is manifestly pointless to
attribute to it a numerical value."
[Ref. 4] A. Bassi, G. Ghirardi. About
the Notion of Truth in the Decoherent Histories Approach:
a reply to Griffiths.
"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 truthvalues to them, as implied by the
theorems of Gleason, Bell and Kochen and Specker."
[Ref. 5] S. Carlip. Quantum Gravity: A
Progress Report.
[Ref. 6] I. Raptis. Quantum SpaceTime
as a Quantum Causal Set.
[Ref. 7] A. Bassi, G. Ghirardi. A General
Argument Against the Universal Validity of the Superposition
Principle.
"The very possibility of performing measurements on a
microsystem combined with the assumed general validity
of the linear nature of quantum evolution leads to
a fundamental contradiction."
"This final state is an entangled state of the microscopic
system and of the apparatus, and it is well known
that (if one assumes that the theory is complete,
i.e., that the wavefunction contains *all* the information about
the system) in the considered case it is not *even in principle*
legitimate to state that the properties associated
to the states M_m> or M_l> are possessed
by the apparatus (the same holds true for the microsystem): as
a consequence, the apparatus is not in any macroscopic definite
configuration. This is the essence of the quantum measurement
problem."
[Ref. 8] I.B. Pestov. On Principle of
Universality of Gravitational Interactions. "So, when general relativity is formulated, a general
logical requirement admissibility of arbitrary systems
of coordinates is postulated, however, it turns out
that in the constructed theory, the dynamic characteristics of the
gravitational field (except for the Einstein equations),
the density of energy and momentum, are described
by nontensor quantities. As a result, it is impossible
to uniquely describe the distribution of energymomentum of any
physical system in the gravitational field. Therefore, there
occurs the notion of nonlocalizability of the gravitational
field. The energy of this field is not localizable,
i.e. there is no uniquely defined energy density."
[Ref. 9] T. Padmanabhan. Combining general
relativity and quantum theory: points of conflict
and contact.
"All energies gravitate thereby removing the ambiguity in the zero level for the energy, which exists in nongravitational interactions. This feature also suggests that there is no such thing as a free, noninteracting field. Any nontrivial classical field configuration will possess certain amount of energy which will curve the spacetime, thereby coupling the field to itself indirectly. Gravitational field is not only nonlinear in its own coupling, but also makes *all matter fields* selfinteracting." T. Padmanabhan. Cosmic inventory of energy densities:
issues and concerns.
"Do we understand any of these components at a fundamental
level or can we relate them to one another in a meaningful
way? Unfortunately, the answer today is 'no'."
[Ref. 10] D.V. Ahluwalia. Three Quantum
Aspects of Gravity.
"The second observation that I wish to report here is
that the collapse of a wave function is associated
with the collapse of the energymomentum tensor. Since
it is the energymomentum tensor that determines the spacetime metric,
the position measurements alter the spacetime metric in a
fundamental and unavoidable manner. Therefore, in
the absence of external gravitating sources (which
otherwise dominate the spacetime metric), it matters, in principle,
in what order we make position measurements of particles
[D.V. Ahluwalia, Quantum Measurement, Gravitation,
and Locality,
grqc/9308007].
Quantum mechanics and gravity intermingle in such
a manner as to make position measurements noncommutative.
This then brings to our attention another intrinsic element of
gravity in the quantum realm, the element of nonlocality."
[Ref. 11] C.J. Isham, J. Butterfield.
On the Emergence of Time in Quantum Gravity.
"The difficulty of finding a buried time in the WheelerDeWitt
equation (and the related difficulty of finding an
'internal time' before quantisation) prompts the idea
that geometrodynamics, and perhaps quantum theory in general,
can  or even should  be understood in an essentially 'timeless' way."
