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 non-trivial *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. 8-10],

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, point-like 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 non-physical 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 non-physical 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 seventy-eight 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
http://members.aon.at/chakalov
http://members.aon.at/chakalov/dimi.html
--
I find the idea quite intolerable that an electron exposed to radiation should choose of its own free will, not only its moment to jump off, but also its direction. In that case I would rather be a cobbler, or even an employee in a gaming-house, than a physicist. 

A. Einstein, Born-Einstein 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,
http://xxx.lanl.gov/abs/hep-th/0005274

"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.
http://xxx.lanl.gov/abs/quant-ph/9901077

"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.
http://xxx.lanl.gov/abs/quant-ph/9711003

"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 self-adjoint 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.
http://xxx.lanl.gov/abs/quant-ph/9912065

"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."
 

[Ref. 5] S. Carlip. Quantum Gravity: A Progress Report.
http://xxx.lanl.gov/abs/gr-qc/0108040
 

[Ref. 6] I. Raptis. Quantum Space-Time as a Quantum Causal Set.
http://xxx.lanl.gov/abs/gr-qc/0201004
 

[Ref. 7] A. Bassi, G. Ghirardi. A General Argument Against the Universal Validity of the Superposition Principle.
http://xxx.lanl.gov/abs/quant-ph/0009020

"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 wave-function 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.
http://xxx.lanl.gov/abs/gr-qc/0112045

"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 energy-momentum 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.
http://xxx.lanl.gov/abs/gr-qc/0110046

"All energies gravitate thereby removing the ambiguity in the zero level for the energy, which exists in non-gravitational interactions. This feature also suggests that there is no such thing as a free, non-interacting field. Any non-trivial 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* self-interacting."

T. Padmanabhan. Cosmic inventory of energy densities: issues and concerns.
http://xxx.lanl.gov/abs/gr-qc/0112068

"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.
http://xxx.lanl.gov/abs/gr-qc/9711075

"The second observation that I wish to report here is that the collapse of a wave function is associated with the collapse of the energy-momentum tensor. Since it is the energy-momentum 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, gr-qc/9308007]. Quantum mechanics and gravity intermingle in such a manner as to make position measurements non-commutative. This then brings to our attention another intrinsic element of gravity in the quantum realm, the element of non-locality."
 

[Ref. 11] C.J. Isham, J. Butterfield. On the Emergence of Time in Quantum Gravity.
http://xxx.lanl.gov/abs/gr-qc/9901024

"The difficulty of finding a buried time in the Wheeler-DeWitt 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."