Subject: On Einstein and realism
Date: Thu, 03 Feb 2005 15:24:17 +0200
From: Dimi Chakalov <>
To: Charles Tresser <>
CC: Michael Clover <>, Tim Palmer <>, Ezra Newman <>, Itamar Pitowski <>

Dear Dr. Tresser,

May I comment on the issue of "alternatives" in the Einstein-Bohr debate [Ref. 1, p. 1]: Either (i) the description by means of the [psi]-function is complete, OR (ii) the real states of spatially separated objects are independent of each other.

It seems to me that there is a third possibility which can be unraveled by zooming on the notion of 'counterfactual definiteness', an implicit assumption in the proof of Bell's theorem [Ref. 2].

You define counterfactuals as "thought experiments that cannot be performed because performing them would violate Physics (like getting back in time to redo an experiment)" [Ref. 1, p. 5].

Hence for two (EPR paradox) or more entangled parties (we cannot write down their "individual" properties as tensor products), the line of reasoning includes -- tacitly or not -- 'counterfactual definiteness' [Ref. 2]. The latter is well-known in psychology,

Please note that the kind of *reality* of entangled parties, in the example at the link above, is a Platonic reality. It contains "counterfactual" or potential states *en bloc*, hence is UNspeakable. We keep this *potential reality* in our brains, but it is not included in present-day QM textbooks. More at

The late Asher Peres never agreed to comment on this *potential reality*. I believe it introduces a brand new kind of determinism in the quantum realm, which is missing in QM textbooks. Surely Einstein and Bohr would have been very happy to see it in math.

I hope to hear from you and your colleagues. Will keep your professional feedback strictly private.

Kindest regards,

Dimi Chakalov


[Ref. 1] Charles Tresser, Weak realism, counterfactuals, and decay of geometry at small scales, quant-ph/0502007 v1.

[Ref. 2] Tim N. Palmer, Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect, quant-ph/0404041 v2.

p. 7: "Fig 1c showed the situation when both the left and right hand particles of an entangled particle pair were measured with magnets oriented in the same direction n. However, in order to establish Bellís theorem, we need to consider correlations between pairs of measurements when the magnets have different orientations, letís say n for the left-hand magnets and n' for the right-hand magnets.

"It is also necessary to assume that it is meaningful to ask: what would the spin of a left-hand particle have been had we actually measured it with magnets oriented in the n' direction (or, conversely, what would the spin of the right-hand particle have been had we actually measured it with magnets oriented in the n direction)? Note that by definition this question could never be actually answered experimentally. In fact it is an example of a counterfactual question, a question about things that didnít happen, but our intuition suggests might have happened."


Subject: Request for references
Date: Fri, 11 Feb 2005 04:09:54 +0200
From: Dimi Chakalov <>
To: László B Szabados <>,
BCC: [snip]

Dear Dr. Szabados,

I have an immodest request. I need references and any other information regarding (i) all non-tensorial variables in GR (Noether currents inclided), (ii) the nature of the resulting "non-locality" in GR, and (iii) the comparison of the "non-locality" in GR with the apparent non-local interactions in QM due to quantum entanglement. The task is to get (iii) done.

In your online article "Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article" from 16 March 2004 [Ref. 1], you explained the meaning of the non-tensorial Christoffel symbols and the linear connection. I don't understand GR (the linear approximation of Einstein's theory [Ref. 2]) and cannot compare the quasi-locality in GR with the non-local interactions in QM, as you can see from my unsuccessful efforts at

In general, I really need to understand GR, since I can't see any *genuine observables* whatsoever [Ref. 3] nor some rigorous proof that the spacetime can indeed be 'asymptotically flat' [Ref. 2] so that I can make some sense of that non-tensorial mesh.

I extend my request for references to all colleagues of yours. Please be assured that I'll keep your feedback strictly private and confidential, and please excuse my violent curiosity.

Kindest regards,

Dimi Chakalov


[Ref. 1] László B. Szabados, Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article, Living Rev. Relativity 7, (2004) 4. Online article, 16 March 2004,

"3.3 The necessity of quasi-locality for the observables in general

"3.3.1 Non-locality of the gravitational energy-momentum and angular momentum

"One reaction to the non-tensorial nature of the gravitational energy-momentum density expressions was to consider the whole problem ill-defined and the gravitational energy-momentum meaningless. However, the successes discussed in the previous subsection show that the global gravitational energy-momenta and angular momenta are useful notions, and hence it could also be useful to introduce them even if the spacetime is not asymptotically flat. Furthermore, the non-tensorial nature of an object does not imply that it is meaningless. For example, the Christoffel symbols are not tensorial, but they do have geometric, and hence physical content, namely the linear connection.

"Indeed, the connection is a non-local geometric object, connecting the fibres of the vector bundle over different points of the base manifold. Hence any expression of the connection coefficients, in particular the gravitational energy-momentum or angular momentum, must also be non-local. In fact, although the connection coefficients at a given point can be taken zero by an appropriate coordinate/gauge transformation, they cannot be transformed to zero on an open domain unless the connection is flat."

[Ref. 2] Hermann Weyl, How far can one get with a linear field theory of gravitation in flat space-time? Amer. J. Math. 66 (1944) 591,

[Ref. 3] Peter G. Bergmann, Observables in General Relativity, Reviews of Modern Physics, 33 (1961) 510-514.


Note: On Wednesday, 23 February 2005 at 17:37:02 +0100 (CET), Laszlo Szabados was very kind to send me a summary of the non-tensorial variables in GR (cf. below). He stressed that "the gravitational energy-momentum and angular momentum, i.e. the gravitational analogs of the classical conserved quantities and observables are non-local. Non-local in the sense that they should be associated to *extended* domains rather than to points."

He went further by emphasizing that "the non-locality in QM is a completely different business. The root of this is that the basic object, the wave function, by means of which the elementary states are described is already an "extended" mathematical objects. This comes from the different nature of the notion of the states and the dynamics of the two theories."

Hence if we wish to compare the "non-locality" in GR with the apparent non-local interactions in QM due to quantum entanglement, as stated in my email above, we should provide some new notions of the states and the dynamics of the two theories. Clearly, we're about to enter the realm of quantum gravity, so don't expect to read something that can be found in QM and GR textbooks.

Also, don't expect to find any math here. The issue is highly speculative, since "even if we start with genuine tensorial variables, then certain important physical quantities turn out to be non-tensorial" (Laszlo Szabados).

Right. So, we need to elaborate some new notions of the states and the dynamics of the two theories, such that they can be presented, with minor distortion, as 'quantum entanglement' in the context of QM, and 'non-tensorial quantities' in the context of GR. Something like a song being played with two entirely different instruments, QM and GR. But the "song" itself should be different from any of its QM and GR presentations, because it must provide the common dynamics of a quantum-gravitational system. Again, please don't reject the speculations below with 'there is no such thing in QM nor in GR'. Of course there isn't. I am trying to speculate on quantum gravity, but will provide only the links to what has been already suggested. And, as you might have already guessed, the "song" itself will be derived from the physics of the human brain.

Regarding the human brain dynamics, see the alleged "non-tensorial" variables expressed as 'context' here. Note that what we call 'context' is "spread over" the whole text. Thus, the 'context' is non-local in the sense that it should be "associated to *extended* domains rather than to points" (Laszlo Szabados). More from Chris Isham here.

In QM, this non-local 'context' comes from the Holon, but it cannot be used for sending information faster-than-light, and "the field equations are still genuine partial differential equations" (Laszlo Szabados).

Now comes the tough part. What is the proper time associated with the Holon and its 'context'? What is the intrinsic dynamics of the Christoffel symbols, namely, in what time do they change? And what could be the common dynamics of a quantum-gravitational system?

Regarding the first question, see the explanation of the notion of 'global mode of spacetime' by reductio ad absurdum here. (Some implications can be read here.) The dynamics is explained with the established notion of 'relational reality' here, and with the proposed notion of 'donkian Hamiltonian' here. (To get a glimpse of the dynamics of the human brain, click here and here.)

As to the second and the third questions, the situation is quite murky, to say the least. Perhaps Laszlo Szabados and Elemer Rosinger can shed some light on the intrinsic dynamics of the Christoffel symbols. I believe they can be interpreted as produced by the Holon, too.

In general, the notion of the Holon can be explained as 'something that pertains simultaneously (global mode of spacetime) to all elements of a set'. Hence the Holon introduces 'quantum wholeness', such that all elements of the set are both ONE (covered by the context delivered by the Holon) and 'many'.

In GR, the Holon manifests itself by those non-tensorial variables. But the whole idea of representing matter by a tensor was "a wooden nose in a snowman", as stated by Einstein. Maybe we should try to mimic Feynman's path integral approach to QFT by elaborating some 'virtual geodesic path' formulation of Einstein's GR, which would include two virtual worlds in the global mode of spacetime, and a real, localized, strictly tensorial world in the local mode of spacetime. This will be an ambitious goal, and if you wish to start with some "extension" of QM, see Erasmo Recami's quant-ph/9706059 here.

I was never able to understand Einstein's GR, and I am very grateful to Laszlo Szabados for his efforts to help me with the non-tensorial mesh in GR. Read about it below.

D. Chakalov
February 24, 2005


Subject: Re: Request for references
Date: Wed, 23 Feb 2005 20:18:38 +0000
From: Dimi Chakalov <>
To: Szabados Laszlo <>

Dear Laszlo,

Thank you very much for your precise and thoughtful reply.

On Wed, 23 Feb 2005 17:37:02 +0100 (CET), you wrote:
> Concerning your questions, I am not sure if it is me that you
> should contact with, because I have worked only in the classical
> general relativity, but not in quantum gravity.
> Thus what I can tell you is relevant in the classical theory.
> In particular,
> > (i) all non-tensorial variables in GR (Noether currents included),
> 1.
> As you know, in the usual formulation of GR the basic variable is
> the metric *tensor*. However, if you want to carry out a Noether-type
> analysis, then you should have a derivative operator that is independent > of the field variables. This may come from an auxiliary, non-dynamical
> metric or connection, or, in the traditional approaches, it is simply
> the partial derivative operator coming from a local coordinate system.
> Then the action of the latter is defined on the metric only if by
> metric you mean the *components of the metric in the coordinate
> system in question*. Unfortunately, however, the partial derivative of
> these components are *not* components of *any* tensor. Essentially,
> these are the Christoffel symbols.
> One might expect that the final results (e.g. the energy-density, a
> special component of the Noether current) was independent of the
> actual coordinate system. However, as is well known for say 80 years,
> this expectation is not correct.
> The situation is not better if you use the background metric/connection: > The final results depend on the choice of the background, and it is
> not clear what could be the physical content of such an expression.
> Thus, to summarize: even if we start with genuine tensorial variables,
> then certain important physical quantities turn out to be non-tensorial.
> In subsection 3.3.1 I argued that this phenomenon is not accidental,
> a consequence of an unfortunate choice for the field variables, but
> this is a consequence of a much deeper fact, namely that the metric
> has a double role: it is a field variable and defines the geometry
> at the same time.

You just hit the nail on the head: *at the same time*. I believe we need
to introduce two kinds of time here,

> Or, in other words, GR is a completely diffeomorphism
> invariant theory, which diffeomorphisms form an incredibly huge set.
> Thus all the observables are associated with the whole spacetime, which
> can be introduced if the spacetime is asymptotically flat, or you should
> have some extended, physical object that breaks this invariance.
> This is the quasi-local case. These quasi-local quantities can be
> introduced even if the spacetime is not asymptotically flat.
> On the other hand, I am arguing against the simple view that
> "coordinate dependent = meaningless".
> If you are interested in the related matter, the so-called pseudotensors,
> you can find several classical and excellent reviews, such as that of
> Trautman, Goldberg, Anderson, etc. An excellent recent review was
> written by Alexander Petrov (Sternberg Astrophysical Institute,
> Moscow).
> 2.
> Another possibility is to choose an orthonormal basis field as the basic
> filed variables rather than the metric. With this choice you describe
> the geometry by the 16 components of the four 4-vectors of the
> basis instead of the usual 10 components of the metric. Thus, with
> this choice you introduced extra gauge freedom into your formalism.
> Again, you can carry out an analogous analysis that I mentioned above,
> and you obtain an expression eg. for the energy density. Interestingly
> enough this expression seems to be tensorial. Unfortunately, however, it
> depends on the actual choice for the basis, i.e. it is *not* gauge
> invariant.
> The root of this gauge dependence is the same as in the pseudotensorial > case. The formalism changed, but the difficulty remained in a new form.
> The classical reference is the basic review by Goldberg, where you can
> find the references for the original papers.
> 3.
> Instead of the metric or orthonormal basis alone, one can use both the
> metric *and* the connection coefficients as independent variables.
> Such is, for example the variation principle of Palatini. In this case
> the connection coefficients are *not* tensorial objects. In the
> presence of a matter filed whose Lagrangian depends on the spacetime
> connection coefficients, the field equations that this variational
> principle give are different from the usual ones. However, for the
> gauge fields, spinor fields and scalar fields the Palatini variation
> gives the familiar equations of motion.
> For the gravitational `field', in addition to the Einstein equations,
> there will be a further field equation linking the connection coefficients
> to the metric. In vacuum or in the presence of the previous special
> matter fields the Palatini variation gives the familiar Einstein theory.
> There are many-many papers using this method, but personally I do not
> prefer this, thus at this moment I cannot give you any explicit
> reference (maybe in Kijowski's paper in Gen.Rel.Grav. in 1996 this is
> mentioned, because he considers this kind of variation).
> But if you type `Palatini variation' into Google, you will certainly
> find the best papers (among the several thousands).
> 4.
> In the previous cases the field variables were *local* objects, in the
> sense that they were associated with points of spacetime.
> Genuinely *non-local* basic variables are the so-called loop variables
> (or in gauge theories the so-called Wilson loops). They are associated
> with closed curves rather than points. The basis idea is that if you
> have a connection, then the parallel transport of any vector along the
> curve is well defined. If the curve is closed, then you can compare
> the vector with that you obtain after parallel propagation. The resulting
> vector will be a linear function of the original vector, and the
> corresponding transformation, called the holonomy, depends both the
> connection and the actual closed curve. Its trace is called in the
> field theory the `Wilson loop'.
> In the Rovelli-Smolin approach of the canonical quantum gravity this
> is one of the basic variables. The other contains the vectors of the
> orthonormal basis at a point, too.
> The basic reference is clearly the famous paper by them in the
> Nucl.Phys. but you can certainly find it in the review paper by Rovelli in
> the Living Reviews home page, too. (That was the first paper in this
> journal.)
> > (ii) the nature of the resulting "non-locality" in GR, and
> > (iii) the comparison of the "non-locality" in GR with the apparent
> > non-local interactions in QM due to quantum entanglement.
> What I say in my review is *not* that GR is a non-local theory,
> I say only that the gravitational energy-momentum and angular
> momentum, i.e. the gravitational analogs of the classical conserved
> quantities and observables are non-local. Non-local in the sense that
> they should be associated to *extended* domains rather than to
> points.

I believe these *extended* domains are the crux of Einstein's GR.

> The field equations are still genuine partial differential equations.
> As far as I can see the non-locality in QM is a completely different
> business. The root of this is that the basic object, the wave
> function, by means of which the elementary states are described is
> already an "extended" mathematical objects. This comes from the
> different nature of the notion of the states and the dynamics of the
> two theories.
> I hope this helps, at least to find some useful references.

It does help; thank you.

Best regards,

Dimi Chakalov
35 Sutherland St
London SW1V 4JU


Note: I was asked by a colleague to explain the idea of 'virtual geodesic path' (VGP) formulation of Einstein's GR. In the notes above, I tried to explain what I mean by 'virtual' in QM and GR: a unified approach to non-local interactions, which might (hopefully) provide a framework for canonical quantum gravity. Very briefly, I denote with 'virtual' both the Wheeler cloud and all non-tensorial variables in GR. This is something like a song being played with two very different instruments, as you can see by comparing the mathematical presentation of the virtual "stuff" in QM and GR. Surely this is "one song" played by Mother Nature, but it seems to me that a direct comparison of the non-local virtual stuff in QM and GR is not possible: the math is totally different, and we need new ideas about some 'common denominator'.

But before jumping into the putative global mode of spacetime, let's see if we can get the job done without it. This was the reason for writing to Charles Tresser and László Szabados and their colleagues. So far only  László Szabados replied.

D. Chakalov
February 11, 2005
Last update: February 24, 2005


I received today a complaint that my interpretation of 'virtual stuff' in QM has not been made clear and decisive. Let me address this complaint here, ensuing from the interpretation of the "collapse" by J. von Neumann. Then I will try to explain my speculation about how this same virtual stuff shows up in GR, in the form of some 'dark stuff', following the metaphor 'one song being played with two entirely different instruments'.

Again, consider the issue of relativistic "collapse", after I. Bloch. The reason why we cannot, even in principle, work out a theory of Lorentz invariant non-locality has been outlined here. Recall that after the so-called collapse or Process I (von Neumann), the pure state density matrix transforms "instantaneously" into a mixture, but for a given quantum system only one component of the mixture is available to ponder on. Also, the wave function of the initial quantum system can be made to cover the whole "asymptotically flat" (I love this phrase) 3-D space, i.e., its support can be unbounded.

Let's suppose, just for the sake of the argument, that the global mode of spacetime does not exist, and try to find out the link between the Hilbert space and Minkowski spacetime without it. In other words, let's drop the postulate of 'global mode of spacetime', and assume that a relativistic collapse was possible to occur in Nature. This means that you could, at least in principle, equate/map the "time parameter" in Schrödinger equation (Process II, von Neumann) to the time parameter in STR, and because the latter is T-invariant, you would be able to trace back the initial state of the quantum system before the collapse. That is, after you perform the measurement, you will be able to trace the history of the quantum system back to its state "immediately prior" the collapse, and then nothing could possibly stop you to trace the entire "history" of the quantum system back to the last instant from its lifetime, as we know from quantum cosmology.

Hence you could discover some time operators in QM, as well as the absolute reference frame in which the collapse "occurs" and its absolute cosmological time. You will also wipe out the Kochen-Specker theorem, because your quantum system would have fixed state which is independent from the measurement context: your quantum system will behave just like a classical system, say, the Sun.

Last but not least, you will establish a direct link between the time parameter read by an inanimate physical clock and the intrinsic "time" of the interference pattern of the-cat-is-alive-and-dead-at-the-same-time in Wigner distribution presentation, hence mapping the negative probabilities of the global mode of spacetime with the observable physical world ascribed to positive probabilities (cf. Dietrich Leibfried, Tilman Pfau, and Christopher Monroe, Shadows and mirrors: Reconstructing quantum states of atom motion, Physics Today 51(4), 22-28 (1998); 2.7MB pdf file from here).

Surely this is impossible, which leaves us with a number of puzzles and painful questions. Shall we say, after Niels Bohr and Asher Peres, that there is no quantum world and "quantum states are not physical objects: they exist only in our imagination"? That nuclear bombs are product of our imagination? Of course not.

But then you say -- look, I can make a relativistic QM from Process II, by replacing the Schrödinger equation with the Dirac equation. But of course you can, Harry. You can even develop a whole standard model of elementary particles, only you won't get any closer to solving the mystery of the quantum world, as known since 1935, after Schrödinger's "Die gegenwärtige Situation in der Quantenmechanik".

The whole issue is about the nature of quantum reality. It's a virtual reality. There is no other way to bridge the gap between the Hilbert space (there is no Hilbert space-time) and Minkowski spacetime. Which brings us to the nature of time, again.

The same line of reasoning applies to the so-called dark matter and dark energy. They too are 'virtual stuff', as I tried to explain here and here. But then you say -- hold on, GR is a classical theory, there is no room for any virtual stuff in it. Yes there is, only it is being 'played with a completely different instrument': the principle of general covariance. Recall the lesson from the hole argument, and read P. Bergmann [Ref. 3] and R. Geroch on 'diffeomorphism freedom' here. It may be quite difficult, if not painful, to consider the possibility that diff-invariant "observables" are being selected from a virtual stuff that lives 'outside spacetime', but the other option is to search for 96 per cent of the universe that remains in some "dark" state. Alternatively, it may not be "dark matter" and "dark energy" but a virtual reality.

In summary: If you honestly believe that GR does not need a crucial update, then you of course are entitled to interpret the "dark" stuff as matter and energy. Fine. But then you'll have to accommodate this whole dark stuff in the current GR -- your way. Just recall the cosmological constant problems, and quit. It's hopeless, because with the current GR and QFT you will have to chose between mutually exclusive solutions, while Mother Nature has managed to employ all of them, by answering your questions with Jain.

Not sure? Okay, wait for the paper by Hooft 't G., entitled: "201 wrong theories for the cosmological constant" (in preparation). Prof. Gerard 't Hooft kindly wrote to me "you are wellcome to provide for the 201st reference in my paper", and I immediately sent him the link to my web site.

Should you have further questions on the virtual reality in QM and GR, please consider requesting the opinion of Prof. Gerard 't Hooft as well. He is a Nobel Prize laureate, while I'm just a psychologist. He has written a textbook in GR which looks totally clear and decisive, while I stick to the opinion of Einstein, in his last lecture of April 14, 1954 (reference here):

"The representation of matter by a tensor was only a fill-in to make it possible to do something temporarily, a wooden nose in a snowman."

D. Chakalov
February 12, 2005
Last update: March 2, 2005


Subject: Re: On Einstein and realism
Date: Sun, 13 Feb 2005 00:00:27 +0200
From: Dimi Chakalov <>
To: Ezra Newman <>
CC: Chris Isham <>

Dear Professor Newman,

I have *great* faith in your H-space [Proc. R. Soc. A363 (1978) 445],

Perhaps R. Penrose couldn't make use of it because was guided by wrong ideas. If you wish to explore the ideas at the link above, please write
me back.

Best regards,

Dimi Chakalov

Explanatory Note: There is no rational reason why I believe in Ted Newman's H-space (E.T. Newman et al. (1978), The metric and curvature properties of H-space, Proc. R. Soc. A363, 445). I have just a hunch that he has discovered the correct presentation of the "fine structure" of what we call "point". Let me try to explain.

If we introduce a timeless global mode of spacetime, which we "insert" between two "neighboring" points from the local mode of spacetime (read the hypothesis here), then it seems to me that the fine structure of the "points" in the local mode will display two virtual worlds with inverted spacetime basis. These two virtual worlds look like material and tachyonic, and are "separated" by a luxonic timeless entity, the remnant from the global mode of spacetime.

Think of this remnant as a water lily which is almost completely open. This is a vivid image of a "point" from the global mode of spacetime, presented -- or shall I say "collapsed"? -- to some 'asymptotically flat spacetime' of the local mode of spacetime. The leaves of the lily display Ted Newman's H-space. They facilitate the timeless negotiation of the "point" with 'everything else in the universe', in line with the rule 'thing globally, act locally'. Recall the postulate that in the global mode of spacetime the whole universe is in a special ONE state called Holon.

Now, close the leaves of the lily, and they will form an arrow toward the next 'end point' along the putative universal time arrow. Hence you can think of the universal time arrow as a chain of states of the lily: open (asymptotically flat local mode of spacetime), then closed (the transition in the gaps in the global mode of spacetime), then open, closed, etc., ad infinitum. Every time you see the water lily open, you have one state (or jacket) that has already been negotiated with 'the rest of the universe', according to the principle of relational reality, while the rest of potential (cat) states are temporary "eliminated" with negative probabilities and remain in the global mode of spacetime, patiently waiting to take part in the negotiation of the next step.

The negotiation of the state of a given quantum system with 'the rest of the universe' is the mechanism of the 'chooser' in the quantum realm, and its final stage (open lily) is fully deterministic, because the Holon is ONE entity, and hence can explicate only one state. It just doesn't play dice, because all sub-systems in the universe can have only one negotiated state in the local mode of spacetime, which complies with 'everything else', in line with the rules of 'relational reality'. It is quite a different matter that we cannot know the states of all sub-system in the universe, and hence our description of this negotiation process in the global mode of time will be inevitably incomplete, hence will display some "probabilistic touch" in computing the relational state of a given quantum system valid for a given instant from the universal time arrow. I believe Einstein would have been be happy with this purely epistemological uncertainty.

Now you will probably say -- but where's the math? Sorry, there is still no math here, because we don't know how to model the relational reality in GR. But if you are psychologist, take a look at Ted Newman's H-space in

E.A. Rauscher and R. Targ (2001), The Speed of Thought, J. Sci. Exploration, 15(3), 331.

Also, if you are familiar with Chi, perhaps you may wish to see some nice clips by Miroslaw Magola. If you don't know what is Chi and say 'I don't believe in that crap', recall another modification of the inertial mass here.

To sum up, if you insist on math, you have a choice. Try Ted Newman's H-space or wait for the paper by G. 't Hooft "201 wrong theories for the cosmological constant" mentioned above.

Needless to say, my hunch about Ted Newman's H-space could be wrong. But if we don't leave for India, how can we discover America?

D. Chakalov
Monday, February 14, 2005