Date: Wed, 22 Mar 2006 16:26:31 +0200 From: Dimi Chakalov To:  cirinag_ngp@sancharnet.in Subject: Re: Are we all afraid of the Truth? Dear Sanjay, Thank you for your reply. > Looked at the link provided by you. Interesting stuff! I sent you the link because you wrote that will "not enter into further details about Time" (physics/0603149 v1, p. 2). I will appreciate your comments on my interpretation of the cosmological fluid and the proposal for 'necessary and sufficient conditions for dynamics' in GR. As to your observation that "Einstein’s field equations are based on logically unacceptable substitution of only the force of gravity by the curvature of the spacetime geometry", let me move one step deeper: we don't know the very mechanism of creating 'inertia'. My speculations are along the lines of a modified Machian theory, in which the notion of 'singularity' is completely removed from the outset by the new dynamics of gravity. Thus, I am very much interested in your professional opinion on the first issue mentioned above.  > Did u get any response from the involved parties? Yes, I got a dark and sombre silence. Hope you'll make a difference, since you are not afraid of the Truth. Best regards, Dimi --  Sanjay M. Wagh, Beyond Einstein ... Are we all afraid of the Truth?  physics/0603149 v1. http://arxiv.org/abs/physics/0603149 p. 2: "The motion of the first physical body is then mathematically  expressible as a rate of change of this number, distance, with respect  to Time. [Time here is a concept related to the "location" of the "hand"  of a clock body relative to the reference physical body. Here, we will not enter into further details about Time, not that these are unimportant.] ... p. 17: "Maxwell’s theory of the electric field remained a torso, because  it was unable to set up laws for the behavior of electric density,  without which there can, of course, be no such thing as an  electromagnetic field. Analogously the general theory of relativity  furnished then a field theory of gravitation, but no theory of the  field-creating masses. ... p. 18: "As Einstein’s field equations are based on logically  unacceptable substitution of only the force of gravity by the curvature  of the spacetime geometry, their solutions cannot form any logically or  scientifically acceptable explanations of observable phenomena. (...)  Einstein had very clearly recognized that a field theory must not  contain any singularities as particles." =============   Date: Wed, 4 Jan 2006 08:53:34 +0200 From: Dimi Chakalov To: Sanjay Subject: First things first Cc: "Isham, Christopher J" Dear Sanjay, Thank you very much for your clarification notes and precise reply. It is, and has always been, a great pleasure to read your papers and study your fundamental ideas. Let me try to explain my impression from your ideas. Please correct me if I got them wrong. You wrote: "The Laws of Physics are then mathematical statements about mathematical structures representing "observable'' or "physical'' bodies. Here, we must, first, assume appropriate mathematical structures to represent physical bodies and, second, make mathematical statements (equations) involving their transformations, which then correspond to, and, hence, *conceptually explain*, observable phenomena." [snip] "As no distinction exists between a reference system and a physical body, these mathematical structure(s) must then "represent" the reference systems. Hence, physical phenomena (changes in physical bodies) become 'changes' to reference systems themselves." First things first. It seems to me that the first phenomenon that needs a conceptual explanation is the following: 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. Many people ignore this crucial challenge of explaining the world of tables and chairs around us, and the result is disastrous. See, for example, Ashtekar & Bojowald [Ref. 1]. Further, you wrote: "This is *analogous* to the case of a category. A category is usually defined in terms of two separate classes, the class of its "objects'' and the class of its "arrows''. However, a category is definable \cite{Law-66, Mac71, banaschewski, macmor} in terms of only the class of its arrows, in an equivalent, object-free, manner. [snip] "Unfortunately, in the setting of a general category, there is no notion of "measures'' that is currently available." I am not confident about topos theory and "transformations or arrows of a category". Please see the latest paper by Chris Isham at It seems to me that we need a new concept of 'reality' to address the first off task above. Please see Finally, you wrote: "... there is no mathematical notion of "measures'' in a general categorical framework that I know about." I believe Chris Isham is the right person to elaborate on this issue. I've been only trying to follow his research program in canonical quantum gravity: "you cannot avoid accepting reality if you are honest", says Einstein, Again, please correct me if I'm wrong. Best regards, Dimi -- [Ref. 1] Abhay Ashtekar and Martin Bojowald, Quantum geometry and the Schwarzschild singularity, gr-qc/0509075 v1, http://arxiv.org/abs/gr-qc/0509075 Class. Quantum Grav. 23 (2006) 391-411, p. 409: "It suggests that the classical singularity does not represent a final frontier; the *physical* spacetime does not end there. (...) If this is borne out by detailed numerical calculations, one would conclude that quantum geometry in the Planck regime serves as a bridge between two large classical regions. Spacetime may be much larger than general relativity has had us believe. (...) Finally, since we restricted ourselves to a spacelike classical singularity, qualitative features of this singularity resolution can be valid only for a spherical collapse of uncharged fields. As explained in section 1, in more general situations the generic classical singularity is likely to be null, representing a Cauchy horizon. Therefore, although one might hope that quantum geometry effects would again extend spacetime beyond this Cauchy horizon, the detailed analysis will be significantly different." General comments on what could be "significantly different" at =========== Subject: Re: gr-qc/0402003 v1 Date: Mon, 23 Feb 2004 16:00:49 +0200 From: Dimi Chakalov To: Sanjay Wagh CC: Mark Stuckey   Dear Sanjay, Thank you for your reply of Mon, 23 Feb 2004 07:54:33 +0530. Just a brief comment/suggestion on the crux of the matter: the field-particle dualism for General Relativity. It is inconsistent with the intention of General Relativity, as explained in your fundamental article "Some fundamental issues in General Relativity and their resolution", CIRI/04-smw01 and gr-qc/0402003 v1 (February 2, 2004). In your words, the problem is that there are no mathematical laws for the singularities of the geometries. We cannot obtain the laws of motion for source particles from only the Einstein field laws since the particles are singularities of the geometry. We have the non-linear laws for the field but what are the laws for the motion, for interactions, of the *source particles* in General Relativity? Your suggestion: if we consider *only the continuum* of the space $\mathbb{B}$ (of gr-qc/0402003), then this problem disappears. Specifically, the Borel automorphisms of $(\mathbb{B}, \mathcal{B})$ can provide us precisely these laws of motion for P-sets and objects. We then have the laws for the field and also for the sources, simultaneously. Of course, self-interactions incorporated in the formalism. Hence we have to address the main issue: the nature of continuum. Once we understand it, we can chose the appropriate language, be it Borel sets or something else. The key point in your proposal -- please correct me if I got it wrong -- is having the laws for the field and also for the sources *simultaneously*. I cannot see how you could solve this task. It seems to me that the only physical system that can (i) handle two "talks" *simultaneously* and (ii) act on itself is the human brain. Please see I cannot provide any math, however. Perhaps you may wish to see Mark Stuckey's "Static for Dynamism: Reductive Pregeometry and Unification", He too is an expert in Borel sets. The only thing we cannot agree upon is the nature of continuum. I'll mark your comments with [S.W.] and mine with [D.C.], followed by the date. Hence your email of today, Mon, 23 Feb 2004 07:54:33 +0530, will be marked as [S.W., 23 Feb 2004], and my reply of today will be marked with [D.C., 23 Feb 2004, current]. Our previous email will be denoted with [S.W., 21 Feb 2004] and [D.C., 21 Feb 2004].   [S.W., 21 Feb 2004]: The approach that I have taken in gr-qc/0402003 is based on the realization that the concept of a point-particle is inconsistent with the basic intention of General Relativity, here meaning Einstein's intention, that of providing a continuum description of physical bodies and physical phenomena. [S.W., 23 Feb 2004]: The problem is that the non-linear laws are only for the field but not the particle (spacetime singularity). There are then no laws of motion, of interactions of particles in General Relativity. I don't know how one deals with only the field laws. As I mentioned above, I do not know how to handle only the field laws. If we have only the laws for the field but not for its source particles, then we have to separately, meaning independently, specify the laws of motion, of interactions, of particles. Without these laws, we have no description and, hence, understanding of dynamics in the physical world. This is what happens with the Maxwellian electrodynamics. It has the Maxwell laws for the electromagnetic field but no laws for the motion or interactions of its source particles, charges. Therefore, we have the independent laws, Newton's laws of motion, for the source particles. Of course, we then need the notion of "force" acting on the particle and must be able to specify this force through an independent statement as is the Lorentz force law. My above point refers precisely to this situation in General Relativity. Importantly, we cannot obtain the laws of motion for source particles from only the Einstein field laws since the particles are singularities of the geometry. We have the non-linear laws for the field but what are the laws for the motion, for interactions, of the source particles in General Relativity? The problem now is that a particle here is a curvature singularity. Then, unless we can think of mathematical laws for the curvature singularities of geometries, we cannot have any laws for the particles here. I were referring to the fact that there are no such mathematical laws for the singularities of the geometries. That is why the field-particle dualism in General Relativity does not have much meaning. I also wish to point out here that, once we consider only the continuum of the space $\mathbb{B}$ (of gr-qc/0402003), this problem disappears. The Borel automorphisms of $(\mathbb{B}, \mathcal{B})$ provide us precisely these laws of motion for P-sets and objects. We then have the laws for the field and also for the sources, simultaneously. Of course, self-interactions incorporated in the formalism. Here, we need precise mathematical description of the processes in a satisfactory physical way. Einstein showed that there are velocity distributions for which particles do not converge to a singularity and, furthermore that, there is no horizon. This is understandable. But, Hawking-Penrose theorems prove things otherway for a generic situation. But, all this used the field-particle dualism for General Relativity. For the reasons that we have been considering, I don't think that theseare any real issues for physical situations of the world.   [D.C., 21 Feb 2004]: We cannot insert two messages into one dimensionless point/event: one message coming from matter (matter tells space how to curve), and another message coming from geometry (space tells matter how to move), [D.C., 23 Feb 2004, current]: This is the problem of having two "talks" *simultaneously* and acting on itself, as mentioned above. You have to "hold on something" in order to "act on yourself". In canonical quantum gravity, I think this problem is insurmountable. See the Hilbert space problem and the Barber Paradox at Math aside, the problem can be explained by recalling a story by Baron Münhausen: you too will have to 'lift' yourself up by pulling up your hair. That's what the human brain does, [D.C., 21 Feb 2004]: The resulting picture is *self-interacting*. As stressed by T. Padmanabhan, the gravitational field is "not only nonlinear in its own coupling, but also makes *all matter fields* self-interacting."   [S.W., 23 Feb 2004]: The formalism of gr-qc/0402003 has the above ingredients. P-sets have measures and these are the source attributes, self-interactions incorporated. Interactions of P-sets and objects may change these attributes. Borel automorphisms, causing these interactions, are non-linear, forming a group with usual composition. Everything there is then highly non-linear and has self-interactions incorporated.   [D.C., 21 Feb 2004]: Just like the human brain, [D.C., 21 Feb 2004]: I'd only say that pseudo-tensors must go away. If so, we perhaps need new math and a new formulation of the energy-momentum tensor.   [S.W., 23 Feb 2004]: Yes, we do require some new mathematics, even for gr-qc/0402003. I am not completely satisfied with the standard ergodic theory used there. It doesn't provide us the platform to directly discuss particles, in the physical sense. The averaging over P-sets (of gr-qc/0402003)  can lead to an averaged conception of some energy-momentum tensor. But, that also does not satisfy me completely. Unfortunately, I am unable to pinpoint that which is what is unsatisfactory here.   [D.C., 23 Feb 2004, current]: Perhaps the nature of continuum can be elucidated by solving the self-referential paradox of the so-called third point, Perhaps we need a new reference object to 'hold onto' -- the whole universe in its Holon state. This state is UNspeakable, but you can easily comprehend it with your brain, Once we understand the nature of continuum, we would be able to search for its appropriate mathematical description. I believe Mark Stuckey can say much more, from his perspective. I invite you and Mark to participate in the creation of a web site dedicated to Albert Einstein's 125th birthday, My tentative contribution has been briefly mentioned at The key ideas are explained at Best regards, Dimi   ======= Subject: Re: gr-qc/0402003 v1 Date: Tue, 24 Feb 2004 15:25:29 +0200 From: Dimi Chakalov To: "Sanjay M. Wagh, Central India Research Institute"      Dear Sanjay, Thank you for your reply of Tue, 24 Feb 2004 16:15:25 +0530. > Therefore, when the field changes, its source attributes (permit me > to call the measures averaged on a P-set by this name) also change. > That is, when a P-set changes its measures also change. Note also > that a P-set is never a singleton set of $\mathbb{B}$. > Therefore, a point-particle is not endowed here with two'' tasks > that you mention. That is: We cannot insert two messages into > one dimensionless point/event: one message coming from matter > (matter tells  space how to curve), and another message coming > from geometry (space tells matter how to move), '' There is no > point-particle here. [snip] > To continue with the above discussion: the crucial point is that > the field and its source are the SAME. We cannot separate them in > any manner whatsoever. Therefore, the issue of two talks'' is > resolved in the manner of this indistinguisability'' of the field and > its source. This is a result of the abandonment of the field-particle > dualism. I understand your idea, thank you. > > The only thing we cannot agree upon is the nature of continuum. > > I am unable to understand the nature of the continuum'' that > you are talking about''. As for me, I am restricting to the space > $\mathbb{B}$, its topology, its measures etc. as a Standard Borel > Space. It's about the nature of infinitesimals that we call "points". I don't know what kind of problems you encountered in reading the explanation of the *self-referential paradox*. The link is, again, I'm not aware of any successful solution to it, Robertson's Non-Standard Analysis (NSA) included. NB: The puzzle stems from the *dynamical* nature of the infinitesimal. We cannot FOLLOW the infinitesimal down the road to the INSTANT in which it will (or would it, really?) become a "point". The notion of time from classical mechanics -- and Einstein's GR is a classical theory -- breaks down BEFORE that crucial transformation from 'something finite but terribly small' to 'genuine point'. WHEN does this miracle happen? Please see again the story about Arhimedes at See also the problems with understanding QM formalism, generated by the notion of time from classical mechanics, If we use this kind of time only, the miraculous transformation above is irreversible. We cannot resurrect a *finite* thing made of NOTHING, that is, made of mathematical "points". Any time we do diff calculus, we invoke a miracle. As I said before, I don't like miracles, even if they work FAPP. You said above that you've been restricting to the space $\mathbb{B}$, its topology, its measures etc. as a Standard Borel Space, and that you're unable to understand my efforts to explain the nature of the continuum. I should be solely blamed for this. Obviously, my explanation was not comprehensible at all. > > [D.C., 21 Feb 2004]: We cannot insert two messages into one > > dimensionless point/event: one message coming from matter > > (matter tells space how to curve), and another message coming > > from geometry (space tells matter how to move), > > True this, for a point-particle acting as a source of the field it > generates. A particle is a curvature singularity of the geometry and > no formalism can tell this point particle how to move. That is what > is the problem with the field-particle dualism in General Relativity. > What you say above supports the abandonment of the field-particle > dualism. [snip] > > [D.C., 23 Feb 2004, current]: This is the problem of having two > > "talks" *simultaneously* and acting on itself, as mentioned > > above. You have to "hold on something" in order to "act on > > yourself". > > Surely, this is correct when we have the field-particle dualism and > when a particle is a point-particle. What you say above is also an > indication that the field-particle dualism needs to be abandoned. > Then a field and its source are identical. > > I may further add the following. A P-set is never a singleton subset > of the space $\mathbb{B}$. So, this problem doesn't arise for it. > Think of a P-set as a continuum with certain properties such as it > being a Borel set. > We have measures definable on it and we call'' the averages of > these measures as the source-properties of the associated Dirac > $\delta$-particle. > This picture of a particle is surely a fictitious one' - arising because > of our associating a Dirac $\delta$-distribution with the measure > averaged' over a P-set. What you refer to as the problem of a > double talk'' applies to this picture of a Dirac $\delta$ particle only. > > > In canonical quantum gravity, I think this problem is > > insurmountable. See the Hilbert space problem and the Barber > > Paradox at > > http://members.aon.at/chakalov/Kuchar.html > > > > Math aside, the problem can be explained by recalling a story by > > Baron Münhausen: you too will have to 'lift' yourself up by > > pulling up your hair. > > Perhaps, I understand this one. The catch here appears to be that > you move (lift yourself up) in relation to other things. Whether one > does so by pulling one's own hairs or in some other way appears > irrelevant. > Perhaps, I may not have understood you correctly here. Have I? What I mean is a famous saying from Lao-tzu: If you realize that all things change, there is nothing you will try to hold onto. The puzzle is not, and cannot, be resolved "relationally". It boils down to the Unmoved Mover, the Aristotelian Prima Cause. See Karel Kuchar at > > [S.W., 23 Feb 2004]: The formalism of gr-qc/0402003 has the > > above ingredients. P-sets have measures and these are the source > > attributes, self-interactions incorporated. Interactions of P-sets > > and objects may change these attributes. Borel automorphisms, > > causing these interactions, are non-linear, forming a group with > > usual composition. > > Everything there is then highly non-linear and has > > self-interactions incorporated. > > I hope that the issue of self-interaction'' is then cleared. To stress > it again: field (continuum)  and source attributes (measures) are > indistinguishable'' in the sense that changes in the one are > interlinked to those of the other one and we cannot separate them > in the formalism of gr-qc/0402003. If some changes are interlinked to other changes in a way that does not, even in principle, allow us to talk about *two* or more separable things, then you're talking about the Holon, The potential state(s) of centipede's legs  _are/is_  an example of this unique phenomenon. > > I invite you and Mark to participate in the creation of a web site > > dedicated to Albert Einstein's 125th birthday, > > > > http://God-does-not-play-dice.net > > Thank you very much for your this kind offer. I will think of > something and would let you know. Anything specific that you > want me to add to this site? Please let me know so that I can think > over that matter. Thank you very much. I believe there is a puzzle which you might find interesting. Please see the alleged collapse of the energy-momentum tensor in D.V. Ahluwalia's The puzzle involves both QM (the measurement problem) and Einstein's GR. If the spacetime metric would "collapse" by QM observations, we wouldn't be alive, or would we? My efforts to solve the measurement problem can be read at Any macroscopic cat states of our neurons would be lethal. If you buy QM and measure a quantum system, the very first thing that will happen is that your brain and the quantum system will be entangled, and *nothing* would have any definite state whatsoever, 'the rest of the universe' included. Hence your brain will break down and could never recall that there is such thing as 'projection postulate', not to mention the Born rule. Best regards, Dimi =================   Subject: Re: gr-qc/0402003 v1 Date: Sat, 21 Feb 2004 12:35:28 +0200 From: Dimi Chakalov To: Sanjay Wagh Dear Sanjay, Thank you very much for your thoughtful reply of Sat, 21 Feb 2004 11:07:47 +0530. It seems to me that you didn't have the chance to look at the second URL from my preceding email of Sat, 21 Feb 2004 01:11:47 +0200, It boils down to the nature of continuum. Let me try to be specific. > To begin with, any Theory of Quantum Gravity appears to me to > be a theory that is primarily statistical in nature Is so, it seems to me that the task of choosing 'one possibility out of infinity' would be a blatant miracle, I personally don't like miracles, and I'm glad to tell you that even my 10-year old daughter was able to understand the issue, > The approach that I have taken in gr-qc/0402003 is based on the > realization that the concept of a point-particle is inconsistent > with the basic intention of General Relativity, here meaning > Einstein's intention, that of providing a continuum description > of physical bodies and physical phenomena. I fully agree. Please see the first link above, from my preceding email. Again, it is all about the nature of continuum. If you're short of time, the proposal for solving the puzzle of continuum is at The story of the "third" point goes back to Lucretius, some 2060 years ago. > Historically, we chose to consider a point-particle in General > Relativity and to associate with it a spacetime geometry, the > Schwarzschild geometry. > A point-particle is a curvature singularity of this spacetime and is > not a part of the smooth spacetime. Then, a point-particle is not a > part of the Theory of the Field that refers to the external > gravitational field of a point-particle. The external field obeys > Einstein's field equations of General Relativity but a curvature > singularity, a point-particle, does not. Therefore, there are no Laws > of Motion, of Interactions, of point-particles in this approach to > General Relativity since this approach cannot provide us the laws > for any spacetime singularities. I believe the issue of spacetime singularities is elucidated in the latest article by Prof. Angelo Loinger, The Black Holes do not exist - "Also Sprach Karl Schwarzschild", http://xxx.lanl.gov/abs/physics/0402088 "The fictive notion of BH was generated by erroneous reflections on the "globe"  r = 2m  of the standard HDW-form. It would not have come forth if the treatises of GR had expounded the Schwarzschild form of solution in lieu of the standard form. ... "Continued gravitational collapse: it is almost evident that if we bear in mind, e.g., Schwarzschild’s and Broillouin's forms, no continued collapse can generate a BH -- and this was just Einstein's opinion [11]." If we adopt the solution to the paradox of continuum, no continued collapse can generate a black hole -- and this was just Einstein's opinion. No continued "collapse" of the universe along the deflation time could reach The Beginning either, I believe this was Einstein's dream. > This is, remarkably, very similar to the case of Maxwellian > electromagnetism of Maxwell and Faraday. In this Maxwellian > (linear) theoretical framework, we consider an electric charge as a > field-producing property (in addition to the gravitational mass) of a > point-particle and this source attribute of a point-particle produces > the external electromagnetic field. The laws of field are Maxwell's > equations and these laws tell us nothing about the laws of motion > of a point-particle, a source particle of the field. The laws of the > source particle, Newton's laws of motion, are entirely independent > of Maxwell's laws. Clearly, the above situation with the standard > approach (based on the field-particle dualism) to GR is, in a > notional sense, similar to this, although Einstein's equations provide > us non-linear laws for the field in GR. I believe these non-linear laws are crucial for understanding the TIMING of the bi-directional "talk" between matter and geometry, after John Wheeler. We cannot insert two messages into one dimensionless point/event: one message coming from matter (matter tells space how to curve), and another message coming from geometry (space tells matter how to move), The resulting picture is *self-interacting*. As stressed by T. Padmanabhan, the gravitational field is "not only nonlinear in its own coupling, but also makes *all matter fields* self-interacting." Just like the human brain, > But, we do not have the laws of motion of curvature singularities, > point particles as yet in this field-particle dualism in GR. > > Ignoring this problem, we may now want to describe a physical > object (but, now, we must remember that there are no laws for its > motion in the approach based on the field-particle dualism in GR). > Then, any physical body will be a collection of spacetime > singularities, a collection of point-particles in this (standard) > approach (based on the field-particle dualism) to GR. But, if the > geometry has curvature singularities, we cannot replace the > collection of curvature singularities by any smoothsource density > function. Mathematically, it follows that what we areattempting > here is an impossibility since the source density must diverge > at the locations of point-particles (making up the physical body) in > order to give us a smooth Cartan's volume form (for the spacetime > with sources treated as a fluid). Thank you for pointing this very important mathematical consideration. I was not aware of it. > Moreover, if we admit spacetimes with naked singularities as well > as the Schwarzschild one, then there are two inequivalent > descriptions of a point-particle in the standard approach to GR - > one with a horizon and another without a horizon. Furthermore, > there are no clear indications as to when we use either of these two > inequivalent descriptions of a point-particle for a physical particle > This is clearly indicative of the inconsistency of this (field-particle > dualism) approach to GR. > > All the above reasons indicate that we need to abandon the > field-particle dualism in any approach to General Relativity. Then, > only smooth spacetime geometries need to be considered. Which of > these smooth spacetimes are to be considered  relevant to Physics > without the field-particle dualism? The answer to this question, > very naturally, requires us to give up thinkingin terms of > point-particles. Then, the concept that we need to give up to > begin with is that of the energy-momentum tensor. Well, I personally am not prepared for such drastic move, or at least not until we explore the brand new possibilities from the treatment of continuum. I'd only say that pseudo-tensors must go away. If so, we perhaps need new math and a new formulation of the energy-momentum tensor. > Clearly, this concept is based on that of point-particles. To obtain > the energy-momentum tensor, we consider a collection of > point-particles and average various physical quantities over this > collection. But, the spacetime singularities, as point-particles, do > not permit us any mathematically meaningful such averaging > procedure. > > In this connection, I wish to further point out that any > higher-dimensional theory will also face these above problems if > we continue to impose the field-particle dualism on it. > > We do not observe'' any extra dimensions than four, three for > the space and one for the time. That is why I restricted myself to > the four-dimensional situation in my investigations. Then, we must > analyze the (general relativistic) situation as it presents itself. That > is what I have done in gr-qc/0402003. > > The moment we recognize that the field-particle dualism is > inconsistent with the intention of General Relativity, that of > providing a continuum description of physical bodies, there is then > no need for Quantizing Gravity, Quantizing Geometries. If we confine ourselves to the current understanding of continuum, I believe it was proven by Prof. Angelo Loinger that the notion of 'quantum gravity' is an oxymoron, Angelo Loinger, "Quantum gravity": an oxymoron, http://arxiv.org/abs/physics/0308042 ... which is why we need new ideas about the nature of continuum. > The need for Quantum Gravity does not > present itself, as can be seen from gr-qc/0402003. On the > contrary, on the basis of the mathematical approach in > gr-qc/0402003, we can think of obtaining an approximate > statistical theory'' that bears a similar relation to the underlying > space ($\mathbb{B}$ of gr-qc/0402003) as thatborne by the > usual statistical mechanics to the classical newtonianmechanics. > A concrete such possibility does present itself. I wish you best of luck with your work. Regards, ====== Subject: Re: The principle of spatial scale-invariance Date: Thu, 21 Feb 2002 05:59:31 +0200 From: "Dimiter G. Chakalov" To: Sanjay Wagh CC: b.j.carr@qmw.ac.uk, robin.booth@ic.ac.uk, k.savvidou@ic.ac.uk,      tirth@iucaa.ernet.in, jayant@iucaa.ernet.in,      nabhan@iucaa.ernet.in, e.zafiris@ic.ac.uk, j.fearns@ic.ac.uk,      i.raptis@ic.ac.uk BCC: [snip] Dear Dr. Wagh, Thank you for your kind reply and for your modified paper, gr-qc/0202005, updated on February 4, 2002. You wrote: "Mach's principle states that the inertia of a particle of matter is the result of its interaction with all other particles in the universe. As a result of the additivity of inertial mass, there must be energy density of gravitational mass "everywhere" in a machian universe." I believe what you call "everywhere" is a special state of the whole universe, which does *not* exist in the local time mode, > I downloaded some of the references that you mentioned. > However, in spite of my sincere efforts to understand the need for > two times, I am sorry to say that I was unable to follow the > arguments leading to such a postulate. The existence of TWO > times must then follow for the newtonian theory too. I didn't suggest "two times" but two *modes* of (one) time, > Are there any specific observational consequences of such a > postulate that can be testable in the weak gravity situation? Not > being an expert in this area, I do not know the answer to this > question. Perhaps, you would be able to tell me more on this issue. The postulate about two modes of time, global and local, is supposed to suggest a new kind of quantum spacetime, There is no theory of quantum gravity so far, and subsequently no observational consequences. The task is to find the correct geometrical presentation of the infinitesimal, That's tough, isn't it? Are you tempted to try p-adic numbers for modeling the infinitesimal I will appreciate your ideas and insights, as well as the feedback from all colleagues of yours reading these lines. With kind regards, Dimiter G. Chakalov http://members.aon.at/chakalov http://members.aon.at/chakalov/dimi.html (last update 20.02.2002)