| Date: Wed, 22 Mar 2006 16:26:31
+0200
From: Dimi Chakalov <dimi@chakalov.net> 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
p. 2: "The motion of the first physical
body is then mathematically
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Date: Wed, 4 Jan 2006 08:53:34 +0200
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."
"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. More at
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.
"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 http://www.God-does-not-play-dice.net/Kiefer.html#Chris_1 It seems to me that we need a new concept of 'reality' to address the first off task above. Please see http://www.God-does-not-play-dice.net/Rosinger.html http://www.God-does-not-play-dice.net/Stachel.html#point 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, http://www.God-does-not-play-dice.net/Kiefer.html#Chris_3 Again, please correct me if I'm wrong. Best regards, Dimi
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
General comments on what could be "significantly different" at http://www.God-does-not-play-dice.net/Smolin.html
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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 http://members.aon.at/chakalov/Wagh.html I cannot provide any math, however. Perhaps you may wish to see Mark Stuckey's "Static for Dynamism: Reductive Pregeometry and Unification", http://members.aon.at/chakalov/Booth.html#PS 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), http://members.aon.at/chakalov/Nature.html#PHI
[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 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. That's what the human brain does, http://members.aon.at/chakalov/Beauregard.html#note
[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, http://members.aon.at/chakalov/Beauregard.html#note
[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, http://members.aon.at/chakalov/Pestov.html#continuum 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, http://members.aon.at/chakalov/Vecchi.html http://members.aon.at/chakalov/McGuire.html#note 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, http://God-does-not-play-dice.net My tentative contribution has been briefly mentioned at http://members.aon.at/chakalov/Seevinck.html#note The key ideas are explained at http://members.aon.at/chakalov/Carlip.html#GR Best regards, Dimi
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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
[snip] > To continue with the above discussion: the crucial point
is that
I understand your idea, thank you. > > The only thing we cannot agree upon is the nature
of continuum.
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, http://members.aon.at/chakalov/Pestov.html#continuum 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 http://members.aon.at/chakalov/Kiefer.html See also the problems with understanding QM formalism, generated by the notion of time from classical mechanics, http://members.aon.at/chakalov/Seevinck.html 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
[snip] > > [D.C., 23 Feb 2004, current]: This is the problem
of having two
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 http://members.aon.at/chakalov/Kuchar.html#1 > > [S.W., 23 Feb 2004]: The formalism of gr-qc/0402003
has the
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, http://members.aon.at/chakalov/faq.html#centipede 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
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 http://xxx.lanl.gov/abs/gr-qc/9711075 http://members.aon.at/chakalov/Matone.html#10 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 http://members.aon.at/chakalov/faq.html#QM 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
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, http://members.aon.at/chakalov/Carlip.html#GR 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
Is so, it seems to me that the task of choosing 'one possibility out of infinity' would be a blatant miracle, http://members.aon.at/chakalov/Linde.html#note 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, http://members.aon.at/chakalov/Kiefer.html > The approach that I have taken in gr-qc/0402003 is based
on the
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 http://members.aon.at/chakalov/Pestov.html#continuum The story of the "third" point goes back to Lucretius, some 2060 years ago. > Historically, we chose to consider a point-particle
in General
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",
"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.
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, http://members.aon.at/chakalov/Schwarz.html I believe this was Einstein's dream. > This is, remarkably, very similar to the case of Maxwellian
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), http://members.aon.at/chakalov/Nature.html#PHI 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." http://members.aon.at/chakalov/Matone.html#9 Just like the human brain, http://members.aon.at/chakalov/Beauregard.html#note > But, we do not have the laws of motion of curvature
singularities,
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
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
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,
... which is why we need new ideas about the nature of continuum. > The need for Quantum Gravity does not
I wish you best of luck with your work. Regards, Dimi
====== Subject: Re: The principle of spatial scale-invariance
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, http://members.aon.at/chakalov/Stachel.html#PS http://members.aon.at/chakalov/Shimony.html > I downloaded some of the references that you mentioned.
I didn't suggest "two times" but two *modes* of (one) time, http://members.aon.at/chakalov/dimi.html > Are there any specific observational consequences of
such a
The postulate about two modes of time, global and local, is supposed to suggest a new kind of quantum spacetime, http://members.aon.at/chakalov/PHI.html#dark_room 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, http://members.aon.at/chakalov/Fearns.html http://members.aon.at/chakalov/Zafiris.html#GPP That's tough, isn't it? Are you tempted to try p-adic numbers for modeling the infinitesimal http://members.aon.at/chakalov/Khrennikov.html ? 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
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