Subject: Relativity of simultaneity
Date: Fri, 7 Dec 2007 11:13:06 +0200
From: Dimi Chakalov <>
To: Vesko <>

Maraba Vesko,

May I take the stand of your students, and ask two questions regarding your latest arXiv:physics/0610046v2 [physics.gen-ph].

1. Consider two observers in relative motion: observer A is at rest at a buss stop, and observer B moves w.r.t. A with constant speed of, say, 60 km/h.

2. At some instant denoted with t_1 by the two observers, they take an instantaneous snapshot of the Sun, such that the time readings of the clocks in their digital cameras stamp their images with some provisional reading denoted with t_1 by the two observers.

3. At a later moment t_2 (after app. 8 min), observers A and B will see the actual state of the Sun, which was existing as 'objective reality out there' at *their* t_1.

Let's assign two three-dimensional cross-sections of the real four-dimensional world to the two observers, in relative motion, at t_2 .

Q1: Will the two observers see different states of the Sun at *their* t_2?

Q2: If observer B moves with constant acceleration w.r.t. A , will the two observers see different states of the Sun at *their* t_2?

Best regards,



Note: I believe my good old friend Vesko remembers our discussions some twenty-three years ago, about the ontological status of 'simultaneous events', after
A. Einstein, Annalen der Physik 17, 891 (1905):

"We have to take into account that all our judgments in which time plays a part are always judgments of simultaneous events. If for instance I say, 'that train arrived here at seven o'clock', I mean something like this: 'the pointing of the small hand of my watch to seven and the arrival of the train are simultaneous events'".

Likewise, the instant denoted with t_1 by the two observers (cf. (2) above) pertains to two 'simultaneous events' in an imaginary now-at-a-distance "reference frame". No need to synchronize the clocks of the two cameras; this is just a Gedankenexperiment based on two imaginary 'simultaneous events'. We may think of them as resembling the quantum correlations producing simultaneous event(s), but the remote analogy may only be valid to the extent to which one could loosely compare quantum entanglement with gravity: "the whole universe must know about everything instantaneously" (Mike Zucker).

The fact that we cannot experimentally verify such simultaneous events does not imply that they cannot exist. For example, we can't employ the preferred reference frames of CMBR, cosmological GWs, or the cosmic equator for physical measurements, yet we're confident that they 'exist'. Another example: the evenly-spread DDE might be acting on the whole 3-D space en bloc, yet such 'simultaneous events' cannot be recorded in any reference frame, because the perfectly smooth DDE is omnipresent: no "point" from 3-D space is affected differently by DDE by stretching the metric of space (many people are tempted to interpret the latter as equivalent to producing actual distances, as inferred from redshifted astrophysical "candles"), and all "points" are being acted upon by DDE as 'one event' that refers now to 'infinitely many simultaneous events'. Otherwise the good old DDE won't be "dark" but will become observable, which would ruin the whole theory of relativity, since we'd have physical access to its preferred reference frame. Also, the vicious DDE would wipe out the whole universe, because it will immediately, before we could blink, pour out from such "drill" in the 3-D space.

We can visualize the action of Dynamic Dark Energy (DDE -- see the "GW lake") only in some non-relativistic presentation. Not surprisingly, it is totally hidden in STR and GR (see below), and can be revealed (but not visualized) only in the proper relativistic theory.

Same with the 'flow of time' (Das „Fließen” der Zeit, cf. Rüdiger Vaas below): it pertains to the whole universe as ONE, hence can be visualized only in its initially wrong, non-relativistic presentation from Isaac Newton.


From: Rüdiger Vaas, Bild der Wissenschaft, Heft 01/2008

Recall the initial assumption that "spacetime can be represented by a 4-dimensional differentiable manifold" (Andrzej Trautman): can we dig out the action of DDE, and perhaps even some 'arrow of spacetime', by elucidating the question of how the 'connected Hausdorff manifold' end up with some differentiable structure? And by the way, what made the Hausdorff manifold connected in the first place? Just ponder on Hausdorff's axioms below.

The underlying puzzle from Lucretius -- how do we get a finite region of space, with its "borders", from uncountably infinite, infinitesimal "points" -- is not even acknowledged.

These are fundamental issues, yet they seem so "obvious" that many physicists mention them en passant, in footnotes (e.g., Robert Geroch and Chris Isham). Just ponder on Georg Cantor's definition of ‘set’ from 1895 (quoted after D. Giulini, arXiv:0802.4341v1, p. 11):

By a ‘set’ we understand any gathering-together M of determined well-distinguished objects m of our intuition or of our thinking (which are called the ‘elements’ of M) into a whole.

Can we unravel some pre-geometric plenum which can replace "our thinking"? We certainly shouldn't allow the human intuition or thinking to act as "gathering-together" binding agent at the most fundamental level of geometry -- 'the grin of the cat without the cat', after Alice.

If such pre-geometric plenum exists and has been tacitly introduced with the initial mathematical assumptions, we should not expect to recover it again, from the physical stuff we drop on the bare spacetime manifold. Stated in philosophical terms, mens agitat molem (Der Geist bewegt die Materie, Vergil, The Aeneid, Ch. 6, 727). Only instead of talking about 'mind' or 'spirit', we introduce a new structure of spacetime and operate with three forms of reality. In other words, we try to model the universe as a brain, and put aside the question of whether some sort of "mental reflection" (perhaps resembling the human mind and consciousness) may or may not emanate from 'the universe as a brain'.

Let's try to be specific regarding present-day GR.

NB: Consider two neighboring sections of spacetime, Hyperfläche 1 and Hyperfläche 2 (see the drawing above), corresponding to the elementary 'tick of time' ("an intrinsic time interval associated to any timelike displacement", T. Jacobson), presented with some shift from Hyperfläche 1 to Hyperfläche 2, such that the canonical data on the two (or are there "two"?) hypersurfaces are "separated" by  dt , projected from the absolute time of Isaac Newton (see also Plato below).

Now, I hope one day Robert Geroch will agree to write a book on the sentence above, as a sequel to his 1978 "General Relativity from A to B", with the provisional title "General Relativity from A to A + dt-and-ds", to explain the emergence of differentiable structure on the spacetime manifold, and the perfectly smooth embedding of "dark energy from empty space" into the perfectly smooth Cauchy surface (otherwise we wouldn't be able to use PDEs, ever).

From: Robert Geroch, Computation and Physics, 12.03.2008

Then perhaps Karel Kuchar would update his 1992 landmark article "Time and interpretations of quantum gravity", and the whole bundle of mysteries involved with the NB sentence above would become comprehensible, to the extent to which even I might be able to grasp it. As of today, I can't.

The only "comprehensible", but in fact highly misleading, representation of spacetime is from Isaac Newton: an absolute 4-D space, depicted with the whole white area in the picture above, complemented with an absolute time, such that its elementary "shift"  dt  happens between two (yes, now we have countable, differentiable, and successive entities) 3-D surfaces of 'absolute now', which belong to an 'universal time arrow' that has been driven by 'the dark energy of X' ever since the non-relativistic (or rather anti-relativistic) inflation stage.

Notice that X, as the substrate of "dark energy", cannot qualify as relativistic object (arguments from October 2005 here), so it is 'gut zu wissen' that in the framework of the theory of relativity X will inevitably look "dark" (cf. E. Linder). Moreover, any ad hoc postulated "scalar field" with custom made EOS won't fit the bill, as shown by T. Padmanabhan.

Going back to present-day GR, there are two interpretations of how the shift   dt  may "happen".

The first, and seemingly "scientific", interpretation would be based on a typical reductionistic, Marxist-Leninist approach to GR: the shift  dt  is determined only and exclusively only from/by the localized physical stuff on the 3-D hypersurace. There would be no quasi-local holistic "context" spanned "over" the adjacent hypersuraces, like Karel Kuchar's Perennials, and no possibility for the phenomenon of 'transience' either; more from George F R Ellis here.

Subsequently, the formulation of quantum gravity, based on Dirac-ADM hypothesis for "splitting the spacetime" (canonical quantum gravity), goes to a dead-end. Look at the x-dots below, and think of them as the coordinate-independent part of the metric known as the "3-geometry", at some "instant" from the linear time read by your wristwatch.

x  x  x  x

x  x  x  x

"As a consequence of general covariance, relativity becomes entirely constrained; the equations of motion are a list of expressions which must vanish" (Seth Major). That's the dead-end. If we get back to classical GR and think of these x-dots as matter fields self-coupled and self-interacting due to gravity, they will be totally frozen in the linear time (C. Rovelli): it is logically impossible for these x-dots to produce their "time", while at the same time evolve in that same time. If we stick to the linear time only, we can't recover the dynamics of background-free GR with some relational approach either.

In summary, if we stick to this Marxist-Leninist approach, we would dealing with just one frozen snapshot from a "film reel", with actual "duration"  dt  . Nothing can run the film, simply because there is nothing "outside" the film reel, nor can the latter act on itself (cf. Antonio Machado).

We need to introduce an additional degree of freedom to these x-dots, to attach well-defined quasi-local "gravitational" energy, both to every x-dot and to the whole domain of 3-D space occupied by these x-dots (the whole Cauchy surface en bloc), and then recover the true dynamics of GR.

Which brings us to the second option, inspired from brain dynamics: the self-interacting human brain is not "frozen", and the brain can act on itself, as we think about our brain, with our brain.

The second option is very subtle (cf. N. Dadhich): the present-day GR (recall Einstein's opinion here) is build only on the necessary condition for the shift above (i.e., the localizable physical stuff on the hypersurace), while the sufficient condition is not yet implemented: it is the so-called Aristotelian Connection which comes from 'the universe as ONE'. This global holistic component of the shift (the additional degree of freedom) requires that the physical stuff on the 3-D hypersurface must not be fixed as 'objective reality out there', which in turn tallies to the well-known interpretation that "the points occurring in the base sets of diffrerentiable manifolds with which general relativity models spacetime should not be reified as physically real" (Butterfield & Isham). Hence we always have the freedom to eliminate things that are not "physically real" or "non-tensorial", but only "over a point" (cf. Hermann Weyl). This is a genuine freedom reserved for the global holistic component of the shift, or else it simply wouldn't have access to the 3-D hypersurface, and we would be forced to accept the Marxist-Leninist approach to GR.

Besides, the "shift" from Hyperfläche 1 to Hyperfläche 2 got to be hidden in GR, or else it would expose the "dynamic dark energy" of 3-D space. Had this shift been "exposed" (say, by being well-defined with the reference fluid of GR), the
lapse function and shift vector in ADM hypothesis would not be 'gauge' but Diff(M)-invariant variables. They would have to be constants in all spacetime models in GR, which possess such 'elementary timelike displacement'. The latter would also be observable, and we would be baffled with the question, 'with respect to what' this elementary timelike displacement takes place. All this would be possible, if we could only pinpoint the reference fluid of GR, in present-day GR (e.g., by invoking some "dust fluid as a physical clock" with non-zero "energy" of the gravitational field, such that we could "fix a time-clock which turns out to be a quantum component of the whole system and so the notions of external and internal time converge", as in G. Montani, F. Cianfrani, arXiv:0802.0942v1 [gr-qc]). However, the reference fluid of GR cannot be exposed -- in any form -- in present-day GR, because it acts as the "backbone of spacetime", and may be revealed only in the full theory of quantum gravity.

All efforts to derive the reference fluid from present-day GR -- namely, after imposing the "splitting" of spacetime -- leads to an incomplete, to say the least, version of quantum gravity, the result from which being that we can't recover the classical limit of such version of quantum gravity -- it will inevitably produce "semiclassical approximation" of "decohered" brains, computers, and tables and chairs. We need a brand new reference object/fluid that is not present in the local mode of spacetime, hence can make the latter 'background-free'.

NB: It is not possible to bring out the dynamics of GR by splitting the spacetime into two "parts", and then "define" the dynamics of objects in one "part" of spacetime (that would be called 'time') with respect to the other "part" (called 'space'). We can do this only in STR, be referring to a fixed grid of background spacetime. In present-day GR, we have no referential background to 'hold onto', and "time" can change just as much as "space" can change, and since "space" can't change, "time" can't change either. If you wish to describe how objects would evolve "relationally" and 'within themselves', you will end up with a dead frozen "block universe" in which the instant 'now' would be an illusion. Then every door-to-door salesman and Information Gathering and Utilizing Systems (IGUSes) would be puzzled, how and where to fit the self-interacting faculty of gravity into such "relational" (John Baez) yet dead frozen world, and how to save the dynamics of GR from its self-inflicted dead end.

The so-called strong hyperbolicity (J. David Brown, arXiv:0803.0334v1 [gr-qc]) can't resolve the inherent mathematical problems of ADM "dynamics", to help reconcile GR with QM.

We must first dig out the backbone of spacetime (the reference fluid) "on" which the very spacetime has been build, in order to keep the classical limit of quantum gravity always at hand. If we lose the classical limit by blurring it with some "semiclassical approximation", we will end up with some totally unacceptable amount of poetry: see, for example, "the amount of time-asymmetry of the individual histories" in Fig. 13, p. 29, from IGUSes J. B. Hartle et al., arXiv:0803.1663v1 [hep-th].

Notice that the problem of classical limit of quantum gravity does not originate from Quantum Theory alone (which would be the case, had the present-day GR been correctly formulated): it is logically impossible for matter fields to produce their "time", while at the same time evolve in that same time, as in ADM hypothesis. Hence there is no possibility for the kind of 'dynamical evolution' presented with hyperbolic PDEs (more from Horst R. Beyer) -- they can't be rigorously defined within ADM hypothesis. This should be expected by all people who understand the phrase 'no simple localisation of energy' used by Tullio Levi-Civita in 1917 (if you examine a Frisbee, all its dynamical quantities will have well-defined instantaneous values at each point from its trajectory w.r.t. a background flat space, and you'll never encounter elliptic differential equations).

It is impossible to "recover" the genuine dynamics of GR by splitting the spacetime into two "parts", and then "evolve" one "part" into the other "part". In order to resolve the logical contradiction which freezes the ADM dynamics (cf. the paragraphs above), the proponents of ADM hypothesis would need some referential background of 'bare spacetime points' (bare finger nails) with respect to which the 'strong hyperbolicity' can be recovered. Thus, the inherent mathematical problems of ADM hypothesis (cf. J. David Brown) cannot be resolved within ADM hypothesis in principle: ADM hypothesis must be mathematically ill-defined (cf. J. David Brown), and should remain mathematically ill-defined, because it cannot and should not "recover" the very thing ('bare spacetime points') that has been expelled from it from the outset.

It is manifestly pointless to "cure" the hyperbolicity of PDEs in ADM hypothesis (J. David Brown), just as it would be pointless to "cure" Einstein filed equations by imposing "second time derivatives" only (see below), or make the metric of Kerr spacetime "geodesically complete". There are many things in present-day GR that are mathematically ill-defined, or "non tensorial" (cf. Hermann Weyl), or lead inevitably to pathological behavior of matter fields which, just like the ultraviolet catastrophe, has never happened (e.g., time-like naked singularities, CTCs, and geodesic incompleteness; see Alan Rendall below), because with the current mathematical apparatus all these "disasters" cannot be cured in principle.

All these "disasters" are rooted on the Marxist-Leninist presumption (see above) that matter fields can fully determine their spacetime, despite the fact that in Einstein GR the spacetime points are not 'physically real' (Butterfield & Isham), and the only entity that can fully determine their spacetime -- the unmoved reference fluid -- is expelled from present-day GR from the outset.

The good news is that the generic "ambiguities" that make ADM hypothesis mathematically ill-defined are needed to preserve the inherent flexibility of the local mode of spacetime, which in turn saves us from the Marxist-Leninist approach to GR -- see above.

NB: In other words, instead of trying to "cure" the problems of present-day GR, we should interpret them as hints to the sufficient condition above. (Notice that the interpretation of the alleged Higgs boson(s) here goes in the same vein of 'potential reality' and flexibility of the local mode of spacetime.)

NB: Notice also that the "shift" from Hyperfläche 1 to Hyperfläche 2 (the shift  ds  -- see the picture below) is totally hidden to all observers living in a perfect continuum (local mode of spacetime), because such "shift" is like 'the absence of water between two adjacent water molecules'. Moreover, the duration of the "shift" is zero (cf. Kevin Brown) to all observers confined in the local mode. Last but not least, the Planck scale cutoff is replaced with the Aristotelian First Cause, in such a way that two cutoffs determine the "boundaries" of the local mode of spacetime, as being wrapped by, and isolated from, the Aristotelian First Cause in the global mode of spacetime.

For these reasons, there are no such things as quantum jumps or spacetime foam à la Wheeler's geometrodynamics. Also, the topology of spacetime and its "quantization" (cf. M. Albers, C. Kiefer, and M. Reginatto, arXiv:0802.1978v1 [gr-qc]) are solved from the outset, and two opposite and "dark" remnants from the global mode of spacetime (currently interpreted as 'cold dark matter' and 'dynamic dark energy from empty space') are expected to emerge in the local mode of spacetime.

In today's GR, these tasks are not feasible, because 'the physical stuff on the hypersurface' cannot fully determine the global properties of spacetime ('fully determine itself', in philosophical parlance). As Matt Visser acknowledged: "What general relativity does not do is to provide any natural way of imposing global constraints on the spacetime — certainly the Einstein equations provide no such nonlocal constraint." This is one of the tasks we expect to be solved in the full theory of quantum gravity, as well as fixing the problems of current GR, exposed in the Cauchy problems for the current Einstein field equations.

So, once we work out the full quantum gravity, we won't "recover" today's GR as some "low energy limit", because the proper GR will be entirely different. Namely, the main problem from the principle of general covariance -- "The requirement of general covariance takes away from space and time the last remnant of physical objectivity" (A. Einstein, Annalen der Physik 49 (1916) 769-822) -- will be resolved, along with the classical limit of QM, and the dynamics of the "waves" of the "metric field" will be rigorously defined, with respect to the newly discovered "reference fluid" (global mode of spacetime) in this full theory of quantum gravity.

If you're adamant in detecting GWs, you need to get grip on the shift as well, because -- like it or not -- you can't detect the "ripples" of spacetime without including the "dark gaps" of the shift  ds  (see the picture below) in the global mode: the present-day GR doesn't allow you to employ 'the proper time [tau]' (C. Rovelli) along spacetime trajectories.


Notice that people (perhaps some Jehovah's Witnesses of ADM Formalism) speculate about adjacent hypersurfaces, "separated" by 'the elementary timelike displacement  dt'  and denoted with  Σt  and  Σt + dt  (see the picture above), as if they have witnessed the expanding cosmological balloon from some non-relativistic, absolute reference frame, in which they had taken a bird's eye view on the expanding space/balloon, hence have witnessed the exact amount of "dark energy" needed to blow up the cosmological balloon by one incremental step, from  Σt  to  Σt + dt , and have of course determined the slope/angle between  ds  and  Ndt , after which have decided to educate the general audience about "seeing back into the cosmos", by referring to some linearized "time variable" hooked (asymptotically?) on the alleged "big bang".

But they need to somehow "blur" the deflation time that is hooked "asymptotically" on The Beginning, to avoid the Cosmic Hen Paradox, yet no real clock made from some physical stuff could survive a roundtrip Gedankenexperiment to the "inflation stage": try to deliver a clock at particular location (say, on your desktop in the University of Chicago) into the inflation stage, and if it survives, bring it back on your desktop, exactly at the same location (hint: use time-symmetric unitary evolution, as in cosmological scenarios). People usually impose some "semiclassical approximation" on the world at the scale of tables and chairs (cf. IGUS Jim Hartle above), but pretend that the linear cosmological time in this "semiclassical approximation" has been miraculously resurrected from the inflation stage (cf. IGUS A. Linde below), by some "graceful exit" (cf. IGUS V. Mukhanov here). And how about the dimensionality of space? It can't be blurred with some "semiclassical approximation", because we can see billions of light years back in the deflation time, while according to Lee Smolin "one of the biggest mysteries is that we live in a world in which it is possible to look around, as see as far as we can" (Three Roads to Quantum Gravity, p. 205). Sorry, these are just too many miracles.

Instead, we should keep the classical limit of quantum gravity always at hand, as stated above. Which brings us back to the shift  ds  in the ADM picture above.

If we interpret the shift  ds  &  dt  in the ADM picture as some entities pertaining to the relativistic world (local mode of spacetime), then nothing can stop us from constructing the notions of 'accelerated shift' and 'accelerated expansion of space', with respect to ... what? This path goes nowhere. The shift  ds  &  dt  does not entirely belong to the physical world called here 'local mode of spacetime'. It could only be "part" from it, or rather a global holistic component of the physical world (cf. the second option above). Can we unravel it from ADM picture?

To the best of my knowledge, none of the Jehovah's Witnesses of ADM Formalism has made an effort to explain to the general audience 'the proper time [tau]' (C. Rovelli) along the hypersurfaces and its relation to the linearized "time variable" on the hypersurface -- the cosmological time read by your wristwatch. (This was the essence of my question from Thu, 24 Oct 2002 20:34:51 +0300, addressed to the leading British expert in quantum gravity, Prof. C. Isham: "what kind of time is implied by 'moving points around' in Diff(M)-invariance, and how can your wristwatch read it.")

From our perspective, the crucial question is this: where is the global holistic component of the shift  ds  &  dt , and how is it fused with the "horizontal" shift on the surfaces  Σt  &  Σt + dt ? In the non-relativistic, and highly misleading, picture from ADM formalism above, people draw some fictional triangles to "explain" this fusion, but only to remind us of Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

In the relativistic presentation, the global "vertical" component of the shift is totally hidden to all relativistic observers (local mode of spacetime), yet it "gets smuggled" into the physical world through the "dark gaps" in the global mode of spacetime.

Notice that the local mode of spacetime is confined inside the 3-D balloon surface (on
the hypersurface), so if we convert the non-relativistic picture below to its proper relativistic presentation (again, the proposal is explained here), the "direction" of  ds  will consume all possible directions in 3-D space (on the hypersurface). Thus, the shift  ds  and its "direction" with be totally hidden (or "dark", if you prefer) to all observers on the hypersurface, because there will be no direction left in which the expansion of 3-D space does not occur. Relativistic observers confined on the hypersurface cannot pinpoint the "direction" of the shift  ds , because they would need to specify a direction which is not occupied by the expansion of 3-D space, to answer the question 'with respect to what'. (Recall that the same problem occurs with measuring the strain of GWs, since it isn't possible to identify any direction in 3-D space, in which GWs do not propagate, in order to specify an undisturbed referential "background" with respect to which one can detect a localized "stretch-and-squeeze" action from GW energy.)

Again, the necessary condition for gravity is a physical body that "curves" the space ...

... while the sufficient condition for "delivering" gravity, in the vicinity of the physical body and -- simultaneously -- around the whole universe, is The Aristotelian Connection. The latter runs in the global mode of spacetime, namely, both "between" the adjacent hypersurfaces (cf. above) and "outside" them (the whole white area in the drawing below).


Noticed an important note from C. Kiefer and B. Sandhöfer:


From: C. Kiefer and B. Sandhöfer,
Quantum Cosmology, arXiv:0804.0672v1 [gr-qc]


And notice, again, the new cutoff from the Aristotelian First Cause, suggested to fix 'boundaries of space' (in the vein of George F R Ellis’ 1984 notion of finite infinity), here; cosmological implications here.

NB: Thus, the global mode of spacetime, in which the 3-D space "expands" and "moves into", is absolutely everywhere on the hypersurface. It is a genuine timeless entity, and is literally omnipresent, hence totally hidden to all relativistic observers on the hypersurface (local mode of spacetime).

Apart from the so-called dynamic dark energy of "empty space", there is no trace left from the "dark" shift  ds  on the 3-D hypersurface:  ds  must be "dark" for any adjacent hypersurfaces, or else there will be physical discreteness exposed in the spacetime, and the latter will no longer be modeled as a 'continuum'. It shouldn't be surprising, then, that many people are bewildered by the "block universe": if we don't consider the global mode of spacetime, the problem of time in the canonical quantum gravity will be inevitable, as there is no way in present-day GR to recover the notion of a 'fleeting image in space which continuously changes in time' (cf. Hermann Weyl below).

And by the way,  ds  must be "dark" and "non-tensorial quantity", or else it would be possible to discover some tensorial presentation of its energy (Hermann Weyl), and ruin the whole GR. There is no 'genuine gravitational energy' in GR, because the beast always gets smuggled through some physical field (cf. R. Penrose, p. 458), as a holistic, non-local input from the "vertical" shift that is embedded in the "horizontal" shift, as explained previously here. Locally, or "over a point", we should always have the freedom to eliminate the gravitational "energy" by hand, with a coordinate/gauge transformation (as noticed by David Hilbert prior to 25 November 1915), or else the gravitational "energy" would be a tensorial quantity, and the "vertical" shift will be exposed on the hypersurface (on the GW lake surface); more from
László Szabados here.

Thus, the issue of 'quasi-local energy conservation in GR' can only be resolved "over" an extended domain of space in which the "non-tensorial context", as fixed in the global mode of spacetime, defines a pinpointed and perfectly localized value of the smuggled "dark" (holistic) input from the "vertical" shift, which in turn shows up on the GW lake surface through the "horizontal" shift, as an "already-localized" type I matter field that had already been altered by the quasi-local energy distribution in that domain. Think of the "energy from gravity" as an input from a "delocalized forest", which is being imposed locally on each of its "trees". The result of which is that the dynamics of each "tree" is EPR-like pre-correlated with 'the rest of trees from the forest', like a shoal of fish (see the x-dots above) swinging along a coral reef (we need to elaborate on the Christoffel symbols and the affine structure to explain this proposal in details).

NB: Notice that in the treatment of STR and QM (derivation of the classical limit of QM from STR), the "vertical" shift from 'potential reality' (global mode) is embedded in the "horizontal" shift (local mode) by entering the Minkowski space through the apex of the cone, which in turn brings us to the research of Kevin Brown and the 'null hypersurface' approach to GR (D.C. Robinson), provided the latter is not "canonical". Notice also that in the proposed PR2 interpretation of QM, the alleged "quantum jumps" are interpreted as artifacts from the inherent inability of a classical clock to handle the two kinds of time in the quantum-gravitational realm. In the canonical formulation of GR, the absence of these two kinds of time results in many artifacts, most notably "black holes" (cf. C. Lanczos and Angelo Loinger) and self-inflicted Cauchy problems for the Einstein equations.

Regarding the latter, notice that in present-day GR they cannot be solved in principle: it is logically impossible for matter fields to produce their "time", while at the same time evolve in that same time, as in ADM hypothesis (see the "dark room" metaphor here). To resolve the inherent problems of ADM hypothesis, a "time-like vector" and a perfectly smooth reference fluid would be needed; namely, something that would do the job of "filling the space time with a fluid which plays the role of real reference frame" (cf. S. Mercuri and G. Montani, gr-qc/0401127v1). However, such 'reference fluid' is expelled from GR from the outset, and you can't add [lambda] to either side of Einstein field equations. With the "dynamic dark energy" of "empty space", we have to start from scratch.

Apart from wishful thinking, there is nothing that can support the splitting of spacetime and the Hamiltonian approach from Paul Dirac. All you can achieve is to make Hermann Minkowski spin in his grave like a helicopter.

Apart from wishful thinking, there is nothing that can support the assumptions about some convenient "constant-t surface" that would play the role of some "smooth Cauchy surface", namely, some smooth (cf. Carl Brans below) spacelike 3-surface cut "exactly once" by each inextendible causal curve. We simply do not have any "causal curve" to begin with.

The proposed new degree of freedom associated with every spacetime "point" (the bundle base space), which may (hopefully) act as a perfectly smooth reference fluid, hence recover the genuine dynamics of GR (cf. T. P. Shestakova, 0801.4854v1 [gr-qc]), has been called 'global mode of spacetime'. It produces holistic effects from 'the universe as ONE', which look like some kind of cold dark "matter" and dynamic dark energy of [you-name-it] in the local mode of spacetime.

Notice that the first effect has been given a very misleading name -- cold dark "matter" (CDM) -- because we don't know any form of matter that can both spin galaxies and keep them together ("holding the crumbs together" -- watch the QuickTime movie below), as well as produce huge "voids".

Cold dark "matter" (CDM)


See the 3-D model of "dark filaments" here

Perhaps people just don't want to talk like parapsychologists, which is why they deeply hope that such effects might be produced by some "matter", even if 90 per cent from such baryonic matter is missing. Imagine this: you visit your local butcher to buy sausages for BBQ party, and he offers you some new special "dark" sausages that have 90 per cent less meat than the normal ones. The two kind of sausages are placed on the same shelf, only one of them has ten times less meat. Then you ask your butcher about the stuff used to make these new sausages, and he replies: 'I can't see it, it looks like some dark frictionless stuff'. But if the butcher doesn't know what this "stuff" could be, he shouldn't define it as "dark". It can't be sausages in the first place, because 'sausages' contain exactly 100 per cent meat (baryonic matter). The only common thing to both kinds of sausages could be the quantum vacuum, correct? If you agree -- welcome aboard!

As to the second effect, 'dynamic dark energy of [X]', the situation is even more puzzling. The crux of the problem has been explained by Larry Kraus as follows (The energy of empty space that isn't zero. A Talk with Lawrence Krauss, July 6, 2006):

"The energy of empty space had to be precisely zero. (...) Symmetries produce two numbers that are exactly equal and opposite because somewhere there's an underlying mathematical symmetry of equations. So that you can understand how symmetries could somehow cause an exact cancellation of the energy of empty space.

"There appears to be energy of empty space that isn't zero!"

The reason why the global mode of spacetime is the only viable DDE candidate is that in the local mode of spacetime the energy of the quantum vacuum (empty space) is indeed precisely zero. There is absolutely no link, no connection whatsoever from the local mode toward the global mode: because of the 'universal time arrow', any "snapshot" in the local mode is made of an already-completed "negotiation" (J. Wheeler) in the global mode.


And that is the essence of 'potential reality' residing in the global mode of spacetime: the separation of the two modes of spacetime is nothing but the "separation" of the potential future (global mode) from the already-produced realm of 'irreversible facts' of the local mode. This is the essence of the "quantization" of spacetime as well: the "separation" of the two modes of spacetime is produced by the universal time arrow, while in the local mode of 'irreversible facts' we enjoy a perfect continuum, at all length scales. Notice also that the topology of spacetime is defined from the outset. (Strangely enough, people utterly refuse to comment on this Ansatz, yet some don't hesitate to express their bold opinion.)

Hence we can 'have our cake and eat it': on the one hand, we have exact cancellation of virtual particles in QFT, such that no residual energy from the quantum vacuum gets "smuggled" into the local mode of spacetime. On the other hand, we have an unlimited, perhaps infinite, pool of 'potential reality' in the global mode, which simply isn't in the local mode. Can't make it more "dark" than that.

On top of everything, we may have to explain both effects in 'one stroke', because the formation of galaxies seems to suggest that the two "dark" and tug-of-war effects of gravity work together.

To see the imprint from the global mode of spacetime, left on the local mode, look at the Smooth Coordinate Presentation Problem, p. 5 and p. 16, from “Exotic Smoothness and Spacetime Models”, by Carl Henry Brans (9 May 2007). Perhaps if we consider the structure of spacetime outlined here, a perfectly smooth transition from Hyperfläche 1 to Hyperfläche 2 (see the picture above) may be possible, in which case the puzzle spotted by Carl Brans would be automatically resolved.

Had the alleged 'smoothness' of the manifold been completely -- that's the key word -- derivable from the properties of the topological space, we would have had a typical explanation of 'smooth manifold', resembling the explanation of 'temperature' by 'kinetic energy', in the sense that everything we know about temperature can be reduced to kinetic energy. Then we would have had cases of "ordinary" manifold smoothness, which would be examined thoroughly in textbooks, and a bunch of exotic anomalies, which would be left for those who are seriously interested in differential geometry and topology, such as Carl Brans.

But life is not that simple. There exist just one kind of 'perfectly smooth transition', which is fixed at the fundamental level of 'pure math' -- the connected Hausdorff topological space. This perfectly smooth transition is neither "exotic" nor "ordinary". It is an exclusive feature of the local mode of spacetime, and is being produced by the Aristotelian First Cause; hence the name suggested is The Aristotelian Connection.

In order to have "points" in the initial topological space -- we assume that it is a primary mathematical entity -- these "points" have to be both individuated and connected by something that should not be present in that topological space. With the exception of such simple cases as the explanation of 'temperature', we always need a one-step-further background (or a one-step-further meta-theory to resolve the undecidable propositions in the theory under consideration, after Kurt Gödel) to define unambiguously some 'structure', even at the 'pure math' level of topological space. And this 'background' cannot be derived completely from the 'structure', if the latter is a primary entity. There should be something "on top of which" such primary structure is being introduced by Mother Nature. And this truly final 'something' is the Aristotelian First Cause and Leibnitzian ideal monad. It is 'the final background', because nothing can go further, not even the human thought: the human brain cannot produce a comprehensible notion of 'the universe as ONE', because our thinking is relational as well.

Which does not mean that 'the final background' is "dark", of course. Perhaps only some Marxist-Leninist philosophers or parapsychologists would consider it "dark". I also believe every butcher can understand this simple metaphysics from Lucretius.

More on 'the final background' from Leibnitz and Döring & Isham here, and from St. Augustine, Lucretius, and Aristotle here. As Carl Brans stated, "progress in theoretical physics has often come as a result of questioning old assumptions." In the case under consideration, the old assumption being questioned is about the Aristotelian First Cause and Leibnitzian ideal monad: many people tacitly presuppose that the two phenomena have no physical or mathematical presentation.

I tend to disagree, since up to 96 per cent from the stuff in the universe comes from -- how shall we call it? --  potential reality grounded on 'the ideal monad without windows'.

Thus, we have three forms of reality to consider: physical reality (local mode of spacetime), potential reality, and the ultimate reality of 'the monad without windows' or Aristotelian First Cause. The pie chart above is based on the presumption that the second and third forms of reality do not exist, hence people calculate their input as if it were produced by type I matter fields.

The correct chart would be quite different: 100 per cent -- exactly 100 per cent -- from the local mode of spacetime consists of intergalactic gas and stars (baryonic matter), since the holistic input from the "vertical" shift (see above) is being transformed as 'nothing but baryonic matter'.

There is no way to "see" the input from the Holon in the global mode, because all physical observations are inevitably, by the laws of STR, directed to facts that are already cast in the respective past light cone, at each instant 'now' from the universal/master time arrow.

However, in the world of 'facts' cast irreversibly at the 'absolute past' of the whole universe and projected in the respective past light cones of the relativistic observers, there should exist a tiny "remnant" from the driving force of 'the universe as ONE', since [lambda] isn't exactly zero in the local mode of spacetime. Viewed from the local mode of spacetime, this puzzling "remnant" may look like 'coming from nowhere', because there is no way we could trace it back to its source -- it really resembles creatio ex nihilo. This is as it should be, because in order to have a Heraclitian arrow of time, each and every step from this arrow must be a newly created "snapshot" of the whole universe (local mode of spacetime), while the "memory" of the universe kept in the global mode of spacetime will be irreversibly enriched from 'the ideal monad without windows' -- the ultimate source of 'the unknown unknown' (cf. John Wheeler). We will certainly be puzzled by such non-unitary transformations of the local mode of spacetime: if we compare it with 'unitary dynamics of a kaleidoscope', it will indeed be enriched with brand new possibilities for its next shift along the Heraclitian arrow of time. You can't cross the same river twice.

Speaking philosophically, the guiding principle here is that the highest possible symmetry is the harmony of symmetry and asymmetry. We simply can't go further that that. C’est la dissymétrie qui crée le phenomène (Pierre Curie). More on my proposal here; just bear in mind that all this "negative mass" and "negative energy densities" belong to the global mode of spacetime, hence in the local mode they will look like a 'timeless potential future'. The implications from this conjecture are outlined here and here.

If the reader has troubles with understanding the holistic effects from 'the universe as ONE', which cannot be traced back to their origin (hence may look "dark" to some Marxist-Leninist philosophers who accept only the teleological, linear time of 'facts'), please write me back, and I will do my best to explain the whole story. Just recall the experiment from your high school, with an U-shaped track and a ball, which you push from one end of the U-shaped track, call it A, to the other one, B. The ball runs down from A, and them goes up, but cannot reach B (the other upper part from the U-shaped track), for reasons you know very well. But if the ball had acquired an additional kinetic energy from the global mode of spacetime, it would easily jump over  B . Now, having acquired such additional kinetic energy, you might think that the ball would violate the so-called 'averaged null energy condition' (ANEC). But if you consider such effect as being produced by the global mode of spacetime, you will never lose your night sleep, like Ed Witten, because such seemingly "anomalous" behavior of the ball will be a holistic effect from the "vertical" shift (see above). It can't jeopardize the classical physics and thermodynamics strictly valid for the local mode of spacetime -- read Eric Linder here; more here.

Going back to philosophy, the putative structure of spacetime boils down to (i) unraveling the so-called torsion (instead of adding some ad hoc postulated "scalar field" to play the role of "dynamic dark energy"), and (ii) upgrading the Levi-Civita connection (cf. R. Aldrovandi and J. G. Pereira, 0801.4148v1 [gr-qc]). Why? Because the linear time that is read by a clock (cf. "already-linearized time") pertains to the local mode only (cf. "inside the train"). There is no such thing as genuine linear time in GR.

The Levi-Civita connection should be upgraded to include the negotiation (the missing torsion in GR) with 'everything else in the universe', which "takes place" in the global mode of spacetime, in such a way that every "point" is able to think-globally-and-act-locally "during" the elementary shift of time dt . My wild and uneducated guess about how this could work "inside" an infinitesimal "point" is outlined here.

Regarding the absence of torsion in GR (cf. A. Trautman), perhaps we need a new spinor field. Consider Ted Newman's H-space. In the latest publication (Carlos Kozameh, Ezra T. Newman, and Gilberto Silva-Ortigoza, Null infinity, H-space and equations of motion, Gen Relativ Gravit 38 (2006) 1559-1564), the crucial notion of 'neighborhood of future null infinity' has been explained in details (p. 1561). Notice, however, that this notion has completely different interpretation in the framework of modified (with some help from Aristotle) 'finite infinity' proposal by George F R Ellis: the cutoff with which we define the 'neighborhood' of the 'boundaries' of spacetime at future null infinity is Aristotelian First Cause. The authors explain their interpretation as follows (p. 1560): "the real part of the world-line yields the classical equations of motion for a ‘particle’ with structure while the imaginary part becomes the spin per unit mass." My comment: place the imaginary part in the global mode of spacetime ("observation space", p. 1563). Further, they elaborate (p. 1563 -- emphasis, comments, and links added): "The parameter space, H-space, should not to be treated as real in any sense -- instead it should  be viewed as an observation space; a screen space that captures certain images of the physical space. In the physical space-time there is a complicated physical system, a gravitating, charged, mass distribution, that creates curvature and an electromagnetic field that can be ‘observed’ only from its asymptotic behavior; we can not ‘see’ individual masses, charges, spins, etc., but instead only the large-scale behavior (such as the whole domain of 3-D space occupied by the x-dots above)." My comment: we should be able to ‘see’ individual masses, as well as detect their wave-like dynamics along the arrow of spacetime, if only we can construct a 'measuring device' that has access to the global mode of spacetime, hence harness the self-acting faculty (see the x-dots above) of 'the universe as a brain'. Finally, Ted Newman et al. acknowledged (p. 1563 ): "Though there is still much to understand, this ‘screen’ view of these H-space curves appears to be essentially correct." I fully agree.

To quote from R. Sverdlov's arXiv:0802.1914v1 [gr-qc] (emphasis added): "In order to visualize the “spinning” that goes on, one can replace infinitesimal points in spacetime by small arrows. However, unlike the way it is normally done, these arrows will not be aligned with a spin axis. Instead, these arrows will be, themselves, spinning around some other axis."


This "other axis" is the global mode of spacetime, which can be visualized only in some non-relativistic presentation (cf. the vertical axis of the "dark water spring" in the "GW lake" here). Once we convert this picture to its proper relativistic presentation (again, the recipe is explained here), the "other axis" will be infinitesimal in the local mode of spacetime. Namely, the "other axis" along which the very 3-D space "moves" is such that the dimensions of physical bodies along it -- in the local mode of spacetime -- will be zero, yet it will "point" to 'the common timeless potential future' of all physical systems in the local mode. The negotiation of their next EPR-like correlated state takes place "along" that "other axis", in line with the rule 'think globally, act locally'. Again, the genuine, non-linear time of GR is not accounted for in present-day GR (cf. C. Rovelli).

Obviously, any attempt at presenting the non-linear dynamics of GR with some linear (polynomial) time ('think globally, and then act locally, and then think again globally', ... etc.), leads to Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

As stressed by Giulini & Kiefer (gr-qc/0611141 v1, p. 16), there should be infinitely many Wheeler-DeWitt equations, each for every "space point", hence every "space point" is endowed with the same "timeless world" of the global mode of spacetime. Otherwise we may live forever with the current ADM recipe (cf. Luis Lehner, gr-qc/0106072v3): "When Einstein equations are recast in a way amenable to a dynamical description, one coordinate, say x_0, is chosen to play the role of ‘time’ with respect to which (emphasis added -- D.C.) the dynamical evolution will referred to."

I wonder what Hermann Minkowski would have said regarding such self-referential "dynamical description" à la Baron Munchausen: if we accept the view that 'spacetime' is one entity, the metric tensor of 3-D space would have to "evolve" within itself, and with respect to itself, just like the GWs. Of course it will be inevitably dead frozen, even if you try some 'relational ontology' based on the linear time (the Buridan donkey paradox).

Stated differently, the task is to provide an answer to Mach's Question (cf. C. Schmid, gr-qc/0409026v1): "What share has every mass in the determination of direction in the law of inertia?" It seems that the whole universe must "know" about everything "instantaneously", and this "knowledge" should be kept in the global mode of spacetime: think globally, act locally. Locally, every spacetime "point" should be endowed with two opposite and "dark" blueprints from its global mode -- the fine-grained structure of the "torsion" of spacetime --  currently interpreted as dark matter (implosion) and dark energy (expansion). Think of them as two opposite "forces" which balance the distribution of the inertial mass, by producing "dark" effects that cannot, not even in principle, be fully derived from the matter content in the local mode of spacetime (which is why some people call these holistic effects "dark", regrettably). Their residual "force" could perhaps produce an observable torsion in the local mode of spacetime, from galaxy rotation to cosmic equator. A balance that is achieved and sustained dynamically should inevitably produce "spin", right? Think of it as resulting from a tangent vector in the global mode of spacetime, attached to every "point" from the local mode, in such a way that its real, 3-D component would swirl the physical stuff, much like you turn the wheel of your car, only an observer confined "inside the wheel" can't trace back the "turning hand" of the 3-D wheel, so the tangent vector looks "dark".

Well, just some gentle suggestions. As Chris Isham boldly declared, I "do not know enough theoretical physics to help with any research in that area". Everything stated here is a personal, "just another crank" opinion.

Now let's see where we can "insert" the putative global mode of spacetime. Look in Bob Wald's textbook:


NB: The "simultaneous events" belong to the potential reality in the global mode of spacetime.

These "simultaneous events" are not facts. They do not form some "three-dimensional surface" either. They are ]between[ each and every event from the 4-D local mode of spacetime. In the local mode of spacetime, they refer to all directions in 3-D space, en bloc: "the whole universe must know about everything instantaneously" (Mike Zucker). These "simultaneous events" pertain to the first part from the rule 'think globally, act locally'. Locally, matter fields coupled (or bootstrapped) via gravity will exhibit a quasi-local dynamical pattern, resembling the collective movement of a shoal of fish: every fish follows a quasi-local geodesic correlated with 'the rest of fish' by the rule 'think globally, act locally'. There is no such thing as "non-local" interactions in the local mode of spacetime, in both quantum and gravitational realms.

In Bob Wald's textbook (p. 4), this hypothetical fine-grained structure of 'the infinitesimal' is buried "in a sufficiently small (notice the poetry - D.C.) neighborhood of a given event". The problems of the dynamic of gravitational systems, resulting from the absence of 'potential reality' in present-day GR, are outlined on pp. 252-268 from Ch. 10.

Notice that, in the context of Abram Zelmanov’s ideas, the global mode of spacetime can be defined as "zero point of reference" (Rabounski & Borissova, arXiv:gr-qc/0304018v4):

"The essence of Zelmanov’s method is simple. As known, components of a tensor value are defined in so-called ortho-frame, a system of orthogonal ideal (straight and uniform) axes, which are tangential to real physical axes (curved and non-uniform) at the zero point of reference (footnote 4).
"Footnote 4: From mathematical viewpoint in every point of real space-time we choose a tangential ideal pseudo-Euclidean space. In other words, components of the tensor are chosen in a tangential pseudo-Euclidean
space, but not real curved and unhomogeneous pseudo-Riemannian space.
"Hence in a real laboratory we do not measure components of a four-dimensional value, bit rather its projections on curved, nonuniform coordinate axes of a real space of reference."

More on 'GR for pedestrians' here and here. For a bit more technical overview, click here, and also notice the problems with 'global existence theorems for the Einstein equations' from Alan Rendall here: a local existence theorem for data of finite energy might be extendable to 'global existence', provided energy is conserved in GR. Only it can't. There is no 'general continuation assurance' in present-day GR: "If it can be shown that the relevant quantity is bounded on any finite time interval where a solution exists, then global existence follows."

The problem goes into the heart of today's GR: the geodesic hypothesis. As acknowledged by Alan Rendall: "In elementary textbooks on general relativity we read that the Einstein equations imply that small bodies move on geodesics of the spacetime metric. It is very hard to make this into a mathematically precise statement which refers to actual solutions of the Einstein equations (and not just to some formal approximations)." (But if we use dynamical determinism, a geodesic is being build just like your brain moves your arm: it has to be flexible, so if you wish to impose some "global existence" on all possible states of your arm, you will end up with a robot.)

We also read in textbooks that GR is 'background independent', in the sense that Mother Nature creates its case-specific spacetime as given by the respective solution of the Einstein equations, once a distribution of masses is specified, prior to which there should be a case-specific spacetime already laid out for the distribution of masses: a bona fide Catch 22 logical contradiction. How does Mother Nature solve this logical conundrum? People shrug their shoulders, yet claim that understand the dynamics of GR, simply because can use the infamous ADM formalism.

But how does DDE 'exist', really? And how did it manage to act on the whole universe en bloc during the inflation? More on September 21, 2008.

One last note on the origin of inertia (physics/0610046 v2, p. 3): "Take as an example the open question of inertia. We do not know why a body resists its acceleration." Perhaps a modified Machian theory of gravity could provide the answer: you can't stir a coffee without disturbing a star. It may sound like poetry to some people, but I believe the issue is of paramount importance to everyone interested in the origin of what we call 'inertial mass'. The prerequisites from GR are outlined here.

As to my Bulgarian friend, it is highly unlikely that he would tackle the 'relativity of simultaneity' in such non-relativistic, now-at-a-distance "reference frame". I wasn't even notified of the conference organized by Prof. Dr. Vesselin Petkov in June 2008. People change.

As John Coleman noticed, "it is extremely difficult to induce penguins to drink warm water".

D. Chakalov
December 7, 2007
Last update: July 21, 2008


Subject: Robert Geroch, Computation and Physics, 12.03.2008
Date: Mon, 24 Mar 2008 02:49:41 +0200
From: Dimi Chakalov <>
To: Bob Geroch <>


I greatly enjoyed your talk at PI. Thank you.

I believe non-computable "numbers" can be handled by the cutoff from the Aristotelian First Cause,

Have you heard about 'the monad without windows'? That's a real math challenge. The physics is outlined at



Subject: Antonio Machado: "Traveller there are no paths, paths are made by walking"
Date: Fri, 28 Mar 2008 13:43:30 +0200
From: Dimi Chakalov <>
To: Werner Israel <>,
Luis Lehner <>,
Jeffrey Winicour <>

Dear colleagues,

If 'paths are made by walking' (A. Machado), then the 'traveller' will have to literally act on himself, in order to "move" within himself and with respect to himself, correct? Please see

I will highly appreciate your professional feedback on the ideas at the link above.

Kindest regards,

Dimi Chakalov



Addendum: I gathered the impression, from our private emails exchanged today (January 3rd), that Prof. Dr. V. Petkov wasn't able to understand my message, so let me state it plain English:

The laws of STR are what makes the energy of 3-D space (a "curious energy that resides in empty space") to look "dark", because STR is designed from the outset to be blind to any phenomenon that (i) operates in an absolute reference frame and (ii) acts on the whole 3-D hypersurface en bloc. (The same "blindness" holds for GR; see ADM hypothesis.)

This is the reasons why the arrow of time, as driven by the so-called DDE, cannot show up in STR in principle: there is no 'now' nor 'moving now' in the theory of relativity, since it would require “the addition of something to the four-dimensional continuum” (Dennis Dieks). Read about this 'addition of something' here. It is from Aristotle, Lucretius, and St. Augustine. And don't mess up with 'consciousness', like Hermann Weyl.






I also gathered the impression that won't be given the chance to speak at the conference organized by Prof. Dr. V. Petkov and his colleagues in June 2008. If true, it is very likely that they will again end up with a fully predictable conference resembling GR17 and
EPS13. They just avoid tough questions. Sad but true.

Just a sample of such questions: if you wish to observe the 'moving now', your first off task is to observe the elementary timelike displacement, to see if the latter does, or does not, 'move' with respect to [aether?] and with particular pace, say, one 'elementary cycle of time' per [whatever -- but not seconds]. If such tasks were feasible, you would be able to expose the Aristotelian First Cause and the "dark" energy of 3-D space in the local mode of spacetime. In other words, such teleological tasks are doomed to fail. They cannot reach the Aristotelian First Cause.

Notice that we cannot define the 'moving now' with [seconds], or define the 'elementary increment of the volume of 3-D space' with notions which make sense only in the 3-D space. The global mode of spacetime can only show up as particular 'dimensionless variable', like the "amplitude" of Quantum Waves and Gravitational Waves.


NB: Recall that GW's "amplitude" is necessarily dimensionless: you can't define the very stuff that determines 'the length of a meter' with [meters], just as you can't define 'the elementary cycle of time' with [seconds]. Yet LIGO Scientific Collaboration -- 490 distinguished Jehovah's Witnesses of GW astronomy -- are chasing the physical push from such dimensionless entity. They can't explain the phase of GWs, nor can they explain how would GWs propagate 'within themselves', and at the same time alter the metric of space, by literally acting on themselves.

Perhaps only Baron Munchausen can perform such self-acting miracle, but LIGO Scientific Collaboration haven't yet acknowledged his contribution to "GW astronomy". Just click the image above.

I very much hope that GR experts will acknowledge that the same type of logical contradiction is involved with the so-called DDE as well. I believe the crux of the matter has been stated above. It is also encrypted in the following phrase:


This seemingly sensible statement from A. Linde requires an absolute and perfect clock of the whole universe, which would provide an absolute and perfect time, such that both 'the observers inside the universe' and some 'ideal or meta observer outside the universe' can reach an agreement on the alleged 'terribly accelerated expansion' in the initial 10-30 seconds, by elucidating the "rate" of expansion of the diameter of 3-D space, measured in [meters] (e.g., "only a few kilometres across") per [second], since 'dimensionless entities' are not favored by philosophers like A. Linde.

Namely, in the initial 10-30 seconds, there were many-many-many-many more elementary increments of the volume of 3-D space per second -- as compared to the first 10-30 seconds from the time interval needed to read these lines -- and then after these 'initial 10-30 seconds' the accelerated expansion of space "settled down" for a while, but apparently it is currently again in some accelerated stage, only not so vicious as it were in the initial 10-30 seconds.



If you can leave the 3-D space of the universe and take the stand of some 'ideal or meta observer outside the universe', you may try to verify such statements, and eventually publish your insights in peer-review academic journals, like A. Linde has been doing since 1980s.


NB: Notice that you may visualize the "expansion" of 3-D space -- be it accelerated or linear -- only by referring to something that is not 3-D space. Thus, if you stick to the basic rule of relativity theory -- 'with respect to what?' -- you are forced to use an initially wrong, and also highly misleading, non-relativistic presentation, such as those above.

Murphy's Law No. 15 reads: Complex problems have simple, easy-to-understand wrong answers. In the case depicted with the pictures above, we don't have a 'wrong answer' but a 'wrong visualization' of a finite time interval hooked on some "big bang", as well as a vast 3-D space with fixed, and absolute, volume. Click on these misleading pictures for more.

You can visualize the expansion of 3-D space (see also Ned Wright's balloon metaphor) and the "ripples" of its metric (see the GW "lake" here) only in some initially wrong, and highly misleading, non-relativistic presentations that display some "background" and "boundaries" for the spacetime, with respect to which 'things make sense', hence can be grasped and visualized by the human brain. Then you try to assure your students and the general audience that you can "remove" these non-relativistic visualizations with math.

Only you can't. You need quantum gravity to explain things that pertain to 'the only truly isolated system' -- the whole universe as ONE -- so you better start telling your students the whole truth.

As mentioned below, there is no sunlight to blindfolded people, so it is 'gut zu wissen' that with the current theory of relativity we are still blind.

I will report here any new developments (if any) on these questions right after the Third International Conference on the Nature and Ontology of Spacetime in June 2008.

"Nobody has ever noticed a place except at a time, or a time except at a place", said Hermann Minkowski one hundred years ago. Specifically, he stressed that "space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality" (cf. Orfeu Bertolami, arXiv:0801.3994v1 [gr-qc], Sec. 1).

Yet people are tempted to separate time from space, in the sense that "time" would refer to some object that changes its states by changing its position in "space", as labeled with some provisional coordinates. And even if this object is in relative rest, it is somehow intuitively obvious that its "clock" would continue to count its "time". Which seems to allude that the object somehow "moves in time", while the 3-D space is always dead frozen: there is no "empty 4-D space" waiting for the cosmological balloon to expand into.

But if we use 'a kind of union' of time and its 3-D space, the 'union' will be dead frozen as well: in present-day GR, the 3-D space does not "move" in any way whatsoever -- recall Karel Kuchar's Perennials. Then such "block universe", along with all its pathologies, would seem inevitable. As Bob Geroch eloquently explained:

"There is no dynamics within space-time itself: nothing ever moves therein; nothing happens; nothing changes. (...) In particular, one does not think of particles as "moving through" space-time, or as "following along" their world-lines. Rather, particles are just "in" space-time, once and for all, and the world-line represents, all at once, the complete life history of the particle."

Then Cauchy problems for Einstein equations and Closed Timelike Curves (CTCs) would be inevitable, while time-orientability would be a rare, and model-dependant, luxury of spacetime, if not a sheer wishful thinking. Most importantly, "what general relativity does not do is to provide any natural way of imposing global constraints on the spacetime — certainly the Einstein equations provide no such nonlocal constraint", says Matt Visser.

But what if the 3-D space itself "moves" along a hypothetical 'universal time arrow' in such a way that "global constraints" on the local mode of spacetime are produced?

Recall that we landed up with "constraints" (cf. Karel Kuchar) because of purely mathematical "reasons": some of the Einstein field equations do not involve second time derivatives, and the textbook interpretation became "they are not dynamical equations but constraints" (cf. T.P. Shestakova).

Of course they will look like "constraints": those 'second time derivatives' refer to the linear time variable (cf. C. Rovelli and the unmonitored brain activity here) from the local mode of spacetime. Each and every instant from this 'already linearized' time is an 'already accomplished' negotiation of the two sides/parties from Einstein equation. In the flat Minkowski space of STR, this linear time can indeed "read" the dynamics of the object in consideration, because the effect from the non-linear "talk" of matter and space (John Wheeler) is vanishing small, and the 'second time derivatives' of such linear time can do the job. Strictly speaking, the dynamics of STR is severely strained by the absence of the feedback from the geometry of space.

Perhaps only the human brain can "read" the non-linear time of GR and QM. Your poor wristwatch can't -- it is locked "inside the train" -- so it will be inevitably "frozen". For if you take a walk "outside the train", your time will be comprised of infinitely many instants from the time of your wristwatch "inside the train", all of which will be "inserted" in the "gaps" (cf. St. Augustine) of the global mode of spacetime "inside the train".

Here comes an obvious question: but how can you rob 'the time inside the train' with an infinite "number" of points in the first place? But of course you can, and that's the beauty of the continuum hypothesis (cf. Kurt Gödel). If you stay 'inside the train' only, you won't feel "robbed" at all, but you will indeed notice some "dark" effects on your train -- see above.

We may recover the 'moving now' of the global Heraclitian time only by enabling the 3-D space to "move": not 'with respect to an aether', but as 'emerging from something else'. But because space and time are such crucial categories, "it is bound to be ferociously difficult to understand their emerging, or even some aspects of them emerging, from 'something else'" (Isham & Butterfield).

More about this 'something else' on Sunday, 21 September 2008. The title of the talk is "The Arrow of Spacetime"; the venue is Munich.

Space is very limited; please get in touch with me by email and book your seat by August 31st. As of today (March 15th), almost all seats are taken. If you miss the talk on September 21st, please note that my last talk will be on Wednesday, 25 November 2015, commemorating the discovery of GR by Einstein, Hilbert, and Levi-Civita (in alphabetical order). At this last talk, there might -- just might -- be some math, only not from me but from my younger colleagues. You never know with 'the unknown unknown'.

Meanwhile, may I suggest to the reader a quiz based on New Scientist (9 February 2008): try to find all the 47 errors in the drawing below.



Just a hint: Closed Timelike Curves (CTCs) are unavoidable in present-day GR (cf. W. Bonnor), which means that if there is a ban on them, it should not be directly exposed in present-day GR. To uncover this ban and subsequently the errors in the drawing above, you need to realize that in present-day GR you can move in 3-D space just as you move it "time", hence CTCs are indeed inevitable. But once you recover the 'reference fluid' (global mode of spacetime) and the genuine dynamics of GR (see above), you will operate with the Heraclitian time produced by the "movement" of 3-D space, and no CTCs nor any other pathologies will be possible: you can't cross the same river twice.

In summary, if we treat the spacetime as 'one entity', after Hermann Minkowski, we should not disentangle the 3-D space from its time, nor should we use any non-relativistic pictures like those above.

Frankly, I can't find any genuinely new idea suggested at this web page. Nor there is any original idea in 'the ultimate cutoff' from Aristotle here and here. All I tried to do was to take some well-known ideas from classical philosophy and metaphysics, neuroscience, and psychology, and drop them in the pot of modern theoretical physics. The only new, to the best of my knowledge, suggestion is about the so-called scale relativity: (i) something has to 'keep together' the physical stuff in vast volumes of space, and (ii) the absolute structure of 3-D space, in terms of absolute volume and absolute spatial relations (inside vs outside, etc.), is in my view unacceptable, because it actually introduces a fixed background in GR: it acts on the physical stuff, without being acted upon. Obviously, the problem is rooted on Paul Dirac's speculations about some Hamiltonian formulation of GR, based on splitting of spacetime into two "parts". I think this Hamiltonian formulation of GR is fundamentally wrong (despite its effectiveness as a calculation tool), firstly because there is 'problem of time' in canonical quantum gravity, but no 'problem of 3-D space'.

Regrettably, Prof. Karel Kuchar hasn't found time in the past two years to resolve this fundamental problem, although all this tallies to his filed of expertise. In my just-another-crank opinion, the only possible solution is the so-called scale relativity principle.

I honestly claim that haven't read any proposal similar to this principle. But given the opinion of the leading British expect in quantum  gravity, Prof. Chris Isham -- "You do not know enough theoretical physics to help with any research in that area" -- I consider it highly unlikely that my proposal would turn out to be original.

I am simply unaware of any similar efforts being posted on the Internet or published on paper. 

If the readers happen to know about similar 'scale relativity principle', please let me know. Thank you.

D. Chakalov
January 3, 2008
Last update: March 15, 2008


Subject: The zeroth theorem (request for opinion)
Date: Thu, 10 Sep 2009 12:34:32 +0300
From: Dimi Chakalov <>
To: J D Jackson <>,
V Arnold <>,
V Kisil <>

Dear colleagues,

I am trying to develop a model of the universe as a 'brain' (after Ulric Neisser's cognitive cycle), but am afraid of the zeroth theorem of the history of science.

In your spare time, please look at

Does this sound familiar to you?

Kindest regards,

Dimi Chakalov



Subject: Re: The canonical Dirac-ADM 3+1 approach to GR
Date: Thu, 13 Mar 2008 15:51:46 +0200
From: Dimi Chakalov <>
To: L. A. Glinka <>

On Thu, 13 Mar 2008 15:59:52 +0300, Message-ID:
L. A. Glinka <> wrote:

> In your statements I find only madman's rubbish, who make pseudo
> science. You are not physicist, you are not mathematician, you are not
> philosopher. On your present level you are only door-to-door salesman.

Tovarish Glinka,

I'm not interested in your emotional attitude.

Is it difficult to say something as a physicist? You've been working in USSR for so many years...

> Not any regards for you.

This isn't polite, Shliachtich Glinka :-)

Take care,


> On 13/03/2008, Dimi Chakalov <> wrote:
> >
> > > The main question is: Where are mathematical and numerical
> > > results of your divagations?
> >
> >
> > Your presumption is that the mathematical apparatus of the newly
> > proposed structure of spacetime is available, or at least that
> > somebody on this planet knows something about it. If this is indeed
> > your presumption, you simply haven't read the text at the link from my
> > initial email. Let me quote:
> >
> > "I honestly claim that haven't read any proposal similar to this
> > principle. (...) I am simply unaware of any similar efforts being
> > posted on the Internet or published on paper. If the readers happen to
> > know about similar 'scale relativity principle', please let me know.
> > Thank you."
> >
> > Moreover, the tasks of presenting the ideas of Aristotle, Lucretius,
> > and St. Augustine with math are not yet solved. I regret that you
> > have completely missed them.
> >
> > If some theoretical physicists had written something about these
> > tasks, I suppose Kuchar, Isham, and Kiefer would have known about
> > it.
> >
> > To sum up, the math is yet to be discovered. I have only tried to
> > explain the main tasks known since Aristotle.
> >
> >
> > > Prof. Gerard 't Hooft said me once: the main proof of theory are
> > > numbers, they should give predictions for experimentators.
> >
> >
> > Only he hasn't offered any solution to the measurement problem in
> > QM. None. Zilch. I believe have offered such solution, but it is based
> > on the concept of 'potential reality' from Aristotle, which, again,
> > nobody has presented with math.
> >
> > As to your model, you should check out Karel Kuchar. Yes, you have
> > lots of math, but it goes nowhere.
> >
> > Please do not waste my time. If you wish to read the text at the link
> > from my initial email, please do it.
> >
> > Take care,
> >
> >
> > Dimi
> >


Subject: Quantum Mechanics 101
Date: Tue, 26 Aug 2008 14:06:45 +0300
From: Dimi Chakalov <>
To: L A Glinka <>,

arXiv:0808.1035v3 [gr-qc], p. 6: "Quantum Gravity (14) is interpreted as nonrelativistic quantum mechanics. It seems to be unlogical."

No, it isn't "unlogical". Not because there is no such word in English language, but because your idea is 'not even wrong'.

You are consistently ignoring the basic basics of QM,

Every door-to-door salesman can understand the arguments at the link above. If you can't, feel free to write me back.




Subject: Re: If time is discrete, ..., if time is continuous, ...
Date: Fri, 14 Mar 2008 02:09:19 +0200
From: Dimi Chakalov <>
To: Gerard Hooft 't <>

Hi Gerardus,

One of your devotees, L.A. Glinka, claimed that you've said the following: "the main proof of theory are numbers, they should give predictions for experimentators."

Which reminded me of my email from Tue, 4 Apr 2006 23:43:30 +0300,

and your footnote on p. 4 from "The mathematical basis for deterministic quantum mechanics", arXiv:quant-ph/0604008v2: "Thus, we do, as yet, use an absolute notion of time. Special and general relativistic transformations are left for future studies."

I wonder if you've made any progress in the past two years. If not, see an alternative approach at

Wishing you best of luck,



Subject: Empirical Symmetries, Slides 28 and 29 (Time and Universe, 2007 Vancouver Workshop)
Date: Thu, 3 Jan 2008 16:58:49 +0200
From: Dimi Chakalov <>
To: Richard Healey <>
Cc: Andrew Wayne <>,
Steven Savitt <>,
Dennis Dieks <>,
Mauro Dorato <>,

Hi Richard,

Perhaps you may wish to see

It looks like I won't be able to speak at the Third International Conference on the Nature and Ontology of Spacetime, so I included some colleagues of yours in the CC: list. Sorry for the bulk email.

Best regards,



Subject: Gut zu wissen
Date: Tue, 25 Dec 2007 22:24:29 +0200
From: Dimi Chakalov <>
To: Rüdiger Vaas <>,
Cc: Vesselin Petkov <>,
Claus Kiefer <>

Hi Rüdiger,

Regarding your short articles in Bild der Wissenschaft, January 2008 (excerpts below): how did you manage to bypass almost all information from my web site, which I'm sure you know since July 2004? You act just like Claus Kiefer!

Time and 3-D space are considered *one* entity, after Hermann Minkowski (Raum und Zeit, in: Vorträge von der 80. Naturforcherversammlung zu Köln, Physikalische Zeitschrift, 10, 104-111, 1908), hence if you wish to speculate about time, recall Albert Einstein: "In the first place, we entirely shun the vague word “space,” of which, we must honestly acknowledge, we cannot form the slightest conception."

And we have a real challenge with 3-D space: recall the so-called "dynamic dark energy". Some simple prerequisites from 1905 (STR) and 1915 (GR) can be read at

Until we understand the nature of space and its "dynamic dark energy", I believe *any* statement about the flow of time, advertised in magazines such as Bild der Wissenschaft, should be supplemented by a clear presentation of our current knowledge of 3-D space. Otherwise people may be tempted to trust your colleague Vesselin Petkov and miss the bold fact that the "dynamic dark energy" of 3-D space is totally outside the framework of the theory of relativity *as well*. And that isn't an illusion.

In other words, there is no sunlight to blindfolded people, so it is 'gut zu wissen' that with the current theory of relativity we are still blind.

In case you wish to write another article for Bild der Wissenschaft and provide the missing information, feel free to drop me a line and I will be glad to help, just by quoting from Claus Kiefer's papers and monographs.

Wishing you and your colleagues from Bild der Wissenschaft all the best for 2008,


Bild der Wissenschaft, Heft 01/2008,

Rüdiger Vaas: "... more and more physicists and philosophers come to the conclusion that the time is not objective. "That to see is perhaps the greatest intellectual challenge with which mankind has ever faced," says the philosopher and physicist Vesselin Petkov from the Concordia University in Montreal, Canada."
"Die Zeit ist eine reale vierte Dimension analog zu den drei Raumdimensionen" (Time is a real fourth dimension analogous to the three spatial dimensions).

"Nur die Vergangenheit ist determiniert, die Zukunft ist dagegen ein Spielraum der Möglichkeiten, von denen zu jedem Zeitpunkt nur eine realisiert wird" (Only the past is determined, the future is, however, a spectrum of possibilities of which, at any given time, only one will be realized).

"Das „Fließen” der Zeit ist im Rahmen der Relativitätstheorie eine Illusion" (The "flow" of time is within the framework of the theory of relativity an illusion).


Subject: Seth Major's students
Date: Thu, 21 Feb 2008 05:10:44 +0200
From: Dimi Chakalov <>
To: Seth Major <>

Hi Seth,

Please pass the link below to your students

You have some very bright kids,

Be fair to them, okay?

As to your crrent project regarding some "knot invariants expressed in terms of q-spin networks", see again the first link. If you find an error, please disregard this email message, and write me back.




Subject: Malcolm MacCallum's General Relativity mailing address list
Date: Thu, 21 Feb 2008 05:03:20 +0200
From: Dimi Chakalov <>

Dear Dr. MacCallum,

I hope my email messages sent last year have been safely received.

Please look at

If you find an error, please write me back. If you can't, may I ask you to pass the link to the people from your General Relativity mailing address list, with the same request.

Kindest regards,

Dimi Chakalov


Subject: The most pertinent question
Date: Fri, 22 Feb 2008 10:52:20 +0200
From: Dimi Chakalov <>
To: Naresh Dadhich <>
Cc: Tilman Sauer <>,
Andrzej Mariusz Trautman <>,
Carlos Kozameh <>,
Ted Newman <>

Dear Naresh,

I don't believe we need branes, extra-dimensions, and all that stuff: please see

A penny for your thoughts!

The opinion of your colleagues will be highly appreciated, too.


Naresh Dadhich, On the derivation of the gravitational dynamics,
arXiv:0802.3034v1 [gr-qc]

"(T)he dynamics of gravity resides in spacetime curvature which must fully and entirely determine it"
"Gravity is an inherently self interactive force and the self interaction could only be evaluated by successive iterations. (...) As two and three dimensions were not big enough for free propagation of gravity, similarly four dimension is not big enough to fully accommodate self interaction dynamics of gravity. Then the most pertinent question is where does this chain end?"


Note: Naresh Dadhich didn't reply to my email from Mon, 24 May 2004 21:18:11 +0300. Mike Turner didn't reply to my email from Thu, 03 Jun 2004 02:47:26 +0300, and I never heard from Jorge Pullin, Bob Wald, and Rafael Sorkin, to name but a few. The only response from Steven Weinberg was that he doesn't have time to read my email. The incomplete list of physicists who ignored my proposals is here.

At least four years have been wasted. I was hoping that will be given a chance to talk at GR17 and EPS13, but my application for oral presentation was denied. All I got so far is either dead silence, from physicists who ignored my proposals, or insults ranging from relatively polite (e.g., C. Isham) to seriously ugly (e.g., L.A. Glinka). As of today, I can't even find one physicist who would endorse the submission of my manuscripts to server. I managed to submit a manuscript regarding the alleged "GW astronomy" only once, and it was immediately deleted. This was communist censorship, plain and simple. And the wasting of taxpayers' savings by LIGO Scientific Collaboration continues: all these 490 experts in GR stubbornly believe that "something that is dimensionless" (Kip Thorne's definition of GW amplitude) may act on the physical world, in line with their "linearized approximation of GR" (they refuse to read Hermann Weyl's article from 1944) and their version of quantum gravity from 1960s (the "invariance angle" from "gravitons"). I call it GW parapsychology.

Under these circumstances, one could hardly expect from me to be nice and polite to these ... well, let's just call them 'people'. I am, and will remain totally frank instead. If someone offers an idea which I consider very interesting and fruitful (e.g., Ted Newman's H-space or Gerard 't Hooft's unpublished proposal here), I will acknowledge it. Alternatively, if someone demonstrates total ignorance of Einstein's GR or attempts to mislead the general audience about Einstein's beliefs, like Steven Weinberg did, I will strike back.

À la guerre comme à la guerre.

D. Chakalov
March 17, 2008
Last update: March 22, 2008


Subject: Please confirm the receipt of this email.
Date: Mon, 24 Mar 2008 01:14:07 +0200
From: Dimi Chakalov <>

Dear colleagues,

I believe you all are interested in quantum gravity. If true, please see an alternative to your efforts at

In my opinion, you are not only wasting your time, but also the money of Perimeter Institute.

May I ask you to confirm the receipt of this email.

If any of you can find an error in the proposal at the link above, please don't hesitate to send me your professional opinion as well.

Thank you for your time.


D. Chakalov

Note: Take, for example, Lee Smolin. He knows about the ideas proposed at this web site since February 2002. It's all about two presentations of time, known since Plato (the 'absolute time' of Platonic Ideas, and the time of their fleeting explications/shadows). Yet in the past six years this gentleman from the Perimeter Institute has not mentioned these widely known ideas, not even once. Is this a 'scrupulous intellectual honesty'?

Watch L. Smolin's ISSYP Keynote Session (Perimeter Institute, 01/08/2007 - 1:00 PM, duration 01:28:14) at


He offered to the kids in the auditorium to "vote" on the two ideas about time, but failed to tell them that both Newton and Leibniz could be right: Newton's absolute time is the 'global time', while the relativistic notion of time is the 'local time'. More at the link from my email above.

Here at this web page I only quoted from one of L. Smolin's book and tried to explain how he missed the fourth road to quantum gravity. He failed to mention my critical remarks sent since February 2002 (the last email recorded at this web site is from 15 September 2006), and has always ignored them. His only "argument", and also last email, was from Sun, 24 Feb 2002 17:30:25 +0000 (BST): "So don't refer me to web pages."

I'm sure Lee Smolin can read web pages, but perhaps he "remembers" only those that suit him.

Do you smell a rat? I do, because kids have the right to know everything we know. What Lee Smolin did to them during his Keynote Session was not fair. And this person is the founding research scientist at Perimeter Institute.

Were Karel Kuchar and C. G. Torre invited at Perimeter Institute, ever?

D. Chakalov
March 24, 2008


Subject: Re: If time is discrete, ..., if time is continuous, ...
Date: Mon, 24 Mar 2008 12:57:18 +0200
From: Dimi Chakalov <>
To: "Gerard Hooft 't" <>

P.S. Regarding my email from Fri, 14 Mar 2008 02:09:19 +0200

and your forthcoming talk at Perimeter Institute (Rm 301, May 01, 2008 - 2:00 PM) ,

I wonder if you intend to mention the ideas at my web site, or will keep quiet, like Lee Smolin,


Note: Surely the Nobel Prize laureate and member of Perimeter Institute’s Scientific Advisory Committee (SAC) is a very busy person, so let me lay out the crux of the matter in just a few sentences.

Consider the so-called dualistic conception of time (cf. Joy Christian): "a classical clock is supposed to register the time external to itself (...). In other words, the time measured by such a clock is presumed to be ‘external’, existing independently of it, whereas its dynamic evolution, although parameterizable by this background time, is viewed to be ‘internal’, specific to the clock itself."

But in background-free theories such as GR, the dynamical evolution must be parameterizable by itself, since there is no difference between the ‘external’ and ‘internal’ time: the system got to produce its "time", while at the same time evolve in that same time. Forget it, Gerardus.

If you ignore the ideas know since Plato and use a linear time only, perhaps only Baron Munchausen could perform such self-acting miracle. But if you model the universe as a brain, you will recover the "background" global time (the non-linear time 'tau', cf. C. Rovelli) that looks "timeless" in comparison to the linear time variable read (supposedly) by your wristwatch. There is no other option to fix the dynamics of GR (cf. J. Stachel) and reconcile it with QM (cf. A. Ashtekar).

I have a feeling that will never be invited to talk at Perimeter Institute and get a glimpse at its "open atmosphere where anybody can criticize anybody, honestly and directly". Or at least not until L. Smolin retires or G. 't Hooft writes his landmark paper "201 wrong theories for the cosmological constant", whichever comes first.

D. Chakalov
March 24, 2008




Subject: Particles do have spacetime feelers
Date: Thu, 18 Mar 2004 12:14:19 +0200
From: Dimi Chakalov <>
To: Vesselin Petkov <>,
     Nasko <>

Dear Vesko and Nasko,

I can't believe that time flies so damn fast. I vividly remember our
talks at the mini-seminars at Nasko's room some twenty years ago. I think he had the best collection of physics papers and books, much better than the one in the Sofia University library, three floors underneath. I learned so much from you. Thank you *very* much!

I just read a beautiful paper by Harvey R. Brown and Oliver Pooley [Ref. 1], which I believe will appear in the forthcoming volume "The Ontology of Spacetime".

Vesko: Please send me your editorial article and any other paper you
have on the energy-momentum tensor and QM,

I think the issue is very subtle; please see Eq. 1 and Footnote 5 in
[Ref. 1], "the complications that quantum physics is likely to introduce to the question of geodesic behaviour."

More on these "complications" at

See also some jokes at

Just like in the good old days! Not that they were good, but at least I was young.

Nasko: Please call me anytime that is convenient for you. I do owe you a lot, and will never forget what I learned from you: particles do have spacetime feelers,

Vesko: If you come to Sofia some day, please call me, perhaps we all could try to make another mini-seminar, over a glass of gin tonic or five:-) And please send my love to Svetla.

Best wishes,

IT Consultant (third from the left),


[Ref. 1] Harvey R Brown and Oliver Pooley (16 March, 2004), Minkowski space-time: a glorious non-entity, physics/0403088.

pp. 2-3: "We have seen that for Einstein the inertial property of matter [footnote 3] requires explanation in terms of the action of a real entity on the particles. It is the space-time connection that plays this role: the affine geodesics form ruts or grooves in space-time that guide the free particles along their way. The intuition was well expressed by Nerlich in 1976:

 ...without the affine structure there is nothing to determine how the
[free] particle trajectory should lie. It has no antennae to tell it
where other objects are, even if there were other objects... It *is
because space-time has a certain shape that world lines lie as they do*. (Nerlich, 1976, 264, original emphasis)
[Nerlich, G. (1976), The Shape of Space, Cambridge University Press, Cambridge.]

"In GR, on the other hand, this view is at best redundant, at worst
problematic. For it follows from the form of Einstein’s field equations that the covariant divergence of the stress-energy tensor field T_µv -- that object which incorporates the "matter" degrees of freedom -- vanishes.

        T^µ v;µ = 0             (1)

"This result is about as close as anything is in GR to the statement of a conservation principle, and it came to be recognised as the basis of a proof, or proofs, that the world-lines of a suitably modelled force-free test particles are geodesics. [footnote 4] The fact that these proofs vary considerably in detail need not detain us.

"The first salient point is that the geodesic principle for free particles is no longer a postulate but a theorem. GR is the first in the long line of dynamical theories, starting with the Aristotelian system and based on that profound distinction between natural and forced motions of bodies, that *explains* inertial motion. The second point is that the derivations of the geodesic principle in GR also demonstrate its limited validity. In particular, it is not enough that the test particle be force-free. It has long been recognised that spinning bodies for which tidal gravitational forces act on its elementary pieces deviate from geodesic behaviour. [footnote 5]

"What this fact should clarify, if indeed clarification is needed, is that it is not simply *in the nature* of force-free bodies to move in a fashion consistent with the geodesic principle. It is not an essential property of localised bodies that they run along the ruts of space-time determined by the affine connection, when no other dynamical influences are at play. In Newtonian mechanics and SR, the conspiracy of inertia is a postulate, and its putative explanation by way of the affine connection is a postulate added to a postulate.

"And it is here that Einstein and Nerlich part company with Leibniz, and even Newton. For both Leibniz *and Newton*, absolute space-time structure is not the sort of thing that acts at all. If this is correct, and we believe it is, then neither Newtonian mechanics nor SR represent, *pace* Einstein, a violation of the action-reaction principle, because the space-time structures in both cases are neither acting nor being acted upon. Indeed we go further and agree with Leibniz that they are not real entities in their own right at all."

"Footnote 3:  To be precise, the fact that particles with non-zero mass satisfy Newton’s first law of motion, not that they possess such inertial mass.

"Footnote 4: See, for example, Misner et al. (1973, §20.6, 471-80).

"Footnote 5: See Misner et al. (1973, 480; ex. 40.8, 1120-1; and §40.9, 1126-31). These authors refer briefly on p. 480 to the complications that quantum physics is likely to introduce to the question of geodesic behaviour. (...)"