Subject: The timeless-ordering
Date: Thu, 09 Dec 2004 04:55:33 +0200
From: Dimi Chakalov <>
To: D Oriti <>

Dear Dr. Oriti,

May I comment on your recent paper [Ref. 1]. Your feedback will be highly appreciated.

I'm afraid the key phrase "depend on an external time parameter as is the case in ordinary quantum mechanics" is utterly unclear, since we don't know how to embed the events produced by QM measurements in Minkowski's cone,

Thus, your next key statement, "(T)he very concept of time is not
fundamental at all and should instead emerge only in a semiclassical
approximation [3]", is also utterly vague, since it depends on the first

I find your proper time formalism and proper time variable very interesting, and invite you to look at my speculations on 'clearly identified notion of causality' in background-independent theories,

Kindest regards,

Dimi Chakalov

[Ref. 1] D. Oriti, The Feynman propagator for quantum gravity: spin foams, proper time, orientation, causality and timeless-ordering,
gr-qc/0412035 v1, December 9, 2004

"In quantum gravity, because of background independence and
diffeomorphism invariance, neither phsyical observables nor physical
states, i.e. none of the basic elements of any canonical formulation of
the theory, can depend on an external time parameter as is the case in ordinary quantum mechanics, (...)."

"(T)he very concept of time is not fundamantal at all and should instead emerge only in a semiclassical approximation [3]."
[3] C. Isham, gr-qc/9210011;

"(O)ne can argue that the notion of causality is actually more primitive than that of time, more fundamental, being already present in the notion of ordering between events, of a fundamental directionality in spacetime, and that as such can be present, as a *seed* of what will then be, in a semiclassical approximation, (...). We agree with this latter point of view.

"The answer [1, 2] is that all current spin foam models do not depend, in their amplitudes, on the orientation of the underlying 2-complex, i.e. they do not depend on the orientation data we identified above. The way this is achieved is quite simple in all models: in the expression for the amplitudes for spin foams the terms that can be understood as contributions from opposite orientations are summed simmetrically thus erasing the dependence on the orientation itself.

"This orientation independence leads to interpreting the current spin
foam models as a-causal transition amplitudes, as we said, i.e. as the
quantum gravity analogue of the Hadamard function of field theory and particle dynamics; when a canonical formulation is available, this sort of transition amplitudes can be equivalently thought of as defining the physical inner product between quantum gravity states, invariant under spacetime diffeomorphisms, or as a covariant definition of the matrix elements of the projector operator onto physical states [14].

"The proper time formalism we have developed could find interesting
applications in itself, with a first step being the study of the
relationship between our group theoretic proper time parameter and the lapse function of canonical quantum gravity or the conformal factor of the covariant formulation, and therefore with the physical proper time for quantum gravity (both the lapse and the conformal factor or spacetime volume element have used in the literature as a proper time variable).

"....... in absence of an external time coordinate, but with a clearly
identified notion of causality."

Note: See also D. Oriti's Ph. D. Thesis "Spin Foam Models of Quantum Spacetime", gr-qc/0311066, particularly Sec. 1.2.1, "Background independence and relationality", and the problem of time in canonical quantum gravity (the freezing of the donkian Hamiltonian), 

There is also a very nice quote from Groucho Marx in D. Oriti's gr-qc/0311066: "Those are my principles, and if you don't like them... well, I have others."

Keeping this piece of wisdom in your mind, see my email to Erich Schoedl below.

D. Chakalov
December 9, 2004

The next question was - what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit. As you will see, the answer is not very far from the truth. The only difference is that the angels sit in a different direction and their wings push inward.

Richard Feynman, Character Of Physical Law, p. 8


Subject: The shape of space
Date: Thu, 09 Dec 2004 14:39:41 +0200
From: Dimi Chakalov <>
To: Erich Schoedl <>,
BCC: [snip]

Dear Dr. Schoedl,

In your online article "What Exactly Is Curved?", 02/09/2003,

you wrote:

"A tensor is typically a linear function designed to take a certain combination of input data, and convert this data to a specific set of output data.  The perfect example of a tensor is the Riemann curvature tensor.  This tensor takes three inputs, the 4-velocity of test particle along a certain geodesic, a small separation to a neighboring geodesic, and the 4-velocity of the same test particle along this neighboring geodesic."

I wonder if you know Graham Nerlich's "The shape of space",

"(W)ithout 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*."

I've been trying to link these "antennae" to the Christoffel symbols, which are 3rd rank tensors, but nothing came out from this exercise.

Why Christoffel symbols? Prof. G. 't Hooft was very kind to explain the issue (private communication, 20 January 2002): "There should not be such a thing as a 'gravitational field stress-energy' at the r.h.s. of Einstein's equations. In a co-moving frame there is no gravitational field, hence no grav. stress-energy! In any other frame where you do have effective grav. fields, you automatically get the correct grav. contribution to the stress-energy from the Christoffel symbols in the covariant derivatives."

I believe geodesics are made in a way similar to the collective movement of a shoal of fish swinging along a coral reef,

It seems to me that there is something similar in GR, in the way a test particle would "anticipate" its neighbors from the "shoal of fish", and would pinpoint its correct tangent vector "online", one-point-at-a-time, thus making a geodesic. See also "Beyond space and time", by Robert Matthews, New Scientist, 17 May 1997,

Perhaps you and your colleagues can help.

Kindest regards,

Dimi Chakalov

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