|Subject: You can't stir a coffee without disturbing a
Date: Thu, 21 Mar 2002 23:39:31 +0200
From: "Dimiter G. Chakalov" <email@example.com>
To: Robin Booth <firstname.lastname@example.org>
CC: email@example.com, firstname.lastname@example.org, email@example.com,
I'm reading your recent gr-qc/0203065 [Ref. 1] with great interest, particularly your ideas about time: "The fourth dimension in General Relativity would then take on a hyperspatial role, providing the additional dimension in Euclidean space in which the three dimensional manifold of the observable Universe can be curved. Time in Quantum Mechanics would continue to be a feature of the Lorentzian metric that overlays Euclidean hyperspace."
May I ask you to help me understand your idea above by explaining the apparent paradox of action-at-a-distance and non-locality associated with QM, which you briefly mentioned in your gr-qc/0106007 [Ref. 2].
Would you consider, for example, an interpretation of action-at-a-distance and non-locality as 'action at zero distance' that could "take place" in some hypothetical global mode of time pertaining to the whole Universe, which could also incorporate the ideas of Mach about gravity? Please see:
Please note that the hypothetical global mode of time is needed for explaining the phenomenon of transience [Ref. 3], the problem of explaining the motion, and the geometrical nature of the infinitesimal. It also provides an entirely different interpretation of the Planck scale, which could perhaps be helpful for elaborating a scale-invariant theory of gravity obeying the principle of general covariance. Let me try to explain.
The paradox of motion, which is the crux of the notion of time, is known since Zeno's first paradox (aporia). It is a paradox in the sense that Mother Nature has managed to reconcile two contradictory requirements in a way that we still can not quite comprehend.
Consider two states of a physical system, [A] and [B] , which must be different-in-time and totally separated, like sequences of snapshots from a film tape, separated by a strip | (=global mode of time).
[A] | [B]
One of the requirements is that [A] and [B] have to be totally separated, otherwise they will merge into one state only, hence there will be no time but some "block universe" with eternal 'now'. The other requirement is that [A] and [B] have to be linked *in some way* enabling the phenomenon of transience [Ref. 3]. Otherwise there is no possibility for defining time as successive foliations of a three dimensional manifold [Ref. 1].
The only way to solve this puzzle, I think, is by adopting the view that at fundamental level the spacetime is both continual and discrete (please see the two URLs above). In other words, there should be a special state of the whole Universe (I call it 'global time mode'), which does not *physically* exist in the states [A] and [B] (I call the latter 'local time mode'), being physically hidden due to the speed of light.
The implications for the nature of Planck scale are striking: the numerical values of any physical quantities describing the "elementary" volume of space, [A] and [B] , can not be reached due to the strip | called 'global time mode'. They are both numerically finite and physically unattainable boundaries of the physical world,
The finite values of Planck "volume" and Planck "time" are due to the finite nature of bodies in 3-D space at our macro-scale of tables and chairs, as measured with real numbers,
I believe Mother Nature is hiding the infinitesimal with the global mode of time, i.e., with the strip | separating the elementary "volumes" [A] and [B].
But do we really need all this heavy metaphysics? It seems to me that in order to describe the way that matter curves spacetime [Ref. 1], we need an *extended* volume of space. Measurement in physics are instantaneous in time, they provide actual information about a singular snapshot only. We can't define spacetime "curvature" over a singular, dimensionless point. Hence the paradox of transience [Ref. 3] is tacitly interwoven into the basic ideas of Einstein's GR. To understand the nature of gravity, I believe we need to solve the paradox of transience [Ref. 3] and to reveal the *dynamics* of the mechanism providing uniquely defined energy density of the gravitational field in each and every [A], [B], etc. valid for their corresponding successive foliations of a three dimensional manifold.
Also, the putative global time mode can be a very powerful tool for solving the puzzle of action-at-a-distance and non-locality associated with QM. Viewed from the local mode of time, as measured with a clock, it provides a 'zero distance' between any two or more "points", [A] , [B] , etc., and can act as some bootstrapping web correlating distant events: you can't stir a coffee without disturbing a star. Hence the implications for Machian gravity and for a dynamical structure at the most fundamental level of the Universe.
This whole story can be easily ignored iff time was non-existent, as advocated by Barbour, Rovelli and others. The problem with such timeless hypothesis is that if there is no time, there is no 3-D space either, meaning that physical bodies won't have *finite* dimensions in space,
Besides, if there was no transience [Ref. 3] and our subjective experience of time was an illusion, how could your brain manage to read this text with some feature of the Lorentzian metric that overlays Euclidean hyperspace [Ref. 1]?
I will highly appreciate your opinion on the issues above, as well as the opinion of all colleagues of yours reading this note. I will be happy to elaborate, if necessary.
Thank you very much in advance.
With kind regards,
[Ref. 1] Robin Booth. Scale invariant
gravity and the quasi-static universe. Imperial/TP/1-02/18, Tue, 19 Mar
2002 23:15:54 GMT,
"Einstein's General Theory of Relativity has proved to
be one of the most successful and enduring theories in physics, and its
predictions have been verified in numerous experiments. However, it stands
alone amongst field theories in that it is not scale invariant. For example,
the differential form of Maxwell's equations, which elegantly describe
the electromagnetic field, do not define any intrinsic scale. Conversely,
Einstein's field equations, which describe the way that matter curves spacetime,
are linked to an apparently arbitrary scale determined by the Newtonian
gravitational constant, G.
"Numerous attempts have been made to develop a theory
of gravitation that is scale invariant, and yet retains the key properties
of General Relativity, such as the principle of general covariance.
"Essentially, time provides the fourth dimension of spacetime
that allows a three-dimensional manifold to possess the property of curvature.
Alternatively, time can be viewed as providing the offset between successive
foliations of a three-dimensional manifold. Interestingly, neither the
General Relativity nor the Quantum Mechanics description of time coincides
closely with our own perception, which tends to view time as a linear flow
of events with a clearly defined past, present and future. These concepts
do not really exist at all in General Relativity time, and only do so to
a limited extent in Quantum Mechanics.
"The concept of a uniquely defined Planck scale is one of the two principal motivations for the pursuit of a quantum theory of gravity, the other being the need for the curvature terms in the gravitational field equation to be quantized in order to be equivalent to the quantized matter fields. If the Planck factor is removed, we need to ask whether there is still a need for a theory of Quantum Gravity, at least in the form currently being sought. There is no fundamental requirement that the gravitational field should have an inherent quantum structure, and it may well be more reasonable to think of the gravitational field as being quantised as a consequence of the matter fields with which it interacts.
"The QSU model also has a number of implications for the role of time. The static nature of the Universe, when viewed from a cosmological reference frame, strongly suggests that at its most fundamental level the Universe does not possess any dynamical structure. If this were to be the case then we would need to reject the concept of time in canonical quantum gravity as being the separation between successive foliations of a three dimensional manifold. The fourth dimension in General Relativity would then take on a hyperspatial role, providing the additional dimension in Euclidean space in which the three dimensional manifold of the observable Universe can be curved. Time in Quantum Mechanics would continue to be a feature of the Lorentzian metric that overlays Euclidean hyperspace.
"Finally, one can speculate that by more clearly defining
the distinction between the realms of General Relativity and Quantum Mechanics,
we can actually move closer towards constructing a paradigm that unifies
the two theories."
[Ref. 2] Robin Booth. Machian General
Relativity: a possible solution to the Dark Energy problem, and a replacement
for Big Bang cosmology.
"In Section "Time", an alternative spacetime structure
was described, which potentially allows processes to occur 'simultaneously',
but at different time coordinates. (...) The spacetime structure also offers
the intriguing possibility that processes operating in the cosmological
reference frame, i.e. across the whole Universe, can occur in the same
time as local processes occurring in the atomic reference frame. If this
were to be the case, then it provides a mechanism for explaining the apparent
paradox of action-at-a-distance and non-locality associated with Quantum
[Ref. 3] Abner Shimony, Implications of Transience for Spacetime Structure, in: S.A. Huggett, L.J. Mason, K.P. Tod, S.T. Tsou, and N.M.J. Woodhouse (eds.), The Geometric Universe: Science, Geometry, and the Work of Roger Penrose. Oxford: Oxford University Press, 1998, pp. 161-172.
"Even more problematic is the role of transience in physical
theory. Classical mechanics, special relativity, and general relativity
differ profoundly in their assumptions about spacetime structure, but in
all three the structure is characterized without any reference to the slipping
away of the present moment into the past."
P.S. Regarding the problem of defining "curvature", in my preceding email
let me quote from Mark Stuckey's "Static for Dynamism: Reductive Pregeometry and Unification":
"In GR for example, spacetime is modeled as a differentiable manifold, as it and its supporting cast of local structures, e.g., tangent and co-tangent spaces, are well-suited for the local description of trans-temporal objects. Wald writes, "It is the notion of 'infinitesimal displacements' or tangent vectors which lies at the foundation of calculus on manifolds." [Wald, R.M. (1984). General Relativity. Chicago: University of Chicago Press, p. 14.] Not surprisingly, the tangent and co-tangent spaces provide the basis for tensor representations of matter, momentum, and energy."
But the quantity proposed by Einstein for the gravitational field stress-energy turned out *not* to be a tensor [Weyl, H. (1922), Space-Time-Matter, Fourth Edition, translated by Henry L. Brose. Reprinted by Dover Publications, New York, 1951, p. 270].
Do you agree with my interpretation suggested at the URL above?
Also, can you think of 'zero distance' interactions in the putative global time mode to resolve the problem in
Carroll O. Alley, Darryl L. Leiter, Yutaka Mizobuchi,
Huseyin Yilmaz. Energy Crisis in Astrophysics (Black Holes vs. N-Body Metrics).
without resorting to any background field in the local mode of time, i.e., NOT along the lines suggested by Huseyin Yilmaz?