Regarding your physics/0311037, "Quantum Gravity Phenomenology", in the November 2003 issue of Physics World:  isn't it true that quantum gravity is needed to understand the very nature of gravity in the classical theory of gravitational field, after Einstein?

See what happens if we treat spacetime as continuum,

http://members.aon.at/chakalov/Montesinos.html

It seems to me that the task of quantizing spacetime is utterly clear, hence we need quantum gravity to understand GR. However, can we get this job done in the framework of canonical quantum gravity? Angelo Loinger says "no" [Ref. 1].

Can you or some of your colleagues remove/bypass/avoid the initial problem of continuum?

Regards,

Dimi
--
http://members.aon.at/chakalov
http://members.aon.at/chakalov/white_paper.html

Reference

[Ref. 1] Angelo Loinger, "Quantum gravity": an oxymoron,
http://arxiv.org/abs/physics/0308042

=========

Subject: Re: gr-qc/0201012
Date: Sat, 12 Jan 2002 09:02:28 +0200
From: "Dimiter G. Chakalov" <dchakalov@surfeu.at>
To: Giovanni Amelino-Camelia <Giovanni.Amelino-Camelia@cern.ch>
CC: moffat@medb.physics.utoronto.ca, baez@math.ucr.edu,
     don@phys.ualberta.ca, jb56@cus.cam.ac.uk, youssef@bu.edu,
     newman@pitt.edu
BCC: [snip]

On Mon, 7 Jan 2002 12:37:55 +0100 (MET), Giovanni Amelino-Camelia wrote:
>
> Dear Dimiter
>
> among your comments to maguejo I sympathize particulrly with
> desire to have planck as absolute cutoff.

I think it is a very special kind of a cutoff, as I tried to explain at

http://members.aon.at/chakalov/Magueijo.html

Let me try to elaborate more on this unique cutoff, a numerically finite but physically unattainable boundary of the physical world. It is highly important not to 'invent the wheel', so I will later try to explain briefly the natureof this puzzling 'final frontier' from philosophical perspective. Let me first stress that a seemingly simple recipe for deriving the Planck constant, as explained by John Baez [Ref. 1], can not reveal the nature of Planck scale. Recall Murphy's Law No. 15: Complex problems have simple, easy-to-understand wrong answers.

What we perhaps need is a much broader framework, including issues such as the cosmological time arrow and all varying "constants", for example, the varying "speed" of light (John Moffat has elaborated extensively on this topic, cf.[Ref. 2]) and the fine structure "constant", 

http://members.aon.at/chakalov/PHI.html#Webb

Suppose all these pseudo-constants can not only change but also adjust dynamically their values -- Panta rei -- in different epochs along the cosmological time, so that their current, transient values would depend on the particular epoch (instant-of-observation) from the cosmological time arrow.Example: the "miraculous" coincidence problem in the cosmological constant problems (e.g., A. Vilenkin, hep-th/0106083).

A radical solution can perhaps be sought along the "disappearance of time" in background-independent theories,

http://members.aon.at/chakalov/right.html#Baez_April97

If the metric is treated as a field which not only affects, but also is affected by, all the other fields present at the particular epoch, then the geometry of spacetime becomes a local degree of freedom of the theory [Ref.1]. Locally, however, there is no "background time parameter", which is a bona fide case for the two modes of time: the global mode of time 

http://members.aon.at/chakalov/PHI.html#dark_room

http://members.aon.at/chakalov/Ashtekar.html

is the only reference object w.r.t.w. one can define the dynamics of all local degrees of freedom, geometry of spacetime included. Hence the global mode of time can be the 'back bone' of background-free quantum gravity, and can provide some self-tuning mechanism determining the temporal values of all pseudo-constants, relative to the corresponding epochfrom the evolution of the universe. Thus, the nature of Planck scale cutoff could be tied up with the nature of The Beginning. It is also a kind of a cutoff, but we can trace back the evolution of the universe only to some "already-physical" state that is tending asymptotically toward The Beginning. Perhaps the case with the Planck scale cutoff is similar, if not identical.

Consider, for example, two observers in two very distant time epochs, in 2002 (Giovanni) and shortly "after" The Beginning (Andrei), i.e., during the putative fast-roll inflation (A. Linde, hep-th/0110195). Giovanni would say that Andrei's universe was "small" compared to his universe in year 2002, and also that Andrei's metric was "expanding" exponentially, 

http://members.aon.at/chakalov/readme1st.html#Kolb

but what would Andrei say about his universe at his epoch? Perhaps Andrei would see his universe exactly as Giovanni sees his in year 2002, thanks to the dynamical self-adjustment of all pseudo-constants. 

Let me try to explain. Do you remember the old joke from Martin Gardner about two people whose ship sank and were left on an island for many years, and one day they found a big Coca-Cola bottle (they know only the small ones), and one of them said "Look, we got shrunken!"

To find out whether or not they got shrunken, they have to compare two causal histories: their history on the island with the one at the Coca-Cola factory. No problem in classical physics, but if you try the consistent (decoherent) history interpretation of QM, you have to think of the state ofa quantum system *between* observations, which exist as 'objective reality' at the very instant of observation (the notion of simultaneity!) but has *not yet* been physically observed due to the finite speed of light. We can't have this luxury in QM, which is why I can't see how one could suggest a theoryof Lorentz invariant nonlocality (unless we employ the global mode of time, but then we have to drop the basic postulate of a 'consistent history').

It seems to me that if Andrei can have some tacit presumption about some *not yet* observable state of Giovanni after, say, 15 billion years, then the two guys could *in principle* compare their universes at their epochs, and agree on the duration of time separating them, the size of their universesand their spacetime metrics, and finally compare the size of objects in the two universes (Coca-Cola bottles, say), and determine which one has *in fact* shrunken. NO WAY!

This is the crucial point: the notion of simultaneity, as in Einstein's paper in Annalen der Physik from 1905,

http://members.aon.at/chakalov/PHI.html#simultaneous_events

We don't have the possibility to think about The Beginning and today "at the same time", and then measure some invariant that does not change under Lorentz transformations. Hence we can't answer the question "what was the value of the speed of light 15 billion years ago, was it bigger, equal, or smallerthat that of today?" If the spacetime metric changes dynamically, a Coca-Cola bottle will be the same size for Andrei in his universe 15 billion years ago, and for Giovanni in year 2002. The dimensions of the bottle will be determined by the corresponding pseudo-constants, and since the latter change, the bottle remains *the same*, for both Andrei and Giovanni. It's all relative to their corresponding universes at their epoch from the cosmological time arrow.

This is another relative-state philosophy, which Ibelieve Hugh Everett would have liked very much!:-) Point is, we don't know and can *not* know the exact duration of cosmological time separating Giovanni and Andrei. We simply can not compare their universes which change along the local, cosmological time. 

So, what do you think about the metric tensor and all "fundamental constants" being local dynamical variables subject to adjustment and fine tuning? Can we make Lorentz invariant measurements on their "true" (if any) values? Myguess is in the negative, since we are physically confined inside our temporary, transient universes, and hence can not compare them from the *local* mode of time.

But what is the so-called global mode of time? Operationally, it can be explained as "the phenomenon which does not allow things to go into zero dimensions, such as a mathematical point",

http://members.aon.at/chakalov/PHI.html#point

Philosophically, the effect of the global mode of time can be explained as follows. There is a very nice paradox called Thompson's lamp: imagine a lamp that is 'on' for 1 min, then 'off' for 0.5 min, then 'on' for 0.25 min, etc.Do we have a limit? If you say 'yes', what is the state of the lamp at the instant of time at the "end" of this limit? We have not two but *three* puzzles here: the state of the lamp at the initial instant (t_1), the state of the same lamp after two min (t_2), and the nature of the cutoff  t_0. The latter can go back to Andrei, 15 billion years ago, but never at The Beginning. The duration of the two instants, t_1 and t_2, can only tend asymptotically toward the Planck length, too. What is also very intriguing here is that the cutoff t_0, with which we measure any *finite* intervals, like  (t_2 - t_0) - (t_1 - t_0) = 2 , can not only go back to Andrei but approach asymptotically t_1 as well.

Hence it seems to me that the true physical model of "point", with which you can develop a complete theory of quantum gravity, should be sought with the Lawvere-Kock Synthetic Differential Geometry: a ring that contains a dimenionless point "inside it", but can never shrink to reach it.

Perhaps you can attach to this ring -- in the global mode of time -- two virtual worlds with inverted spacetime basis, 

http://members.aon.at/chakalov/Ford.html

Think of these two virtual worlds as two "waves" which, in the case of a quantum world (cf. the URL above, H2 , [delta] taking some finite value sufficiently bigger than zero), produce a third, *quantum* wave at the localmode of time. This is my feedback to the idea of Chris Isham about a radically new quantum theory [Ref. 3], which he has been suggesting for over sixteen years now,

http://members.aon.at/chakalov/readme1st.html#Isham

In the global mode of time (the 'dark room', please see above), the two "waves" are NOT YET quantum waves.

Si non e vero e bene trovato, eh?;-)

Regards,

Dimi

P.S. You can read this email also at

http://members.aon.at/chakalov/Giovanni.html

May I suggest, for your convenience, to download my web site, less than 550 KB, from

http://members.aon.at/chakalov/chakalov.zip

Please unzip in some empty folder and open  Giovanni.html  with your web browser.

If you wish to read the whole story, open  index.html .

All files were scanned with Norton AntiVirus 2002, v8.00.41C, virus definitions from 9 January 2002, and were found virus free.

D.
 

References

[Ref. 1] John C. Baez. Higher-Dimensional Algebra and Planck-Scale Physics, January 28, 1999.
http://xxx.lanl.gov/abs/gr-qc/9902017

"It is reasonable to suspect that any theory reconciling general relativity and quantum theory will involve all three constants c, G, and h. Planck noted that apart from numerical factors there is a unique way to use these constants to define units of length, time, and mass. For example, we can define the unit of length now called the 'Planck length' as follows: (...)
...
These two lengths become equal when  m  is the Planck mass. And when this happens, they both equal the Planck length!"
 

[Ref. 2] J.W. Moffat. A Model of Varying Fine Structure Constant and Varying Speed of Light.
http://xxx.lanl.gov/abs/astro-ph/0109350
 

[Ref. 3] J. Butterfield, C.J. Isham. Spacetime and the Philosophical Challenge of Quantum Gravity.
http://xxx.lanl.gov/abs/gr-qc/9903072

"4. Start ab initio with a radically new theory.

"The idea here is that both classical general relativity and standard quantum theory emerge from a theory that looks very different from both. Such a theory would indeed be radically new. (...) So the kind of theory envisaged here would somehow be still more radical than that; presumably by not being a quantum theory, even in a broad sense -- for example, in the sense of states giving amplitudes to the values of quantities, whose norms squared give probabilities."