Dear Dr. Dadhich,

I like your recent paper [Ref. 1] very much. I think quantum gravity is needed for understanding the world around us, at the scale of tables and chairs.

You stressed that (i) spacetime must have micro-structure which could accord to quantum principle, and (ii) [lambda] cannot be zero and hence any quantization scheme should have to address it. [Ref. 1]

Regarding the first issue, I've been trying to introduce a *global mode of spacetime* which keeps the potential outcomes of all physical interactions in a special holistic state called Holon. These potential outcomes are "the same for all observers", hence constituting an absolute reference frame needed for the quantization of spacetime,

http://God-does-not-play-dice.net/Carlip.html#1

Following the principle by David Hilbert quoted below, the meaning of "the same for all observers" can be understood with a simple experiment at

http://God-does-not-play-dice.net/Azbel.html#self

Please note that these potential outcomes are UNspeakable,

http://God-does-not-play-dice.net/McGuire.html#note

As to the enigmatic [lambda], please see the cancellation process in

http://God-does-not-play-dice.net/about.html#NB

It can go down to the the Planck length and back to the scale of tables and chairs,

http://God-does-not-play-dice.net/Yang.html

I will be happy to elaborate, should you or your colleagues are interested.

Best regards,

Dimi Chakalov
--
A sentence about nature, expressed in coordinates, is only then a proposition about the objects in nature, if the sentence has a content which is independent of the coordinates. ("Ein in Koordinaten ausgedrüuckter Satz über die Natur ist nur dann eine Aussage über die Gegenstände in der Natur wenn er von den Koordinaten unabhängig einen Inhalt hat.")

D. Hilbert, Grundsätzliche Fragen der modernen Physik, Lecture I. Hamburg, July 26, 1923
 

Reference

[Ref. 1] Naresh Dadhich, Universality, Gravity, the enigmatic [lambda] and Beyond, gr-qc/0405115 v1

"The quantum principle is universal. Going by the guiding principle of universality, it must be expressible as a property, like the speed of light, of spacetime. This has unfortunately not happened. What is required is exactly what Minkowski did to SR by synthesizing the speed of light into the spacetime structure. This is however very difficult because synthesis of quantum principle with the spacetime would ask for discrete structure which is in contradiction with the inherent continuum of spacetime. However so long as this doesn't happen quantum theory will remain incomplete. Thus for completion of quantum theory it would be required that spacetime must have micro-structure which could accord to quantum principle. It is the geometry of that which would synthesize quantum principle with the spacetime. This is an open question of over 100 years standing.
...

"We remain bound to the 4-dimensional spacetime and there is no background spacetime relative to which spacetime is being quantized.
...

"Finally, we have argued quite forcefully that [lambda] cannot be zero and hence any quantization scheme should have to address to it [12]. I think that there must exist some basic link connecting [lambda] with the Planck length which needs to be discovered. That may hold the key to the problem."

===============

Subject: Re: The enigmatic [lambda]
Date: Fri, 28 May 2004 05:53:42 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: cirinag_ngp@sancharnet.in
CC: Naresh Dadhich <nkd@iucaa.ernet.in>, nabhan@iucaa.ernet.in,
     smajor@hamilton.edu, yang@castu.tsinghua.edu.cn,
     gj_ni@yahoo.com, cmw@wuphys.wustl.edu, wfdavis@davis-inc.com,
     amallios@cc.uoa.gr

Dear Sanjay,

Thank you for your reply. May I ask you to send your comments to my email address only: I don't want to start some discussion list.

> The Lambda-term is a part of the Einstein field equations because
> we demand the vanishing of the divergence of both the sides of the
> Einstein field equations on the basis of the conservation principles
> and the Lambda-term appears in the most general form of the
> geometric side of these equations. True this. This has what has led
> to the idea of ``dark energy''  and much efforts are directed at
> modelling the role of this dark energy in determining the
> cosmological model.

Sure, but we totally ignore the main problem,

http://God-does-not-play-dice.net/Hongsheng.html

I will reply to your comments in a separate private email.

Best regards,

Dimi
--
http://God-does-not-play-dice.net

===============

Subject: Re: The enigmatic [lambda]
Date: Fri, 28 May 2004 21:17:26 +0300
From: Dimi Chakalov <dimi@chakalov.net>
To: Sanjay M Wagh <cirinag_ngp@sancharnet.in>

Dear Sanjay,

Thank you, once more, for your email of Fri, 28 May 2004 08:28:45 +0530. It seems to me that you've chosen a very different approach to the main problem of the so-called dark energy, and the whole bundle of questions raised at

http://God-does-not-play-dice.net/Dadhich.html

This is great, since we need to examine the enigmatic [lambda] from different perspectives. My approach is outlined at

http://God-does-not-play-dice.net/Hongsheng.html

http://God-does-not-play-dice.net/Professor_X.html#Negative_Mass

> However, the problem is again the same: matter and geometry are
> separately treated even in these equations. But, any such treatment
> is completely against the very basis of the conception of any
> dynamic geometry (field) as representation of matter, ie, the metric
> of geometry changing as matter fields change.

Here's the crux of the issue: we have two entirely different entities, apples [the metric of geometry] and oranges [matter fields], which change *in time*.

In what 'time'? The puzzle is that in GR we define 'spacetime' only and exclusively only as 'structural quality of the gravitational field'.

So, we have a bi-directional "talk" between apples and oranges, which is totally "outside" and "before" fixing the spacetime. The latter is the end result, the final outcome from the "talk" that creates spacetime. Not surprisingly, nothing moves in this frozen static spacetime, as stressed by Bob Geroch,

http://God-does-not-play-dice.net/Pullin.html#3

The enigmatic [lambda] is NOT there.

Going back to the paradox of the bi-directional "talk" of our apples and oranges, please note that we have the same paradox in human brain dynamics,

http://God-does-not-play-dice.net/white_paper.html#brain

I believe the solution to the paradox of human brain dynamics can be applied to the same end-result paradox of the talk between our apples and oranges. In both cases we anticipate the "end result", but because we do that on a *perfectly continuos* manifold, we need the putative global mode of spacetime.

This is the crux of the problem: a *perfectly continuos* manifold down to the Planck scale, and back to the scale of tables and chairs. If we try the current spin network hypotheses, we cannot recover the continuous nature of 4-D spacetime, as acknowledged by Lee Smolin,

http://God-does-not-play-dice.net/Smolin.html#smooth

See also the problems in Ashtekar's background-free program,

http://God-does-not-play-dice.net/Kiefer.html#relational

We are not allowed to consider some *real* gaps needed for the aplles-oranges talk, in which the end-result is still in the state of 'being negotiated'.

We cannot pinpoint these gaps in the (local mode of) spacetime, and hence cannot find the enigmatic [lambda] either. It's all in the global mode of spacetime, just as in the case of the human brain.

See also the interpretation of the affine structure, by Graham Nerlich,

http://God-does-not-play-dice.net/Nerlich.html#3

The very notion of affine structure implies anticipation. We define and compute a geodesic as 'locally straightest path' on a sheet of paper,

http://God-does-not-play-dice.net/Frank.html#note

but how does it emerge 'out there'? Does Mother Nature make a geodesic statistically, by try and error?

> Surely, quantum theoretical formalism provides us only statistical
> inferences.

Surely we cannot develop quantum gravity from statistical inferences.

I hope to deliver my thoughts on a new quantization scheme at GR17 in Dublin,

http://God-does-not-play-dice.net/GR17.html

It's about the quantum gravity of He Who Does Not Play Dice: the whole universe modeled as a human brain. I believe we can have a perfectly continuos and background-free local mode of spacetime, and a brand new absolute reference frame in the global mode of spacetime. More from Steve Carlip,

http://God-does-not-play-dice.net/Carlip.html#1

BTW it's worth noting that the end-result paradox mentioned above is still haunting the Objective Reduction (OR) hypothesis of Roger Penrose, based on his interpretation of the gravitational "self-energy",

http://God-does-not-play-dice.net/Penrose.html#Hameroff

You have something that is supposed to 'roll over' a particular threshold, and then -- voila! -- you have OR and subsequently *events*. Only you cannot ask the question of what is going on "before" the final stage called OR. Roger Penrose can calculate it on a sheet of paper, but he hasn't answered any of the questions raised during the discussion of his OR hypothesis at Q-Mind Forum, from 1998 to 2000.

Now, Sir Roger has agreed to share his insights at GR17 in Dublin on Friday, July 23rd, with a lecture entitled "Fashion, Faith, and Fantasy in Modern Physical Theories",

http://www.dcu.ie/~nolanb/gr17_social_programme.htm#Public Lectures

I *love* this title! See also a similar lecture by Kip Thorne,

http://God-does-not-play-dice.net/Kopeikin.html#Kip

Can't wait!!!

The only problem, as of today, is that I am allowed to compete with all your colleagues with a tiny little poster,

http://God-does-not-play-dice.net/about.html#poster

It's like that: [all your colleagues at GR17] vs [Einstein & poster].

Do you believe somebody will come to see my poster? I'm still waiting to hear from you regarding my proposal for Einstein's 125th birthday,

http://God-does-not-play-dice.net/Wagh.html#QM

Best regards,

Dimi
--
http://God-does-not-play-dice.net
 
 

Note: I've conjectured that [lambda] is NOT living in the local mode of spacetime, since it has to be effectively zero there, namely, 'tending asymptotically toward zero' due to the dynamical nature of the cancellation process. It's all about the dynamical nature of "points".

Let me emphasize that the global mode of spacetime is validated by the requirement for a perfect (not coarse-grained) continuum in the local mode of spacetime. Another reason why [lambda] is not living in the local mode of spacetime is that the "thickness" of the latter needs to be effectively zero but not strictly zero. If it were strictly zero, the elementary increment of the cosmological time will be strictly zero as well, leading to a 4-D "block universe" (perdurance) and the whole bundle of controversies with the creation of such "block universe", such as the definition of any finite cosmological time interval: the sliding cut-off is only in the global mode of spacetime.

The concrete idea of the elementary increment of the cosmological time is here; some speculations on the topological transitions in the cancellation process can be read here. The first two hurdles toward this brand new Quantum Cancellation Theory (QCT) are (i) the hypothetical symmetry called 'space inversion' that has to be included in the active diffeomorphism invariance, and (ii) the problem of 3-D space in GR.

Then comes the re-examination of Mach's principle and the origin of inertia (cf. J. Barbour and H. Pfister, Mach's Principle: From Newton's Bucket to Quantum Gravity, Birkhäuser, Boston, 1995), since we have the "instantaneous" fixing of the inertial mass (the resistance of a body to a change in motion) not by "distant stars" but by 'everything else in the universe', just as in the case of the Holon in the quantum world. Then perhaps we will approach the correct mathematical presentation of what is currently interpreted as 'energy-components of the gravitational field' and 'spacetime curvature'.

Please follow the links, and don't forget that quantum theory gives us only statistical predictions about outcomes from QM measurements, but it says nothing about the nature of the quantum world and its transition to the classical world. Hence Einstein's dictum "God casts the die, not the dice".

I've been working on this project since May 1989, but cannot squeeze it on a poster. Perhaps many people, not just Ed Witten, cannot sleep because of the enigmatic [lambda]. I hope this can help, not only for their sound sleep but also for the development of QCT which should be design with the main priority of explaining the emergence of spacetime. The task is known since 1935. It's about time.
 

D. Chakalov
May 29, 2004
Last update: June 1, 2004
--
Is it not possible that perhaps gravitation is due simply to the fact that we do not have the right coordinate system?

Richard Feynman, "Lectures on Physics"
 

The representation of matter by a tensor was only a fill-in to make it possible to do something temporarily, a wooden nose in a snowman.

Albert Einstein, April 14, 1954