Dear Professor Margon,

I spotted your name in "Before the Bang: Who Turned the Key?"
http://www1.cac.washington.edu/alumni/columns/
march96/universe1.html

"Margon has addressed this question, too. As he told the Washington Post last year, "One would think that if someone has trouble reconciling religion with physics, they would like the big bang. It has beautiful elements of ultimate mystery."

Perhaps we can postpone the reconciliation of religion with physics. It sounds to me like blending papaya with tuna fish.

I believe a tentative solution to the "ultimate mystery" can be sought in the following text from Ned Wright,

"Balloon Analogy in Cosmology",
http://www.astro.ucla.edu/~wright/balloon0.html

"But the balloon analogy is a 2-dimensional model, and the center of the balloon and the space around are not part of the 2-dimensional Universe. In our 3-dimensional Universe, these points could only be reached by traveling in a 4th spatial dimension (not the time dimension of 4-D spacetime), but there is no evidence that this dimension exists."

If this 4th spatial dimension does exist in Nature as some 'global mode of spacetime',  T , then perhaps the physical time measured with a clock,  t , can be modeled with a curve tending asymptotically toward the Beginning placed at  T=0 . The simplest way to say this is by postulating Txt=1 , bearing in mind that there is no direct evidence that this 4th spatial dimension exists *physically* as a privileged reference frame

http://members.aon.at/chakalov/Krasnikov.html#4

Hence the choice of local time,  t , is arbitrary in GR,

http://members.aon.at/chakalov/Shimony.html#Butterfield_Isham

and we hit all sorts of problems with  t , like the problem of  t  in canonical quantum gravity, the problem with the inner product in the Hilbert space of physical states (they have to be both invariant under Diff(M) and somehow conserved in t ), the problem of Perennials,

http://members.aon.at/chakalov/intro.html#Kuchar93

and the problem of  t  in quantum cosmology,

http://members.aon.at/chakalov/Halliwell.html#3

We may also speculate that a physical observer measuring t  would gather the impression that  T  refers to 'the only truly isolated system' with frozen  t  , as implied by Wheeler-DeWitt equation. Strangely enough, this same physical observer would try to detect some GR "waves",

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

although no physical device could measure the component of these "waves" along  T .

To cut the long story short, I don't think these ideas are original, but couldn't find them in Ned Wright's tutorial pages.

The interesting stuff comes if we think of  T  and  t  as two parameters of Arthur Koestler's Holon,

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

http://members.aon.at/chakalov/LHC.html#Holon

but I'm afraid that's a bit too difficult to digest, like blending papaya with tuna fish. I fear that you and your colleagues might not like it at all.

But I'm wondering, can you cook something better?

Best regards,

Dimi Chakalov
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.
 

Note: Two days ago, I tried to explain the hypothetical global mode of spacetime  T  (please see above) to my 17-year old son Nicky, since he and his teenager gang are my 'test bed' for PHI -- my forthcoming CD ROM is intended for very young people and for those who have retained a young spirit and open mind. My son got it for nearly 3 min. Let's see if it will work for the readers of these lines.

Imagine a circle like your wristwatch, and you sitting at point '9' at  T . Blow up the circle by increasing its radius (=expansion of the universe, after the inflation scenario; see Shinji Tsujikawa, hep-ph/0304257, p. 9, Fig. 1). Since you're in the global mode of spacetime  T , you have the privilege of expanding the circle up to the stage at which the radius of the circle will be infinite and any tangent vector at the point '9' will be zero. Zilch. You will be on a perfect flat 1-D line. But immediately after this special state, you will be again in a 2-D space, only this time it will be with a negative curvature, like a torus.

At this point my son looked at me with big open eyes, since these stories are not quite popular in the rap "music", I suppose. But I quickly regained his interest by adding the following explanation.

Imagine that you can break the circle at the points '12' and '6', so the same will happen to your neighbor at point '3'. The points '9' and '3' do not move, they simply belong to either a sphere or wind up on a torus, and then go back to sphere, like the circle of your wristwatch. What is a torus, dad? A doughnut, Nicky! Now he got it all. Besides, there is a nice screen saver in Windows 98 and above, which shows the non-smooth transition of sphere to torus and back, which my son knows very well. All this mental exercise took no more than 3 min, as read by my good old wristwatch.

I didn't ask Nicky to tell me how the center of the wristwatch will be instantaneously teleported upon the sphere-torus-sphere... transitions, and whether a left glove in the sphere will be converted into a right glove in the torus, but I told him an old joke about how a mathematician can catch a lion in Sahara. First, he will make sure that there is at least one lion available, then he will build a cage, go inside it, and will invert the space w.r.t. the cage surface, such that all points from inside will be teleported outside, and the other way around. Then the mathematician will wind up outside the cage, and the poor lion will be trapped inside! [Relieved, my son picked some cash and left the house to catch up with his (girl)friends.]

This is just some background prerequisites for understanding the ideas about topology of space: the 'center of the wristwatch' is supposed to model a "point" on a smooth differentiable manifold in a new, extended active group of transformations or 'moving points around'. This might sound strange, but recall that in Feynman path integral approach we have the same 'sniffing' of all virtual paths, only we can't build quantum gravity from the standard model.

Perhaps this could help us understand, and eventually solve, two big puzzles. Read about them here and here, and keep in mind that the mechanism of inflation is pre-build in the dynamics of the 'center of the wristwatch', in the exponential expansion of  T  near the break point, by jumping from sphere to torus and back. Hence we inevitably discover this blueprint from  T  in the local mode of spacetime, along with CPT-invariance, but our current inflationary models presume that The Beginning has been some 13,7 billion years ago, as inferred from the physics of the universe in the local mode of spacetime.

Is this true? Jain! It is both true and false. Surely the universe has a beginning, only inside each and every moment 'now', as projected from the 'center of the wristwatch', it undergoes a genuine re-creation. Hence in such Phoenix Universe the "beginning" and the "end" are well-hidden inside each and every "point" of the 3-D space, since every "point" belonging to the 3-D space is being continuously created along the universal time arrow (recall the old story about the dragon chasing its tale here, as explained on 31 July 2001). Briefly, the spacetime is dual, and so is the "age" of the universe. Its ultimate "fate" is undecidable (cf. Paul Frampton and Tomo Takahashi, astro-ph/0211544; Hitoshi Kitada, gr-qc/9910081). Thank God, everything is possible: "Time is Nature's way to keep everything from happening all at once" (John Wheeler).

Driven by the optimistic remark of John Wheeler (he is a deeply religious person obsessed by anti-theism, and told me that he saw this famous remark written on a wall in a coffee bar in Austin), I've been trying (without success so far) to cast this story in the framework of Kruskal-Szekeres diagram, since I believe the so-called black holes are artifacts: they are "accessible" in the global spacetime only, just like the break points from the example above. I don't believe in "information loss" either (cf. Claus Kiefer, gr-qc/0304102). Nothing should be lost in the universe, it just goes "temporarily" in the global mode of spacetime (much like Jungian archetypes, but that's a bit different story).

I will be very happy to learn about the "rotation" of the universe, since its "spin" (see M. Everaldo de Souza here) should come from  T  as well. We can't visualize "spin", it's simply what Wolfgang Pauli called 'klassisch nicht beschreibbare Zweideutigkeit'. Sounds nice, but now we need math to unravel all blueprints from  T  left in the local mode of spacetime, and get the job done.

All questions and comments will be appreciated.

Dimi Chakalov <dchakalov@surfeu.at>
May 2, 2003