P.S. Here is a quote from Max Tegmark's essay:

"The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 10^28 meters from here. This distance is so large that it is beyond astronomical, but that does not make your doppelgänger any less real. The estimate is derived from elementary probability and does not even assume speculative modern physics, merely that space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate."

I believe your readers know that the "distance" between the May issue of Scientific American and its doppelgänger can not be calculated. The estimate is derived not from "elementary probability" but from wishful thinking: the problems of defining 'probability' in a multiverse are widely known.

May I suggest Dr. Tegmark to check up his math. If he is right, I hope to find his doppelgänger article in section "Antigravity" in the same May issue of Sci American that is just 10 to the 10^28 meters from here.

D.C.
 

On Fri, 25 Apr 2003 19:40:58 +0300, Dimi Chakalov wrote:
>
> Dear Sir,
>
> There is something very strange in the current issue of Scientific
> American of April 24th: "Parallel Universes", by Max Tegmark
> (April 14, 2003),
>
>
http://www.sciam.com/print_version.cfm?articleID=
000F1EDD-B48A-1E90-8EA5809EC5880000
>
> "A common feature of all four multiverse levels is that the simplest
> and arguably most elegant theory involves parallel universes by
> default. To deny the existence of those universes, one needs to
> complicate the theory by adding experimentally unsupported
> processes and ad hoc postulates: finite space, wave function
> collapse and ontological asymmetry."
>
> Surely Dr. Tegmark knows very well the unresolved problems of
> Einstein's GR,
>
> http://members.aon.at/chakalov/Nature.html#note
>
> Perhaps it would be a better idea if he focuses his professional
> efforts on the real issues in his field of expertise, not "parallel
> universes" or New Age.
>
> Yours faithfully,
>
> Dimi Chakalov
> http://members.aon.at/chakalov
> --
> Dead matter makes quantum jumps; the living-and-quantum
> matter is smarter.

=====

Explanatory note: What makes the story about Max Tegmark's "Parallel Universes" really bizarre is that he is professional cosmologist and knows very well that the so-called cosmic equator in the cosmic microwave background radiation (see below) does not support any of the three possible space topologies.

According to Einstein's GR, we have three possibilities, depending on the distribution of matter and energy: Euclidean, spherical, or hyperbolic. All this is explained in the April 1999 issue of Scientific American, "Is Space Finite?", by Jean-Pierre Luminet, Glenn D. Starkman and Jeffrey R. Weeks. Max Tegmark did quote this article, and he should be fully aware of the fact that the puzzle of space topology is far from clear: (i) 96 per cent of the universe consists of some unknown stuff called 'dark matter' and 'dark energy', and (ii) the most reliable observational data do not support any of the three possible space topologies.

What if Mother Nature is smarter and has managed to employ all three possibilities for space topology? Perhaps in the global mode of spacetime we have both spherical and hyperbolic topologies pertaining to two virtual worlds, material and tachyonic, while in the local mode of spacetime we have a perfectly flat space -- on a single "point" only. Hence we observe, along the universal time arrow, a "mixture" of all three cases, and have two ages for the universe: finite in the local mode of spacetime, and infinite (indecisive) in the global mode of spacetime, as explained in my FAQ.

Of course, all this will be wrong if only Dr. Tegmark can tell us what is the topology of space by using the format "either - or", and then calculate the "distance" between him and his blond doppelgänger, just 10 to the 10²⁸ meters from here.

It seems highly unlikely the the moment of truth will come out soon, however. The story goes even more blurred and messy. In a recent astro-ph/0307282 of July 16, 2003, "The significance of the largest scale CMB fluctuations in WMAP", submitted to Physical Review D, we read the following:

"In other words, we have ruled out the "plain bagel" small universe model. A more ambitious six-parameter "everything bagel" circle search, corresponding to the general case of arbitrary topologies, is currently being carried out by Spergel and collaborators, and will be presented in a forthcoming paper [35]. This should provide decisive evidence either for or against the small universe hypothesis. If this circle search confirms our finding that small universes cannot explain the anomalies, we will be forced to either dismiss the anomalies as a statistical fluke or to search for explanations elsewhere, such as modified inflation models [21-26]. Even the fluke hypothesis might ultimately be testable, since it may be possible to improve the signal-to-noise of the large scale power spectrum beyond the WMAP cosmic variance limit by employing cluster polarization [36, 37] or weak gravitational lensing [38] techniques."

In plain English: we're waiting for some "decisive evidence either for or against the small universe hypothesis" from David Spergel et al. (in preparation).

I bet that the so-called small universe hypothesis will be sacked. If so, we'll be presented with two alternative routes:

1. Explore that Big Mess of the topology of the universe by some newly modified inflation models. The zoo of inflation models is enormous; read about it here. Perhaps Alex Starobinsky could suggest yet another, custom-made inflation model, to explain exactly how stars could have started forming only 650 million years after Time Zero. Only the Big Mess will grow bigger and endless. Why? Because 96 per cent of the stuff is unknown, and it is precisely this unknown "dark" stuff that determines the topology of space and the mechanism of "inflation", if any. If we trust the current inflationary scenarios, we live in an eternal universe in which an infinite amount of 3-D space is produced. Infinite -- nothing more, nothing less. Then there will be an infinite number of regions very similar
to ours and an infinite number of existing observers, perhaps very similar to us (cf. Ken D. Olum, gr-qc/0303070). We should expect our neighbors to pop in very soon (the number of their visits could have been infinite as well), and explain where we went wrong with Hawking's chronology protection conjecture, Penrose's cosmic censorship hypothesis, and the conflict between quantum physics and gravity in general. Then everything will be just fine.

2. Acknowledge the possibility above and start from scratch. We need to understand the nature of 3-D space in classical GR. First things first.

Watch this space!

Dimi Chakalov
Sunday, April 27, 2003
Latest update: Sunday, August 3, 2003

====

Subject: The topology of the universe
Date: Mon, 21 Jul 2003 15:57:05 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: max@physics.upenn.edu, angelica@higgs.hep.upenn.edu, alstar@itp.ac.ru, dns@astro.princeton.edu
CC: mturner@oddjob.uchicago.edu, c.doran@mrao.cam.ac.uk, gerlach@math.ohio-state.edu, Gary.F.Hinshaw.1@gsfc.nasa.gov, Charles.L.Bennett.1@gsfc.nasa.gov, guth@ctp.mit.edu, shinji@resceu.s.u-tokyo.ac.jp, unruh@physics.ubc.ca, don@phys.ualberta.ca

Dear Colleagues,

Please see the update at

http://members.aon.at/chakalov/Tegmark.html#either_or

A penny for your thoughts!

Regards,

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

=====

Subject: How much entropy do we "see" in the cosmic equator?
Date: Wed, 23 Jul 2003 14:42:38 +0300
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Willy Fischler <fischler@physics.utexas.edu>, Amit Loewy <loewy@physics.utexas.edu>, Sonia Paban <paban@zippy.ph.utexas.edu>
CC: Robert McNees <mcnees@zippy.ph.utexas.edu>, Tom Banks <banks@physics.rutgers.edu>

Dear Colleagues,

Regarding your hep-th/0307031: I'm wondering, how much entropy do we "see" in the cosmic equator,

http://members.aon.at/chakalov/Tegmark.html#March_6

Regards,

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

=====

Subject: Cosmic equator in the cosmic microwave background radiation
Date: Thu, 06 Mar 2003 16:17:43 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: max@physics.upenn.edu
CC: mukhanov@theorie.physik.uni-muenchen.de,
     faris@math.arizona.edu, David.Coule@port.ac.uk,
     hkj@iucaa.ernet.in, tirth@iucaa.ernet.in, jayant@iucaa.ernet.in,
     nabhan@iucaa.ernet.in, claudio.garola@le.infn.it,
     afsar@iopb.res.in, M742503402@cs.com, les@mppmu.mpg.de,
     dopliche@mat.uniroma1.it, saul@astro.cornell.edu,
     kip@tapir.caltech.edu, SMOOT@smoot1.lbl.gov,
     carroll@theory.uchicago.edu, mturner@oddjob.uchicago.edu,
     contact@gyre.org
 
 

Congratulations, Max! I'm very happy that you found a "cosmic equator" in CMBR, "some extra, so far unexplained structure in the CMB." [Ref. 1]

Are you missing something? See the interpretation of "point" in 3-D space at

http://members.aon.at/chakalov/Nature.html ,

and recall that this "point" could be the result of cancellation of two worlds, material and tachyonic [Ref. 2],

http://www.hep.upenn.edu/~max/dimensions.html

http://members.aon.at/chakalov/Professor_X.html#Negative_Mass

There is no "intrinsic time" attached to this "point", as you explained eloquently in your gr-qc/9702052. [Ref. 2]

On the other hand, everything you can observe is "inside" spacetime. Hence it is NOT surprising that the creative mechanism of spacetime and its "reference frame" can NOT be observed even indirectly, by a perfectly smooth isotropic CMBR.

You've told BBC News Online that "If we could only see another 380,000 light-years we would be able to see the beginning of the Universe." [Ref. 1]. Well, I'm a bit skeptical. Maybe the "beginning" and the "end" of the universe are well-hidden inside each and every "point" of the 3-D space. See again my feedback to Nature above.

I'm just trying to help you: "We did not expect this and we cannot yet explain it." [Ref. 1]

I will appreciate the opinion of your colleagues as well.

Take care,

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

References
 

[Ref. 1] Map reveals strange cosmos, by David Whitehouse, BBC News Online, Monday, 3 March, 2003, 13:23 GMT,
http://news.bbc.co.uk/2/hi/science/nature/2814947.stm

In producing the image, Dr Tegmark removed all sources of contaminating foreground radiation leaving only the cosmic background itself.
...

Having produced the cleanest map of the CMB yet, Dr Tegmark displayed it in an unusual manner. Instead of a flat projection on a computer screen, he showed the data as ripples on a sphere - "after all the CMB comes from a sphere", he says.

"Space continues outside the sphere but this opaque glowing wall of hydrogen plasma hides it from our view. If we could only see another 380,000 light-years we would be able to see the beginning of the Universe," he told BBC News Online.

Looking for evidence

And he added: "We found something very bizarre; there is some extra, so far unexplained structure in the CMB.

"We had expected that the microwave background would be truly isotropic, with no preferred direction in space but that may not be the case."

Looking at the symmetry of the CMB - measures technically called its octopole and quadrupole components - the researchers uncovered a curious pattern.

They had expected to see no pattern at all but what they saw was anything but random.

"The octopole and quadrupole components are arranged in a straight line across the sky, along a kind of cosmic equator. That's weird.

"We don't think this is due to foreground contamination," Dr Tegmark said. "It could be telling us something about the shape of space on the largest scales. We did not expect this and we cannot yet explain it."

It may mean that the CMB is clumpier in some directions than others. Some theories of the structure of the Universe predict this but observational evidence to support it would be a major discovery.

[Ref. 2] Max Tegmark. On the dimensionality of spacetime.
http://www.hep.upenn.edu/~max/dimensions.html
http://xxx.lanl.gov/abs/gr-qc/9702052

Footnote 4: "The only remaining possibility is the rather contrived case where data is specified on a null hypersurface. To measure such data, an observer would need to "live on the light cone", i.e., travel with the speed of light, which means that it would subjectively not perceive any time at all (its proper time would stand still)."
 
 

==========

Subject: Cosmic equator in the cosmic microwave background radiation
Date: Sat, 08 Mar 2003 00:19:37 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Charles.Bennett@gsfc.nasa.gov, halpern@physics.ubc.ca,
     Gary.Hinshaw@gsfc.nasa.gov, jarosik@pupgg.princeton.edu,
     Alan.Kogut@gsfc.nasa.gov, limon@pupgg.princeton.edu,
     meyer@oddjob.uchicago.edu, page@pupgg.princeton.edu,
     dns@astro.princeton.edu, tucker@physics.brown.edu,
     Ed.Wollack@gsfc.nasa.gov, wright@astro.ucla.edu
CC: max@physics.upenn.edu
 

Dear Colleagues,

Regarding the "cosmic equator" at

http://news.bbc.co.uk/1/hi/sci/tech/1413707.stm ,

perhaps you may be interested to read

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

I will appreciate your critical comments.

Regards,

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

=======

Subject: Re: Cosmic equator in the cosmic microwave background radiation
Date: Wed, 12 Mar 2003 04:38:35 +0200
From: Dimi Chakalov <dchakalov@surfeu.at>
To: Charles.Bennett@gsfc.nasa.gov, halpern@physics.ubc.ca,
     Gary.Hinshaw@gsfc.nasa.gov, jarosik@pupgg.princeton.edu,
     Alan.Kogut@gsfc.nasa.gov, limon@pupgg.princeton.edu,
     meyer@oddjob.uchicago.edu, page@pupgg.princeton.edu,
     dns@astro.princeton.edu, tucker@physics.brown.edu,
     Ed.Wollack@gsfc.nasa.gov, wright@astro.ucla.edu,
     max@physics.upenn.edu
CC: gangui@iafe.uba.ar, mariocastagnino@citynet.net.ar,
     msouza@fisica.ufs.br
 
 

I'm thrilled to learn that a solution to the problem of Max Tegmark

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

has been suggested by Alejandro Gangui, in

Alejandro Gangui, In Support of Inflation, Science, 291(5505), 837-838 (2 Feb 2001)

and

Alejandro Gangui, A Preposterous Universe, Science, 299(5611) 1333-1334 (28 Feb 2003); astro-ph/0303048.

"According to theory, it is at this precise time, nearly 14 billion years ago, that the CMB became polarized. (...) These rules will help us understand why the CMB should be linearly polarized."
...
"But the CMB is not perfectly isotropic. It has a tiny "quadrupole anisotropy", first discovered by experiments onboard of the COBE satellite [2]. Hence, from any point of view, the orthogonal contributions to the final polarization will be different, leaving a net linear polarization in the scattered radiation. Theorists believe that this is how the CMB polarization detected by DASI, and recently confirmed with data from the Wilkinson Microwave Anisotropy Probe (WMAP) satellite [8], arose.
...
"That is why we know with certainty that the CMB polarization shows the uncontaminated dynamics of the primordial seeds at recombination.
...
"As more independent experiments confirm and extend these findings, the CMB polarization will become the next gold mine of cosmology."

I wish you best of luck in exploring the next gold mine of cosmology.
 

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