A Cosmology based on a Chaos-borne Hubble Law

Otto E. Rossler

Division of Theoretical Chemistry, University of Tubingen, Auf der Morgenstelle 8, 72076 Tübingen, F.R.G.

Abstract

A recent classical-mechanical finding, Fermi deceleration, implies a classical Hubble-like law. While its exact size is still open, it is bound to co-determine empirical reality. Some old and new questions concerning the size and the age of the cosmos arise. The current enigma of early old galaxies supports the prediction of a potentially much larger and older cosmos. So does Riccardo Giacconi's finding of ultra-high-redshift x-ray point sources.

(October 8, 2004)

Recently, a classical-mechanics based Hubble-like law was described [1,2]: Light rays

negotiating galactic clusters that are in random motion with up to 1 percent the speed of light (as is realistic) suffer a distance-proportional redshift through "Fermi deceleration." The latter phenomenon was discovered by Loskutov et al. [3] on a chaotic billiard: A fast-moving, low-mass billiard that is subject to random grazing-type collisions with slowly moving high­mass boundaries suffers a distance-proportional loss of momentum called Fermi deceleration [3]. The repelling grazing-type boundaries of Loskutov et al. can be replaced by attracting high-mass point centers - with the same grazing-type interactional effect. The slow attracting centers may be galaxies or clusters of galaxies and the billiard may be a light ray. The size of the effect depends on the density, mass and speed of the attracting centers.

The size of the effect appears to be neither too large nor too small to accomodate the empirical Hubble law [1]. If this preliminary result is taken as a cue, the implied lack of cosmic expansion re-opens the age-old question of the size of the cosmos. Fortunately, perhaps, a general-relativistic size limitation remains in charge if the mass density in the cosmos is uniform. In this case, not too much is changed compared to the standard paradigm: The cosmos can still be a pulsatile cosmos, for example, albeit so on a longer time scale.

If the assumption of a uniform mass density is dropped, on the other hand, the general­

relativistic bound is no longer finite. This stationary solution to the original Einstein equations was discovered by Benoit Mandelbrot [4], a fact which is not very well known. If the fractal dimensionality of the mass distribution is assumed to be unity (so that twice as large a radius contains not eight times but only twice as much mass - as in an ultra-light hole­ ridden Swiss cheese), the Schwarzschild radius which limits the size of the cosmos becomes infinite. For twice as much mass by definition has twice-as-large a Schwarzschild radius (and so on), so that no finite limit is reached in the present case. An exactly 1-D Mandelbrot cosmos is both stationary and unbounded. Peebles almost immediately found that the empirical fractal dimensionality of galaxies is about 1.2 up to large distances [5]. This and subsequent data can be re-evaluated by dropping the original assumption of a progressive lack of volume as the remaining distance to the primordial fireball shrinks toward zero. The validity of Peebles' near-unity result will thereby be extended to covering the greater part of the visible universe.

If this prediction is correct, a "Brunian cosmos" (in honor of Giordano Bruno) of potentially unbounded extension in both space and time becomes an option again- But would not the other "pillars of the big bang" automatically preclude so far-reaching a conclusion? Surprisingly, this is not the case. The cosmic background radiation -- the strongest ally -- would assume the role of "mean cosmic temperature" in the sense of Assis [6]. The also observed large-scale fluctuations in the WMAP would reflect a giant honeycomb structure that lies beyond the range of current telescopes (although some infrared and x-ray sources may already be pointing the way). The three other major pillars - primordial nucleosynthesis, inflation and accelerated expansion - would have to wait in line until the gross features have been straightened out. The third (large-distance dimming) may, by the way, prove reducible to Peebles' little-known (1+z)--4 formula [7], cf. [8].

But how about the riddles newly imported by a modern Brunian cosmos? First, in the absence of a far-from-equilibrium big bang, the persistent far-from-equilibrium state of the observable universe becomes incomprehensible. A gravitational effect partially anticipated by Einstein in 1912 [9] may possibly solve the mystery: Any particle in rectilinear motion inside a Newtonian (or Einsteinian) void enjoys a forward acceleration [10], cf. [11]. If this is so, gravitational energy gets "recycled" into kinetic energy in a Carnot-like manner. The same mechanism, by the way, could explain - jointly with Hawking radiation [12] - the second major new riddle that arises: the empirical "non-devouredness" of almost all matter by age-old black holes.

The main asset of a classical explanation of cosmological redshift, when held against the backdrop of the standard model, seems to lie in the fact that it introduces no hypotheses. lt only uses facts that are implicit in classical (post-Newtonian) mechanics and special and general relativity anyhow. lts predictions are irrefutable once their size has been correctly determined. What is surprising is only how many accepted hypotheses suddenly lose their hard-won plausibility.

Nevertheless it would be nice to have direct evidence as well. Very faint distant x-ray point sources appear to possess redshifts in excess of 30. This is because, on the one hand, the sensitivity ofx-ray telescopes is presently 1000 times greater than that of light telescopes [13]

- so that they can look 30 times (squareroot of 1000) deeper into space in principle - and, on the other, x-ray point sources continue to pop up at the lowest brightnesses [13]. This empirically suggested, two-tiered conclusion is incompatible with the big bang scenario (which leaves no room for redshifts beyond about 10 for massive objects). lt is about tobe decided by direct redshi:ft measurements in progress [13]. A hard - if weaker - fact is the recent optical discovery of strongly redshifted old galaxies 12 billion light years away, which has put cosmology into a full-fledged crisis [14,15]. While almost any way out appears acceptable at the time being, the above explanatory scenario was arrived at independently.

To conclude, the classical-mechanical finding of Fermi deceleration has upset the decades­ old belief that only a relativistic mechanism can account for the Rubble law. By coincidence, an empirical crisis holds cosmology in its grip in which fiddling with the usual culprits (like the star formation rate in young galaxies) seems insufficient to rescue the big bang model. In

,.:;uch a situation, even an at first sight alien, chaos-borne ray of light can acquire a warm glow.

Acknowledgments

I thank Christophe Letellier, Heinrich Kuypers, Dieter Fröhlich, Normann Kleiner, Peter Weibel, Erwin Wendling, Hans Diebner and Florian Grond for discussions. For J.O.R.

References

[1] O.E. Rossler, D. Fröhlich and N. Kleiner, Time-symmetric Hubble-like law: Light rays grazing randomly moving galaxies show distance-proportional redshift. Z. Naturforsch. 58 . 807-809 (2003).

[2] O.E. Rossler, Cosmic shear's temporal fluctuations generate a distance-proportional redshift in both time directions: Minibang theory. Chaos, Solitons & Fractals 12, 1335- 1338 (2004).

[3] A. Loskutov, A.B. Ryabov and L.G Akinshin, Analysis of billiards with time-dependent boundaries. Facta Universitatis Series Mechanics, Automatic Control and Robotics 11, 99- 116 (2001).

[4] B.B. Mandelbrot, CR. Acad. Sci. Paris A 280, 618 (1975).

[5] M. Seldner and P.J.E. Peebles, Astrophysical J 215, 703 (1977).

[6] A.K.T. Assis, "Relational Mechamics." Montreal: Apeiron 1999.

[7] P.J.E. Peebles, Principles of Physical Cosmology. Princeton University Press 1993, p. 226.

[8] O.E. Rossler, "Darkness intensified: Existence of a nonlinear threshold in redshift­ induced dimming." Z. Naturforsch. 54, 453-454 (1999).

[9] A. Einstein, Does there exist a gravitational effect analogous to electrodynamic induction?

"Collected Papers," English Translation edition, Vol. 4, pp. 126-129. Princeton University

Press 1996.

[10] O.E. Rossler, A morphogenetic instability in gravitation. Physica D 2004 (invited paper submitted).

[11] The term "Fermi acceleration" was already reserved by Loskutov et al. [3] for a different mechanism (the heating-up of billiards subject to repetitive head-on collisions with moving boundaries). Thus, a new term (“Einstein acceleration”?) will be needed for the present mechanism which has nothing to do with billiards and, by the way, does not extend to light, provided it is going to be confirmed.

[12] S.W. Hawking, Particle creation by black holes. Commun. Math. Phys. 33, 323 (1973).

[13] R. Giacconi, Kepler lecture, held at the University of Tübingen, July 2003.

[14] J.-M. Bonnet-Bidaud, Le big bang face à ses contradictions, Ciel&espace No. 412, 42- 44, September 2004.

[15] Editorial: Mature galaxies in young universe at odds with theory, Scientific American online, September 2004.

Remark added in 2020: Since this paper was written in 2004, Cryodynamics – explaining cosmology causally for good – got discovered; so this text remains just a step on the road.