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  • Author: O. Rössler x
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Redshift obeys adiabatic invariance. From this fact it follows that not only the individual photons are dimmed by a factor of z + 1 (if z is the redshift in percent), but the photon flux is reduced by the same factor once more. Hence the luminosity of any source is in the presence of redshift dimmed by a factor of (z+1)2. This model-independent result possibly “explains away” the excess dimming of strongly redshifted Type-la super-novae, discovered in 1998.


A new experiment in the foundations of quantum mechanics is proposed. The existence of correlated photons -first seen by Wheeler -can be taken as a hint to devise a ‘‘double-wing’’ delayed choice experiment in Wheeler’s sense. A path choice (polarization choice) measurement made on the one side should then block an interference type measurement made on the other side (‘‘distant choice’’). A precondition for the combined measurement to work in theory is that the correlated photons used are of the ‘‘prepolarized’’ (Selleri) rather than the ‘‘unpolarized’’ (Böhm) type. A first EPR experiment involving prepolarized photons was recently performed by Alley and Shih. It may be used as a partial experiment within the proposed experiment.

in Chaos

A modified Rinzel-Keller equation of reaction-diffusion type is investigated analytically. Both on the ring and on the linear fiber, the possible existence of wavetrains containing an arbitrary finite number of impulses is demonstrated. The longest wavetrain shown explicitly consists of ten pulses. Unlike other approaches, the present method varies many parameters simultaneously. An implicit algebraic equation is formulated which contains all possible wave solutions of the system. This equation is then solved with a standard technique (Powell's algorithm). The results obtained extend the findings of other authors. The method can be applied, after appropriate modification, to other piecewise linear systems, that is, to other prototype reaction-diffusion systems

A variant to the well known Danziger-Elmergreen equation of hormonal regulation is analyzed geometrically by analytical methods. The new method of Poincaré half maps is employed. Several chaotic regimes are found.


An open three-variable mass action kinetics is presented which exhibits chaotic behavior under numerical simulation. The elementary reactions of this system are at most of second order and satisfy the requirements of thermodynamics as long as the system is closed.

A new class of dissipative structures is proposed that live in real space rather than phase space. A light ray passing through a soup of randomly moving gravitating masses is a case in point. It suffers a “dynamic path elongation” since the random pushes and pulls have a greater probability of increasing than decreasing its path length. Time reversal then re-shrinks the path in question in a conspirational manner, while a close-by nonselected path gets expanded. This is a new statistical-mechanics phenomenon. The latter at the same time qualitatively reproduces the well-known Hubble phenomenon of distance-proportional light-path expansion in the cosmos. A preliminary quantitative estimate, based on the Birkinshaw equation with an assumed bias factor of three, is also presented.


An analytical solution to the Wigner-Weisskopf problem (an excited two-level atom in inter-action with a radiation field), obtained for both finite-and infinite-length boxes, is re-examined in terms of the qualitative behavior implied. As the equations and the plots of the solutions show, there is a major difference between the behavior of the finite system (with discrete spec-trum) and that obtaining in the large-system limit. In the first case, a pulse-shaped wave "travels down the line" and comes back (and is sent off again) many times, completely "losing its shape" in the process (and subsequently re-gaining it on a much longer time scale infinitely often, due to the presence of a Poincare recurrence). In the large-system limit, on the other hand, a delta-impulse-like wave travels down the line only once (in finite time), and there is also no loss of shape upon its return after infinite time. Thus, there is no longer any even temporary "smearing out" of the initially sharply localized energy, and hence no "mixing" in the intuitive sense of the word. Nonetheless a dense spectrum is found (similarly as in the distribution theoretical case of an isolated delta-impulse in an infinite domain), and hence weak mixing in the sense of Lebowitz. The contradiction can be resolved at the expense of having to abandon some symmetry: by assuming the atom adjacent to two cavities of incommensurate lengths. Then the infinite system limit is unchanged (no return in finite time), but the transition is characterized by intuitive mixing of increasing effectiveness.

By investigating the reaction diagram in its own right, it is possible to solve the problem of enumerating all the different types of mass action kinetics up to second order. The amount of non isomorphic complex sets for a given number of species and of non isomorphic reaction networks and reversible reaction networks which can be derived from a given number of complexes is given.