Short Summary of a New Idea: Cryodynamics

Otto E. Rossler, Faculty of Science, University of Tubingen, Germany

Abstract

A brief history and description of cryodynamics is offered. While still in its infancy, it is already strong in basic findings and predictions. It is a classical science the quantum version of which still waits to be formulated. It is highly promising technologically. A new fundamental science is a rare event in history. The basic insight is to picture randomly moving hyperbolic tree trunks in Sinai’s “rolling tennis ball in an orchard game” (Harry Thomas’ term), but flipped upside down so that the trees are hollow funnels pointing downwards.

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Cryodynamics is a classical field which appears to be new. It is a sister discipline to thermodynamics and automatically has as many implications as the latter despite its belated discovery. So far but a few features have been elaborated. For example, its deterministic entropy function is identical to the Sackur-Tetrode equation as given by Diebner, but with inverted sign (“ectropy”). If confirmed it allows for a combined entropic and ectropic model of the universe. Then all direction-of-time bound models of the universe lose their validity. The problem of black hole recycling which poses itself in this case is still unsolved in spite of Hawking’s early stab.

Held against this big scenario, what is presently on hand is still limited. It is the discovery that if you subject a fast-moving low-energy classical particle to successive grazing-type encounters with attractive, rich-in-kinetic-energy particles, then the low-energy particle loses kinetic energy on average to the high-energy ones (“energetic capitalism”). This is very unexpected and paradoxical. Nevertheless the idea goes back to Zwicky in 1929 and Chandrasekhar in 1943, although it was not elaborated at the time.

The “miracle” is that if you invert the direction of time, the opposite behavior is implicit. All of the conceptual problems of thermodynamics are re-encountered. The second major feature is that the new phenomenon is numerically elusive for stiffness reasons. While the increasing disorder of entropy increase, valid in the repulsive case is a numerically stable feature in statistical thermodynamics, the decreasing order of ectropy increase, valid in the attractive case is not numerically stable. Very minor numerical deviations suffice to destroy the on-going decrease of entropy. This explains why in the thousands of multi-particle simulations done so far in galactic dynamics, to mention only this subcase, the phenomenon was never encountered numerically so far.

Another reason for the lack of resonance up until now is the fact that thermodynamics has always been understood as a statistical theory, with probability-theoretic axioms employed to describe it. While this is not false, it eschews the underlying deterministic, chaos-theoretic mechanism. The thereby incurred intrinsic inaccuracy did not cause much damage in thermodynamics so far, but cannot be transported over to cryodynamics. Cryodynamics does not emerge without prior acknowledgement of deterministic chaos as its root. (This new fact strongly constrains the accuracy of quantum mechanics — backwards in time — which is quite unexpected.)

Let me explain the simplest example which also worked numerically in the first two successful simulations so far. A fast-moving low-mass particle is subjected to encounters with a Newtonian potential trough into which it dips-in and then gets out again. If the trough is periodically or nonperiodically approaching and receding (modulated in its depth), a net effect results: a loss of energy of the traversing fast particle. If we invert time after a while, the exact opposite occurs up to the initial point, to from then on give way to the previous behavior, but now in the opposite direction of time.

The best way to understand all this is to invert the sign of the potentials. Then the opposite phenomenon, familiar from statistical thermodynamics, occurs: The periodically modulated trough is now replaced by a periodically modulated mound or tree. It is obvious that the recurrent unequal increases and decreases in the height of the hyperbolic mound amount to a qualitatively different effect in their sums.

To see this, think of a ball running frictionlessly through a forest of (at first fixed) trees with softly rising features. Then the ball will from time to time climb up a little and come down again – without losing or gaining in its net kinetic energy. Now let the trees be moving slowly at random (or periodically). Then the two cases – of the tree approaching the path of the up-climbing particle or receding from it – have different strengths (different mean heights). This explains dissipation. On inverting time after a while, the net gain becomes a net loss for the moving particle — until the initial condition is re-arrived at. Then the gaining streak sets in again, now in the new direction of time.

When we leave the repulsive case by inverting the tree stems into mirror-symmetric troughs, then the opposite thing happens to a ball running on the surface of this inverted landscape. This is the new phenomenon of cryodynamics, proved to the mental eye.

After this geometric proof, the numerical challenge clearly is on – especially so after the successful two cases published by Klaus Sonnleitner and Ramis Movassagh, respectively. The new science is waiting to be put on a broader computational basis.

Why is this important? The new cosmology that is implied clearly is not a sufficient motivation, given the fact that most everyone is happy with the old paradigm. So all that remains as a convincing reason for further research is an economically challenging application.

Such an application could be provided by the ITER, a hot-fusion reactor based on the Tokamak design: a torus-shaped, millions-of-degrees hot plasma that is magnetically confined in a metal ring. The plasma must not touch the (necessarily much colder) confining walls. This design is intrinsically unstable dynamically: The plasma tends to break out from the toroidal magnetic confinement to suddenly touch the wall somewhere to let the overall temperature collapse. No working prototype exists for decades. The current hope that following another quarter of a century, the machine will work, is being upheld with many billions of euros already sunk-in. Here, cryodynamics can be of help in principle. The paradoxical option: apply a heat bath of even hotter attractive particles at the location of the budding instability. Then these hotter attractive particles – like the inverted tree trunks – will cool the too hot nucleons, thus curbing the budding local protrusion.

“Cooling by hotter attractive particles” is the essence of cryodynamics. The hotter particles could be electrons shot-in concentrically into the budding hot spot. This is no problem in principle since even very much hotter electrons are easy to generate in small, dirigible-beam accelerators.

The idea was published under the title “Is hot fusion made feasible by the discovery of Cryodynamics?” in Advances in Intelligent Systems and Computing, Volume 192, pp. 1–4, Springer-Verlag 2013. It can still be patented since no design details were mentioned. This is a very lucrative technological proposal. No country or nation is interested so far nor are the oil companies.

Acknowledgments

Thank you that I was allowed to tell you the whole story in as brief a form as I could. I thank Dan Stein, Eric Klien, Christophe Letellier, Nico Heller, Heinz Clement and Jozsef Fortagh for discussions. Paper presented at the “CQ Colloquium” of the University of Tubingen on June 28, 2013. For J.O.R. (Submitted to Nature.)

As long as a recently published proof (European Scientific Journal March 2013 edition vol.9, No.9 ISSN: 1857–7881(Print) e-ISSN 1857–7431) remains unchallenged by the scientific community, this question is not only scientifically sound but also maximally important.

It would be great if this uncommon call for scientific assistance by imaginative readers across the world would find the resonance it deserves . Einstein would be delighted.

It is a riddle and almost a scandal: If you let a particle travel fast through a landscape of randomly moving round troughs – like a frictionless ball sent through a set of circling, softly rounded “teacups” inserted into the floor (to be seated in for a ride at a country fair) – you will find that it loses speed on average.

This is perplexing because if you invert time before throwing in the ball, the same thing is bound to happen again – since we did not specify the direction of time beforehand in our frictionless fairy’s universe. So the effect depends only on the “hypothesis of molecular chaos” being fulfilled – lack of initial correlations – in Boltzmann’s 19th century parlance. Boltzmann was the first to wonder about this amazing fact – although he looked only at the opposite case of upwards-inverted cups, that is, repulsive particles.

The simplest example does away with fully 2-dimensional interaction. All you need is a light horizontal particle travelling back and forth in a frictionless 1-dimensional closed transparent tube, plus a single attractive, much heavier particle moving slowly up and down in a frictionless transversal 1-dimensional closed transparent tube of its own – towards and away from the middle of the horizontal tube while exerting a Newtonian attractive force on the light fast particle across the common plane. Then the energy-poor fast particle still gets statistically deprived of energy by the energy-rich heavy slow particle in a sort of “energetic capitalism.”

If now the mass of the heavy particle is allowed to go to infinity while its speed and the force exerted by it remain unchanged, we arrive at a periodically forced single-degree-of-freedom Hamiltonian oscillator in the horizontal tube. What could be simpler? But you again get “antidissipation” – a statistical taking-away of kinetic energy from the light fast particle by the heavy slow one.

A first successful numerical simulation was obtained by Klaus Sonnleitner in 2010 – still with a finite mass-ratio and hence with explicit energy conservation. Ramis Movassagh obtained a similar result independently and proved it analytically. Both publications did not yet look at the simpler – purely periodically forced – limiting case just described: A single-degree-of-freedom, periodically forced conservative system. The simplest and oldest paradigm in Poincaréan chaos theory as the source of big news?

If we invert the potential (Newtonian-repulsive rather than Newtonian-attractive), the light particle now gains energy statistically from the heavy guy – in this simplest example of statistical thermodynamics (which the system now turns out to be). Thus, chaos theory becomes the fundament of many-particle physics: both on earth with its almost everywhere repulsive potentials (thermodynamics) and in the cosmos with its almost everywhere attractive potentials (cryodynamics). The essence of two fundamental disciplines – statistical thermodynamics and statistical cryodynamics – is implicit in our periodically forced single-tube horizontal particle. That tube represents the simplest nontrivial example in Hamiltonian dynamics including celestial mechanics, anyhow. But it now reveals two miraculous new properties: “deterministic entropy” generation under repulsive conditions, and “deterministic ectropy” generation under attractive conditions.

I would love to elicit the enthusiasm of young and old chaos aficionados across the planet because this new two-tiered fundamental discipline in physics based on chaos theory is bound to generate many novel implications – from revolutionizing cosmology to taming the fire of the sun down here on earth. There perhaps never existed a more economically and theoretically promising unified discipline. Simple computers suffice for deriving its most important features, almost all still un-harvested.

Another exciting fact: The present proposal will be taken lightly by most everyone in academic physics because Lifeboat is not an anonymously refereed outlet. But many young people on the planet do own computers and will appreciate the liberating truth that “non-anonymous peer review” carries the day – with them at the helm. So, please, join in. I for one was so far unable to extract the really simplest underlying principle: Why is it possible to have a time-directed behavior in a non-time-directed reversible dynamics if that time-directedness does not come from statistics, as everyone believes for the better part of two centuries? What is the real secret? And why does the latter come in two mutually at odds ways? We only have scratched at the surface of chaos so far. Boltzmann used that term in a clairvoyant fashion, did he not? (For J.O.R.)