At all levels of nature we see the emergence of "narrative elements". We are reminded of Scheherazade who interrupts her beautiful story to start another one, even more beautiful. In nature also we have the cosmological history that includes the history of matter, life, humans, and so on till we come to our individual history associated to our consciousness. At all levels we observe events associated with the emergence of novelties, we may associate with the creative power of nature.
These narrative historical aspects are part of complexity. Complex systems share the feature to exhibit a great variety of behaviors. Take an example from chemistry: the Belousov-Zhabotinsky reaction mentioned above. The details are irrelevant here, let us suppose that there are two species of molecules: "red" ones and "blue" ones; moreover they transform one into the other. The behavior of the system depends on the external constraints. Close to equilibrium the collisions are random. There may only appear short living local flashes of color. But far from equilibrium the behavior of this system changes radically. It becomes in succession red then blue then again red. This periodicity indicates the existence of long-range correlations due to the non-equilibrium conditions. "At equilibrium matter is blind, far from equilibrium it begins to see" (Ilya Prigogine3).
The fascination of these physical experiments lies in the fact that small variations in a tiny building block of matter manifest themselves as large changes in biological processes. The paradox of modern scientific research in this field lies in the fact that the greater the detail in which we seek "pure" mechanisms or given sub-particles, the more confirmation we have of the validity of quantum mechanics and the more important information we have on the structure of matter. On the other hand, starting from elementary particles, the more we study interactions with biological systems and ecosystems, the more we discover the complexity, irreversibility, and intrinsic aleatory character of nature. In chaos, we
3From the foreword to Tiezzi (2003a).
rediscover the spontaneity of evolutionary history: a universe in which God plays dice, to invert Einstein's phrase4.
God was the supreme guarantee of physical determinism. For Einstein, protagonist of the first "heroic" phase of quantum physics, physical determinism applied to any process. However, Max Born5 once told Einstein that a deterministic universe was innately anathema to him. Born admitted that Einstein might be right, but added that determinism did not seem to hold in physics, much less in other fields. Born criticized Einstein's comment that God does not play dice6, observing that Einstein's deterministic world needed chance. Born's wife Hedwig had previously written to their "dear friend Albert" that she could not admit a universal law according to which everything was predetermined, including whether or not she vaccinated her child against diphtheria7.
Both uncertainty equations are related to the complex relation between the observer and the experiment. The first one deals with position and momentum, the second one deals with energy and relaxation time. Both equations assume time reversibility and are valid in a given instant: the momentum is related to the derivative of space with respect to time and the relaxation time is related to the lifetime of the elementary particle in the excited state. Both equations are valid in the quantum physics paradigm and deal with conservative quantities (mass, energy), but not with living systems or evolutionary quantities.
Space and time are categories belonging to different logical types, which should not be confused. By nature, time is evolutionary and irreversible, whereas the space is conservative and reversible. A reversible quantity cannot be differentiated with respect to an irreversible one. It is not possible to compare evolving quantities, such as the life span of the Einstein's twins, in the framework of reversible mechanics. If we deal with evolutionary (living) systems, we may introduce a third concept: Thermodynamic Uncertainty related to the intrinsic irreversible character of time (Tiezzi, 2006a).
Let us say that a thermodynamic uncertainty arises from the experimental existence of the arrow of time and from the experimental evidence that, during the measurements,
4On 4th December 1926, Einstein wrote to Max Born that although quantum mechanics was worthy of respect, an inner voice told him that it was not yet the right solution because it did not enable us to penetrate the secret of the Great Old Man, who he was sure did not play dice with the world (Science and Life, Letters 1916-1955, letter no. 52 in A. Einstein, H. and M. Born). Max Born considered that there was a profound divergence of viewpoint between Einstein and the following generation, to which Born regarded himself as belonging, though only a few years younger than Einstein. In a previous letter (29th April 1924, no. 48 of the above collection) Einstein observed that the ideas of Niels Bohr on radiation were interesting but he himself did not wish to be led away from rigorous causality. He added that he could not tolerate the idea that an electron exposed to radiation could freely choose when and in which direction to jump. Were this so, he said he would prefer to be a shoemaker or a gambler rather than a physicist. In the introduction to this collection of letters, Werner Heisenberg comments that Einstein agreed with Born on the fact that the mathematical formalism of quantum mechanics, which originated in Gottingen and was subsequently elaborated at Cambridge and Copenhagen, correctly represented the phenomena occurring inside the atom, but that he did not recognize quantum mechanics as a definitive or even exhaustive representation of these phenomena. The theme that God does NOT play dice recurs elsewhere in the Born-Einstein correspondence (e.g., Einstein's letters of 7th September 1944 and 12th October 1953, nos. 81 and 103, respectively).
510th October 1944 (letter no. 84 in Science and Life).
6The expression "God plays dice" obviously had an irrational overtone for Einstein, but, as we shall see, not for us.
79th October 1944 (letter no. 82 in Science and Life).
time goes by. Since during the interval of the experiment (measurement) time flows, also the conservative quantities (energy or position) may change leading to a further uncertainty.
Recently astrophysics discovered that the mass of a star is related to the life span of the star itself. The larger is the mass, the less is the life span. This finding may also be related to the uncertainty principle. It seems that there is a sort of uncertainty relation between space and time, where space is related to mass, energy, and the conservative quantities.
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