Acta Biotheoretica

, Volume 41, Issue 1–2, pp 105–117 | Cite as

Les brisures de symetrie du temps

  • Alexandre Laforgue

The symmetry breakings of time



Atoms theory and symmetry theory dominated physics. Symmetry propagation and interactions verify the Curie principle. But its violation by symmetry breaking is spontaneous.Fragility is creative. An information breaks a generalized symmetry.

Results on symmetry breakings are not valid for fuzzy symmetries. The breaking of a fuzzy symmetry leads only to a pour symmetry (Fig.1).

Homogeneity breaking, and atom of time are not usual concepts. We examine in this work symmetry breakings which generate the living time.

Relativistic Time-Space Breaking

  1. II A.

    Medium and environment of living define ordinary referential of space and referential of time. Astronomical phenomena following classical mechanics and microphysical phenomena following quantum mechanics can be written with the same t coordinate.

  2. II B.

    Relativity corrections. Schrödinger's Quantum mechanics (Eq.0) approximately governs molecular systems (Relativity corrections can be expressed as physical effects in the above defined referential).

  3. II C.

    Time reversal symmetry. The well-known Wigner's transformation determines the microscopic reversibility.

  4. II D.

    The three essential particle-vacancy equilibria. This transformation is verified by all particle-vacancy reciprocity. Vacancy moves like particle but with negative moment and positive kinetic energies. Only three biochemical equilibria admit this time reversal symmetry, namely: oxydo-reduction, acido-basicity, fluidity-viscosity. In these case, reacting electron, solvated proton, water molecule are respectively antagonist of the corresponding vacancy.

  5. II E.

    Fuzzy character of time reversal symmetry. Dirac's equation does not admit this symmetry which only appears at the “non relativistic” limit of quantum phenomena. Hence particle-vacancy reciprocity is fuzzy according to the experimental evidence. (Laforgue et al., 1988).


Oriented Time

  1. III A.

    From the universal reversible time, an additional breaking generates the oriented time, both in the astronomical and in the living matter.

  2. III B.

    Irreversibility for the environment. We refer to Prigogine and Stengers (1988).

  3. III C.

    Irreversibility for the living matter. We refer to Lochak (1986). Because equation (0), above discussed, is “microreversible” the second breaking could come from an additional term vanishing in the stationary states but increasing with time in evolutionary processes.

  4. III D.

    Negative times. Taking into account the fuzzy character of the time reversed symmetry, the third breaking cannot suppress completely the occurrence of negative times. Reversed time is controlled by direct time. Except in the three above reported cases, time reversal symmetry is not verified by the medium. Free motion of the particle following eg.(0) or of the vacancy following time reversal reciprocal equation takes place only during short jumps from an interaction site to an other. Fig. 2 schematizes the law of motion of the electric charge corresponding to the transport by proton or by proton vacancy in an unitary field (fluctuations are neglected). The reserved jumps are estimated in the range of 10−12s. It is not excluded that such a jump can control a direct phenomenon.

  5. III E.

    The living time. Biological phenomenon appears as an oriented set of events. Nevertheless latency or exaltation phases could be perceived. This modulation could be described by positive and negative times additional to the basic time. (Negative can be interpreted as above)


Living produces Time

  1. IV A.

    That were not understandable, if time was only a frame, in which change occurs. Taking chance as frame and time as effect, we regard biological activity as integrating reversible and irreversible time. Living synchronizes internal and external time by its own effort as it results (Lestienne, 1990) from Chronobiology.

  2. IV B.

    Time modulation. Let us consider the dy1...dyi...dyp changes in the variables of the systems, dy={dyi} has produced dt. We proof (eq.(1) to (4)) that time is modulated by a φ(y) speed coefficient depending on the medium. tmodulated=tφ (y) −1

  3. IV B.

    The production of reversible time (e.g.acido-basicity) determines time modulation. As above reported it remains some reversibility effects (jumps of negative time) which modulate time. E.G., if an important amount of reagent is necessary to modify an acid-base equilibrium, φ(y) is small.

  4. IV D.

    Time modulation and activation-repression reciprocity. As well-known, long tmodulated means repression, short tmodulated means exaltation. Extrema of ϕ are symmetrical because particle and vacancy are reciprocal. Nevertheless reciprocity is not perfect. E.g., on fig. 3, the wet receptor determines the cell increasing, the dry receptor the cell senescence of a certain alga (Lück, 1962).

  5. IV E.

    Irreversible time production. Medium accepts entropy. Hence it acts in the second breaking of time. Living extracts the free energy from the medium, like a dissipative structure. That insures an operative point far from the thermodynamical equilibrium.


Consumption of Time

  1. V A.

    The three followings correspond to the more trivial time consumption.

  2. V B.

    Rhythmical time. Free energy flux is favourable to the arising of order in space or time. This later gives a structure to the living time.

  3. V C.

    Mutual dependence of reversible time and rhythms. Time irreversible structure can be controlled by the above considered particle-vacancy equilibrium. Consequently the living time (modulated and structured) is a chemical time connected to molecular properties and to statistical thermodynamics.

    Practically, the connection between chronobiology and chemistry is important. The use of drugs could be interpreted as a response to an aggression against biorhythms.

  4. V D.

    Lifetime. The dead-birth rythm can be broken in two ways: evolution or indefinite life. This later is non exceptional for the living matter, e.g. in the vegetals where it is connected with the chlorophyllic assimilation; the time reversal significance of which is evident.

  5. V E.

    The plan of the alchemist. Indefinitely life has fascinated individuals. Do the human species becomes better adapted by a longer life?



  1. 1.

    Atoms of time could exist.

  2. 2.

    Biological time is defined by the breaking of five generalized symmetries, namely: Minkovski's space symmetry, reversibility, homogeneity, rhythmicity, generations reproduction.

  3. 3.

    Environment and medium determine non relativistic, oriented, structured time.

  4. 4.

    At the microphysical scale, a fuzzy time reversal symmetry takes place, the breaking of which is not complete. Reversible time and dominating irreversible time are integrated in living phenomena.

  5. 5.

    Three fundamental particle-vacancy reciprocities admit a part of reversibity. Irreversibility governs the all others phenomena.

  6. 6.

    Time is produced chemically.

  7. 7.

    A new perspective is the connection between chemical equilibria and rhythms including the time of the life.



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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Alexandre Laforgue
    • 1
  1. 1.Université de ReimsReims Cedex

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