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J. Maruani
the Copenhagen interpretation of quantum mechanics. In Gould’s extension of Darwin’s theory to whole species [12], the ecosystem acts as an ‘observer’ reducing the
species ‘wave packet’ (population variety) generated by ‘subquantum’ (genotype)
fluctuations. This is somehow similar to an open quantum system [49] and then possibly relevant to the Lindblad, extended Liouville equation [50]. In addition, the fact
that the nucleic acids bearing the genetic material are amenable to quantum theory
raises the question as to whether the internal dynamics of these biomolecules over
extended durations does not also play a role in the highly coordinated, structural and
functional changes of speciation or radiation.
In the biological sciences, only determinist approaches to microevolution have
indeed been rationalized. There is no real understanding of the macroevolution in
which we are embedded—not just external observers as in the physical sciences. But
if biological phenomena are indeed a manifestation of quantum laws at the macroscopic level, then constructive and destructive interferences may operate also among
living systems. The Feynman path integral formulation could then be used to clarify the link between determinist processes and finalist manifestations, and possibly
uncover selected trajectories in phylum evolution.
In this paper, we tried to prepare the ground and lay the foundations for a quantum
theory of biological evolution. This approach is different from the standard studies
of the structure and dynamics of biomolecular systems by using quantum chemical
methods, or from the investigations of specific biological processes such as enzymatic
activity, photosynthesis, or magnetoreception, which involve quantum mechanisms
as electron or proton tunnelling or long-range coherence. It is also different from the
application of concepts borrowed from thermodynamics or cybernetics in order to
rationalize teleological aspects of biological processes. It is a provisional attempt to
elaborate an understanding of phylum trajectories that would reconcile the finalist
and determinist views through a quantum path integral approach.
Fermat’s shortest optical path and Hamilton’s minimal action integral do not
imply intelligent design, except perhaps in the very laws of wave mechanics! We
temptatively proposed as a quantity to be optimized for a biological trajectory in
a space-time ecosystem a convolution of ‘complexity’ and ‘fitness’, which have
to be defined in a way allowing pitch waves expressing nucleic-acid structures to
produce interference fringes. Investigations are in project on the relevance of various
definitions of these concepts for applying effectively to available paleontological
data.
As recalled earlier, unexpected catastrophes also play an important role in biological evolution. In addition, as pointed out by Henri Poincaré, small uncertainties in
initial conditions may lead to unpredictable effects. This led to the theory of deterministic chaos, which involves nonlinear equations [51]. However, while modern
celestial mechanics, an ancient fortress of determinism, shows numerous examples of
distinct, regular and chaotic motions, little was done in biology, except in population
dynamics [52]. Gould’s assumption that organisms are selected by the environment
not only by additive (linear), but also by combined (nonlinear) effects of gene mutations [12] may make it necessary to incorporate chaotic effects in a full understanding
of biological teleology, at least at departures of punctuated equilibria.
J. Maruani
the Copenhagen interpretation of quantum mechanics. In Gould’s extension of Darwin’s theory to whole species [12], the ecosystem acts as an ‘observer’ reducing the
species ‘wave packet’ (population variety) generated by ‘subquantum’ (genotype)
fluctuations. This is somehow similar to an open quantum system [49] and then possibly relevant to the Lindblad, extended Liouville equation [50]. In addition, the fact
that the nucleic acids bearing the genetic material are amenable to quantum theory
raises the question as to whether the internal dynamics of these biomolecules over
extended durations does not also play a role in the highly coordinated, structural and
functional changes of speciation or radiation.
In the biological sciences, only determinist approaches to microevolution have
indeed been rationalized. There is no real understanding of the macroevolution in
which we are embedded—not just external observers as in the physical sciences. But
if biological phenomena are indeed a manifestation of quantum laws at the macroscopic level, then constructive and destructive interferences may operate also among
living systems. The Feynman path integral formulation could then be used to clarify the link between determinist processes and finalist manifestations, and possibly
uncover selected trajectories in phylum evolution.
In this paper, we tried to prepare the ground and lay the foundations for a quantum
theory of biological evolution. This approach is different from the standard studies
of the structure and dynamics of biomolecular systems by using quantum chemical
methods, or from the investigations of specific biological processes such as enzymatic
activity, photosynthesis, or magnetoreception, which involve quantum mechanisms
as electron or proton tunnelling or long-range coherence. It is also different from the
application of concepts borrowed from thermodynamics or cybernetics in order to
rationalize teleological aspects of biological processes. It is a provisional attempt to
elaborate an understanding of phylum trajectories that would reconcile the finalist
and determinist views through a quantum path integral approach.
Fermat’s shortest optical path and Hamilton’s minimal action integral do not
imply intelligent design, except perhaps in the very laws of wave mechanics! We
temptatively proposed as a quantity to be optimized for a biological trajectory in
a space-time ecosystem a convolution of ‘complexity’ and ‘fitness’, which have
to be defined in a way allowing pitch waves expressing nucleic-acid structures to
produce interference fringes. Investigations are in project on the relevance of various
definitions of these concepts for applying effectively to available paleontological
data.
As recalled earlier, unexpected catastrophes also play an important role in biological evolution. In addition, as pointed out by Henri Poincaré, small uncertainties in
initial conditions may lead to unpredictable effects. This led to the theory of deterministic chaos, which involves nonlinear equations [51]. However, while modern
celestial mechanics, an ancient fortress of determinism, shows numerous examples of
distinct, regular and chaotic motions, little was done in biology, except in population
dynamics [52]. Gould’s assumption that organisms are selected by the environment
not only by additive (linear), but also by combined (nonlinear) effects of gene mutations [12] may make it necessary to incorporate chaotic effects in a full understanding
of biological teleology, at least at departures of punctuated equilibria.