460
J. Maruani
in Eq. (15), whose virtual paths would interfere similarly as in Eq. (18) to yield the
real evolution path. The combination of complexification and selection would then
naturally lead to punctuated evolution, and macromutations yielding speciation and
radiation would be understood as quantum biodynamics tunneling effects (‘shape
resonances’).
Consider a species S a endowed with generic genome G a (e g, Fig. 4a), which
evolves along the ages (both through Darwinian progressive selection and unexpected
catastrophic events) to two different species S b (G b ) (e g, Fig. 4b) and G c (S c ) (e g,
homo sapiens). Genomes G a , G b and G c can be expressed as complex systems of
waves, and there are multiple paths (sequences of mutations) that can lead from
‘state’ G a to state G b or G c . This situation is more complex than that shown in
Fig. 2a, where each light wave diffracts independently of other light waves. In a way,
the Archaeothyris extinct species potentially includes all further mammals, as the
white light in Fig. 2a includes all visible colors (which will diffract differently due
to their different wavelengths), or alternatively as x-rays will have their wavelength
increase (and energy decrease) as a function of the angle, cf. Equation (9b), in inelastic
scattering by electrons.
Here we assume that the evolution path followed by S a (G a ) to S b (G b ), for instance,
is such that the evolution functional E [q], defined as a convolution of complexity and
fitness functionals in Eq. (15), is minimal with respect to the extended coordinate q
defining the (possibly time-dependent) structure of the genome interacting (through
its phenotype) with the environment. As in the quantum mechanics of matter waves,
Eq. (18), the genome ‘finds’ the optimal path by ‘feeling’ the other paths, due to the
wave character of its molecular structure.
The probability amplitude for a genome to be in state G b at time t b
after being in state G a at time t a is a sum of contributions, one for each path leading
from G a t a to G b t b . The contribution of a given path would be written: N exp (2π i
E/μ), where N is a normalization factor independent of the path, E is the evolution
functional computed along the considered path, and μ is an evolution quantum which
Fig. 4 Left a: Life restoration of Archaeothyris, a synapsid ancestor of mammals that lived 306
My ago #. Right b: Leopard on a tree in Kruger National Park, South Africa*. # From https://en.
wikipedia.org/wiki/Archaeothyris. * Picture taken by Pr Jan Dillen on the road from Phalabowra
airport to Mopani camp
J. Maruani
in Eq. (15), whose virtual paths would interfere similarly as in Eq. (18) to yield the
real evolution path. The combination of complexification and selection would then
naturally lead to punctuated evolution, and macromutations yielding speciation and
radiation would be understood as quantum biodynamics tunneling effects (‘shape
resonances’).
Consider a species S a endowed with generic genome G a (e g, Fig. 4a), which
evolves along the ages (both through Darwinian progressive selection and unexpected
catastrophic events) to two different species S b (G b ) (e g, Fig. 4b) and G c (S c ) (e g,
homo sapiens). Genomes G a , G b and G c can be expressed as complex systems of
waves, and there are multiple paths (sequences of mutations) that can lead from
‘state’ G a to state G b or G c . This situation is more complex than that shown in
Fig. 2a, where each light wave diffracts independently of other light waves. In a way,
the Archaeothyris extinct species potentially includes all further mammals, as the
white light in Fig. 2a includes all visible colors (which will diffract differently due
to their different wavelengths), or alternatively as x-rays will have their wavelength
increase (and energy decrease) as a function of the angle, cf. Equation (9b), in inelastic
scattering by electrons.
Here we assume that the evolution path followed by S a (G a ) to S b (G b ), for instance,
is such that the evolution functional E [q], defined as a convolution of complexity and
fitness functionals in Eq. (15), is minimal with respect to the extended coordinate q
defining the (possibly time-dependent) structure of the genome interacting (through
its phenotype) with the environment. As in the quantum mechanics of matter waves,
Eq. (18), the genome ‘finds’ the optimal path by ‘feeling’ the other paths, due to the
wave character of its molecular structure.
The probability amplitude
after being in state G a at time t a is a sum of contributions, one for each path leading
from G a t a to G b t b . The contribution of a given path would be written: N exp (2π i
E/μ), where N is a normalization factor independent of the path, E is the evolution
functional computed along the considered path, and μ is an evolution quantum which
Fig. 4 Left a: Life restoration of Archaeothyris, a synapsid ancestor of mammals that lived 306
My ago #. Right b: Leopard on a tree in Kruger National Park, South Africa*. # From https://en.
wikipedia.org/wiki/Archaeothyris. * Picture taken by Pr Jan Dillen on the road from Phalabowra
airport to Mopani camp