3 The Dirac Electron and Basic Physical Concepts
65
of the resulting particle at velocity v by the Compton formula, which connects the
mass increase to the radius decrease:
m v = /2r v c = γ /2r C c = m 0 γ.
(3.33)
A velocity increase in the outer motion entails an amplitude decrease in the inner
motion. This may be the deep reason why c is a limiting velocity for all motions,
and why inertial frames play a specific role in relativity theory. However, contrary
to what we stated in our previous paper [22], the contraction of the radius with
increasing velocity should appear as uniform [49, 50] and not just along the direction
of the motion.
3.5 Homologies in the Hierarchy of Complexity and Dimensional
Analysis of Fundamental Physical Properties
‘Analogy is the key to the understanding of . . . the universal law that governs all things as a
whole and every thing in its detail’.
(Attributed to Hermês ho Trismégistos)
This part is intended to trigger reflections on possible impacts of the inner structure, as discussed above, of the Dirac electron on the properties and interactions of
structures generated at the various levels of complexity.
The number and nature of the quantities that can be defined in a given field of
science (physics, chemistry, biology, ecology, . . .) is a matter of convenience and,
whenever it is possible, of coherence. This is true also for the units that can be
designed to measure or, at least, to scale these quantities. In fact, thousands of units
have been used (and are still in use) in various periods of history (and various regions
of the world) to quantify scores of quantities: from distance, duration, and weight to
radioactivity level, viscosity grade, earthquake strength, nutritional value, or music
interval [51]. However, since Aristotle, and even more since Galileo, it has been
admitted that physics, especially mechanics, is a science more fundamental than
others. This led to a mechanistic vision of Nature, which prevailed until it became
partly challenged by the paradoxes of relativity and quantum theories [52, 53].
This paradigm of modern sciences is based on an analytical and deterministic
approach to natural phenomena, which has made obsolete the holistic and finalistic
vision of traditional sciences. Nevertheless, it is still admitted that the biological
realm, even though it keeps obeying physical laws, has properties and laws of its
own (called emergences in the theories of complex systems), including holistic and
finalistic characters [54]. In the 19th century, Louis Pasteur (who refuted the old
belief in spontaneous generation) expressed an even more radical view, contrasting
with the prevailing materialistic and reductionist views:
‘Who tells you that the steady progress of science will not compel scientists who will live
in a hundred, a thousand years . . . to state that life has existed from all eternity, not matter
. . . . Who ensures me that in ten thousand years, one will not consider that it is from life . . .
that it is impossible to proceed to matter?’
65
of the resulting particle at velocity v by the Compton formula, which connects the
mass increase to the radius decrease:
m v = /2r v c = γ /2r C c = m 0 γ.
(3.33)
A velocity increase in the outer motion entails an amplitude decrease in the inner
motion. This may be the deep reason why c is a limiting velocity for all motions,
and why inertial frames play a specific role in relativity theory. However, contrary
to what we stated in our previous paper [22], the contraction of the radius with
increasing velocity should appear as uniform [49, 50] and not just along the direction
of the motion.
3.5 Homologies in the Hierarchy of Complexity and Dimensional
Analysis of Fundamental Physical Properties
‘Analogy is the key to the understanding of . . . the universal law that governs all things as a
whole and every thing in its detail’.
(Attributed to Hermês ho Trismégistos)
This part is intended to trigger reflections on possible impacts of the inner structure, as discussed above, of the Dirac electron on the properties and interactions of
structures generated at the various levels of complexity.
The number and nature of the quantities that can be defined in a given field of
science (physics, chemistry, biology, ecology, . . .) is a matter of convenience and,
whenever it is possible, of coherence. This is true also for the units that can be
designed to measure or, at least, to scale these quantities. In fact, thousands of units
have been used (and are still in use) in various periods of history (and various regions
of the world) to quantify scores of quantities: from distance, duration, and weight to
radioactivity level, viscosity grade, earthquake strength, nutritional value, or music
interval [51]. However, since Aristotle, and even more since Galileo, it has been
admitted that physics, especially mechanics, is a science more fundamental than
others. This led to a mechanistic vision of Nature, which prevailed until it became
partly challenged by the paradoxes of relativity and quantum theories [52, 53].
This paradigm of modern sciences is based on an analytical and deterministic
approach to natural phenomena, which has made obsolete the holistic and finalistic
vision of traditional sciences. Nevertheless, it is still admitted that the biological
realm, even though it keeps obeying physical laws, has properties and laws of its
own (called emergences in the theories of complex systems), including holistic and
finalistic characters [54]. In the 19th century, Louis Pasteur (who refuted the old
belief in spontaneous generation) expressed an even more radical view, contrasting
with the prevailing materialistic and reductionist views:
‘Who tells you that the steady progress of science will not compel scientists who will live
in a hundred, a thousand years . . . to state that life has existed from all eternity, not matter
. . . . Who ensures me that in ten thousand years, one will not consider that it is from life . . .
that it is impossible to proceed to matter?’