Abiogenesis and the Second Law of Thermodynamics
425
8 The Universe and Quantum Theory
Dirac derived a consistent relativistic quantum theory for electrons, showing in particular the entanglement between matter and anti-matter; for a recent history and update,
see [96]. However, Einstein’s theory of general relativity and quantum mechanics
still remain incompatible. Hence it would seem to be an impossible undertaking to
bring together the topics expressed in the header above. This task becomes even more
difficult in view of the existing cosmological contradictions, such as the accelerating
expansion of the universe, the formation of black holes via a collapsing star, the
information paradox, the nature of the black hole singularity etc., see e.g. MersiniHoughton [97, 98] for a critical appraisal. Solutions to these quandaries should most
likely be found in appropriate modifications of classical black hole dynamics to
incorporate fundamental quantum mechanical effects.
Our present incipient aim has been to promote an evolutionary procedure, representing and interpreting abiogenesis, and encompassing the whole biosphere from
first principles. A first step in this direction was the development of ZEUS, a
Zero Energy Universe Scenario, conveying a plausible picture [95] commensurate
with Darwin’s theory of evolution, from the microscopic ranks to the cosmological
domain, see also [70]. A natural starting point for a quantum mechanical treatment
à la ZEUS would be to extend the relativistic energy-momentum formulation to a
non-positive definite metric, while keeping the fundamental commutation relations
with their conjugate variables intact. This simple directive is a reminder of Kant’s
dictum more than two hundred years ago: space and time are the two essential
forms of human sensibility. In other words, the aphorism states that evolved life
forms perceive and experience phenomena in our environment, set in this perspective. Hence physics, the knowledge of nature, connect material degrees of freedom
such as energy-momentum, with their conjugate immaterial partners space-time. In
QM they are correlated through the usual commutation relations recognized by every
physics student today.
In terms of the energy given by the mass relation E = mc
2 , m the mass, c the
velocity of light, τ the time, and
v the velocity, the classical Klein-Gordon equation
for a non-zero rest-mass particle reads, with E 0 = m 0 c
2 , m 0 the rest-mass and
p = m
v,
−
E
2
0
c 2 = =
p
2
−
E
2
op
c 2
(8.1)
The matching relation for the conjugate variables introducing the familiar
eigentime expression τ 0 obtains
−c
2
τ
2
0 = =
x
2
− c
2
τ
2
(8.2)
In order to be consistent with QM, we extend the definition of the usual conjugate pairs energy-time and momentum-space to their operator equivalents; the time
425
8 The Universe and Quantum Theory
Dirac derived a consistent relativistic quantum theory for electrons, showing in particular the entanglement between matter and anti-matter; for a recent history and update,
see [96]. However, Einstein’s theory of general relativity and quantum mechanics
still remain incompatible. Hence it would seem to be an impossible undertaking to
bring together the topics expressed in the header above. This task becomes even more
difficult in view of the existing cosmological contradictions, such as the accelerating
expansion of the universe, the formation of black holes via a collapsing star, the
information paradox, the nature of the black hole singularity etc., see e.g. MersiniHoughton [97, 98] for a critical appraisal. Solutions to these quandaries should most
likely be found in appropriate modifications of classical black hole dynamics to
incorporate fundamental quantum mechanical effects.
Our present incipient aim has been to promote an evolutionary procedure, representing and interpreting abiogenesis, and encompassing the whole biosphere from
first principles. A first step in this direction was the development of ZEUS, a
Zero Energy Universe Scenario, conveying a plausible picture [95] commensurate
with Darwin’s theory of evolution, from the microscopic ranks to the cosmological
domain, see also [70]. A natural starting point for a quantum mechanical treatment
à la ZEUS would be to extend the relativistic energy-momentum formulation to a
non-positive definite metric, while keeping the fundamental commutation relations
with their conjugate variables intact. This simple directive is a reminder of Kant’s
dictum more than two hundred years ago: space and time are the two essential
forms of human sensibility. In other words, the aphorism states that evolved life
forms perceive and experience phenomena in our environment, set in this perspective. Hence physics, the knowledge of nature, connect material degrees of freedom
such as energy-momentum, with their conjugate immaterial partners space-time. In
QM they are correlated through the usual commutation relations recognized by every
physics student today.
In terms of the energy given by the mass relation E = mc
2 , m the mass, c the
velocity of light, τ the time, and
v the velocity, the classical Klein-Gordon equation
for a non-zero rest-mass particle reads, with E 0 = m 0 c
2 , m 0 the rest-mass and
p = m
v,
−
E
2
0
c 2 = =
p
2
−
E
2
op
c 2
(8.1)
The matching relation for the conjugate variables introducing the familiar
eigentime expression τ 0 obtains
−c
2
τ
2
0 = =
x
2
− c
2
τ
2
(8.2)
In order to be consistent with QM, we extend the definition of the usual conjugate pairs energy-time and momentum-space to their operator equivalents; the time