waves, based on Maxwell’s equations, we have here another metaphor: The
interactive transmitter SERVING LIFE Broadcasting on Channel SELF: A Poisson
Distributed Ultra-Wide Broadband. Obviously communication between life forms
requires some form of intelligence. Although this is a highly controversial term, we
will only use it in its most trivial sense, i.e. in the meaning to pick out or understand
something, but also to discern, distinguish, differentiate and recognize. One may
e.g. refer to the laws of physics, like gravity or the second law of thermodynamics,
as governing teleomatic processes, or as a programmed activity, restricted to action
or behaviour owing its goal-directedness to the influence of an evolved program
during evolution.
12 Conclusion
In the introduction we elaborated on the essential ingredients to promote a reliable
and consistent scenario for the evolution of cosmos from the “Beginning” to the
“End”. We did start with conjugate operator arrays presenting a platform for a
theoretical discourse of maximum generality, including quantum-classical treatments, relativistic practices, teleomatic laws and teleodynamic processes from
Gödel’s incompleteness theorem to Einstein’s laws and the extension of Darwin’s
theories to the Paradigm of Evolution.
In order to augment the present formulation with the cosmological challenges,
we return to one of the key quantities in the gravitational enigma, viz. the emergence of an initially nonrotating black-hole object, Eq. (3.7), with M characterized
as a spherical mass distribution, which does not change sign when m → −m, see
Sect. 3 for details.
As might be anticipated from the density matrix representation in Sect. 6, there
exist proximate relations between the simple form derived, Eqs. (6.7–6.9) and
Yang’s celebrated concept of ODLRO, Off-Diagonal Long-Range Order, [28], and
Coleman’s notion of an extreme state [29], see e.g. [6, 31, 36] as well as references
therein. We will here demonstrate that our black hole type entity is a direct analogue
of the organization of ODLRO. In addition we will extend the discussion to a Kerrtype [8] rotating black hole characterized by its mass and angular momentum, see
also Ref. [44].
From Eq. (3.7), with r 2l, i.e. with the particle-antiparticle superposition
inside the Schwarzschild boundary, solving for the canonical vectors in analogy
with Eqs. (4.14′) and (4.15′) one obtains for the “vacuum” base vectors 0
j i and 0
in terms of the mass m for the particle and with m for the antiparticle, i.e.
0
j i ¼
1
ffiffi ffi
2
p ð m
j i À i m
j iÞ
ð12:1Þ
278
E.J. Brändas
interactive transmitter SERVING LIFE Broadcasting on Channel SELF: A Poisson
Distributed Ultra-Wide Broadband. Obviously communication between life forms
requires some form of intelligence. Although this is a highly controversial term, we
will only use it in its most trivial sense, i.e. in the meaning to pick out or understand
something, but also to discern, distinguish, differentiate and recognize. One may
e.g. refer to the laws of physics, like gravity or the second law of thermodynamics,
as governing teleomatic processes, or as a programmed activity, restricted to action
or behaviour owing its goal-directedness to the influence of an evolved program
during evolution.
12 Conclusion
In the introduction we elaborated on the essential ingredients to promote a reliable
and consistent scenario for the evolution of cosmos from the “Beginning” to the
“End”. We did start with conjugate operator arrays presenting a platform for a
theoretical discourse of maximum generality, including quantum-classical treatments, relativistic practices, teleomatic laws and teleodynamic processes from
Gödel’s incompleteness theorem to Einstein’s laws and the extension of Darwin’s
theories to the Paradigm of Evolution.
In order to augment the present formulation with the cosmological challenges,
we return to one of the key quantities in the gravitational enigma, viz. the emergence of an initially nonrotating black-hole object, Eq. (3.7), with M characterized
as a spherical mass distribution, which does not change sign when m → −m, see
Sect. 3 for details.
As might be anticipated from the density matrix representation in Sect. 6, there
exist proximate relations between the simple form derived, Eqs. (6.7–6.9) and
Yang’s celebrated concept of ODLRO, Off-Diagonal Long-Range Order, [28], and
Coleman’s notion of an extreme state [29], see e.g. [6, 31, 36] as well as references
therein. We will here demonstrate that our black hole type entity is a direct analogue
of the organization of ODLRO. In addition we will extend the discussion to a Kerrtype [8] rotating black hole characterized by its mass and angular momentum, see
also Ref. [44].
From Eq. (3.7), with r 2l, i.e. with the particle-antiparticle superposition
inside the Schwarzschild boundary, solving for the canonical vectors in analogy
with Eqs. (4.14′) and (4.15′) one obtains for the “vacuum” base vectors 0
j i and 0
in terms of the mass m for the particle and with m for the antiparticle, i.e.
0
j i ¼
1
ffiffi ffi
2
p ð m
j i À i m
j iÞ
ð12:1Þ
278
E.J. Brändas