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M. Svrˇ cek
transgressing the law of nature due to the hierarchical way of quantization—first the
electrons are quantized and the nuclei remain classical, and then they are quantized a
posteriori. But quantum mechanics demands simultaneous quantization, regardless
how heavy the nuclei are compared to the electrons. Sutcliffe and Woolley ask: “The
interesting question is how to get from the quantum theory of an Isolated Molecule to
a quantum theory of an individual molecule by rational mathematics.” The problem is
thus, on “what” quantum theory the mentioned rational mathematics do apply. If we
understand quantum theory as quantum mechanics based on the original Copenhagen
interpretation, employing the Schrödinger equation for particles in the many-body
systems, we find no answer. The input of electrons and nuclei in the mechanical
Schrödinger equation exhibits a full symmetry regarding both types of particles. As
we will see in this paper, many-body systems are running in dual mode, and we need
to search the answer not under the mechanical pattern, but under the field concept
where simultaneous quantization can be performed.
The concepts “isolated system” and “individual system” are well defined in the
classical world, but only the first one has a similar meaning in the microworld,
whereas the second one needs a radical redefinition on the quantum level. However,
in speaking about elementary particles as “individual systems”, there is no problem.
The problems start when we try to apply this concept to composite systems like
molecules or crystals.
In regard to the phenomena mentioned above, the explanation calls for the concept of clamped-nuclei, but, as just said, this concept, from the viewpoint of an
exact quantum mechanical many-body formulation, does not work. The Copenhagen
interpretation must be incomplete in this respect.
3 The Paradox of Time Irreversibility
The fundamental problem of both classical and quantum physics is still the question
of the arrow of time. Why does time have a direction?
A half century ago, Santilli, then a nuclear physicist, stated, what he called a noreduction theorem [13]: “A macroscopic irreversible system cannot be consistently
reduced to a finite number of elementary constituents all in reversible conditions and,
vice versa, a finite number of elementary particles all in reversible conditions cannot
consistently characterize a macroscopic irreversible system.” He further said, claiming that he has discussed this problem with Heisenberg and Dirac and that none of the
quantum theory founders knew the answer: “The above theorem establishes that irreversibility originates at the most ultimate structure of nature.” Till now the scientific
community does not seem to take this paradox seriously, nevertheless Santilli continues: “During the 20th century it was generally believed that the irreversibility over
time of our macroscopic environment was “illusory” (sic) because, when macroscopic events are reduced to their elementary particle constituents, irreversibility
“disappears” (sic) and one recovers nice elementary particles in the reversible conditions necessary for the applicability of special relativity, quantum mechanics and
M. Svrˇ cek
transgressing the law of nature due to the hierarchical way of quantization—first the
electrons are quantized and the nuclei remain classical, and then they are quantized a
posteriori. But quantum mechanics demands simultaneous quantization, regardless
how heavy the nuclei are compared to the electrons. Sutcliffe and Woolley ask: “The
interesting question is how to get from the quantum theory of an Isolated Molecule to
a quantum theory of an individual molecule by rational mathematics.” The problem is
thus, on “what” quantum theory the mentioned rational mathematics do apply. If we
understand quantum theory as quantum mechanics based on the original Copenhagen
interpretation, employing the Schrödinger equation for particles in the many-body
systems, we find no answer. The input of electrons and nuclei in the mechanical
Schrödinger equation exhibits a full symmetry regarding both types of particles. As
we will see in this paper, many-body systems are running in dual mode, and we need
to search the answer not under the mechanical pattern, but under the field concept
where simultaneous quantization can be performed.
The concepts “isolated system” and “individual system” are well defined in the
classical world, but only the first one has a similar meaning in the microworld,
whereas the second one needs a radical redefinition on the quantum level. However,
in speaking about elementary particles as “individual systems”, there is no problem.
The problems start when we try to apply this concept to composite systems like
molecules or crystals.
In regard to the phenomena mentioned above, the explanation calls for the concept of clamped-nuclei, but, as just said, this concept, from the viewpoint of an
exact quantum mechanical many-body formulation, does not work. The Copenhagen
interpretation must be incomplete in this respect.
3 The Paradox of Time Irreversibility
The fundamental problem of both classical and quantum physics is still the question
of the arrow of time. Why does time have a direction?
A half century ago, Santilli, then a nuclear physicist, stated, what he called a noreduction theorem [13]: “A macroscopic irreversible system cannot be consistently
reduced to a finite number of elementary constituents all in reversible conditions and,
vice versa, a finite number of elementary particles all in reversible conditions cannot
consistently characterize a macroscopic irreversible system.” He further said, claiming that he has discussed this problem with Heisenberg and Dirac and that none of the
quantum theory founders knew the answer: “The above theorem establishes that irreversibility originates at the most ultimate structure of nature.” Till now the scientific
community does not seem to take this paradox seriously, nevertheless Santilli continues: “During the 20th century it was generally believed that the irreversibility over
time of our macroscopic environment was “illusory” (sic) because, when macroscopic events are reduced to their elementary particle constituents, irreversibility
“disappears” (sic) and one recovers nice elementary particles in the reversible conditions necessary for the applicability of special relativity, quantum mechanics and