Megascopic Quantum Phenomena
285
equations are at fault? Of course, no! On the contrary, the Copenhagen interpretation
was formed in a very accurate, tangible and original way. However the simple characteristics of the hydrogen atom, did not reveal the whole truth about a many-body
quantum system alongside yielding an inappropriate relationship between the micro-,
the macro- and the mega-world. As will be demonstrated in this paper, there is also
the controversial problem regarding the occurrence of the alleged quantum jumps,
which have no origin in the original Copenhagen microscopic formulation. Hence
this article will promote a so-called ‘second quantum floor’ describing megascopic
quantum phenomena, in contrast to the ‘first floor’, defined by the standard description of microscopic phenomena within the Copenhagen interpretation. We will in
addition expound, which heretofore being unexplained or even misinterpreted, upon
the phenomena that belong to this ‘second floor’.
2 The Clamped-Nuclei Paradox
Let us start with the simplest formulation of the many-body problem based on the
Schrödinger equation. Solving it exactly is in practice impossible, and therefore its
simplified solution known as the Born-Oppenheimer (B-O) approximation [3] is
widely used. Quite recently Sutcliffe and Woolley [4] offered an extensive historical justification of the development of quantum theory, in particular the quantum
chemical solution of Schrödinger’s equation, discussing the applicability as well as
the limitations of Potential Energy Surfaces (PES) in quantum chemistry. As conclusion they wrote: “This qualitative modification of the internal Hamiltonian, the
extra choice of fixed nuclear positions in the ‘electronic’ Hamiltonian, is ad hoc in
the same sense that Bohr’s quantum theory of the atom is an ad hoc modification
of classical mechanics. An essential feature of the answer is put in by hand. We
know that both modifications have been tremendously useful and our point is not
that something else must be done in practical calculations on molecules. The point
is how the successful description of molecules involving the clamped-nuclei modification at some stage can best be understood in terms of quantum mechanics. In the
case of the Bohr atom the resolution of the inconsistency in mechanics applied to
the microscopic realm was achieved quite quickly with the formulation of quantum
mechanics; in the molecular case, no such resolution is at present known.”
In other words, we have enough numerical verifications available, but what we
need, is the elucidation why the clamped-nuclei modification works so well. Their
statement is an imperative challenge to everybody. In passing we should not forget
that two scientific sub-disciplines, quantum chemistry and solid state physics, are
mostly dependent on the B-O approximation, making them two sand-castles. This
begs the question: What can we expect: the confirmation of the B-O approximation
that satisfies our desire for perfection—or a disclosure of something new that goes
beyond our contemporary knowledge of physics and chemistry? We will contend in
this paper that the latter is closer to the truth.
285
equations are at fault? Of course, no! On the contrary, the Copenhagen interpretation
was formed in a very accurate, tangible and original way. However the simple characteristics of the hydrogen atom, did not reveal the whole truth about a many-body
quantum system alongside yielding an inappropriate relationship between the micro-,
the macro- and the mega-world. As will be demonstrated in this paper, there is also
the controversial problem regarding the occurrence of the alleged quantum jumps,
which have no origin in the original Copenhagen microscopic formulation. Hence
this article will promote a so-called ‘second quantum floor’ describing megascopic
quantum phenomena, in contrast to the ‘first floor’, defined by the standard description of microscopic phenomena within the Copenhagen interpretation. We will in
addition expound, which heretofore being unexplained or even misinterpreted, upon
the phenomena that belong to this ‘second floor’.
2 The Clamped-Nuclei Paradox
Let us start with the simplest formulation of the many-body problem based on the
Schrödinger equation. Solving it exactly is in practice impossible, and therefore its
simplified solution known as the Born-Oppenheimer (B-O) approximation [3] is
widely used. Quite recently Sutcliffe and Woolley [4] offered an extensive historical justification of the development of quantum theory, in particular the quantum
chemical solution of Schrödinger’s equation, discussing the applicability as well as
the limitations of Potential Energy Surfaces (PES) in quantum chemistry. As conclusion they wrote: “This qualitative modification of the internal Hamiltonian, the
extra choice of fixed nuclear positions in the ‘electronic’ Hamiltonian, is ad hoc in
the same sense that Bohr’s quantum theory of the atom is an ad hoc modification
of classical mechanics. An essential feature of the answer is put in by hand. We
know that both modifications have been tremendously useful and our point is not
that something else must be done in practical calculations on molecules. The point
is how the successful description of molecules involving the clamped-nuclei modification at some stage can best be understood in terms of quantum mechanics. In the
case of the Bohr atom the resolution of the inconsistency in mechanics applied to
the microscopic realm was achieved quite quickly with the formulation of quantum
mechanics; in the molecular case, no such resolution is at present known.”
In other words, we have enough numerical verifications available, but what we
need, is the elucidation why the clamped-nuclei modification works so well. Their
statement is an imperative challenge to everybody. In passing we should not forget
that two scientific sub-disciplines, quantum chemistry and solid state physics, are
mostly dependent on the B-O approximation, making them two sand-castles. This
begs the question: What can we expect: the confirmation of the B-O approximation
that satisfies our desire for perfection—or a disclosure of something new that goes
beyond our contemporary knowledge of physics and chemistry? We will contend in
this paper that the latter is closer to the truth.