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M. Svrˇ cek
expect to be told what to do in terms of some programme, expressed in terms of
formulae or recipes.”
This is indeed a very important objection. We will demonstrate a relation between
Bohm’s dilemma of wholeness versus fragmentation and the problem of isolated
versus individual as formulated by Sutcliffe and Woolley. The microscopic quantum
world simply does not match our concepts of individual or fragmented, albeit these
words have clear and well-defined meanings on the classical level. And further it is
most astonishing to compare how the authors mentioned characterize this problem
and evaluate its complexity. Bohm emphasized that the challenge is more difficult
than the problem of relativity confronting Einstein, while Sutcliffe and Woolley
emphasized that it is harder to solve than the problem of quantum theory for Bohr.
The fourth excerpt reads:
4. “Here, we may hope to get some clues by considering problems in a domain where
current theories do not yield generally satisfactory results, i.e. one connected with
very high energies and very short distances. With regard to such problems, we
first note that the present relativistic quantum field theory meets severe difficulties which raise serious doubts as to its internal self-consistency. There are the
difficulties arising in connection with the divergences (infinite results) obtained
in calculations of the effects of interactions of various kinds of particles and
fields. It is true that for the special case of electromagnetic interactions such
divergences can be avoided to a certain extent by means of the so-called ‘renormalization’ techniques. It is by no means clear, however, that these techniques
can be placed on a secure logical mathematical basis. Moreover, for the problem
of mesonic and other interactions, the renormalization method does not work
well even when considered as a purely technical manipulation of mathematical
symbols, apart from the question of its logical justification. While it has not been
proved conclusively, as yet, that the infinities described above are essential characteristics of the theory, there is already a considerable amount of evidence in
favour of such a conclusion.”
This is entirely a quantum field problem. Quantum mechanical patterns, derived
from the classical Hamilton-Jacobi formalism, don’t seem to lead to any similar
difficulties. The question is rather, whether an analogical quantization of the classical electro-magnetic field Langrangian will provide us with the full quantum field
pattern, especially when it is used in closed systems such as nuclei in quantum chromodynamics. Note that original field patterns of quantum electrodynamics represent
only the scattering process of a few free particles in vacuum. We will here analyze these inconsistencies in applying such a limited pattern to bound-state massive
systems like molecules and crystals.
The final Bohm quotation contains the exchange with Sheldrake:
5. Bohm: “‘How is time to be understood?’ Now, in terms of the totality beyond
time, the totality in which all is implicate, what unfolds or comes into being in any
present moment is simply a projection of the whole. That is, some aspect of the
M. Svrˇ cek
expect to be told what to do in terms of some programme, expressed in terms of
formulae or recipes.”
This is indeed a very important objection. We will demonstrate a relation between
Bohm’s dilemma of wholeness versus fragmentation and the problem of isolated
versus individual as formulated by Sutcliffe and Woolley. The microscopic quantum
world simply does not match our concepts of individual or fragmented, albeit these
words have clear and well-defined meanings on the classical level. And further it is
most astonishing to compare how the authors mentioned characterize this problem
and evaluate its complexity. Bohm emphasized that the challenge is more difficult
than the problem of relativity confronting Einstein, while Sutcliffe and Woolley
emphasized that it is harder to solve than the problem of quantum theory for Bohr.
The fourth excerpt reads:
4. “Here, we may hope to get some clues by considering problems in a domain where
current theories do not yield generally satisfactory results, i.e. one connected with
very high energies and very short distances. With regard to such problems, we
first note that the present relativistic quantum field theory meets severe difficulties which raise serious doubts as to its internal self-consistency. There are the
difficulties arising in connection with the divergences (infinite results) obtained
in calculations of the effects of interactions of various kinds of particles and
fields. It is true that for the special case of electromagnetic interactions such
divergences can be avoided to a certain extent by means of the so-called ‘renormalization’ techniques. It is by no means clear, however, that these techniques
can be placed on a secure logical mathematical basis. Moreover, for the problem
of mesonic and other interactions, the renormalization method does not work
well even when considered as a purely technical manipulation of mathematical
symbols, apart from the question of its logical justification. While it has not been
proved conclusively, as yet, that the infinities described above are essential characteristics of the theory, there is already a considerable amount of evidence in
favour of such a conclusion.”
This is entirely a quantum field problem. Quantum mechanical patterns, derived
from the classical Hamilton-Jacobi formalism, don’t seem to lead to any similar
difficulties. The question is rather, whether an analogical quantization of the classical electro-magnetic field Langrangian will provide us with the full quantum field
pattern, especially when it is used in closed systems such as nuclei in quantum chromodynamics. Note that original field patterns of quantum electrodynamics represent
only the scattering process of a few free particles in vacuum. We will here analyze these inconsistencies in applying such a limited pattern to bound-state massive
systems like molecules and crystals.
The final Bohm quotation contains the exchange with Sheldrake:
5. Bohm: “‘How is time to be understood?’ Now, in terms of the totality beyond
time, the totality in which all is implicate, what unfolds or comes into being in any
present moment is simply a projection of the whole. That is, some aspect of the