Megascopic Quantum Phenomena
341
conflict in detail: “The net result is that in all physics nothing has shown up indicating
an intrinsic difference of left and right. Just as all points and all directions in space
are equivalent, so are left and right. Position, direction, left and right are relative
concepts. In language tinged with theology this issue of relativity was discussed
at great length in a famous controversy between Leibniz and Clarke, the latter a
clergyman acting as the spokesman for Newton [115]. Newton with his belief in
absolute space and time considers motion a proof of the creation of the world out
of God’s arbitrary will, for otherwise it would be inexplicable why matter moves
in this rather than in any other direction. Leibniz is loath to burden God with such
decisions as lack “sufficient reason.” Says he, “Under the assumption that space be
something in itself it is impossible to give a reason why God should have put the
bodies (without tampering with their mutual distances and relative positions) just at
this particular place and not somewhere else; for instance, why He should not have
arranged everything in the opposite order by turning East and West about. If, on the
other hand, space is nothing more than the spatial order and relation of things then
the two states supposed above, the actual one and its transposition, are in no way
different from each other… and therefore it is a quite inadmissible question to ask
why one state was preferred to the other.””
Weyl attempts to reconcile these opposite views from a new perspective of the
theory of relativity after three centuries: “If nature were all lawfulness then every phenomenon would share the full symmetry of the universal laws of nature as formulated
by the theory of relativity. The mere fact that this is not so proves that contingency
is an essential feature of the world. Clarke in his controversy with Leibniz admitted
the latter’s principle of sufficient reason but added that the sufficient reason often
lies in the mere will of God. I think, here Leibniz the rationalist is definitely wrong
and Clarke on the right track. But it would have been more sincere to deny the principle of sufficient reason altogether instead of making God responsible for all that
is unreason in the world. On the other hand Leibniz was right against Newton and
Clarke with his insight into the principle of relativity. The truth as we see it today is
this: The laws of nature do not determine uniquely the one world that actually exists,
not even if one concedes that two worlds arising from each other by an automorphic
transformation, i.e., by a transformation which preserves the universal laws of nature,
are to be considered the same world.”
Does Weyl’s statement hold in universally physics? In classical physics including
Einstein’s relativity, we need not have to care about Leibniz’ principle of sufficient
reason, since this principle is of teleological origin. We have also seen that in the
classical solution of superconductivity this principle is hidden behind a multiplicity of solutions, the first one leading to ideal conductivity and the second one to
superconductivity, in full agreement with Weyl’s interpretation. However, this construal is not valid in quantum physics, since quantum physics is causal and hence
cannot observe teleological phenomena. After a rigorous use of Goldstone’s theorem, we have obtained a superconducting ground state, which is identical to the
ground states of insulators with J-T distorted nuclear positions. This is of course
not enough for a quantum explanation of superconductivity. The quantum nature of
Leibniz’ principle must be first discovered, and only then might the quantum essence
341
conflict in detail: “The net result is that in all physics nothing has shown up indicating
an intrinsic difference of left and right. Just as all points and all directions in space
are equivalent, so are left and right. Position, direction, left and right are relative
concepts. In language tinged with theology this issue of relativity was discussed
at great length in a famous controversy between Leibniz and Clarke, the latter a
clergyman acting as the spokesman for Newton [115]. Newton with his belief in
absolute space and time considers motion a proof of the creation of the world out
of God’s arbitrary will, for otherwise it would be inexplicable why matter moves
in this rather than in any other direction. Leibniz is loath to burden God with such
decisions as lack “sufficient reason.” Says he, “Under the assumption that space be
something in itself it is impossible to give a reason why God should have put the
bodies (without tampering with their mutual distances and relative positions) just at
this particular place and not somewhere else; for instance, why He should not have
arranged everything in the opposite order by turning East and West about. If, on the
other hand, space is nothing more than the spatial order and relation of things then
the two states supposed above, the actual one and its transposition, are in no way
different from each other… and therefore it is a quite inadmissible question to ask
why one state was preferred to the other.””
Weyl attempts to reconcile these opposite views from a new perspective of the
theory of relativity after three centuries: “If nature were all lawfulness then every phenomenon would share the full symmetry of the universal laws of nature as formulated
by the theory of relativity. The mere fact that this is not so proves that contingency
is an essential feature of the world. Clarke in his controversy with Leibniz admitted
the latter’s principle of sufficient reason but added that the sufficient reason often
lies in the mere will of God. I think, here Leibniz the rationalist is definitely wrong
and Clarke on the right track. But it would have been more sincere to deny the principle of sufficient reason altogether instead of making God responsible for all that
is unreason in the world. On the other hand Leibniz was right against Newton and
Clarke with his insight into the principle of relativity. The truth as we see it today is
this: The laws of nature do not determine uniquely the one world that actually exists,
not even if one concedes that two worlds arising from each other by an automorphic
transformation, i.e., by a transformation which preserves the universal laws of nature,
are to be considered the same world.”
Does Weyl’s statement hold in universally physics? In classical physics including
Einstein’s relativity, we need not have to care about Leibniz’ principle of sufficient
reason, since this principle is of teleological origin. We have also seen that in the
classical solution of superconductivity this principle is hidden behind a multiplicity of solutions, the first one leading to ideal conductivity and the second one to
superconductivity, in full agreement with Weyl’s interpretation. However, this construal is not valid in quantum physics, since quantum physics is causal and hence
cannot observe teleological phenomena. After a rigorous use of Goldstone’s theorem, we have obtained a superconducting ground state, which is identical to the
ground states of insulators with J-T distorted nuclear positions. This is of course
not enough for a quantum explanation of superconductivity. The quantum nature of
Leibniz’ principle must be first discovered, and only then might the quantum essence