Megascopic Quantum Phenomena
351
system. Hence a second type of Bohr complementarity for the many-body level is
requested.
This suggestion does not sound weird, since a second type of complementarity was
already requested a long time ago by one of the co-founder of quantum mechanics
Pascual Jordan. In his now almost forgotten paper [134] he wrote: “We assume here
an idealised photographic plate: Each photon hitting it will be absorbed, and a single
photon will with certainty activate a certain silver grain… If we assume the exposed
silver grain to be indeed in a state of well-defined decision as to its developability,
then we must conclude that it is not merely voluntary resignation on our part if we
do not describe the silver grain in terms of wave functions of its single atoms. Doing
so would entangle us in contradictions, as we have already seen above. Therefore
the physical situation itself must contain guarantees that such contradictions cannot
take place—and only a second type of complementarity can give this guarantee.
There must exist in the silver grain a certain situation by which its description in
terms of atomic wave functions is made impossible—only in this manner can the
grain function as it does… It is then apparent that the situation—though it is clear
to a certain extent—does not allow a complete and final analysis; there remain open
certain questions. For one cannot avoid the difficulties merely by describing the silver
grain (or an analogous part of any observational instrument) as a “mixture” of the
form of the statistical matrix; this would not help us much, for it cannot describe
an increase of entropy any better than the Schrödinger equation of a “pure case.” It
seems to me that entirely new conceptions are necessary.”
This infers an extra quality of complementarity imparting a new type of quantum
transitions on the many-body level, which cannot be deduced from any known rules
of quantum physics. It entails a new axiom, and this axiom was requested by Jordan
in the same paper [134]: “This leads us to acknowledge that it is both possible and
necessary to formulate a physical axiom not formulated hitherto. Above we held it
to be part of the definition of macrophysics, to show no complications in the manner of complementarity, but to allow a complete “objectivation” of phenomena in
space and time. But usually one defines macrophysics only by stating that it deals
with great numbers of microphysical individuals—and this is another and a different definition. We need therefore a special axiom to express the empirical fact that
these two definitions define the same thing—that really each large accumulation of
microphysical individuals always shows a well-defined state in space and time—that
a stone never, unlike an electron, has indeterminate coordinates. One often vaguely
believes this to be guaranteed already by Heisenberg’s p : q > h; but in fact this
relation only provides a possibility and not a necessity for the validity of our axiom.
Let us assume that, in our experiment involving the photon, the photographic plate
be removed, but that we have an arrangement whereby a macro-physical stone will
fall according to the decision of the photon. Then, if we strictly assume v. Neumann’s
view, the stone comes to possess a wave function which makes it undecided whether
it does fall or does not, and an observer has the opportunity to compel the stone to a
decision by the mental process of forgetting that interference between the two wave
functions of the falling stone would be possible. Schrödinger’s famous cat is another
illustration of this point. I think we can summarize the situation by saying that indeed
351
system. Hence a second type of Bohr complementarity for the many-body level is
requested.
This suggestion does not sound weird, since a second type of complementarity was
already requested a long time ago by one of the co-founder of quantum mechanics
Pascual Jordan. In his now almost forgotten paper [134] he wrote: “We assume here
an idealised photographic plate: Each photon hitting it will be absorbed, and a single
photon will with certainty activate a certain silver grain… If we assume the exposed
silver grain to be indeed in a state of well-defined decision as to its developability,
then we must conclude that it is not merely voluntary resignation on our part if we
do not describe the silver grain in terms of wave functions of its single atoms. Doing
so would entangle us in contradictions, as we have already seen above. Therefore
the physical situation itself must contain guarantees that such contradictions cannot
take place—and only a second type of complementarity can give this guarantee.
There must exist in the silver grain a certain situation by which its description in
terms of atomic wave functions is made impossible—only in this manner can the
grain function as it does… It is then apparent that the situation—though it is clear
to a certain extent—does not allow a complete and final analysis; there remain open
certain questions. For one cannot avoid the difficulties merely by describing the silver
grain (or an analogous part of any observational instrument) as a “mixture” of the
form of the statistical matrix; this would not help us much, for it cannot describe
an increase of entropy any better than the Schrödinger equation of a “pure case.” It
seems to me that entirely new conceptions are necessary.”
This infers an extra quality of complementarity imparting a new type of quantum
transitions on the many-body level, which cannot be deduced from any known rules
of quantum physics. It entails a new axiom, and this axiom was requested by Jordan
in the same paper [134]: “This leads us to acknowledge that it is both possible and
necessary to formulate a physical axiom not formulated hitherto. Above we held it
to be part of the definition of macrophysics, to show no complications in the manner of complementarity, but to allow a complete “objectivation” of phenomena in
space and time. But usually one defines macrophysics only by stating that it deals
with great numbers of microphysical individuals—and this is another and a different definition. We need therefore a special axiom to express the empirical fact that
these two definitions define the same thing—that really each large accumulation of
microphysical individuals always shows a well-defined state in space and time—that
a stone never, unlike an electron, has indeterminate coordinates. One often vaguely
believes this to be guaranteed already by Heisenberg’s p : q > h; but in fact this
relation only provides a possibility and not a necessity for the validity of our axiom.
Let us assume that, in our experiment involving the photon, the photographic plate
be removed, but that we have an arrangement whereby a macro-physical stone will
fall according to the decision of the photon. Then, if we strictly assume v. Neumann’s
view, the stone comes to possess a wave function which makes it undecided whether
it does fall or does not, and an observer has the opportunity to compel the stone to a
decision by the mental process of forgetting that interference between the two wave
functions of the falling stone would be possible. Schrödinger’s famous cat is another
illustration of this point. I think we can summarize the situation by saying that indeed