Megascopic Quantum Phenomena
343
[119]: “There are two forms of argument which reach their conclusion ‘on the basis of
considerations of symmetry’. One, the symmetry argument proper, relies on a metaprinciple: that structurally similar problems must receive correspondingly similar
solutions. A solution must ‘respect the symmetries’ of the problem. The second
form, rather less important, assumes a symmetry in its subject, or assumes that an
asymmetry can only come from a preceding asymmetry. Both exert a strong and
immediate appeal, that may hide substantial tacit assumptions.”
The first part of van Fraassen’s argument is quite clear and there is full agreement in the scientific community regarding its interpretation. Even if we get several
asymmetric states as solutions of symmetric equations, i.e. if the original symmetry is broken, the asymmetric states together form a set which respects the original
symmetry of the problem. However, the second form is not clear at all, and there
is no unified view how to interpret it. One group of physicists attempts to explain
it within the causal laws of physics. Usually imperfections and random fluctuations
are taken into account. Stewart and Golubitsky in their book [120] describe the role
of imperfections as follows: “We’ve said that mathematically the laws that apply to
symmetric systems can sometimes predict not just a single effect, but a whole set
of symmetrically related effects. However, Mother Nature has to choose which of
those effects she wants to implement. How does she choose? The answer seems to be:
imperfections. Nature is never perfectly symmetric. Nature’s circles always have tiny
dents and bumps. There are always tiny fluctuations, such as the thermal vibration
of molecules. These tiny imperfections load Nature’s dice in favour of one or other
of the set of possible effects that the mathematics of perfect symmetry considers to
be equally possible.”
There is no doubt that imperfections play an important role in macroscopic objects.
The Norton dome is a nice example of this. Nonetheless, Norton emphasises the
difference between the real and ideal dome [121]: “However, we do not even have a
falsified prediction. The dome is not intended to represent a real physical system. The
dome is purely an idealization within Newtonian theory. On our best understanding
of the world, there can be no such system. For an essential part of the setup is to locate
the mass exactly at the apex of the dome and exactly at rest. Quantum mechanics
assures us that cannot be done. What the dome illustrates is indeterminism within
Newtonian theory in an idealized system that we do not expect to be realized in the
world.”
Such idealizations are of course not convincing enough for many physicists to
take the Norton dome seriously, particularly when there are no applications to the
real world. Norton reckons all objections against the dome and the indeterminism in
classical physics [121]: “What’s wrong with the dome? Many believe that the dome
somehow lies outside what is proper in Newtonian theory. Three distinct bases for this
judgment are described below, along with my reasons for finding them unconvincing.
(1) Does the dome employ an incomplete formulation of Newtonian physics? (2) Is
the dome “unphysical”? (a) Unphysical as gauge (over-description). (b) Unphysical
as false. (c) Unphysical as pathological. (d) Unphysical through under-description.
(3) Does the dome use inadmissible idealizations?”
343
[119]: “There are two forms of argument which reach their conclusion ‘on the basis of
considerations of symmetry’. One, the symmetry argument proper, relies on a metaprinciple: that structurally similar problems must receive correspondingly similar
solutions. A solution must ‘respect the symmetries’ of the problem. The second
form, rather less important, assumes a symmetry in its subject, or assumes that an
asymmetry can only come from a preceding asymmetry. Both exert a strong and
immediate appeal, that may hide substantial tacit assumptions.”
The first part of van Fraassen’s argument is quite clear and there is full agreement in the scientific community regarding its interpretation. Even if we get several
asymmetric states as solutions of symmetric equations, i.e. if the original symmetry is broken, the asymmetric states together form a set which respects the original
symmetry of the problem. However, the second form is not clear at all, and there
is no unified view how to interpret it. One group of physicists attempts to explain
it within the causal laws of physics. Usually imperfections and random fluctuations
are taken into account. Stewart and Golubitsky in their book [120] describe the role
of imperfections as follows: “We’ve said that mathematically the laws that apply to
symmetric systems can sometimes predict not just a single effect, but a whole set
of symmetrically related effects. However, Mother Nature has to choose which of
those effects she wants to implement. How does she choose? The answer seems to be:
imperfections. Nature is never perfectly symmetric. Nature’s circles always have tiny
dents and bumps. There are always tiny fluctuations, such as the thermal vibration
of molecules. These tiny imperfections load Nature’s dice in favour of one or other
of the set of possible effects that the mathematics of perfect symmetry considers to
be equally possible.”
There is no doubt that imperfections play an important role in macroscopic objects.
The Norton dome is a nice example of this. Nonetheless, Norton emphasises the
difference between the real and ideal dome [121]: “However, we do not even have a
falsified prediction. The dome is not intended to represent a real physical system. The
dome is purely an idealization within Newtonian theory. On our best understanding
of the world, there can be no such system. For an essential part of the setup is to locate
the mass exactly at the apex of the dome and exactly at rest. Quantum mechanics
assures us that cannot be done. What the dome illustrates is indeterminism within
Newtonian theory in an idealized system that we do not expect to be realized in the
world.”
Such idealizations are of course not convincing enough for many physicists to
take the Norton dome seriously, particularly when there are no applications to the
real world. Norton reckons all objections against the dome and the indeterminism in
classical physics [121]: “What’s wrong with the dome? Many believe that the dome
somehow lies outside what is proper in Newtonian theory. Three distinct bases for this
judgment are described below, along with my reasons for finding them unconvincing.
(1) Does the dome employ an incomplete formulation of Newtonian physics? (2) Is
the dome “unphysical”? (a) Unphysical as gauge (over-description). (b) Unphysical
as false. (c) Unphysical as pathological. (d) Unphysical through under-description.
(3) Does the dome use inadmissible idealizations?”