Comments on
'Basic Concepts and their Interpretation' by H.D. Zeh,
Chapter 2 in:
E. Joos, H.D. Zeh, et al.,
Decoherence and the Appearance of a Classical World in Quantum Theory
Springer 2003
by Arnold Neumaier
http://www.mat.univie.ac.at/~neum/zeh.tzt
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The remarks are based on the version available at
http://www.rzuser.uni-heidelberg.de/~as3/Dekoh2.pdf
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The proposed basis lacks almost everything I want to see in a
fundamental theory. My standards are higher than what I find in most
of the discussions in the literature, including those in Zeh's chapter.
I like decoherence as a tool, but it does not belong into the
foundations on the most basic level, where everything
should be precisely defined. Its role is rather to explain how
putative good foundations give rise to classical phenomena.
To deserve the status of a foundation of physics, upon which everything
else can rest safely, every concept must be precisely and
unambiguously defined on the formal level - so that it could be taught
to an intelligent computer -, before it can be used.
Only what is done on such a basis can be considered as fundamental.
Only the objects defined in this way may be considered as 'beables'
on the level of the mathematical model of the world that good
foundations are supposed to provide.
Good foundations start with a few formal postulates telling which
objects are assumed to be objective at the fundamental level, and
a few axioms defining the properties assumed about these objects.
Everything else must proceed from there in a logical, unambiguous
manner, without introducing new concepts except if they can be
completely defined in terms of those already present.
I do not require that everything can be _calculated_ exactly, but
I _do_ require thet everything is _defined_ exactly, using only
concepts defined before, or specified in the beginning as irreducible
and fundamental.
Thus a detector cannot be an irreducible device that is introduced
in an ad hoc manner, but must be defined as a set of 10^25 nuclei or
10^24 atoms or whatever is taken as the basic building blocks of the
theory.
Seen from this perspective, Chapter 2 by Zeh is just a philosophical
prelude, not a 'foundation' - too many words, too few definitions.
Too many unanswered questions. I start with my critique on p.17 since
there the more formal part seems to begin.
What is a state? Apparently a wave function. Any? Only normalizable
ones? Only normalized ones? In which way is lambda*psi (considered
different from psi on p.18) observationally different from psi?
As far as the consensus among physicists is concerned, the only
observable consequences are in terms of expectations
=psi^*f psi/psi^*psi,
hence states must be rays and not wave functions.
What is the relationship between the state psi of a large system
and the state psi' of a subsystem? Does the latter exist, rigorously,
on the fundamental level? Always? Sometimes? When exactly?
Footnote 7 on p.20 indicates that these states do not always exist.
If so, they cannot be the right kinematical concept. Kinematical
objects must have a meaning at all times to serve their purpose.
What is a detector? What is detected? How?
Under which microscopic conditions does a measurement happen?
What is a filter (p.17)? What does it mean to find a system, which is
objectively in the state psi, with some probability in the state |n>?
After all, it it always 100% in some definite state. Or isn't it?
but then why is it in a definite state before measurement?
Does 'finding a system in some state' require an observer who finds it?
If so, how is the observer defined, on the fundamental level?
How does he/she/it find what it finds? On p.30, a 'subjective observer'
is introduced. What is he/she/it, on the fundamental level? What is
subjective about him/her/it?, What does it mean that an observer is
'aware' of something, in terms of the fundamentals? How many subjective
observers are there? In the paragraph it almost looks like there are
infinitely many of them. How do these observers evolve?
How do probabilities emerge from an objective description?
What is the difference between 'formal probabilities' (p.19) and
observable probabilities?
On p.20, Zeh seems to invoke expansion coefficients. But these have a
meaning only if a particular basis is chosen. If the system is a single
spin, do you expand in terms of up/down or in terms of left/right?
Clearly, one must consider this in the light of the interactions.
If the interactions are simple enough, one can tell what the basis
is supposed to be; the least needed is to give unambiguous rules for
selecting the basis. In any case, good foundations must be basis
independent, so the rules for picking a basis must be deducible from
information assumed to be present at the axiomatic level where
everything is defined.
On p.19, line 5, a measurement devise makes its entrance.
No definition is given what it means in terms of what is already known.
It looks like another fundamental notion. But clearly it cannot be one.
Moreover, it is taken as 'defined regardless of time'. But clearly,
it is a multiparticle system with the ordinary Schr"odinger dynamics,
hence intrinsically time-dependent, and one can actually see in many
cases the pointer move from 0 to its final position which defines a
measurement result.
p.20: What is a pointer position? Another undefined concept,
hence another fundamental entity?? Clearly unsatisfactory.
In the discussion of the Copenhagen interpretation on p.38, a case
seems to be made against events occuring 'outside the laws of nature'.
How would they be described occuring 'within the laws of nature'?
Or does Zeh's physics dispense with events altogether? What then of
the events we see happen all the time? Are they 'apparent events'
(p.39)? Human illusions that in fact don't happen? Or what is a real
event?
Classical analogues of all my questions could be answered on a formal
level in classical mechanics (which is a well-founded theory,
though it conflicts with experiment because the dynamics is not quite
ok). I'd expect a similar level of clarity in quantum foundations.
In summary, I find the proposed foundations vague to the point of
bordering on meaninglessness (from a foundational perspective),
Everything built upon such foundations is highly questionable.
In particular, I cannot accept _any_ of the conclusions listed
on p. 40, and I don't think the necessity of any of them has been
demonstrated convincingly.