Multiple Descriptions of Reality
part 1: The Statistical Mechanic, 12/12/05
The following is part of an unfinished text about the interpretation of
quantum theory and thermodynamics, which I try to put together for
several months. I finally decided to post the main ideas, perhaps
comments from my readers would
help me finish it (or perhaps give up on it).
In my humble opinion, the Copenhagen interpretation and the philosophy
Niels Bohr is still the best approach to understand quantum theory and
physics in general. The core idea of this philosophy, as I understand
it, is the following: There is one reality, but multiple
of this reality are necessary. These descriptions are incompatibel, but
the correspondence principle explains why we do not observe
In particular, the measurement of observables requires the classical
description of the observer (usually including a measurement device),
while quantum mechanics describes the evolution of the objects in a
The classical description is in this case a coarse-grained macroscopic
description. This is necessary, since the observer cannot describe or
store her own microscopic state.
As long as physics requires an observer, the split in two different
descriptions cannot be avoided.
The microscopic description is fundamental in the sense that we can
(almost) arbitrarily choose objects for our experiments. We can choose
objects in a laboratory (e.g. elementary particles), or we can choose a
certain region of space-time(e.g. a black hole) and (try to) determine
its quantum state.
The classical, macroscopic description is fundamental, because we
cannot extend the microscopic description to the whole universe. The
observer cannot determine or describe her own quantum state and has to
describe herself and her measurement devices using a coarse-grained
description, reducing the description to a few variables.
The correspondenc principle indicates when to switch from one
description to the other and how to choose the split between both
descriptions; A quantitative formulation requires the calculation of
While the classical description includes spacetime and in particular a
time parameter, the quantum theory of gravity may not contain this
I may elaborate more on these ideas, but it is enough for now.
part 2: The Statistical Mechanic, 12/13/05
The following are some additional remarks to my previous post
about multiple descriptions of reality.
i) Every measurement decreases our total knowledge of the universe.
This is a simple consequence of the fact that every measurement is a
physical process, which necessarily increases entropy (if results are
recorded and stored).
Of course, measurements are still very useful, since we arrange them
such that we gain knowledge about some objects we are interested in and
reduce our knowledge about those degrees of freedom we are not
interested in (e.g. the internal microstate of the measurement device).
The split between observer and observed object is thus inevitable.
An obvious consequence is the fact that a wavefunction of the universe
cannot be determined. But it may be interesting to calculate certain
approximations (the original Hartle-Hawking wave function describes the
universe with one variable and ignores all other degrees of freedom).
ii) The collapse of the wavefunction ...
... is simply the change of descriptions. Since the observer uses a
preferred reference frame it is not necessary to find a Lorentz
invariant description of this collapse. It is sufficient that different
observers cannot register contradicting evidence and in particular that
they cannot observe non-local signals. We know that both quantum
mechanics and quantum field theory provide for this consistency.
iii) The use of multiple descriptions applies also to classical
...and is not restricted to quantum theory (as already discussed by
However, in this case, the microscopic and macroscopic description are
based on the same classical physics [*] and thus the correspondence
is very easy to understand; Simple averages of the microscopic degrees
of freedom provide for the macroscopic description in the limiting case
of a large number of elements.
As we know, there is a close relationship between thermodynamics and
quantum theory, e.g. if one performs a Wick rotation. I wonder if this
fact can help to understand the correspondence principle better.
So far I have only discussed two fundamental descriptions of reality. I
save some more remarks and the explanation of the phrase 'multiple
descriptions' for later [**].
[*] While the microscopic description is invariant under
time-reversals, the macroscopic description is not. This is an example
of what I meant with 'incompatibel' in the first post.
[**] It should be obvious that it has nothing to do with the ideas
proposed by Brian Josephson.
part 3: The Statistical Mechanic, 12/14/05
This is the 3rd (and for now last) post on the concept of multiple
descriptions of reality, following this and this post.
i) Predictions are not possible ...
...strictly speaking, already in the context of classical physics, as
illustrated in figure 1 below.
A physicist at point i tries to predict the state at f, but in order to
do this would need information along a spacelike hypersurface, which
she cannot determine before reaching point f. Fig. 1 indicates the
light cones at points i and f.
Of course, the workaround is to move the experiment into a laboratory
as depicted in Fig. 2, and the laboratory walls L provide boundary
conditions which make predictions possible. Indeed most of the effort
of real experiments (the vacuum chambers etc.) is about shielding a
quantum system prepared in state |i> from the environment, so that
it can evolve to state |f> without disturbance; The split between
quantum description and classical description of the observer (+
environment) is not arbitrary.
However, while one can shield an experiment from electromagnetic and
other matter fields, it is not possible to shield gravitation.
Fortunately, gravitation is a very weak interaction and the universe is
mostly empty, thus we can usually neglect
ii) Gravitation and quantum theory
There are two cases where gravitation does play a role: If the
difference of energy eigenvalues, E(i+1) - E(i), is very small, the
unknown gravitation field of the environment can affect the system
enough that a quantum description becomes impossible. This may be
important if one tries
to establish a quantum description of macroscopic objects.
The second case is of course quantum gravity. It seems that the
detection of single gravitons would require massive, planet-sized
detectors and obviously the gravitational field of such a
detector/observer would affect the quantum state of the observed
iii)The classical description contains 'time'...
as a necessary pre-requisite (or a priori in the language of Kant). It
is not a scientific concept which can be derived or falsified. (As an
exercise, try to describe an experiment which would potentially falsify
the existence of time.) However, the quantum description may not
contain the concepts 'time' and 'space', e.g. in a quantum theory of
gravitation or M-theory. Again, a correspondence principle would be
needed to decide how to switch descriptions; e.g. a perturbation theory
around a given spacetime background [*].
iv) Observers may use different descriptions for the same situation.
In the thought experiment of 'Wigner's friend', Wigner uses a classical
description for himself and
also his friend uses a classical description for himself; But Wigner
describes his friend using quantum theory.
(However, consider the previous remarks.) But this does not lead to
There are multiple descriptions for the same reality, not just
two, which finally explains the title of my three posts [x].
[*] I should mention that there is a subtle and interesting
technicality involving the constraint equations of general relativity;
But a discussion would be too long for this post and require some math.
[x] Instead of multiple descriptions I could have used the
phrase complementarity, as it was understood by Bohr.
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