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 of 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

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 particular experiment.

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 decoherence effects.

While the classical description includes spacetime and in particular a time parameter, the quantum theory of gravity may not contain this concept.

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

i)

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)

... 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)

...and is not restricted to quantum theory (as already discussed by Niels Bohr). However, in this case, the microscopic and macroscopic description are based on the same classical physics [*] and thus the correspondence principle 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

i)

...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 it [*].

ii)

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 graviton.

iii)

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)

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 observable contradictions. There are

[*] 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

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