[TomS]

Hallo, anbei ein anderer Text zur Energieerhaltung

Q22 Does many-worlds violate conservation of energy?
First, the law conservation of energy is based on observations within each world. All observations within each world are consistent with conservation of energy, therefore energy is conserved.
Second, and more precisely, conservation of energy, in QM, is formulated in terms of weighted averages or expectation values. Conservation of energy is expressed by saying that the time derivative of the expected energy of a closed system vanishes. This statement can be scaled up to include the whole universe. Each world has an approximate energy, but the energy of the total wavefunction, or any subset of, involves summing over each world, weighted with its probability measure. This weighted sum is a constant. So energy is conserved within each world and also across the totality of worlds.

One way of viewing this result - that observed conserved quantities are conserved across the totality of worlds - is to note that new worlds are not created by the action of the wave equation, rather existing worlds are split into successively "thinner" and "thinner" slices, if we view the probability densities as "thickness".

Außerdem noch der folgende Text zu Wahrscheinlichkeiten; Details dazu sind m.W.n. noch umstritten

Everett demonstrated [1], [2] that observations in each world obey all the usual conventional statistical laws predicted by the probabilistic Born interpretation, by showing that the Hilbert space's inner product or norm has a special property which allows us to makes statements about the worlds where quantum statistics break down. The norm of the vector of the set of worlds where experiments contradict the Born interpretation ("non-random" or "maverick" worlds) vanishes in the limit as the number of probabilistic trials goes to infinity, as is required by the frequentist definition of probability. Hilbert space vectors with zero norm don't exist (see below), thus we, as observers, only observe the familiar, probabilistic predictions of quantum theory. Everett-worlds where probability breaks down are never realised.
Strictly speaking Everett did not prove that the usual statistical laws of the Born interpretation would hold true for all observers in all worlds. He merely showed that no other statistical laws could hold true and asserted the vanishing of the Hilbert space "volume" or norm of the set of "maverick" worlds. DeWitt later published a longer derivation of Everett's assertion [4a], [4b], closely based on an earlier, independent demonstration by Hartle [H]. What Everett asserted, and DeWitt/Hartle derived, is that the collective norm of all the maverick worlds, as the number of trials goes to infinity, vanishes. Since the only vector in a Hilbert space with vanishing norm is the null vector (a defining axiom of Hilbert spaces) this is equivalent to saying that non-randomness is never realised. All the worlds obey the usual Born predictions of quantum theory. That's why we never observe the consistent violation of the usual quantum statistics, with, say, heat flowing from a colder to a hotter macroscopic object. Zero-probability events never happen.

Of course we have to assume that the wavefunction is a Hilbert space vector in the first place but, since this assumption is also made in the standard formulation, this is not a weakness of many-worlds since we are not trying to justify all the axioms of the conventional formulation of QM, merely those that relate to probabilities and collapse of the wavefunction.

Bzgl. experimenteller Tests habe ich folgendes gefunden:

It has frequently been claimed, e.g. by De Witt 1970, that the MWI is in principle indistinguishable from the ideal collapse theory. This is not so. The collapse leads to effects that do not exist if the MWI is the correct theory. To observe the collapse we would need a super technology which allows for the “undoing” of a quantum experiment, including a reversal of the detection process by macroscopic devices. See Lockwood 1989 (p. 223), Vaidman 1998 (p. 257), and other proposals in Deutsch 1986. These proposals are all for gedanken experiments that cannot be performed with current or any foreseeable future technology. Indeed, in these experiments an interference of different worlds has to be observed. Worlds are different when at least one macroscopic object is in macroscopically distinguishable states. Thus, what is needed is an interference experiment with a macroscopic body. Today there are interference experiments with larger and larger objects (e.g., fullerene molecules C70, see Brezger et al. 2002 ), but these objects are still not large enough to be considered “macroscopic”. Such experiments can only refine the constraints on the boundary where the collapse might take place. A decisive experiment should involve the interference of states which differ in a macroscopic number of degrees of freedom: an impossible task for today's technology. It can be argued, however, that the burden of an experimental proof lies with the opponents of the MWI, because it is they who claim that there is a new physics beyond the well tested Schrödinger equation. As the analysis of Schlosshauerl 2006 shows, we have no such evidence.

The MWI is wrong if there is a physical process of collapse of the wave function of the Universe to a single-world quantum state. Some ingenious proposals for such a process have been made (see Pearle 1986 and the entry on collapse theories). These proposals (and Weissman's 1999 non-linear decoherence idea) have additional observable effects, such as a tiny energy non-conservation, that were tested in several experiments, e.g. Collett et al. 1995. The effects were not found and some (but not all!) of these models have been ruled out, see Adler and Bassi 2009.

Much of the experimental evidence for quantum mechanics is statistical in nature. Greaves and Myrvold 2010 made a careful study showing that our experimental data from quantum experiments supports the Probability Postulate of the MWI no less than it supports the Born rule in other approaches to quantum mechanics. Thus, statistical analysis of quantum experiments should not help us testing the MWI, but I might mention speculative cosmological arguments in support of the MWI by Page 1999, Kragh 2009, Aguirre and Tegmark 2011, and Tipler 2012.