2008-05-16

The main feature of the m.w.i. is the absence of a 'collapse' of the wave function and the believe that the

various 'branches' of a wave-function are equally real [*].

One consequence is that the m.w.i inevitably needs to assume the reality of the one wave function Ψ of

the whole universe, since it is impossible to separate the wave function of macroscopic bodies from the

environment. But this leads immediately to two problems: First, it seems impossible in principle for any

observer to determine the wave function of the universe (as I argued previously, e.g. here and here).

The second problem is that one needs to make assumptions about quantum gravity [x] and in particular

that incorporating general relativity will not alter quantum theory as we currently understand it.

Notice that in quantum mechanics Ψ depends on the time parameter t, implicitly assuming the existence

of classical clocks. Where do such classical clocks come from in m.w.i.?

If we consider quantum field theory, it is formulated in a classical (flat) background geometry. Since one

cannot explain the existence of the classical entities corresponding to this background within m.w.i., it

requires a complete theory of quantum gravity - and of course we do not know yet what it is. (But if it

turns out that superstring theory is correct, the multiple universes of the string landscape and the many

worlds could perhaps be a perfect match.)

The question of the preferred basis has been discussed at length in the literature and the usual assumption

of m.w.i. proponents is that decoherence will provide for a preferred basis. I do not need to repeat the

arguments here but would only add that decoherence usually considers a quantum system coupled to its

environment. But the very existence of such an environment is dubious in my opinion, if one has to consider

the wave function of the universe to begin with.

In the words of H.D.Zeh [x]: "If the Quantum Universe is thus conceptually regarded as a whole, it does not

decohere, since there is no further environment. Decoherence is meaningful only for subsystems of the

Universe, and with respect to observations by other subsystems."

While H.D.Zeh understands this as an argument in favor of m.w.i., I think it shows the opposite: One can

ultimately not use decoherence to solve the problem of the preferred base, without additional assumptions.

Another issue that is often discussed is the fact that m.w.i. considers all 'branches' of the wave function as

equally real, no matter how small the associated probability. In particular, this would include a large number

of absurd worlds (e.g. worlds where crucial quantum experiments have failed, as noticed by John Bell).

And since quantum theory (without 'collapse') is invariant under time reversal one has to conclude that the

collection of all possible worlds shows no preferred direction of time, which leaves me with the question where

the 2nd law comes from. Of course, this is a difficult problem for other theories and interpretations as well,

but I think it is much more severe for m.w.i.

Finally, I should mention that Ian Durham has posted an argument against m.w.i., but I have to admit that I

do not fully understand it yet 8-)

So where does all that leave us? While m.w.i. considers Ψ, the wave function of the universe, to be the

ultimate reality, the Copenhagen interpretation assumes that wave functions are a description of reality and

acknowledges that (at least currently) one needs more than one description.

I think this is an approximation I can live with for now.

[*] I recommend this video lecture with Sidney Coleman talking about the interpretation of quantum theory if

you have enough time (about 1h). Also, I recommend this list of several posts about quantum theory and m.w.i.

as an introduction to this topic.

[x] H.D. Zeh, The Physical Basis of The Direction of Time, chap. 6, in particular p. 174 of the 5th ed.

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