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So, I'm reading Max Tegmark's Our Mathematical Universe (Knopf edition, p. 229). He's discussing Everett/MWI for a bit and I'm not really paying attention and then I wake up to this:

[I]t's time to update the quantum textbooks to mention decoherence (many still don't) and to make clear that the Copenhagen interpretation is better thought of as the Copenhagen approximation: even though the wave function probably doesn't collapse, it's a very useful approximation to do the calculations as if it does collapse when you make an observation.

Now, I believe I have read (elsewhere, e.g., on this site) that these interpretations do not make any difference whatsoever* when it comes to predictions. But here, apparently (at least that is how I read the above), it is claimed that MWI and Copenhagen actually differ in predictions (and that MWI has the right predictions). Is that correct? (This would make it slightly more difficult to be agnostic about choosing your favourite interpretation for the time of day, right?)

NB: I'm not specifically asking whether the wavefunction collapses or not.

*As in: zip, nada, zilch, exactly $0$.

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see en.wikipedia.org/wiki/Einselection –  Christoph Jan 22 at 11:53

3 Answers 3

I've never seen a single prediction based upon MWI. I've also never heard of the Cophenhagen interpretation called an approximation. If that were the case, then the Copenhagen interpretation must fail in at least one limit. Does Max provide such limits?

Both of these statements seem to lean towards sensationalism than towards mathematical rigor.

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The wave function collapse is an approximation, it is supposed to be intanstaneous but we know that it is not. Moreover with if that postulate was true it would make quantum mechanics not coherent. –  agemO Jan 22 at 8:16

I agree with mcFreid, I just thought I would contribute my two cents: for some people, collapse happens just in your mind when you learn the result of the (say, Stern-Gerlach) experiment; before you do, the Schroedinger equation just evolves probabilities that imply correlations (like spin up -- upper path, spin down -- lower path). Decoherence may show why density matrix is diagonal in some basis instead of being more complicated, but it does not explain why definite result is obtained in measurement. When we find out which way the atom went, we also find out the spin projection (since we believe the two are correlated) and the projection rule requires that we project the spin state accordingly.

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You're asking an excellent question about whose answer there's major controversy among today's most active quantum mechanics researchers. Historically, a lot of people used to claim that Copenhagen predicts the same thing as MWI, but different physicists who claim to subscribe to the Copenhagen approximation often disagree with each other about how to define it. This vagueness may be the main reason that the Copenhagen interpretation has dropped notably in popularity among quantum information researchers in recent years. The MWI makes the clear prediction that the wavefunction never collapses, so there's in principle nothing stopping arbitrarily large quantum computers from working. In contrast, the Copenhagen interpretation says that the wavefunction will collapse when you make an observation, but provides no equation defining what physical process counts as an observation. Critics therefore ask whether a human consciousness is required, or whether it suffices to have, say, an animal, a video camera or a camera doing the observing. It a really small object can count as an observer, then the wavefunction could collapse inside a quantum computer, preventing it from functioning. To shed more light on this controversy, it's therefore really interesting to try to build a large quantum computers and see whether it works. /Max Tegmark

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Yes in fact the problem is that the concept of "measurement" is not defined anywhere, so you cannot say it is true or false or an approximation, it is just not defined –  agemO Jan 22 at 14:47
    
@agemO: Born, von Neuman, and others defined effects of a measurement. They didn’t define precisely what an experimenter must do to effect a measurement, but likewise, nobody clearly defined what one must do in practice to specify a reference frame – does it make frames of reference an undefined notion? –  Incnis Mrsi Aug 21 at 18:13
    
Yes indeed but it is not a complete definition since we don't know what happen to the rest of the system, if it follow a unitary transformation, if MQ is deterministic etc. –  agemO Aug 24 at 20:26

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