Arguments for and against Many Worlds? I would like to hear the best arguments for and against the Many Worlds interpretation of QM.
 A: in my opinion, the best argument is that removes the need to postulate a collapse of wavefunction, and explains the source of the randomness of quantum events as a single observer splitting in multiple version of the same observer entangled to each eigenstate of the observed system
the weak aspect of the many worlds interpretation is that it doesn't give a natural explanation of probabilities as the magnitudes-squared of amplitudes, this is still required to be assumed 
A: Everettians are trying to pull wool over your eyes... If it only were that simple that our world keeps branching with time with a preferred basis, and we subjectively find ourselves in one branch. There are two major problems with this interpretation.


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*Different branches can and will recombine in the future. This is seldom emphasized, but this throws a wrench in the interpretation. In fact, for a system in thermal equilibrium, branching and recombination happens at an equal rate. It's only thanks to the fact that locally, we are out of equilibrium that one-way branching makes any approximate sense at all.

*There's no canonical preferred basis in general, not even macroscopically. Decoherence works most of the time at macroscopic scales, but with many important exceptions. If decoherence were universal at macroscopic scales, do you think we'd be able to observe double slit experiments or superconductivity or quantum optics? Even more troubling is the fact that the basis to be chosen can depend contextually upon future decisions, as in the delayed choice experiment.

*In the many minds interpretation, subjectively fixing the conscious state of the observer still leaves most of the rest of the universe in an indeterminate superposition. Only those coarse-grained properties of the "world out there" corresponding to our internal conscious states will be determined by entanglement. Those Everettians who try to tell you subjective experiences are what causes the entire universe to split into many worlds are bluffing.

*If the other worlds out there have some objective existence, how come we can't extract information from them, except in very special cases where we have a coherent variation in the phase and amplitudes between the many branches which then recombine? Not only that, after recombination, the separate worlds lose their separate identities. Besides, a coherent variation rules out the possibility of a complex intelligent observer, at least in the part of the wave function which varies coherently.
Do you really see?
A: Has the MWI produced any new physics? What I mean is not people who subscribe to it doing new physics, but people doing new physics because they were thinking within that interpretation. If the answer is nothing, then this, in my eyes, is a very strong argument against it. Of course this could apply to other interpretations. 
I am not sure if I am clear. What I mean is for example, is there a calculation or a derivation or anything like that, which would have not been done (at least for some time) had there been no MWI.
Edit: I take the comment about David Deutsch as an example of what I was asking for, hence my answer should be viewed as a point in favour for the usefulness of MWI. 
A: For:


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*Collapse is an awkward non unitary concept in the C.I. and likely to be the source of most of the so called paradoxes (like Schrodinger's Cat etc.). Many worlds does not have collapse and thus avoids those paradoxes. It frees one from assuming the "add on" of collapse.

*Quantum entanglement finds a "local" meaning.

*Removes randomness from quantum theory (although for an observer it does not remove any randomness).
Against:


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*Huge proliferation of universes for explaining the observations of an observer. In a way it does not respect the Occam's razor. (Many worlders claim MWI respects it since this interpretation has an economy of principles).

*The problem of preferred basis.

*Defining a suitable measure of probability to achieve Born rule.

*Other universes can not be observed. (A variation of saying it does not respect Occam's razor)

*It is rather a psychological way of thinking about Q.T. rather than a real ontology.
A: Having studied some David Deutsch material recently here are some other points:
For


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*A Multiverse framework for considering whether there is "something beyond" traditional quantum theory. EDIT Thus providing a framework for investigating quantum gravity. Deutsch sees the Multiverse as an as yet undiscovered theory, motivated by Everett, Quantum Computation and certain properties of General Relativity.

*A possible "explanation" for Quantum Computation speedups (EDIT ADDITION) That is for those quantum computations in the BQP Complexity class.
Against


*

*Those Probability and Preferred Frame problems

*The fact that the theory has split into many sub-theories (e.g. Decoherence, Many Minds, Multiverse, etc) that there is no single model to evaluate any more.

*(Related to 2 perhaps) Everett did not publish enough to clarify exactly what the theory actually said in several respects.
A: It is called "interpretation" for a reason: Ultimately, it all describes the same physics, i.e., so far there is no statement "X" that would be true in the MWI and false in Bohmian QM or the Classical Interpretation. Now, if two ways of explaining something lead to entirely the same results, then for all practical purposes these two ways are identical. In my opinion, it is therefore purely a matter of taste to which of the available interpretations one ascribes.
It is only when results between different interpretations become inconsistent that we can rule one of them out.
Which reminds me of a funny text I read on this topic: You can prove to yourself that the MWI is correct by committing "quantum suicide": Think of Schroedinger's cat, but you are the cat. If the MWI is correct, then there will always be a world in which you aren't dead yet. You should notice that you aren't dead, and after repeating the experiment for a sufficiently long time you can conclude that, with high probability, the MWI is correct. If, however, the classical interpretation is correct, you'll just die with high probability :-( Thus, I say "Don't try this at home!"
A: There's no experimental proof one way or the other. The only way to tell is Occam's razor.
There's two interpretations of Occam's razor. One says that the number of laws should be small. The other says the number of entities should be. I can't prove one of them is correct philosophically, but given that the laws could fit readably on a single note card, and there are 10^80 particles (which are distinct entities), I'd go with the former.
The many-worlds interpretation has strictly fewer laws. That is to say, the laws that make it up exist entirely within the Copenhagen interpretation, where they govern entangled particles. As such, no matter what language you use, the many-worlds interpretation will come out smaller.
Edit: My mistake. I can prove one is correct philosophically. The proof of Occam's razor is basically that all the prior probabilities have to add to one, and if it didn't decrease as complexity increased, they'd add to infinity. This gives a lower limit to how fast probability must decrease.
It applies to number of laws and number of entities, but it just means that exactly 10^80 particles is 80 orders of magnitude less likely than 1. 10^80 to 10^81 is still about as likely as 1 to 10.
When you deal with laws, you're not talking about how many bits the theory is. You're talking about the theory itself. If it takes 267 bits to express, and it's an exact set of 267 bits, that's analogous to there being exactly 10^80 particles.
A: The largest problem with "Many Worlds" interpretations is they do not currently offer testable hypotheses.
A: MWI is an example of misunderstanding of what the wave function is about and it introduces unnecessary "universes" that do not follow from experimental data. It does not solve any conceptual problem. On the contrary. Besides, it is not verifiable. Briefly, it is a funny example of nonsense in science.
A: In addition to the many good answers already posted, Scott Aaronson points out that the MWI interpretation is rather "brittle", in the sense that the discovery of pretty much any tiny experimental deviation from the Schrodinger equation would probably require completely scrapping the MWI interpretation. It's hard to imagine a situation in which it would need to be slightly tweaked, but its main spirit would survive unscathed:

we do more-or-less know what could be discovered that would make it reasonable to privilege “our” world over the other MWI branches.  Namely, any kind of “dynamical collapse” process, any source of fundamentally-irreversible decoherence between the microscopic realm and that of experience, any physical account of the origin of the Born rule, would do the trick.

A: I don't understand why nobody has mentioned the apparent violation of conservation of energy. Am I naive here for thinking that a quantum mechanical trigger that allows the bifurcation of world lines, violates the conservation of energy?
A: A good argument against is Occham's razor. Another is the fact that it is not an experimental testable hypothesis.   The best argument I think against it is the fact that the only reasons for Many-worlds are based in human language, whose intuition is only developed for a classical setting, as such any human meta-reasoning cannot be expected to apply to non-classical areas, there are no mathemtical or scientific reasoning involved.
A: http://lesswrong.com/lw/r5/the_quantum_physics_sequence/
One of the best introductions for MWI out there. Answers queries relating to Occam's razor.. and why it's more than our fantasy..
A: The conservation of energy: This is exactly what I have been thinking about. In MWI  the total energy of universes is  constantly increasing as we are multiplying ourselves along with universes. This clearly violates the law of conservation  of mass and energy law. While in case of CI there is always one reality after collapse of all other possibilities thus conserving the mass. (AFTAB KHAN) 
_6÷
