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This was posted on here in someone's Phys.SE answer:

No, in the many worlds interpretation, every parallel universe is real, but in consistent histories, once you choose your projection operators, only one possibility is real, and all the others are imaginary. This makes consistent histories a lot more like Bohmian mechanics with the world the Bohmian particle sits in being more real than the rest. Why should one world be more real than the others? There is no reason. T[w]o copies of you living in a parallel world, they are more real than you are.

If as he says, each copy of you believes they are more real than the other, is he saying CH and BM are many worlds in disguise? Or are there no copies of you in CH and BM?

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  • $\begingroup$ The [w] is misleading. he/she means that : for a copy of you living in a parallel world he/she is more real, than you. Each parallel world copy thinks itself is the real one. $\endgroup$ – anna v Jan 15 '13 at 20:52
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Answer

There are no 'copies of you' in CH and BM.

Elaboration

Calling these theories 'the MWI in disguise/denial' is a frequent criticism e.g. Deutsch (1996):

In short, pilot-wave theories are parallel-universes theories in a state of chronic denial.

You can find (generally pro-MWI) physicists/philosophers arguing to this day that this is the case, and pro CH/BM physicists/philosophers arguing the opposite, so it's certainly not a question anyone will give you a conclusive answer to.

However...

In CH there are probability branches, as there are in the MWI, although only one is considered to actually happen; unlike in the MWI where every possibility happens and all are considered as real as each other. I'm not enough of an expert on CH to talk about its distinctions from the MWI aside from those that are metaphysical, but in this regard there are definite distinctions; see Cabello (2016) for a superficial differentiation.

In BM there is a guidance equation that exists on configuration space (3N dimension, where N is the number of distinct particles considered; this obviously gets a little more convoluted when QFT becomes involved). The dimensionality is slightly different when taking into account relativity/spin, but we'll stick with the spinless nonrelativistic version for simplicity.

To many Bohmians this guidance equation is real i.e. there is a hyperdimensional wave that guides particles (known as beables). These beables, unlike particles in the MWI, only exist in our three dimensional world; it just happens that the wave that guides their movement exists over many more dimensions. Valentini (2008) gives a reasonably extensive argument against them being considered the same.

Whatever your thoughts there are clearly some differences so however you choose to see it, I'm not sure how productive arguing over this is since it's a purely metaphysical debate - the maths of BM has shown to have computational advantages for some fields in specific applications (as well as several more dubious benefits), so the interpretation itself shouldn't be discarded no matter whether you want to redefine how 'real' other dimensions are in it or not. In this regard, I can't comment on CH.

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