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http://iopscience.iop.org/1742-6596/174/1/012024

In the above link we see TP Singh arguing that only Copenhagen will work for a theory of quantum gravity. Some of his key points are "quantum theory becomes nonlinear at the Planck mass/energy scale." which he states would mean that you would need a nonlinear Schrödinger equation, which he claims only the Copenhagen interpretation of quantum mechanics can provide.

Is this right?

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Could you elaborate on the reason you have doubts?! –  Michiel May 25 '13 at 9:24
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This paper looks like nonsense to me. I wouldn't waste too much time thinking about its refutation. –  user1504 May 25 '13 at 12:34
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I just made a bunch of comments, I will try to say it again more compactly: The question, as stated, misrepresents Singh's position. Singh doesn't mention the Copenhagen interpretation at all. He offers a choice between two types of "realist" theory, many worlds, and an "objective collapse" theory in which the wavefunction spontaneously evolves into special eigenstates because of nonlinear dynamics. –  Mitchell Porter May 25 '13 at 13:22
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The Copenhagen interpetation is a "subjective collapse" theory, in which the wavefunction isn't a real thing, it's more like a probability distribution, a device that makes predictions, and the "collapse" is just the modification to the wavefunction that you make when an observation gives you new information. –  Mitchell Porter May 25 '13 at 13:23
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@MitchellPorter seems like a perfectly good answer to me, why not make that out of it?! –  Michiel May 25 '13 at 14:28

2 Answers 2

The first thing that seems a little silly to me about this paper is that he's worrying about interpretations of a theory of quantum gravity, but we don't have a theory of quantum gravity. Even in standard quantum mechanics, the interpretations are not testable, are not needed for any application of quantum mechanics, and belong to philosophy, not science. Since they're irrelevant to standard quantum mechanics, there's no a priori reason to imagine that they're relevant to a theory of quantum gravity, which we don't have yet.

Quantum gravity has problems in general with talking about observers. E.g., if your system is the entire universe, you don't have any external observer who can make measurements on it. It's possible that this is of deep significance and holds a clue as to how to construct a theory of quantum gravity. It's also possible that it's completely unimportant, just as observers are an inessential concept in standard QM.

The standard presentation of MWI assumes perfect linearity, which explains why the parallel universes can't influence one another. This lack of "cross-talk" is what makes it impossible to test MWI against CI empirically. GR is nonlinear, so it's reasonable to assume that a hypothetical theory of quantum gravity would be nonlinear. The natural inference seems to me to be not that this is a problem for MWI but that it conceivably makes MWI testable.

Singh talks about the hole argument, and that whole part of the paper seems extremely flaky to me. The classical hole argument is resolved by understanding what is and isn't an observable in GR. Now he's trying to apply it to quantum gravity, but he doesn't make any effort to consider the issue of what is and isn't an observable in quantum gravity.

He talks about specific toy models of nonlinear quantum mechanics, apparently with the motivation of associating their nonlinearity with the CI's wavefunction collapse. But it's far from clear to me that this association holds. In a nonlinear quantum mechanics, you're going to get all kinds of new phenomena. There is no reason to think that out of all these phenomena, somehow something will pop out that acts like CI with wavefunction collapse as an actual physical process.

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...what part of the paper was the hole problem referred to in? –  Drew Bowers May 26 '13 at 1:27
    
@DrewBowers: section 3.2 –  Ben Crowell May 26 '13 at 18:58

A limit on the variation of the speed of light arising from quantum gravity effects

http://www.nature.com/nature/journal/v462/n7271/full/nature08574.html

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Quantum gravity theories wiped out by a gamma ray burst

http://arstechnica.com/science/2009/10/quantum-gravity-theories-meet-a-gamma-ray-burst/

"A value this close to the Planck length means that quantum gravity models in which there's a linear relationship between photon energy and speed are "highly implausible." That leaves other quantum gravity options open, including those in which the the relationship is non-linear."

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I like the links you attached, but is the kind of non linearity talked about by TP Singh –  Prathyush May 25 '13 at 20:57

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