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I am trying to understand how gravity might prevent the creation of macroscopic quantum superpositions, such as a Schrodinger Cat state.

I am not asking about decoherence. Also, Penrose has a great paper in which he calculates a decay time of a quantum superposition of different spacetime geometries, but this isn't what I'm talking about. Interestingly, a group of researchers showed that relativistic time dilation at different heights on the Earth’s surface was enough to decohere a macroscopic quantum superposition pretty quickly. They showed that an isolated gram-scale object in a superposition of locations vertically separated near Earth’s surface by 1mm would decohere in around a microsecond. This implies that even a “perfectly isolated” Schrodinger’s Cat experiment could never even get off the ground if located anywhere near a planet; however it says little about performing such an experiment in deep space with flat spacetime curvature. But even though the word “gravitational” appeared in its title, the article was really about time dilation.

So far, I haven’t found an article that deals with how the gravitational effects of a macroscopic object in different locations would correlate to measurable differences elsewhere in the universe, and how this would prevent macroscopic quantum superpositions. If it were the case that an isolated system described by |dead> caused some correlated event different than an isolated system described by |alive>, then the superposition |Ψ> = |alive> + |dead> could not exist. I haven’t done the calculation yet, but I suspect that gravity would destroy a macroscopic superposition very quickly.

Of course, the question is not really whether gravitational effects are relevant to the existence of quantum superpositions. Of course they are. The sun could not exist in a superposition of a state in which it is located at the center of our solar system and a state in which it is located a light-year away, as the differences between such states would be heavily correlated to measurable differences in other places in the universe. The question is at what scale are gravitational effects relevant to the existence of quantum superpositions. That may place an upper limit to the size of quantum superpositions and the applicability of QM. (This whole notion that there is no limit, in principle, to the size of objects in interference experiments is driving me crazy, but I’ll save that rant for another time.) If the answer happens to be such as to prevent any kind of Schrodinger’s Cat or Wigner’s Friend experiment anywhere in the universe, no matter how isolated, then we can finally stop being confused by (and hearing about) these thought experiments.

Before I spend time doing these calculations or trying to reinvent the wheel, it would be great to know if it’s already been done. Do you know of any such calculation, article, or research?

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  • $\begingroup$ I was also surprised to read that gravitational differences are perceptible between different altitudes on earth, but it seems a little more intuitive if you consider that slopes upward toward ridges & peaks are mostly concave, "undoing" some of the gravity of the earth, whose shape is convex. However, I've even read that those differences are measurable within the heights of tall buildings...! $\endgroup$ – Edouard May 9 at 23:09
  • $\begingroup$ I don't think Penrose has a theory of how this happens, more like a general gut feeling that decoherence and gravity are related. He also hasn't made a specific quantitative prediction, only an order of magnitude estimate. I don't mean to say that the experiment isn't worth doing. But "how gravity influences decoherence" is a question that even the proponents of this non-mainstream idea aren't exactly sure how to answer. $\endgroup$ – Prof. Legolasov May 10 at 14:51
  • $\begingroup$ Also, the paper you linked talks about decoherence due to the time dilation coming from the external gravity field causing various internal degrees of freedom to interact with each other. Penrose's proposal, unless I'm mistaken, is that the superposition principle breaks down when two parts of the system gravitate with each other. Hence, these are very different effects. $\endgroup$ – Prof. Legolasov May 10 at 15:00
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I am very skeptical about the conclusions reached in "a group of researchers showed that relativistic time dilation at different heights on the Earth’s surface was enough to decohere a macroscopic quantum superposition pretty quickly. They showed that an isolated gram-scale object in a superposition of locations vertically separated near Earth’s surface by 1mm would decohere in around a microsecond."

In optics, it is not unusual for, e.g., a femtosecond light pulse to be separated into a continuum of components having different wavelengths, for the components to be filtered, and then the components recombined to form a new pulse having a different shape. This is a coherent process, requiring mutual coherence between all the components. It's not quite the usual kind of coherence; it just means that the relative phases of the components are known precisely.

In the case where oscillators (e.g., atoms) are placed at different heights in a gravitational field, even if they start out with the same phase (start oscillating at the same moment), they will slip out of phase due to gravitational time dilation. However, their relative phases will be precisely knowable, so all aspects of the original configuration can be recovered. In other words, no information is gained or lost, and therefore "decoherence" has not occurred.

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