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Theoretically, nothing prevents a really massive object to be in a superposition of two spatial locations, even far away one from the other. Then I guess spacetime would also show the superposition of two corresponding gravitational wells. Could this be observed somehow ? Now measuring the gravitational field would provide a way to measure the object position and thus give it a specific one. Could this impose a limit to the mass of an object in superposition (in the line of: when heavy enough its position gets automatically measured by whatever is subject to its gravity) ? If yes, what would be the order of magnitude of such a limit ?

Qmechanic
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Stéphane Rollandin
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  • "Theoretically, nothing prevents a really massive object to be in a superposition of two spatial locations, even far away one from the other.". I don't know why you would say that. Both experiment and theory prevent that from happening just fine. What the theory doesn't prevent is your uncertainty about the object to be arbitrarily large, but you can't superimpose two quantum states that for a heavy object that are localized in two different places, you would have to have extremely low temperatures for that, so that the radiation field doesn't collapse your fragile state. – CuriousOne Mar 11 '16 at 09:02
  • @CuriousOne. I did not suppose the state is fragile. Let's suppose it is not fragile. – Stéphane Rollandin Mar 11 '16 at 09:10
  • Science doesn't work by pretense. Yes, you can imagine preparing such a state and they have been prepared in atomic physics experiments, but the interaction with the radiation field will destroy it. Actually, since you are also asking for gravity, gravity will destroy it, for sure. Is that your question? That one can do this for a few atoms is only possible because gravity is so weak. – CuriousOne Mar 11 '16 at 09:18
  • @CuriousOne. What pretense ? I am clarifying my thought experiment in response to your objection, because you were assuming something that is not assumed in the question. Now if you can direct me to a theoretical reason why a massive object (not "complex", "big", "fragile": "massive") can not be in a superposition of spatial locations, please do, this will be a fine answer. – Stéphane Rollandin Mar 11 '16 at 09:27
  • Because the massive object interacts "massively" with the em field and that performs the equivalent of a measurement on it. After that you will always find it in one of two places. Gravity will do the same. If the background is cold, the wavelengths of the background photons are long and the "precision" of the decohering measurement will be low, hence the decoherence timescale will be long enough to do this on the atomic scale. – CuriousOne Mar 11 '16 at 09:36
  • @CuriousOne. Could you please add some precisions or references to what you say and make it an anwser ? Notably it is not clear to me why an EM field would automatically interact with the object (aren't you assuming some structure in the object again ?). As for "gravity will do the same", well, I did not assume that the object is in a non-vanishing gravitational field. Actually, that's a bit the gist of my question, if you read it again. – Stéphane Rollandin Mar 11 '16 at 09:43
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    I think this is actually a pretty interesting question, but the answer is probably not really known. Here is a recent interesting article related to this matters. – glS Mar 11 '16 at 10:08
  • @glS. If you don't mind, I will write an answer myself based on the paper you linked. – Stéphane Rollandin Mar 12 '16 at 08:35
  • Sure, go ahead!... – glS Mar 12 '16 at 12:33

2 Answers2

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You say:

Theoretically, nothing prevents a really massive object to be in a superposition of two spatial locations, even far away one from the other.

but a massive object cannot be maintained in a superposition for very long due to quantum decoherence. Strictly speaking it's not the mass that matters but rather the number of degrees of freedom, but in practice the more massive an object is the more degrees of freedom it has.

Anyhow, any macroscopic object has such a short decoherence time that it is never likely to be observed in a superposition of states. As far as I know, the largest object ever to show quantum behaviour is an oscillator built by Andrew Cleland's group at Santa Barbara, which was around 50 - 100 microns in size.

Having said this, it has been suggested that a gravitational field would act as one of the mechanisms for decoherence, and this is known as gravitational decoherence. So far there is little in the way of experimental studies, but a Chinese team will shortly be launching a satellite to test whether entangled states can be maintained between the ground and a satellite.

John Rennie
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  • Thanks. This all makes sense but as we discussed in the question comments with CuriousOne, my question is really a thought experiment and does not assume large degrees of freedom in the object (neither a much active environment actually), only that it is massive. And as glS pointed out, there is actually a paper discussing a possible implementation. – Stéphane Rollandin Mar 11 '16 at 10:56
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I'm answering my own question by refering to a paper linked by glS in a comment (Is Gravity Quantum ?, Bahrami & al., 2015).

The authors feel that although a satisfying theory of quantum gravity is still missing at the moment, they "can safely claim that, should gravity be quantum, [the spatial superposition in a massive quantum system] would be manifested by the superposition of gravitational fields".

They go on proposing an experimental setup that could, amazingly, actually test that possibility in the not too far future by directly probing the gravitational field of a mesoscopic system (of mass about 100 ng) prepared in a superposition of two different positions. They seem confident that it should be possible to keep all non-gravitational interactions (notably van der Waals) negligible in that "technically demanding" experiment.

Edit:

A new paper appeared: Probing a Gravitational Cat State: Experimental Possibilities.

Stéphane Rollandin
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