I'm trying to learn quantum mechanics and this is a question that came to mind. I tried searching for it online, but I couldn't find a good answer (or at least one I could understand). From what I understand, you should theoretically be able to determine the position of a quantum object by observing the spacetime-curvature around it, but that goes everything I'm learning.
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5$\begingroup$ "you should theoretical be able to determine the position of a quantum object by observing the spacetime-curvature around it" We only have "rough" ideas how gravity works at the quantum level, let alone gravity affects superposition. The answer to this question is a lot more involved than it seems. $\endgroup$– joseph hCommented Mar 18 at 8:15
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$\begingroup$ Re "that goes everything": Do you mean "that goes against everything"? Or something else? $\endgroup$– Peter MortensenCommented Mar 19 at 0:45
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$\begingroup$ Relevant: Penrose interpretation $\endgroup$– user76284Commented Mar 19 at 2:33
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$\begingroup$ I would have thought that anything that determines the location of a particle in superposition would break down the superposition and any potential interference pattern. While a particle in superposition is in "transit" it does not interact with the outside world and so it does not affect the spacetime around it. Any attempt to try and measure a change in the spacetime around it amounts to an interaction and measurement. No? $\endgroup$– KDPCommented Mar 19 at 12:16
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$\begingroup$ For example, if we use a two path interferometer and use "spacetime detectors" to obtain "which way" information, this would be no different than obtaining which way information by any other method. You cannot cheat the system. $\endgroup$– KDPCommented Mar 19 at 12:21
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2 Answers
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The short answer is we do not know.
Our best theory of gravity, general relativity, tells us that the curvature of spacetime follows Einstein's equation,
$$ G_{\mu\nu} = \frac{8\pi G}{c^4}T_{\mu\nu},$$
where $T_{\mu\nu}$ is the stress-energy tensor of any matter present. This is a classical (non-quantum) quantity. Your quantum object will, however, will produce a quantum observable $\hat{T}_{\mu\nu}$ as its stress-energy. This a square (quantum) peg that does not fit in the round (classical) hole. There are roughly two ideas of how this could be made to work. The first is make the square peg round, by taking the expectation value of $\hat{T}_{\mu\nu}$, while keeping gravity classical,
$$ G_{\mu\nu} = \frac{8\pi G}{c^4}\langle\hat{T}_{\mu\nu}\rangle.$$
The second is to make the round hole square by replacing general relativity by a quantum version of itself,
$$ \hat{G}_{\mu\nu} = \frac{8\pi G}{c^4}\hat{T}_{\mu\nu}.$$
Both approaches are mired with theoretical difficulties that we do not know how to solve.
However, we do have a qualitative idea of how the different approaches would answer your question. In the first case, trying to measure an object's position through gravity would result in measuring the mass distribution of its wave function without causing it to collapse to a single position. In the second, the measurement would collapse of the wave function, and you would observe the object to be gravitationally in exactly one of its possible positions.
So far, we are not able to test this experimentally, basically because we are:
- Not good enough at measuring gravity on short distances.
- Not good enough at preparing macroscopic objects (with sufficient gravitational pull) in quantum states with sufficient spatial spread.
However, experimental progress is being made on both fronts, and some experimentalists are hopeful that we will experimentally answer these questions in the next decade(s).
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10$\begingroup$ +1 for starting with "we do not know". $\endgroup$ Commented Mar 18 at 15:35
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2$\begingroup$ Note this recent paper on classical gravity coupled to quantum matter: link.aps.org/doi/10.1103/PhysRevX.13.041040 $\endgroup$ Commented Mar 18 at 18:18
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2$\begingroup$ Key takeaway here is that the gravity coupled via expectation value is not really a good option and has some pathological behaviour, and the proposal is that the gravitational field is generated stochastically, and objectively collapses the quantum wavefunction $\endgroup$ Commented Mar 18 at 18:20
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3$\begingroup$ @OutisNemo String theory tries to resolve this. The problem is that no one has come up with a version of string theory that works (i.e. is experimentally testable), despite a whole lot of effort, to the point where it's no longer the darling child it once was. (There's also a number of other "GR+quantum" approaches which have their own level of popularity.) $\endgroup$– R.M.Commented Mar 18 at 18:48
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2$\begingroup$ @OutisNemo It's not really simpler, at least currently. If you want to know more, it's probably better to ask a separate question. $\endgroup$– R.M.Commented Mar 18 at 20:41
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Spacetime that is dynamically curved by the presence of mass/energy is a key feature of general relativity. Quantum mechanics, on the other hand, typically assumes a spacetime background that is flat and static. Although this allows quantum mechanics to be combined with special relativity, it does not allow it to be combined with general relativity. A successful (and experimentally verified) merger of quantum mechanics with the dynamic spacetime of general relativity would give us a theory of quantum gravity. However, at the current time we do not have a generally accepted theory of quantum gravity (although there are some candidates) and the experiments that would be required to verify such a theory seem to be a long way beyond our current or foreseeable technology.
So, in short, we do not know how the curvature of spacetime is affected by a quantum object - and we do not even know whether that is a meaningful question to ask.
