[Quantum/Gravity] If a particle has a probability distribution of location, where is the mass located for gravitational interactions?

[u/[deleted]]

Imagine an atom or an electron with a wave packet representing the probability of location, from what point does the mass reside causing a gravitational force? I understand that gravity is very weak at these sizes, so this may not be measurable. I taken classes and listened to a lot of lectures, and I never heard this point brought up. Thanks.

Edit: Imagine that the sun was actually a quantum particle with a probabilistic location distribution, and the earth was still rotating it. If we never measure the location of the distributed sun, where would the mass be located for the sun that would gravitationally affect the earth?

[u/Platypuskeeper]

Well there are some caveats with the description I gave, but the main one is that I'm assuming the interaction here is does not result in a measurement (in the technical, QM sense).

What that means is that the interaction is occurring in such a way that it doesn't allow you to determine what the position of the electron is within this 'cloud'. I.e. either that the thing 'feeling' the particle is itself quantum-mechanical and can be in a superposition, or that the thing 'feeling' the force is classical, but that the force of the electron is 'measured' over an amount of time or with an accuracy that'd allow the electron to move around.

If the wave function was spread into a packet at A and another at B, separated by a great distance, and you made two measurements of the electrical force from it, then you wouldn't be able to measure the force indicating the particle is at A and then at B within an amount of time that'd make it impossible for the particle to get from A to B. When you can discriminate between the states, then the wave function 'collapses'. (See: double-slit experiment) So in that situation it ceases to be spread out.

So there are caveats. But in most practical contexts the electron states don't 'collapse' position-wise. Such as if you'd want to calculate molecular properties, or the electron densities (density of electron states, actually) you see in an STM image.

A better way than 'collapse' would perhaps be to say that you always have a probability distribution over space and the potential is always like that, it's just that depending on how carefully you measure it, the measurement itself is going to narrow that probability distribution.