So let's say you are doing a double slit experiment. Also, let's use electrons.
My question is, won't the gravity of the electron affect the earth, thereby causing it decoherence and its wave function to collapse (or for MWI, entanglement and loss of information to the environment, preventing interference)?
The reason why I think this would happen is because you could tell which path the electron took based off its tidal effects on the earth: everything is a detector.
Yes, everything is a detector, but you need to quantify which things your system interacts with (and how strongly). Gravity is in some sense a poor example, because the quantum details of gravity are still an unsettled question (and gravity is a weak force regardless), so let's bypass that red-herring by replacing gravity with the electromagnetic field:
As your charged electron accelerates one way or another in a Stern-Gerlack apparatus or double-slit experiment, in theory it should radiate electromagnetic waves. Moreover, you would expect to be able to determine its position, by measuring differences of how particles in the environment are affected by the electron's EM field, right?
Basically, the reason you still observe interference fringes is because the coupling with the environment is weak. (Whereas if you gradually adjust the experimental parameters to increase the strength of coupling to the environment, then the fringes gradually fade.) Weak means that if you do the math, it isn't possible even in principle to infer sufficient information from the environment.
You might enjoy some of Zeilinger's journal-papers such as experimental demonstration of slit interference fringes with buckyballs (which are over a million times more massive than electrons), including demonstration of gradual decoherence (controlling the strength of interaction with the environment). You could also look at QM papers on weak measurement, or decoherence theory.
"everything is a detector"
This can't be true, or else there would be no such thing as persistent entanglement.
As @Conifold points out, the electron's charge should be a far more potent source of environmental disturbance, anyway. Why doesn't the charge of the electron leave a trace as it passes through the slits - some persistent disturbance of the charged particles that make up the atoms that make up the filter?
The answer must be that the coupling in both cases (electromagnetic, gravitational) genuinely does not cause decoherence. In the case of gravitation, I would think it's just the extreme weakness of the interaction. In the case of electromagnetism, I'm not so sure.
This answer is a placeholder, written in a rush. I will return to it and improve it a few days from now, if no-one has written a better one.
