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But hold on: consider the double-slit experiment: the electron to be fired at the slits is forever entangled with the continually collapsing electron gun! So shouldn't the shot-out electron be constantly collapsing as it travels towards the slits? But then GRW entails that there can never be interference patterns!

Okay there must be some simple solution to this. Here's my attempt at a solution, do let me know your thoughts...

The electron gun (g) is itself in a superposition since its components are all Gaussians. So simplify the gun superposition to just two of its high amplitude components (i.e. two distinct points where its Gaussian peaks):

#|x1-x100>g + #|x2-x100>g

which means that the gun is in a position superposition of two x-axis ranges.

Now separate out the electron it's about to fire:

#|x1-x100>g|x100>e + #|x2-x101>g|x101>e

...so that the electron is in a superposition of being at 100 and 101 (on the x-axis), and is entangled with the gun.

Okay now the gun fires:

(#|x1-x100>g(#|x100>e + #|x101>e)) + (#|x2-x101>g(#|x101>e + #|x102>e))

Boom!

(#|x1-x100>g(#|x100>e + #|x101>e + #|x102>e)) + (#|x2-x101>g(#|x101>e + #|x102>e + #|x103>e))

Just look at that electron wave function spread as if it wasn't entangled with the gun!

And because the two slits are at x104, the electron can go through them both...

#|x1-x100>g|x104>e + #|x2-x101>g|x105>e

But then start spreading out again, interfere, then collapse somewhere on the screen.

I think that must be how it works?