QUOTE:
Mass is defined asymptotically, yes, but the mass term always comes in the combination Mr, so when r→−∞, where the angular part of the metric goes as r2, you have to replace r by |r| to see what happens. So M goes to −M. Look up the Penrose diagrams in Hawking and Ellis for example. And look up the Kerr metric (too long for these "comments"). If you do AdS/CFT you are doing quantum, and you won't avoid thermalization. Only the classical theory would seem to allow you to get out, God knows in which universe– G. 't Hooft Sep 6 '12 at 16:18

Thought experiment (???)
Is it possible to modify the double slit experiment as follows:
Instead of having a phosphor screen where electrons hit it, it is being replaced by an array of magnets so that for each path the electron will be routed back to the source so that they are fired again at the double slit

Now make some measurements in this system with a detector being placed at one slit (so as to collapse the intereference pattern), and then repeat the measurement again without the detector (so that the intereference pattern can appear again)

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Background of this thought experiment. After reading a bit about matrix mechanics again in wikipedia (and have questions clarified by Acuriousmind). I learnt that the state vector collapses after measurement because it is being mapped to one of the observable's eigenstates (e.g. position or momentum)

For conjugate variables that don't commute this result in the state of the system being mapped to one observable having some well defined eigenstate while the conjugate observable become a superposition of eigenstates of that other observable

@ACuriousMind
Based on what I understand from reading that brief section on matrix mechanics in wikipedia, a measurement will map the state (e.g. say of an electron) into an observable's eigenstate (e.g. position eigenstate). Now since position and momentum are conjugate variables, it means the momentum state of that electron is a superposition of momentum eigenstates (hence the uncertainty)

Our setup above can presumably be described by some hamiltonian $H$ which has potential energy terms that is due to the electric field used to route the electrons back, and the kinetic energy term will…

@Acuriousmind

If the electron was not being previously measured, then it will still be in some superposition of position states as the Hamiltonian evolves it and we will expect an interference pattern

But since the above electron has been measured, will it become unable to give an interference pattern since it is being collapsed into the state $|e^-_{(2)}\rangle$, thus it can no longer be changed (since the collapse causes all other position state contributions to go to zero)?

https://en.wikipedia.org/wiki/Wave_function_collapse

@ACuriousMind
Perhaps in maths the above is written like this:
$$\hat{H}_{doubleslitsetup}=T_{e-}(\dot{\mathbf{r}})+V_{routing tube}(\mathbf{r})$$
where $V_{routing tube}(x,y,z)$ is the electric potential within the tube (Not sure how to model this in the simplest way).

Consider an initial state of the electron as a superposition of position states
$$|e^-\rangle=\sum_i c_i|x_i\rangle$$
$$\langle e^-|e^-\rangle=1$$
There exists a detector at a slit such that a position measurement causes the following: