What happens to the uncertainty principle if....

[borib]

TL;DR Summary

What happens to the uncertainty principle if we could build this experiment

I just read the Feynman Lectures about the electron gun experiment with two holes in the middle wall.

It demonstrates that if we don't look at the electrons while they travel toward the detector there is an interference pattern in the probability curve of the electrons similarly to what happens with waves. But if we try to measure which hole the electron passes through the probability pattern changes and the electrons behave like bullets.

At the end of the lecture there is a further experiment this time with a wall with rollers --> here <--
I don't understand much the details of the latter experiment but it turns out that even in this situation is not possible to break the uncertainty principle.

My question is what would happen in the following situation:

We have the middle wall but this time the two holes are replaced with two detectors that perform the following actions:

- retrieve all the information about the electron speed, angle/direction, spin, hole A or B, etc...
- block the electron
- shoot another electron or the same electron with the same speed, angle/direction, spin etc... that has been retrieved before it was stopped.

This way the new electron has the same properties that would have had the original electron if it was not watched by the machines and it goes on toward the backstop with the movable detector described in the lecture.

What is the probability curve of such situation? Will it have interference or not?

 

[DrClaude]

- retrieve all the information about the electron speed, angle/direction, spin, hole A or B, etc...

This can only be done within the constraints of the uncertainty principle.

This way the new electron has the same properties that would have had the original electron if it was not watched by the machines and it goes on toward the backstop with the movable detector described in the lecture.

That's not possible, since you have performed a measurement on the electron.

What is the probability curve of such situation? Will it have interference or not?

You will end up with two independent sources of electrons, so no interference.

 

[borib]

@DrClaude Thanks for the explanation. I've also been told that quantum cloning is not allowed.
But we can perform imperfect cloning instead: https://en.wikipedia.org/wiki/Quantum_cloning ?

 

[DrClaude]

@DrClaude Thanks for the explanation. I've also been told that quantum cloning is not allowed.
But we can perform imperfect cloning instead: https://en.wikipedia.org/wiki/Quantum_cloning ?

You don't need cloning if you do not care about the initial electron. You could transfer its state to a new electron, which would be indistinguishable from the original. But to do this, you would need access to the full state of the original electron, which would require here an apparatus at least as big as the two slots, so you would lose any which-way information.

 

[borib]

But to do this, you would need access to the full state of the original electron, which would require here an apparatus at least as big as the two slots, so you would lose any which-way information.

Just to understand, are you saying that in theory is possible but is just a problem of the dimensions of such machine?

 

[DrClaude]

Just to understand, are you saying that in theory is possible but is just a problem of the dimensions of such machine?

I am saying that the theory requires the machine to be at least as wide as the two slits to be able to perform what you want.

Anything smaller will correspond to a measurement of position (which slit information), so there can be no interference.