# What happens to the uncertainty principle if

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.

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?

• But there is no technology (and I think there will never be) that can measure both the position and velocity of the electron simultaneously. May 27 '20 at 9:34
• So you would never be able to eject the electron from the detector in exactly same way it came towards the detector May 27 '20 at 9:37
• You're right, I was thinking something like just the direction maybe? Just to know where it was directed before interrupting the trajectory. May 27 '20 at 9:50

You won't get an interference pattern. This was very nicely explained by @Vivekanand Mohapatra, but there is a more simple reason why. The interference never happens.

In the original double slit experiment, you get the interference when the electron's wavefunction crosses both slits and interferes with itself, which causes a change in the probability distribution. But the catch is that when you measure the electron, the wavefunction collapses, and the electron now has a definite position. That is why it behaves like a normal particle and you don't get the pattern.

But, in this case, the electron is detected (which means it is measured) before it can cross the slit. So the electron now has a particular, set position (and it behaves like a particle). So even if you can do imperfect cloning, the new electron produced has no wave properties. Because it's path has already been set; and there is no probability distribution for it. So, it cannot interfere with itself and produce the infamous wave patterns.

Uncertainty principle is not about whether we can calculate the physical observables simultaneously or not. It works for the non-commutating operators only, which means we cannot have simultaneous eigenstates for those operators.

Okay, there are many "quantum mechanical terms" which you should know before. you understand why your solution won't work.

The short answer is you can never calculate each and every value of the properties you mentioned, i.e, cloning is not allowed in quantum mechanics. So you just cannot copy an electron exactly, which is why we don't get the interference pattern in the second para you wrote in your question.

• comment down if you still have doubt. May 27 '20 at 7:53
• Thanks for your answer. What would happen then if we perform an imperfect cloning? Only the necessary properties: en.wikipedia.org/wiki/Quantum_cloning Or if we clone different properties in different similar experiments. May 27 '20 at 8:20