Delayed double slit experiment

[Sergionuevo]

Hello! I have this doubt with a variation of the double slit experiment:
Let us suppose that we are sending electrons to the screen. When both slits are open, the wave function at a given point x of the screen is the sum of the functions phi1 and phi2, respectively corresponding to reach x through slit 1 or slit 2. If we put a photon source near one of the slits, if one electron crosses the slit it will scatter one photon. If we place also a photodetector in a proper position, every time that we detect a photon we can say that the electron crossed that slit, and according to the theory, the wave function collapses to phi1. As a result, no interference pattern is observed. Here is my problem: if we place the photodetector very far, so that the scattered photon is detected AFTER the electron reaches the screen, the wave function does not collapse before the electron reaches the screen. Then, in this case I think that we would find interference pattern, and also we would detect later with the photodetector which slit had been used by the electron.
Is this right? Thank you very much for your help!

 

[lugita15]

I'm not sure about your scenario at first glance, but let me describe some phenomena that are somewhat similar. If you have a device that records which slit the particle went through, and then before the particle reaches the screen you destroy the device so completely that it would be impossible even in principle to reconstruct the data, then the particle will display an interference pattern. This is known as a quantum eraser experiment.

Another thing you might find interesting is that if you let the particle go through the slits, and then after some period of time (but before it reaches the screen) you find out which slit it went through, it will not display an interference pattern. You could say (although this is controversial) that instead of making the decision of whether to go through one or both slits when it actually came to the slits, it only made up its mind about what it did in the past after it was already past the slits! This is known as a delayed choice experiment. As John Wheeler pointed, you could do this at an astronomical scale, where you can get light from which was gravitationally bent by a cluster of galaxies into one or both of two paths, and then after billions of years the light arrives on earth, and you can either do a measurement of which path it came from, or you can choose not to do such a measurement, and then depending on that it will either show interference or not when you allow the light to fall on a screen. So you could say that the light has now chosen what it originally did billions of years ago!

 

[San K]

If you have a device that records which slit the particle went through, and then before the particle reaches the screen you destroy the device so completely that it would be impossible even in principle to reconstruct the data, then the particle will display an interference pattern.

there will be no interference pattern if all you do is simply destroy the device.

This is known as a quantum eraser experiment.

the quantum eraser experiment is not about destruction of the device/detector

 

[lugita15]

there will be no interference pattern if all you do is simply destroy the device.

Strictly speaking I'm talking about destroying the record the device made, but presumably the record is inside of the device.

 

[San K]

Strictly speaking I'm talking about destroying the record the device made, but presumably the record is inside of the device.

lets say we destroy the device (say by burning it) and the record inside the device also gets destroyed...and all this happens prior to photon reaching the screen...

there will still be no interference pattern...

 

[lugita15]

lets say we destroy the device (say by burning it) and the record inside the device also gets destroyed...and all this happens prior to photon reaching the screen...

there will still be no interference pattern...

Hmmm, isn't the definition of a quantum eraser experiment one in which the information about a measurement is destroyed?

 

[Cthugha]

Hmmm, isn't the definition of a quantum eraser experiment one in which the information about a measurement is destroyed?

No, it is not. You prepare a system in a state which would give you some information about one property of the system if you performed a measurement. Now you have the choice to leave the system in that state or change the state such that a measurement will not give any information about that property anymore. Typically one changes for example the polarization of photons to decide whether information is present or not.

The important point is that you do not perform a measurement and destroy information afterwards - this does not work - but do just destroy the possibility to perform a measurement that would give you some kind of information.