Double slit experiment with magnetic traps

[Marcin]

1. Is it possible to perform the following, modified double-slit experiment with single electrons/electron beam: The slits are separated in such a way, that each leads to a separate magnetic trap. The traps have oppositely directed magnetic fields, so that the electrons entering them move in circles in opposite directions.
2. If 1., is it possible to measure magnetic induction on the axes of both circles, produced by electrons moving around the circles? There should be enough of them to produce a current with measurable intensity and measurable induction.

Goal is to check whether electrons in separate traps remained in superposition by measuring magnetic induction, which will determine the current.

 

[hagopbul]

when the electron move in circular motion wouldn't start to accelerate ?

 

[Marcin]

when the electron move in circular motion wouldn't start to accelerate ?

Indeed, it's centripetal acceleration.

 

[PeroK]

1. Is it possible to perform the following, modified double-slit experiment with single electrons/electron beam: The slits are separated in such a way, that each leads to a separate magnetic trap. The traps have oppositely directed magnetic fields, so that the electrons entering them move in circles in opposite directions.
2. If 1., is it possible to measure magnetic induction on the axes of both circles, produced by electrons moving around the circles? There should be enough of them to produce a current with measurable intensity and measurable induction.

Goal is to check whether electrons in separate traps remained in superposition by measuring magnetic induction, which will determine the current.

It seems to me that you simply have an elaborate mechanism for detecting which slit the electron went through?

 

[Marcin]

It seems to me that you simply have an elaborate mechanism for detecting which slit the electron went through?

No. My goal is to keep superposition, to have the same electrons in both traps :) I've read, that even strong electric/magnetic fields do not cause the collapse of electron wavefunction.

 

[hagopbul]

intersting i didnt hear of entanglement that include acceleration

 

[Marcin]

intersting i didnt hear of entanglement that include acceleration

Me neither, but entanglement is not superposition.

 

[PeroK]

No. My goal is to keep superposition, to have the same electrons in both traps :) I've read, that even strong electric/magnetic fields do not cause the collapse of electron wavefunction.

The wavefunction only collapes when a measurement is made. The electron remains in a superposition of the two possible spatial paths until you measure (or gain information about) what path is has taken. If you measure a current in one loop, then effectively the wave-function will collapse.

Keeping an electron in superposition is relatively easy. The superposition simply evolves through a magnetic field. In the Stern-Gerlach experiment, for example, the superposition of two spatial wavefunctions coupled to spin orientation is actually created by the magnetic field. It's the interaction with the screen (being detected) that eventually collapses the wave-function.

 

[Marcin]

The wavefunction only collapes when a measurement is made. The electron remains in a superposition of the two possible spatial paths until you measure (or gain information about) what path is has taken. If you measure a current in one loop, then effectively the wave-function will collapse.

Keeping an electron in superposition is relatively easy. The superposition simply evolves through a magnetic field. In the Stern-Gerlach experiment, for example, the superposition of two spatial wavefunctions coupled to spin orientation is actually created by the magnetic field. It's the interaction with the screen (being detected) that eventually collapses the wave-function.

Thanks for the comprehensive reply. I don't want to measure the current directly, but the magnetic induction, that the current induces. The idea is to make the indirect measurement, that will not cause the collapse.

 

[PeroK]

Thanks for the comprehensive reply. I don't want to measure the current directly, but the magnetic induction, that the current induces. The idea is to make the indirect measurement, that will not cause the collapse.

It amounts to the same thing: information about which way the electron went.

 

[Marcin]

It amounts to the same thing: information about which way the electron went.

Are you sure, that the sole transfer of information causes the collapse, no matter how the information is transferred?

 

[Marcin]

It amounts to the same thing: information about which way the electron went.

Are you sure, that it's impossible to measure, that electron went both ways?

 

[PeterDonis]

Are you sure, that it's impossible to measure, that electron went both ways?

You can't measure that the electron was in both traps, because then there would have to be two electrons, not one.

 

[PeterDonis]

Are you sure, that the sole transfer of information causes the collapse, no matter how the information is transferred?

You don't even need a measurable "transfer of information" to cause collapse. Any interaction with the environment will do it. For example, these "magnetic traps" that you describe will be made of lots and lots of atoms. The electron will interact with those atoms, and that in itself could be enough to cause collapse, even without any intended measurement of current or magnetic induction. Experimenters in QM often have the problem of preventing the quantum object they want to measure from interacting with something else before they have a chance to make it interact with the measuring device.

 

[Vanadium 50]

It seems to me that you simply have an elaborate mechanism for detecting which slit the electron went through?

No. My goal is to keep superposition, to have the same electrons in both traps :)

That may be your goal, but I don't think you've achieved this. I think all you've done is exactly what @PeroK said: devised n elaborate mechanism for detecting which slit the electron went through.

 

[PeroK]

Are you sure, that the sole transfer of information causes the collapse, no matter how the information is transferred?

That's one way to look at it. In a way "collapse" is really one way to describe or interpret the process of gaining information about a quantum system. It starts in a superposition of a certain observable - in the case of the double-slit that of the electron's path/position. As long as you do not obtain any information about the electron's path, the electron behaves according to that superposition. But, if you gain information about the path, then the electron behaves according to the "collapsed" wavefunction that describes only that path.

In this sense, and contrary to the popular science myth, an electron cannot be in two places at once. Not if "being in a place" means you have information that the electron was there.

 

[Marcin]

You don't even need a measurable "transfer of information" to cause collapse. Any interaction with the environment will do it. For example, these "magnetic traps" that you describe will be made of lots and lots of atoms. The electron will interact with those atoms, and that in itself could be enough to cause collapse, even without any intended measurement of current or magnetic induction. Experimenters in QM often have the problem of preventing the quantum object they want to measure from interacting with something else before they have a chance to make it interact with the measuring device.

What do you think about the same experiment with magnetic field, that does not cause the collapse:
https://physics.stackexchange.com/questions/322739/double-slit-experiment-done-with-magnetic-fields

 

[PeroK]

What do you think about the same experiment with magnetic field, that does not cause the collapse:
https://physics.stackexchange.com/questions/322739/double-slit-experiment-done-with-magnetic-fields

I looked at the first response and it asks: "Why would the fields collapse the wave function?" Exactly!

Collapse isn't a physical process that is induced by an EM field. On the contrary, QM describes the unitary evolution of the state of the electron in an EM field.

I believe you may be confused about what collapse means and why it is part or orthodox QM.

 

[Marcin]

I looked at the first response and it asks: "Why would the fields collapse the wave function?" Exactly!

Collapse isn't a physical process that is induced by an EM field. On the contrary, QM describes the unitary evolution of the state of the electron in an EM field.

I believe you may be confused about what collapse means and why it is part or orthodox QM.

It was my reply to @PeterDonis who wrote: "Any interaction with the environment will do it (cause the collapse)".

 

[PeterDonis]

What do you think about the same experiment with magnetic field, that does not cause the collapse

The magnetic field described there is not at all like the magnetic traps you described in your scenario. The magnetic field is a simple thing and so is its interaction with the electron. The magnetic trap contains a magnetic field, but it also contains lots of atoms, which, as I said, can also interact with the electron. The latter interaction is what can cause collapse (and what experimenters working with magnetic traps have to work so hard to avoid, for example by cooling the traps to near absolute zero).

 

[PeroK]

It was my reply to @PeterDonis who wrote: "Any interaction with the environment will do it (cause the collapse)".

I missed Peter's responses while I was typing one of mine. It can happen with this user interface.

 

[Marcin]

I missed Peter's responses while I was typing one of mine. It can happen with this user interface.

No problem. Do you agree with his latest answer: "The magnetic trap contains a magnetic field, but it also contains lots of atoms, which, as I said, can also interact with the electron. The latter interaction is what can cause collapse"

 

[PeroK]

No problem. Do you agree with his latest answer: "The magnetic trap contains a magnetic field, but it also contains lots of atoms, which, as I said, can also interact with the electron. The latter interaction is what can cause collapse"

I would say this is a separate, practical issue. These experiments can be very delicate to set up. For example, in quantum computing it's very difficult to keep the system in the state it should be in and prevent the "environment" from spoiling things.

From that point of view it's difficult to conduct certain QM experiments. In these cases, I imagine, the electron would simply disappear from your experiment.

From that point of view, controlled superpositions can be hard to maintain.

 

[vanhees71]

The wavefunction only collapes when a measurement is made. The electron remains in a superposition of the two possible spatial paths until you measure (or gain information about) what path is has taken. If you measure a current in one loop, then effectively the wave-function will collapse.

Keeping an electron in superposition is relatively easy. The superposition simply evolves through a magnetic field. In the Stern-Gerlach experiment, for example, the superposition of two spatial wavefunctions coupled to spin orientation is actually created by the magnetic field. It's the interaction with the screen (being detected) that eventually collapses the wave-function.

You don't need to measure anything to "decohere" (which is what you obviously mean by "collapse"). It's enough to bring your system in thermal equilibrium with the environment, which is very easy to do (unfortunately for many applications you'd need to keep things coherent).

 

[PeroK]

You don't need to measure anything to "decohere" (which is what you obviously mean by "collapse"). It's enough to bring your system in thermal equilibrium with the environment, which is very easy to do (unfortunately for many applications you'd need to keep things coherent).

I wasn't thinking of decoherence, simply orthodox collapse (which you may or may not subscribe to). In any case, it may be worth explaining what you mean in the context of the "magnetic traps" in the original post.

 

[Marcin]

That may be your goal, but I don't think you've achieved this. I think all you've done is exactly what @PeroK said: devised n elaborate mechanism for detecting which slit the electron went through.

I disagree, because after the measurement of magnetic induction in both traps I still know nothing about the paths of individual electrons.

 

[PeterDonis]

I disagree, because after the measurement of magnetic induction in both traps I still know nothing about the paths of individual electrons.

Yes, you do: you know that there is an electron in one trap and no electron in the other. So you know the electron went through the slit in front of the trap that has an electron in it.

 

[Marcin]

Yes, you do: you know that there is an electron in one trap and no electron in the other. So you know the electron went through the slit in front of the trap that has an electron in it.

You are right on one condition: that there was a collapse. But you can know it only by the measurement. You can't use the ad infinitum argumentation: the electron is in just one of the traps, because there was a collapse. Why there was a collapse? Because the electron is in just one of the traps.

 

[PeterDonis]

You are right on one condition: that there was a collapse.

No, what I have said is true for any interpretation of QM, including no collapse interpretations. In a no collapse interpretation like the MWI, there are two branches of the wave function after the measurement, one in which the electron is in the trap behind slit #1 and the magnetic induction measurement shows it there (and the observer observes that), and one in which the electron is in the trap behind slit #2 and the magnetic induction measurement shows it there (and the observer observes that).

you can know it only by the measurement.

The magnetic induction measurement...is a measurement. That's why we use expressions like, oh, say, "measure the magnetic induction" (which is what you said in the OP of this thread) to describe it.

 

[PeroK]

You are right on one condition: that there was a collapse. But you can know it only by the measurement. You can't use the ad infinitum argumentation: the electron is in just one of the traps, because there was a collapse. Why there was a collapse? Because the electron is in just one of the traps.

This is perhaps a good time to pause, reflect and consider learning a bit more about QM, what it says and what it doesn't say.

There is not a lot of point in arguing about things that are well-established, theoretically and experimentally.

 

[Marcin]

This is perhaps a good time to pause, reflect and consider learning a bit more about QM, what it says and what it doesn't say.

There is not a lot of point in arguing about things that are well-established, theoretically and experimentally.

Thx for all the answers.

 

[Marcin]

The magnetic induction measurement...is a measurement. That's why we use expressions like, oh, say, "measure the magnetic induction" (which is what you said in the OP of this thread) to describe it.

Correct. The difference is that I don't measure the effect or presence of a single electron, but the effect caused by the whole bunch of them. This is my idea of preventing the collapse of individual electrons, however stupid it sounds.

 

[PeterDonis]

I don't measure the effect or presence of a single electron, but the effect caused by the whole bunch of them.

In other words, you run a large number of electrons through the experiment, and then measure the magnetic induction in each of the traps?

This is my idea of preventing the collapse of individual electrons

It won't.

First, you'll have the problem that magnetic traps can't store large numbers of electrons--the Pauli exclusion principle prevents it (there are only a small number of states the electrons in the trap can be in, and once those states are filled you're done, the trap can't hold any more electrons).

Second, when you do the magnetic induction measurement, you'll just get two numbers for magnetic induction that will be approximately equal (since each electron has basically a 50-50 chance to go into one trap vs. the other). You won't get anything that shows interference between the electrons (which pretty much invalidates the point of doing a double slit experiment in the first place).

Third, even though you have multiple electrons in both traps, you haven't "prevented collapse"; you've just changed the states that the electrons collapse into when you make the magnetic induction measurement, as compared to the case where you only have one electron and it has a 50-50 chance to be in either trap. (The states change because if the presence of multiple electrons in the trap affects the energy levels of the states, due to the Coulomb repulsion between the electrons.)

 

[Marcin]

@PeterDonis I get it, you've made it clear. Thank you.