Double slit one source same as no slits with two sources?

[bahamagreen]

Instead of using a single source and two slits, imagine just using two sources the same distance apart as were the slits...

The two sources are controlled by a device that has two modes of operation, selected by a two position switch labeled D and R:

D is "determined" - the emission from the left and right sources is determined respectively by a file of 0s and 1s (half of each) and an experimental run is comprised of n periods of t of only single emissions. The "which path" knowledge is known before, during, and after the experimental run.

R is "random" - the emission from the left and right sources depends on a radioactive substance that has a p=.5 decay during the same period as t above, run for the same n periods, wherein a decay causes an emission from the left source and no decay an emission from the right source. The "which path" knowledge is unknown before, during, and after the experimental run.

No interference pattern with the switch set to D? Interference pattern when set to R?

 

[DrChinese]

For there to be interference, it must not be possible - in principle - to determine the source path. Knowing it (or not) is not a factor.

In this example, that does not occur with either setup. So no interference.

 

[Nugatory]

In the standard form of the experiment, both slits contribute to the probability of a particle being detected at any given point on the screen; these contributions interfere and that's why we get an interference pattern as we accumulate detections. But in your variant only one source at a time can contribute, so there can't be an interference pattern.

Indeed, if I'm understanding you properly, your setup is equivalent to a double slit experiment in which at any moment one of the two slits is closed and the other open, and the device controls which.

 

[bahamagreen]

I was reading Feynman's analysis of the double slit experiment... he demonstrates that experimentally the electron is only found going through one or the other slit, never both at the same time.

My thought experiment attempts to experimentally match that output of the slits by replacing them with two sources.

"In principle" includes a lot... what kind of arraignment could make it not be possible - in principle - to determine the source path? How is the "R" setting leaking out which source path?

 

[Nugatory]

I was reading Feynman's analysis of the double slit experiment... he demonstrates that experimentally the electron is only found going through one or the other slit, never both at the same time.

Yes, if our experiment is set up so that we can find which slot the electron goes through, then our experiment always finds that it went through one slit or the other. We also find that we never get an interference pattern in these experiments.

My thought experiment attempts to experimentally match that output of the slits by replacing them with two sources.

You've succeeded. As I said above, your experiment is equivalent to always having one or the other slits closed; that's clearly a setup in which we can confidently say that the electron went through one slit (the open one) and not the other (the closed one) so no interference pattern is the predicted and unsurprising result. The changes in the device as its actuators open and close the slits or (in your version) flip the switch that controls the source provide the which-path information.

(It's important that this is a "device", something macroscopic that cannot be in a long-lived coherent superposition of "activates left-hand source" and "activates right-hand source").

"In principle" includes a lot... what kind of arraignment could make it not be possible - in principle - to determine the source path? How is the "R" setting leaking out which source path?

The R setting isn't leaking anything, just the fact that the device is either activating one source or the other is sufficient to know that one source or the other has been activated.

To make it impossible in principle to know which source has emitted a given particle we'd need both sources to be continuously emitting single particles at a low rate with complete coherence between the two. One of the easier and more practical ways of doing this is to have a single source illuminating a barrier containing two slits - call each slit a "source" and you're there.

 

[bahamagreen]

The R setting isn't leaking anything, just the fact that the device is either activating one source or the other is sufficient to know that one source or the other has been activated.

That sounds more like knowing "it went one of two paths" rather than knowing "which path". I'm not seeing how the presence of the second slit as a potential path isn't like the presence of the second potential source.

What I was really doing was thinking about the domain of "in principle" as it approaches vanishing into HUP... trying to remove the detectors at the slits and push the "which way" before the slits by using two sources as proxies for the slits.

How about if I use just one source of electrons but include a magnetic coil that takes two values to deflect them, experimental runs similarly controlled by D or R (a list or a radioactive decay)... so "two paths" without using a double slit?

 

[bahamagreen]

After some thinking... is the difference that the double source no slit setup incorporates a macro switching device to emit the electrons (so above the HUP so "in principle")?

 

[Nugatory]

After some thinking... is the difference that the double source no slit setup incorporates a macro switching device to emit the electrons (so above the HUP so "in principle")?

The uncertainty principle is completely irrelevant to this discussion, but I'm not sure what difference you're asking about.

The quantum system you proposed, which includes the macroscopic switching device, cannot be in a superposition of "left-hand source emitted the particle" and "right-hand source emitted the particle". If the system were in such a state, then it would be impossible in principle to find the which-path information - not because it's hard to find it, or because we haven't looked, but because it is completely meaningless to associate which-path information with a state that is a superposition of both paths. But the system is not in such state, it's in the state "No superposition, one or the other source emitted the particle and if we don't know which it's just because we haven't bothered to find out"

 

[PaleMoon]

For there to be interference, it must not be possible - in principle - to determine the source path. Knowing it (or not) is not a factor.

i have a problem with this possibility. does it imply two kinds of events?

consider two different events:
the particle emits a photon between the slits and the screen.
the particle passes through one of the slits.
measuring them will give you which path information.
but there is a difference.
it is possible to modify the setup to measure the direction of the photon without modifying the interference pattern.
but if you examine the particle near tne slits you modify the pattern.
it seems to me that these events are different
even if the particle's decay is a microscopic event it belongs to things like measurement.
but a particle passing through a slit is a virtual event without reality.

 

[Mentz114]

i have a problem with this possibility. does it imply two kinds of events?

consider two different events:
the particle emits a photon between the slits and the screen.
the particle passes through one of the slits.
measuring them will give you which path information.
but there is a difference.
it is possible to modify the setup to measure the direction of the photon without modifying the interference pattern.
but if you examine the particle near tne slits you modify the pattern.
it seems to me that these events are different
even if the particle's decay is a microscopic event it belongs to things like measurement.
but a particle passing through a slit is a virtual event without reality.

This is overcomplicating your problem.

If you apply the general principles it is straightforward.

1. Knowing 'which path' does not affect the state. Getting this information can affect the physical state.
2. Information is not free. Work must be done on a system to extract information.
3. If this causes any decoherence between the possibilities the interference can be diminshed or lost completely. The more information extracted the less visible the interference.

 

[PaleMoon]

you are right.
the two cases are different
in the case of the particle emitting a photon we have nothing to do. just wait for it.+

 

[Mentz114]

..
in the case of the particle emitting a photon we have nothing to do. just wait for it.+

Photons carry momentum so there will be an exchange of momentum between the particle and the photon. The photons momentum increases as the wavelength diminishes, so to get a resolution of the order of the slit separation the energy of the photon would be of the same order of that of the particle and the deflection would be huge.
It is very unlikely that your scheme will work and it is no exception to the general rule that the more information is got the greater the decoherence.

 

[PaleMoon]

It is very unlikely that your scheme will work and it is no exception to the general rule that the more information is got the greater the decoherence.

can you give me a sentence in which you find a scheme? (i am not sure that this answer is for me)