The Ensemble Interpretation and the Double Slit Experiment

[jbergman]

TL;DR Summary

How does the Ensemble Interpretation explain the double slit experiment?

I am a big fan of Ballentine's book on QM and was reading the discussions about the Ensemble Interpretation. Although, I am not an expert on these matters I reject the idea of the wave function collapse as a fundamental postulate of QM. Instead, I've come to the conclusion that we don't understand measurement well enough and instead believe that measurement alters the state of that being measured in a way that gives the appearance of collapse.

What I can't quite resolve with the Ensemble Interpretation is how it explains the double slit experiment. From what I understand, one can send electrons through a double slit and still get interference even if they are sent hours apart. Therefore, in some sense a particle must be interfering with itself. This doesn't feel consistent with the Ensemble Interpretation, does it? It feels more Everettian.

I'm hoping that someone can explain how to think about this in the Ensemble Interpretation.

 

[PeterDonis]

From what I understand, one can send electrons through a double slit and still get interference even if they are sent hours apart.

You can get interference in the sense that the pattern that will eventually be built up on the detector screen will be an interference pattern, yes. But you can't see interference in a single electron's impact--that's just a dot somewhere on the detector screen.

Therefore, in some sense a particle must be interfering with itself.

In some interpretations, yes, this is how the interference pattern is accounted for. But not in all of them. In the ensemble interpretation, the interference pattern is simply a manifestation of the quantum mechanical rules that apply to electrons in this experimental setup; those rules say that, if you have a large ensemble of electrons, all identically prepared, and all sent through the identical apparatus (whether in a beam all at once or one at a time with hours in between makes no difference), you will get an interference pattern on the screen. The ensemble interpretation simply doesn't make any claims at all about what an individual electron will do; it just says the QM rules lead to an interference pattern for a large ensemble of electrons. And that is what we observe; as above, we only see the interference pattern when a large number of electrons have gone through the apparatus.

 

[jbergman]

In the ensemble interpretation, the interference pattern is simply a manifestation of the quantum mechanical rules that apply to electrons in this experimental setup; those rules say that, if you have a large ensemble of electrons, all identically prepared, and all sent through the identical apparatus (whether in a beam all at once or one at a time with hours in between makes no difference), you will get an interference pattern on the screen. The ensemble interpretation simply doesn't make any claims at all about what an individual electron will do; it just says the QM rules lead to an interference pattern for a large ensemble of electrons. And that is what we observe; as above, we only see the interference pattern when a large number of electrons have gone through the apparatus.

Great explanation! That the ensemble interpretation doesn't make an claims about the individual electron in this case, I find a bit irritating. I would describe as more of a non-interpretation.

Also, I might argue a bit that the interference manifests itself in the probability distribution where a single electron will hit the screen. So even with a few electrons, one could build a classifier to guess whether the electrons came from an interfering ensemble or not.

 

[PeterDonis]

That the ensemble interpretation doesn't make an claims about the individual electron in this case, I find a bit irritating. I would describe as more of a non-interpretation.

Proponents of many other interpretations would agree with you. But the fact remains that QM is consistent with all of these interpretations; none of them can be ruled out.

the interference manifests itself in the probability distribution where a single electron will hit the screen.

But you can't compare that probability distribution to the result of a single electron, or a few electrons. You have to collect enough data to be able to do meaningful statistics.

even with a few electrons, one could build a classifier to guess whether the electrons came from an interfering ensemble or not.

No, you couldn't. See above.

 

[Nugatory]

That the ensemble interpretation doesn't make an claims about the individual electron in this case, I find a bit irritating.

There’s something not to like about every interpretation. This is it for the ensemble interpretation.

 

[PeroK]

I reject the idea of the wave function collapse as a fundamental postulate of QM. Instead, I've come to the conclusion that we don't understand measurement well enough and instead believe that measurement alters the state of that being measured in a way that gives the appearance of collapse.

That's what collapse is: the sudden (non-evolutionary) change in the state of a system. If you say "measurement alters the state of that being measured", then that is the definition of collapse.

 

[Demystifier]

That the ensemble interpretation doesn't make an claims about the individual electron in this case, I find a bit irritating.

Welcome to the club!

 

[jbergman]

That's what collapse is: the sudden (non-evolutionary) change in the state of a system. If you say "measurement alters the state of that being measured", then that is the definition of collapse.

I disagree. Collapse implies a non-reversible change of state. Instead, I believe that the system has a whole continues to evolve in a reversible way and that it only looks like a collapse when you look at that subsystem you were measuring when instead it is just the projection that looks like a collapse.

 

[PeroK]

I disagree. Collapse implies a non-reversible change of state. Instead, I believe that the system has a whole continues to evolve in a reversible way and that it only looks like a collapse when you look at that subsystem you were measuring when instead it is just the projection that looks like a collapse.

If a measurement is reversible, how do you reverse it?

 

[jbergman]

But you can't compare that probability distribution to the result of a single electron, or a few electrons. You have to collect enough data to be able to do meaningful statistics.

If you made a guess after one electron hit the screen as to whether there was interference by choosing the scenario which has a higher probability at that location on the screen, then you would do better than a random guess. In fact you could repeat the experiment 1000 times with different setups, firing a single electron each time. Now, I guess you could say this is again an ensemble of some sort, but if you did this in different locations with large time gaps in between, I think it strains the idea that this isn't a phenomenon associated with a single particle.

 

[jbergman]

If a measurement is reversible, how do you reverse it?

Quantum Erasers? But to answer your question in another way, in thermodynamics we have non-reversible macroscopic systems but that doesn't mean that the laws of physics at microscopic levels are nondeterministic. Instead, with measurement we are dealing with complex systems that can give the appearance of non-reversiblity. I am not aware of an experiment that rules out my claim but experiments like the quantum eraser experiment do suggest that an irreversible collapse is incorrect.

 

[PeterDonis]

Instead, I believe that the system has a whole continues to evolve in a reversible way and that it only looks like a collapse when you look at that subsystem you were measuring when instead it is just the projection that looks like a collapse.

What you are describing is the many worlds interpretation. Which is a perfectly valid interpretation, but it's not the ensemble interpretation. So which interpretation do you want to discuss? You can't discuss one based on assumptions that only apply to the other; that doesn't make sense.

 

[PeterDonis]

Quantum Erasers?

No. Quantum erasers do not erase actual measurement results. They only "erase" things that would have been recorded as measurement results, if the eraser had not been applied. But this is just a garden-variety experimental manipulation: a quantum eraser is just another unitary operation added to the "internals" of the experiment, before any result is recorded. Don't be misled by all the pop science hype.

 

[jbergman]

What you are describing is the many worlds interpretation. Which is a perfectly valid interpretation, but it's not the ensemble interpretation. So which interpretation do you want to discuss? You can't discuss one based on assumptions that only apply to the other; that doesn't make sense.

My understanding from other threads is that wavefunction collapse isn't a postulate of the Ensemble Interpretation as described by Ballentine, so it would be consistent with the beliefs mentioned above.

I opened the discussion to learn more about the Ensemble Interpretation to see if it was compatible with my instinctual understanding of QM. But interpreting the double-slit experiment in that framework raises a fundamental problem with it as highlighted by your initial response.

Personally, I am uncomfortable with the Many Worlds Interpretation as espoused by DeWitt, although the original Everettian version is probably closer to what I believe to be the truth.

 

[PeterDonis]

My understanding from other threads is that wavefunction collapse isn't a postulate of the Ensemble Interpretation as described by Ballentine

This is true, but it's also true that Ballentine, and the ensemble interpretation in general, assumes that measurements have single outcomes. And that means there has to be something else going on besides straightforward reversible unitary evolution, because straightforward reversible unitary evolution does not give single outcomes for measurements. Measurements having single outcomes out of multiple possibilities is not reversible.

So if your position is "everything is reversible", then, as I said, you are talking about the MWI, not the ensemble interpretation.

 

[jbergman]

This is true, but it's also true that Ballentine, and the ensemble interpretation in general, assumes that measurements have single outcomes. And that means there has to be something else going on besides straightforward reversible unitary evolution, because straightforward reversible unitary evolution does not give single outcomes for measurements. Measurements having single outcomes out of multiple possibilities is not reversible.

This is getting to the heart of the matter and I can't refute what your saying here at the moment. But my understanding is that measurement could involve entanglement between that what is being measured and the measurement system in such a way that a projective measurement on a subsystem looks like a collapse.

So an alternative postulate could be that measurement involves a change to the entire system such that a projective measurement on a subsystem will be a single outcome.

I've come to this half-baked idea after discussions with other more accomplished physicists than myself.

As to how and why something like this would be true, it's not hard to imagine that measuring the position of a particle involves disturbing it's momentum. Again, these ideas are half-baked and I need to work through these details formally.

 

[PeterDonis]

my understanding is that measurement could involve entanglement between that what is being measured and the measurement system in such a way that a projective measurement on a subsystem looks like a collapse.

Again, there are interpretations that take this view (with some corrections to the way you are wording it), but the ensemble interpretation is not one of them. So you need to make up your mind which interpretation you want to talk about. If you want to talk about the ensemble interpretation, then you need to use the ensemble interpretation, not some other one.

 

[PeterDonis]

these ideas are half-baked

Personal theories and personal speculations are off limits here at PF. I have assumed so far in this thread that you were asking about the ensemble interpretation as it appears in the mainstream literature on QM interpretations. That is what the responses you are getting are about.

 

[jbergman]

Personal theories and personal speculations are off limits here at PF. I have assumed so far in this thread that you were asking about the ensemble interpretation as it appears in the mainstream literature on QM interpretations. That is what the responses you are getting are about.

As stated before, I am/was trying to investigate whether the Ensemble interpretation is compatible with my ideas about QM. It looks like it isn't based on your assertion that it doesn't support measurement in the way that I described along with the fact that it doesn't say anything about the state of a single electron.

 

[PeterDonis]

As stated before, I am/was trying to investigate whether the Ensemble interpretation is compatible with my ideas about QM.

Then this thread is now closed since what you want is not what PF is for.