Particle vs Wave Interpretations of QM

[PeterDonis]

But then the interference pattern becomes much too fine to be resolved:

Interference pattern of what? The plastic is not measuring impact positions. It's measuring tracks. What would an "interference pattern" of tracks even look like?

To be concrete, my prediction is that if this experiment is run, the plastic will show two bundles of tracks, one coming from slit #1 and the other coming from slit #2, with a finite angle between them where zero tracks appear. The proton wavelength being very short means the tracks are expected to be very narrow, but the directions of the tracks are what's important, not their widths.

What is your "interference" prediction for what the tracks will look like?

 

[gentzen]

What is your "interference" prediction for what the tracks will look like?

I thought the intention was to have an experiment where interference can be observed, like for example in
https://www.oeaw.ac.at/fileadmin/In..._Paradigms_Tested_in_the_Mesoscopic_World.pdf

Since the experiment is based on a thermal source, i.e. a classical mixture of external and internal molecule states, one may wonder why interference is possible at all.

The setup is as above, but complemented by a nanofabricated SiN structure close behind the second collimation slit. Many slits are each etched ∼ 50 nm wide and into the 200-nm-thick SiN membrane to form a grating with a period of 100 nm. About 20–30 such slits are illuminated by the molecular beam. The coherence width covers about 10 such slits. Figure 24.4a,b shows interference patterns for thermal beams of C60 and C70 respectively.

Because protons are charged, I would probably not try to use a thermal source. But still, I would not accelerate them too much. Then, if the detector screen is sufficiently far away (might be expensive, because we have to work in vacuum), I might have the chance to actually see a diffraction pattern.

If not, then I can also do this experiment with electrons instead of protons, and some thin crystal sample in a transmission electron microscope instead of a manufactured grating. The detection of tracks in the plastic will stay roughly the same.

For this sort of experiment, since the detector screen is rather far away, the tracks in the plastic would point in the direction from the sample to the detection spot.

The proton wavelength being very short means the tracks are expected to be very narrow,

The plastic determines how narrow the tracks can be. The wavelength of the proton is much shorter than that.

 

[PeterDonis]

I thought the intention was to have an experiment where interference can be observed

As I understand it, @Roberto Pavani intended a scenario basically as follows:

(1) Start with a double slit experiment setup which is arranged so that, with a normal detector screen, i.e., one that shows a dot for each individual particle impact, the dots on the screen will gradually build up an interference pattern when both slits are open.

(2) Remove some portion of the detector screen and replace it with a thick layer of something that can record the tracks of particles passing through it--the plastic film that was described was what he said, but it could equally well be, say, a bubble chamber.

Then the question is, what kinds of tracks will be recorded?

@Roberto Pavani had specified protons as the particles, but that was just because he wanted to have something charged to go with the kind of track detector he was imagining. Electrons would work just as well, and I think there have been actual double slit experiments done with electrons, but not with protons. So we could take the parameters from an electron experiment and use those if we wanted concrete numbers.

 

[gentzen]

Then the question is, what kinds of tracks will be recorded?

My prediction is that the starting positions of the tracks will show the same interference pattern as the normal detector screen. And in such a setup, the angular resolution provided by the tracks will be insufficient to determine through which slit the particle went. (Because the slit is far-away and the distance between the slits is very small.)
(My reasoning is that the spatial resolution of a plastic detector screen is not significantly worse compared to the resolution of a normal detector screen.)

And in a setup where it is possible to determine through which slit the particle went, based on the tracks, any "predicted" double-slit (or grating) interference pattern would have a resolution much finer than the "nm resolution" provided by the plastic detector screen.

 

[renormalize]

So the amplitude for every track that has a nonzero amplitude at all will only have a contribution from one slit. Hence, no interference.

OK, I think we'll have to agree to disagree, at least until one of us finds an appropriate reference or does an actual calculation. But before I go further, I want to make sure I understand your claim. Consider the 2-slit configuration using a cloud chamber to display tracks and focus strictly on the "on-axis" response (i.e., just the region of the chamber that is directly above the point centered between the slits):

My prediction is that the electron tracks will be strictly vertical there (shown in red), whereas you predict that we'll see either the blue or the green tracks (presumably with equal probability) that point back to the individual slits. Do I have that right?

 

[PeterDonis]

My prediction is that the starting positions of the tracks will show the same interference pattern as the normal detector screen.

I hadn't thought about that explicitly, but if my claim that the tracks are sufficient to record which path information is correct, my prediction for this would be that no interference pattern would be shown.

My prediction is that the electron tracks will be strictly vertical there (shown in red), whereas you predict that we'll see either the blue or the green tracks (presumably with equal probability) that point back to the individual slits. Do I have that right?

Pretty much. My prediction is that, for each individual run of the experiment, we'll see either one of the blue tracks or one of the green tracks, and over a large number of runs, the tracks will fall into two bundles, a blue one and a green one.

Note, though, that as you've drawn the diagram, my prediction is that there will be many more tracks of both colors--the blue ones will be a fanout from the right slit, and the green ones will be a fanout from the left slit. Your prediction, I take it, would be that there would be just one fanout, the red one, from a point halfway between the slits.

I think we'll have to agree to disagree, at least until one of us finds an appropriate reference or does an actual calculation.

I don't think a calculation in itself will help, since it's really the premises behind the calculation that are the focus of our disagreement, specifically whether the tracks are sufficient to record which path information or not. Saying yes leads you to one calculation, the one I've been implicitly imagining; saying no leads you to another, the one you've been implicitly imagining. But I don't think our dispute is over how to do either calculation; it's over which one reflects the actual physics of the experiment. The only way to resolve that for sure is to actually do the experiment.

It would certainly be interesting, though, if any theoretical analysis of this scenario appears in the literature. So far I have not been able to find one.

 

[PeterDonis]

in a setup where it is possible to determine through which slit the particle went, based on the tracks, any "predicted" double-slit (or grating) interference pattern

If the tracks are sufficient to record which path information, why would there be any interference at all?

 

[Roberto Pavani]

My prediction is that the electron tracks will be strictly vertical there (shown in red),

This sounds reasonable to me.

My reasoning was simply that, for light, the Poynting vector at the central interference maximum is normal to the screen. By analogy, I wondered whether the local probability current for matter waves might also be normal to the screen at that location.

I am not claiming that this is correct. In fact, the purpose of my question was precisely that I did not know what the recorded tracks would look like.

My initial choice of protons was because I thought they might be easier to track in a plastic detector.

However, one could instead use electrons and a small cloud chamber (or similar track detector) with high-speed imaging. The conceptual question would remain the same.

 

[Roberto Pavani]

As a side remark, one of the reasons I found the "red track" picture intuitive is the following.

If one computes the probability density distribution in the region between the slit plane and the detector screen, one obtains a 3D interference structure. Of course, this says nothing about the trajectory of any individual particle, but it does provide information about the spatial distribution of probability (and perhaps some intuition about the associated probability current).

At the central bright fringe, my naive expectation would be that the local probability current is approximately normal to the screen, which is why I found the "red tracks" picture appealing.

I am not presenting this as an argument, only as the intuition that motivated my original question.

 

[gentzen]

It would certainly be interesting, though, if any theoretical analysis of this scenario appears in the literature. So far I have not been able to find one.

People working on the theoretical side of electron microscopy and charge particle optics know how to compute such scenarios. The question is, how did they learn those fundamentals, and how do they refers to them in their papers. Here is how a Ph.D. dissertation I consulted while working on crystal effects computations did it:

2.1. Transmission Electron Microscope (TEM). Figure 1 shows the basic configuration of a transmission electron microscope and ray diagrams for imaging and diffraction mode [4–6].

[4] P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley, and M. J. Whelan, Electron Microscopy of Thin Crystals (Krieger, Malabar, 1977).
[5] J. C. H. Spence, Experimental High-Resolution Electron Microscopy (Oxford, New York, 1988).
[6] A. W. Agar, R. H. Alderson, and D. Chescoe, Principles and Practice of Electron Microscope Operation (Oxford, New York, 1988).

I have not read any of those books, I didn't even know of their existence. I have read (very old) papers by Hirsch, Howie, and Spence. I have also seen references (in papers) to

L. Reimer, H. Kohl, Transmission Electron Microscopy, 5th Edition, Springer, 2008.

which is a book I do own and have read in parts. (The first edition of that book appeared in 1985.)
I now asked Google for the standard reference textbooks in the TEM field, to get a better idea of whether Reimer & Kohl is a "useful" reference:

Textbook (Main Authors)	Primary Focus	Target Audience	Mathematical Depth
Williams & Carter	Practical operation, crystallography, analytical TEM	Materials scientists, beginners	Moderate / Highly visual
Reimer & Kohl	Physical image formation, wave optics	Physicists, advanced users	Very high / Rigorous
Spence	Atomic resolution (HRTEM), image simulation	Structural researchers, experts	High / Specialized
Hirsch et al.	Crystal defects, dynamical theory	Solid-state physicists, historical baseline	Very high

"Transmission Electron Microscopy: A Textbook for Materials Science" by David B. Williams and C. Barry Carter
„Transmission Electron Microscopy: Physics of Image Formation“ by Ludwig Reimer and Helmut Kohl
"High-Resolution Transmission Electron Microscopy" by John C. H. Spence
"Electron Microscopy of Thin Crystals" by P. Hirsch, A. Howie, R. Nicholson, D. W. Pashley, and M. J. Whelan

Many of the relevant topics are at least mentioned in Reimer & Kohl, but I personally find the presentations found in introductory chapters of various Ph.D. dissertations more coherent (but also much shorter and less extensive).

---

Conceptually, in the vacuum between sample and detector, you mostly get a statistical collection of wavefunctions of a single electron at a fixed energy. The electron optics can use static electric and magnetic fields to focus or otherwise transform those wavefunctions before the detector. At the detector surface before the measurement, you now have such a wavefunction of a single electron, and you can use that wavefunction to "predict" momentum or intensity, or a combination of both at different local spots on the detector surface.

 

[gentzen]

in a setup where it is possible to determine through which slit the particle went, based on the tracks, any "predicted" double-slit (or grating) interference pattern

If the tracks are sufficient to record which path information, why would there be any interference at all?

Because conceptually, you have a wavefunction of a single electron (or rather a statistical collection of them) at the surface of the detector, which stays the same, independent of whether you use a normal detector screen or a plastic detector screen. And if you take the modulus squared of that wavefunction, the resulting spatial probability distribution shows an interference pattern. And because this is a theoretical "predicted" interference pattern, its resolution can be much smaller than a nanometer. And when you average it over a nanometer, all contrast of the interference is gone.

Experimentally, I imagine making the distance D between sample and detector small, when I want to be able to determine which slit information, and making that distance D big, when I want to see an interference pattern.

 

[Roberto Pavani]

Here a little simulation (python code attached as txt)

 

[renormalize]

Here a little simulation (python code attached as txt)

Very nice and rather similar to the electromagnetic Poynting-vector interference plot in post #83. But what do the arrows depict? Perhaps the expectation values of the 3-vector momentum/probability-current density? (I can't Google translate your image title to English!)

 

[Roberto Pavani]

Yes, that is essentially the idea.

Sorry for the Italian title in the figure. Translated, it reads:

"Double-Slit Experiment: Probability Density and Probability Current"

The arrows are meant to represent the local direction of the probability current. The background color represents the probability density

$|\psi|^2$

The current is computed from

$\mathbf{j} = \mathrm{Im}(\psi^* \nabla \psi)$

up to an overall constant factor.

I was not able to produce arrows whose length also reflects the current magnitude, so they should be interpreted qualitatively as direction indicators only.

 

[PeterDonis]

Because conceptually, you have a wavefunction of a single electron (or rather a statistical collection of them) at the surface of the detector, which stays the same, independent of whether you use a normal detector screen or a plastic detector screen.

But the two detectors are detecting different observables. Heuristically, the normal detector screen is detecting position, so it makes sense to look at the wave function in the position representation. But the track detector (plastic, cloud chamber, whatever), heuristically, is detecting momentum, so here it makes sense to look at the wave function in the momentum representation. What does that look like?

 

[Demystifier]

I think that asking these questuons is what brings the confusion.

Sorry, I can't resist.

 

[martinbn]

Sorry, I can't resist.

View attachment 373173

But it doesn't fit! I didn't obejct to the questions because they were philosophical. I objected because they didn't make sense. Take for example the very first question

Is the Moon itself the same thing as its wave function?

How could the Moon possibly be the same thing as its wave function!!

ps It is funny you gave Einstein as a model example, when you disagree with him on the foundations of QM and relativity.

 

[Fra]

But it doesn't fit! I didn't obejct to the questions because they were philosophical. I objected because they didn't make sense. Take for example the very first question

How could the Moon possibly be the same thing as its wave function!!

So you think the obvious answer is no (and I agree). Then what is their relation? Because at the same time they arent unrelated.

If we take wavefunction to conceptually represent the observational contexts information about the system.

Then the "wave function of the moon" can not explicitly not encoded in the moon itself - it must be physically encoded in the moons environment. So the are not the same.

The moon might as well ask, is the environment the same thing as my information about it? And that answer is the same.

i don't find any interpretation of QM satisfactory. I see that, however, as a separate issue from trying to treat the Moon as a giant electron and imagining that it has no classical trajectory. And that in some sense it doesn't exist unless someone is looking at it.

It is the assymmetry between the observed and the observing system that allows us to avoid the hard questions.

The difference between the moon and an atom examlp is simply one of relative scales, asking questions as if the moon was a quantum system is a way to NOT avoid the hard questions.

QM needs the assymmetry, it is when we challenge the assymmetry by considering a macroscopic system, as part of the quantum system that the question is unavoidable. Avoiding the question because "for practical matters" we dont need QM to describe the moon is valid, but conceptually avoing the challenge.

I think some of us dont want to avoid it, we want to knock our heads until its solved. I think unification questions, will not allow us to repeat the trick infinitely. At some point, there is no "bigger context". Like it would be for atomic scale system. I think the reason we dont understand the hiearchy of interactions all the way down to when spacetime dissolves, is related to this. At some point, we have to also ask, what DIFFERENCE does it make wether the moon is there or not?

(Here we're tangenting on the indivisibliltiy thread, where we discussed wether the "actual configuration" must be part of the equations or motion - or not. This is directly related to what is the difference between the moon, and someones information about the moon, and what difference does it make for the evolution)

/Fredrik

 

[PeterDonis]

How could the Moon possibly be the same thing as its wave function!!

It is in the MWI.

 

[PeterDonis]

what is their relation?

That depends on which interpretation of QM you adopt. You appear to be adopting an "information interpretation", where the wave function just encodes information we have about the system. (Note that "information" is vague, though: what information, exactly? Generally when you try to unpack this, you end up saying that the wave function encodes information about the probabilities of possible measurement results.)

But there are other interpretations. In the MWI, for example, as I just posted in response to @martinbn, the wave function is the system--more generally the wave function is the physical reality, there is nothing else. (You could say that the wave function is a mathematical representation of the physical reality, but that's just quibbling: the point is that in the MWI the wave function represents the actual physical state of everything in the same way that particle positions and velocities do in Newtonian mechanics.)

As the guidelines for this subforum note, interpretation debates are not resolvable, since all interpretations make the same experimental predictions. So at some point any discussion of interpretations has run its course and is just going around in circles, with people simply restating their opinions. This thread is probably getting close to that point now.

 

[martinbn]

It is in the MWI.

What is a good reference for this?

 

[PeterDonis]

What is a good reference for this?

Any reference by an MWI proponent. But see my post #110 in response to @Fra for some more unpacking.

 

[Fra]

It is in the MWI.

It is? Not sure if i want to know how?

Maybe that explains why it is one of the few interpretations I never really made sense of.

/Fredrik

 

[PeterDonis]

It is? Not sure if i want to know how?

In the sense I described in post #110.

 

[martinbn]

(You could say that the wave function is a mathematical representation of the physical reality, but that's just quibbling: the point is that in the MWI the wave function represents the actual physical state of everything in the same way that particle positions and velocities do in Newtonian mechanics.)

That's what I thought, but then the question is still meaningless. It is the same as asking in Newtonian physics if a particle is the same as its position and velocity.

 

[PeterDonis]

the question is still meaningless

If you give it the literal intepretation you are, yes. But many would not; they would just interpret it as shorthand for what I described in post #110.

It is the same as asking in Newtonian physics if a particle is the same as its position and velocity.

Perhaps a better phrasing would be that the state of the particle is the same as its position and velocity in Newtonian physics, and in the MWI the state of the overall system (and in the last analysis, the whole universe) is the same as the wave function.

 

[PeterDonis]

And note that the original question by @Demystifier that prompted this subthread, in context, was:

Is the Moon itself the same thing as its wave function? If not, then what exactly the Moon is? Can the Moon itself be described by a mathematical object?

That looks to me like he was asking "what mathematical object describes the Moon", not "is the Moon literally the same thing as its wave function".

 

[Demystifier]

How could the Moon possibly be the same thing as its wave function!!

So you say that it is not the same thing, i.e., your answer to my question is a clear "no". Thus you admit that my question has a clear answer, which implies that it is not meaningless.

 

[martinbn]

So you say that it is not the same thing, i.e., your answer to my question is a clear "no". Thus you admit that my question has a clear answer, which implies that it is not meaningless.

No, I am saying that it is meaningless that they could be the same thing, the map and the territory situation.

Can you clarify if you meant the question literary what it says or not? And if not, what exactly did you mean?

 

[Demystifier]

No, I am saying that it is meaningless that they could be the same thing, the map and the territory situation.

Can you clarify if you meant the question literary what it says or not? And if not, what exactly did you mean?

As an example, you said that it would be meaningless to say that a classical particles is the same as its position and momentum. But I would say that it would be quite meaningful, in the sense that it would really mean that a classical particle has no other properties than its position and momentum. And if someone objected that it also has mass, one could argue that it has not, because the mass is not a property of the particle itself, but is a parameter in the Hamiltonian. In other words, the kinematics of a classical particle consists in its position and momentum (as functions of time), while everything else (such as mass of the particle) belongs to the dynamics.

So if we accept such terminology, then it makes perfect sense to ask whether the quantum particle is the same thing as its wave function, in the same sense in which the classical particle is the same thing as its position and momentum. And, as has been already said here, in some interpretations of QM, namely many worlds (and also in the objective collapse theory, which, however, is not just an interpretation, but an alternative theory with slightly different measurable predictions), it is indeed the case that the quantum particles is the same thing as its wave function.

Of course, you may object to such terminology, that "to be the same as" means "to have no other properties than". But that's just a terminology. A terminology can be chosen at will, and when one defines reasonably clearly what one means by certain terminology, then it starts to make sense.