Instantly reformable wave packets instead of "particles"?

[Idunno]

TL;DR Summary

Is it consistent with quantum mechanics to say that quantum objects are instantly reformable, real, wave packets? Also, might collapse be related to energy density of a packet going over threshold?

Hello,

I am a high school physics teacher, and I have been thinking about a way to model quantum mechanics in an intuitive way in order to teach it better, but I don't want to lead my students down the wrong path. I am certainly no expert in quantum theory. In looking at the guidelines, I realize this might not be postable, as it probably comes under the category of a “personal theory”, but I don’t really have any other avenue to ask this. I showed it to some people (experimentalists) at my local university, and they said “you need to talk to a theorist”. Problem is, I don’t know any theorists, and the ones at my university all seem too busy. So I’m hoping to get some help here.

What I have come up with boils down to two questions:

Question (1) Is it consistent with Quantum Mechanics to say that quantum objects (photons, electrons, protons, etc.) are instantly reformable, real, wave packets?

To clarify this as best I can, by "real," I mean that energy exists wherever the wave packet is not cancelling itself out. So that, if a wave packet is split into two, or becomes very big, it can nevertheless instantly reform (shrink (or expand?) upon measurement conditions) and thus instantly move energy about itself? Notice this instantaneous movement of energy is "internal" to the "particle" and not instantaneous movement from particle to particle.

In this view, all the energy of the wave packet is part of "one thing" so that if it reforms to a small spot, all the energy of the quantum object instantly goes to that spot. This would be the main sense that it is a "particle" (it's all together), but, otherwise, the idea of a “particle” doesn't fit too well, as instead of thinking that there is an infinitesimal billiard ball like object moving about that the wavefunction mysteriously influences the path of, you take wavefunctions as real things that are instantly reformable, they can become as small as you want when you measure them and they shrink.

Of course, I am no expert, but to my mind the main issue with this view is that energy moves instantly, which on the surface seems to violate relativity. However, this seems like it would be OK, since it is internal to the "particle" and not instantaneous transmission from particle to particle? It seems like the reasons that make entanglement consistent with relativity would apply to this?

Question (2): Is it possible that the reason why packets instantly reform (wavefunction collapse) is that the energy density goes over some threshold?

To clarify, assuming that the answer to question (1) is yes, I am wondering about what seems like an obvious question (which I've never seen addressed anywhere). In a classical wave, the energy is proportional to the squared amplitude. In QM, the squared amplitude relates to the probability of finding a particle in some region. Might there be a connection? It seems to me that the simplest way that there might be a connection is that if the energy density of a region of the wave packet goes over some threshold (gets "too high") then this might trigger collapse. I don't know what this threshold might be, but if it's true, it seems to explain a lot to my undereducated mind. It's like the wave packet gets out of equilibrium when the energy density gets too high, and this triggers collapse.

Take the example of a wave packet (photon) coming towards a detector. The detector is modeled as a bunch of electron wave packets confined to boxes. Assume all the detector electrons are not in sync, they are all independent with different timing. As the photon wave packet starts to mingle with the detector electrons it interferes constructively and destructively. The idea is that if there is a "good" phase match in some region, then the energy density increases in that region. If the phase match is good enough, then the photon will go over threshold and the wave packet will instantly reform to that region. In the middle of the wave packet the amplitude is intrinsically higher, so the idea is that it is more likely that that region will go over threshold, since an "OK" phase match will take it over threshold, but on the edge of the packet, where the intrinsic amplitude is less, you need a very good phase match to take it over threshold and collapse the packet to that region, so it happens less often on the edge of the packet. I naively imagine that a similar scheme would apply to an electron packet coming towards a detector, where the interaction is mediated by virtual photons, which I know little about.

If the probability of getting a good phase match is the same throughout the packet interfering with the detector, then the probability of collapse (with detector electrons that are not in sync, with a random distribution in their timing) to a region is proportional to the energy density, which, classically is proportional to the squared amplitude. Thus you get a reason for the Born rule with this scheme.

You also get a reason for randomness and unpredictability with this scheme. If you cannot know the relative timing of two wave packets, you cannot predict where and when a packet will go over threshold.

There is more to be said about all this, but I should stop here, as I don't want to make too long of a post. So, please tell me how this sounds. If it is consistent with QM, it seems like an intuitive model for QM to my mind, and you get a reason for randomness, which seems good. To be abundantly clear, I'm far from an expert in QM, just asking.

 

[charters]

What you suggest would broadly be classified as an objective collapse, dynamical modification of quantum theory. These approaches match QT is some regimes, but not all.

Your particular modification involves a detector triggering a positive collapse. This won't be able to account for the so called interaction free or negative result experiments. In standard QT, the observation that a detector did *not* click also triggers a collapse - to every other eigenstate where a detector isn't present/making a measurement. I don't see how your story could explain this.

For teaching high schoolers, I would advise just sticking to the standard textbook presentation.

 

[Idunno]

What you suggest would broadly be classified as an objective collapse, dynamical modification of quantum theory. These approaches match QT is some regimes, but not all.

Your particular modification involves a detector triggering a positive collapse. This won't be able to account for the so called interaction free or negative result experiments. In standard QT, the observation that a detector did *not* click also triggers a collapse - to every other eigenstate where a detector isn't present/making a measurement. I don't see how your story could explain this.

I'm not sure I'm following you, but I think I can reply like this:

Would splitting a photon in two and only having one detector be an example of negative result or interaction free collapse? So you split a single photon in two with a beam splitter and the components of the photon go off in different directions. Usually you have two detectors, and 50% of the time you get collapse at one detector, 50% at the other. But if you only have one detector, and just empty space at the other spot, if your detector fails to click, then what happens?

In my scheme, the fact that part of the photon is not being detected (not interacting) ups the need for a really good phase match at the existing detector. The more the wave packet is not being detected (not interacting with anything), the better the phase match has to be to get it to collapse where it is interacting. If the detector fails to trigger, the energy that is impinging on the existing detector reflects (or instantly joins the other part) after failing to interact with the detector material (failing to find a good enough phase match), and eventually joins the other part when it interacts with something. Think the scheme can handle this? By the negative result, you know where the energy instantly moves to, it joins the other component eventually.

For teaching high schoolers, I would advise just sticking to the standard textbook presentation.

Would love to if there was a intuitive model out there. But there doesn't seem to be.

An intuitive model would be really great. For instance, instead of saying something monumentally confusing like "electrons have properties of both particles and waves" I would be able to say electrons are instantly reformable wave packets such that all the energy is part of "one thing"". Which is far more understandable with a bit of explaining. The problem with the first statement is that it doesn't tell you in just what way an electron is like a particle and in what way it is like a wave, the second statement does. It would be great to be able to say something like the second.

 

[charters]

If the detector fails to trigger, the energy that is impinging on the existing detector reflects (or instantly joins the other part) after failing to interact with the detector material (failing to find a good enough phase match), and eventually joins the other part when it interacts with something

This is a little better, but notice how the "threshold" you mentioned before isn't really relevant. The collapse trigger is just the presence of the detector, not only when a certain condition of the detector is met. Above and below threshold interactions are both collapsing.

More importantly, this is still an objective collapse model, so you have an observer independent, non-unitary process happening when microscopic particles interact with macroscopic detectors. This is still a modification of QT that undermines the universal validity of QT. In QT, unitarity is an axiom, as is the idea that what we designate as the detector is arbitrary. You would need to define this micro/macro distinction as a preferred scale, and introducing this cut will identify some mesoscopic regime where your predictions diverge from QT. You will also have to explain how a soup of micro particles condense into a macroscopic star, where there's no a priori concept of a detector. There are minority ideas kind of similar to this floating around, mainly the GRW equation, which is a spontaneous collapse trigger. But most people have given up on identifying objective collapse with a detector based trigger.

An intuitive model would be really great.

But if you aren't careful, your intuitive will leave the students with some wrong beliefs, so it is probably better to be vague and unclear in the normal/mainstream way. At least they'll be normally situated for future study. In my opinion, you need to get into decoherence to really do justice to these foundational issues beyond the standard textbook axioms, but I don't know if this is realistic for your situation.

 

[PeterDonis]

Is it consistent with Quantum Mechanics to say that quantum objects (photons, electrons, protons, etc.) are instantly reformable, real, wave packets?

Only on certain interpretations of QM. For high schoolers, I would not want to present QM in a way that is interpretation dependent.

In fact, there isn't any interpretation of QM that describes it quite the way you are. So really you are inventing your own interpretation of QM, which I think is even less appropriate for high schoolers than presenting it in a way that is only consistent with some well-known interpretations, but not others.

The key thing that all interpretations of QM have, which basic QM as usually presented in textbooks and as actually used to make experimental predictions does not have, is some kind of ontology--some kind of claim about what is "really going on" behind the scenes of the observations and measurements. There is no single accepted account of this, which is why QM interpretations are still a contentious issue. For high schoolers, the most I would say about all this is what I just said--that there is no single accepted account of what is "really going on"; QM as it is actually used makes no commitments about that, but only makes predictions about experimental results (and those predictions are usually of probabilities of different possible results).

 

[PeterDonis]

Would love to if there was a intuitive model out there. But there doesn't seem to be.

Yes, and the reason for that is that QM simply does not work the way our intuitions, which evolved in a classical environment, think things should work. That is why there is no single accepted interpretation of QM.

IMO, the proper response to this, for high schoolers, is not to make up your own intuitive interpretation. It is to be up front with them about the fact that there is no single accepted interpretation, and to refrain from committing to one in the course of teaching. QM's experimental predictions, and the methods used for making them, can be taught without making any such commitments.

 

[Idunno]

This is a little better, but notice how the "threshold" you mentioned before isn't really relevant. The collapse trigger is just the presence of the detector, not only when a certain condition of the detector is met. Above and below threshold interactions are both collapsing.

Threshold is still relevant, I think. If some of the wave packet is not interacting, the phase match has to be even better in the interacting part, if it's good enough, it goes over threshold, and collapse happens (all the energy is instantly relocated). The threshold is simply moved to a higher energy density.

More importantly, this is still an objective collapse model, so you have an observer independent, non-unitary process happening when microscopic particles interact with macroscopic detectors. This is still a modification of QT that undermines the universal validity of QT. In QT, unitarity is an axiom, as is the idea that what we designate as the detector is arbitrary. You would need to define this micro/macro distinction as a preferred scale, and introducing this cut will identify some mesoscopic regime where your predictions diverge from QT. You will also have to explain how a soup of micro particles condense into a macroscopic star, where there's no a priori concept of a detector. There are minority ideas kind of similar to this floating around, mainly the GRW equation, which is a spontaneous collapse trigger. But most people have given up on identifying objective collapse with a detector based trigger.

You're kind of talking over my head, but to try to answer, in this interpretation, collapse is happening all the time, with or without a detector, whenever wave packets interact, or they enter a field, like a magnetic field. So wave packets in condensed matter (like a star) get confined and collapse without a detector. I'm also getting that you don't like objective collapse. OK. Further, collapse happening due to an energy threshold might also work with magnetic fields and spin, not just interfering wave packets.

I was trying to figure out how this might work for spin, and the thought I had was that a spherically symmetric charged wave packet has no magnetic field (as charge in circulating evenly in all directions), but a non symmetric wave packet does produce a field (charge is circulating unevenly). I have no idea if this is right, but I went with it, cause it's fun. So then, a spherically symmetric charged packet (with no magnetic field) enters a magnetic field. Suddenly the circulating charge is forced about, and in keeping with an energy threshold idea, the energy can go over threshold in one direction, reforming the wave packet. It then changes shape to non symmetrical (like a teardrop maybe? I don't know) and now produces a magnetic field. Depending on what direction went over threshold, it's either producing a field consistent with "spin up" or "spin down".

Nice thing is, it doesn't have to be spinning to produce this field. So no confusion there about how electrons don't really spin, just chalk it up to non symmetrical wave packets (if I can say that, again, no idea if i can). Also a reason why a neutron can have a spin. Other nice thing is that the wave packet can retain its shape after, and if it encounters another identical magnetic field, it is deflected the same way.

Nice intuitive picture, if I can say it. :)

But if you aren't careful, your intuitive will leave the students with some wrong beliefs, so it is probably better to be vague and unclear in the normal/mainstream way. At least they'll be normally situated for future study. In my opinion, you need to get into decoherence to really do justice to these foundational issues beyond the standard textbook axioms, but I don't know if this is realistic for your situation.

I'm not about to lead students down the wrong path, so I'm not about to teach this way unless it's "approved". However, even if my collapse question/hypothesis is no good, it seems to me to be much better to state that it's Ok to think about quantum objects as instantly reformable real wave packets, if that is consistent with QM. It's just so much less confusing and less vague than saying quantum objects have properties of particles and waves at the same time.

For instance, in this interpretation, there is no confusion about electrons around the atom, and whether or not they are orbiting. Electrons are simply wave packets attached to the nucleus because of their negative charge. They are standing waves confined to a spherical volume, and the balloon like pictures of s,p,d,f orbitals are pictures of their packet envelopes. They then instantly reform if hit by a photon of the right energy. There is no wondering how a tiny billiard ball like object can be orbiting yet not accelerating whose postion is mysteriously influenced a imaginary wavefunction. Isn't that better? Less confusing?

 

[PeterDonis]

even if my collapse question/hypothesis is no good, it seems to me to be much better to state that it's Ok to think about quantum objects as instantly reformable real wave packets, if that is consistent with QM.

I disagree; see below.

It's just so much less confusing and less vague than saying quantum objects have properties of particles and waves at the same time.

I don't think you should not be telling your students that either.

IMO, what you should be telling your students, if you really want to give them the best picture of QM that you can at their level, is that QM consists of two parts:

(1) A set of mathematical models rules for predicting the results of experiments, which has been confirmed by various experiments to very high accuracy, up to a part in a trillion; combined with a very minimal "interpretation" that just says how the various mathematical entities in the models and rules correspond to the real objects and phenomena that are used and observed and measured in the real world;

(2) A whole family of "interpretations" that amount to various ways of telling stories about what is "really going on" behind the scenes when experiments whose results are accurately predicted by the rules in #1 are run. There is no consensus among physicists about which of these interpretations is the "correct" one--in fact, many physicists do not believe any of them are correct, and expect that future advances in physics will either uncover new interpretations that no one has yet thought of, or will show that QM itself--the set of models and rules in #1 above--is just an approximation to some deeper theory.

All of the stuff you are posting here--including "quantum objects have properties of particles and waves at the same time"--falls under #2 above--and what's more, it's not even one of the interpretations in #2 that have been discussed and debated among physicists, but just something you came up with yourself, which makes it even less appropriate for discussion in a high school class. If you are going to talk about specific QM interpretations at all, you should learn about the ones that physicists have discussed and debated, and those are what you should tell your students about (with very strong reminders that there is no consensus among physicists about whether any of them are "right"), not an interpretation you made up yourself. Otherwise, IMO, you will be doing your students a huge disservice.

 

[PeterDonis]

I'm not about to lead students down the wrong path

If you're really serious about this, I strongly recommend that you consider the points I have raised. You admit that you are not an expert in QM; but I'm not sure you realize just how strongly that limits your ability to usefully go beyond the minimal version of QM that I described in #1 of my previous post. Please understand that I am not criticizing the fact that you are not an expert in QM; we all have lives and jobs and nobody, and no teacher, can be expected to be an expert in every subject that comes up in the course of our lives and jobs. I am simply trying to point out some consequences of your admitted lack of expertise that you might not have considered, because I think they're important things to consider in pursuing your stated goal (which I wholeheartedly agree with) of not leading your students down the wrong path.

To illustrate what I mean by limitations, here is how you describe electrons in atoms:

Electrons are simply wave packets attached to the nucleus because of their negative charge. They are standing waves confined to a spherical volume, and the balloon like pictures of s,p,d,f orbitals are pictures of their packet envelopes.

There's a problem with this: each of these orbitals can contain two electrons, not one. (Consider, for example, the 1s orbital of a helium atom in its ground state.) The two electrons have opposite spins. But there's no room in your "wave packet" description of electrons for them to have spin; how can a wave packet have spin? This is question I would expect a bright student to ask. How would you answer it?

There's another problem with it as well, one which is not obvious with electrons in atoms, but which is made evident by experiments run on free electrons. Schrodinger encountered this issue when he originally attempted to construct an interpretation of an electron's wave function similar to yours: he basically said the electron was a little packet of charge density, whose shape was described by its wave function. The problem with this was that when electrons are actually detected--for example, when they hit the screen of a cathode ray tube (which is unfortunately not as easy to give an everyday life example of now that TVs with picture tubes are no longer common )--they are always detected as little dots, which in general bear no resemblance to the wave function they had just before the detection.

For example, electron diffraction experiments showed a wavelike pattern similar to that shown when light is diffracted, but with the intensity of the electron source turned down sufficiently, the pattern always resolved into individual dots, which only formed the complete pattern over time as the results of many runs were accumulated. (This also happens with light when the intensity of the source is turned down sufficiently, by the way.) But the wave function describing each electron has the shape of the diffraction pattern, not of a single dot. This was a key observation that made Schrodinger's interpretation untenable, and led to Born proposing the interpretation of the wave function as a probability amplitude.

Just to be clear: I am not saying that there is some other QM interpretation that tells a consistent, intuitively satisfying story about all quantum experiments. There isn't; that's why there is no consensus among physicists about QM interpretations. For physicists doing active work in the field, they generally either remain agnostic about interpretations, or use whichever one seems most appropriate for the particular experiment they are doing or the particular theoretical model they are working on. But for high school students, I really think the best approach is to not adopt any particular interpretation, but to just tell students that there is no consensus about QM interpretations and leave it at that. If the students get really curious about interpretations, you could cover some of the most studied ones.

 

[Idunno]

Only on certain interpretations of QM. For high schoolers, I would not want to present QM in a way that is interpretation dependent.

I agree. I think that if I ever do teach it, I should mention multiple interpretations. I'd just rather have an intuitive one. Help the students more. Situation is that it is now in the cirriculum, but optional, and I don't currently teach it, but I would like to if I can do a good job. Seeing it in the cirriculum stimulated me to think of a good way to teach it. A bunch of thoughts later, and here I am posting this.

In fact, there isn't any interpretation of QM that describes it quite the way you are. So really you are inventing your own interpretation of QM, which I think is even less appropriate for high schoolers than presenting it in a way that is only consistent with some well-known interpretations, but not others.

Whether or not it's appropriate depends on if it's consistent with QM, isn't it? So is it? That's the question. And again I agree with presenting multiple interpretations, but in the end, I want to do a good job, instead of confusing the heck out of everyone.

From the replies so far, it seems like the answer to Question 1 is sort of "yes". That's progress for intuition, I hope. As for Question (2). I certainly don't know. It's very interesting to me that the posible connection between squared amplitude of a classical wave and the Born rule is never discussed, seem like an obvious question?

The key thing that all interpretations of QM have, which basic QM as usually presented in textbooks and as actually used to make experimental predictions does not have, is some kind of ontology--some kind of claim about what is "really going on" behind the scenes of the observations and measurements. There is no single accepted account of this, which is why QM interpretations are still a contentious issue. For high schoolers, the most I would say about all this is what I just said--that there is no single accepted account of what is "really going on"; QM as it is actually used makes no commitments about that, but only makes predictions about experimental results (and those predictions are usually of probabilities of different possible results).

But if you could get a story that gives you an intuition, where there were a set of postulates you could use to logically deduce quantum phenomena, wouldn't that be better?

With the Kinetic Molecular theory (materials are composed of atoms in constant motion) you can logically deduce that gases should expand when heated, with no mathematics. Plus a bunch of other phenomena. The two postulates enable logical deduction. Intuition is possible.

Whereas with QM, there are no postulates that enable logical deduction without mathematics. This is a terrible situation. So my proposal is:
(1) All quantum objects are real wave packets that have a presence everywhere in the universe.
(2) These wave packets are instantly reformable. Energy can be moved about instantly within them.
(3) Instant reformation happens due to the energy density going over some threshold. This is often through waves interfering constructively. If part of the packet is not interacting, this increases the threshold needed for collapse.

If (1) and (2) are OK, maybe that's progress? (3) seems to be obviously debatable, just an idea I have that seems to work to my undereducated mind. Wondering if it's worth pursuing and why it's never discussed?

If you accept these three postulates, it seems to me that you can logically deduce the results of the double slit experiment. You send a single wave packet (larger than the slits) through some slits. Most of the time it collapses on the slit material, or is reflected. But sometimes it makes it through, because some of the packet is not interacting with anything, some of it is going through the slits. Then it heads to the detector screen cancelling itself out in some areas. The detector screen is a bunch of electron wave packets that can be promoted to make a signal. The wave packet starts interfering with the detector electrons. Which one will make a signal?

Obviously where the wave packet is cancelling itself out there will be no signal, there is no amplitude to take over threshold. But in regions where it is not constructively interfering with itself, going over threshold is possible. It is most likely where the squared amplitude is greatest, as you just need an OK phase match, but in other areas you need a very good phase match. Over time, the signals are consitent with the double slit pattern and the Born rule.

The fact that I can deduce that with those postulates seems like a good thing? Yes?

 

[PeterDonis]

Whether or not it's appropriate depends on if it's consistent with QM, isn't it?

What does "consistent with QM" mean? QM here has to mean the mathematical model and the predictions it makes. How can you check the consistency of a story told in vague ordinary language with a precise mathematical model? You can't. Nobody has ever done any such thing with any QM interpretation. That's not what interpretations are for.

if you could get a story that gives you an intuition, where there were a set of postulates you could use to logically deduce quantum phenomena

These are two different things. We already have a set of postulates that you can use to logically deduce all quantum phenomena: that's the mathematical model I described in #1 of post #8. But no such model will be "a story that gives you an intuition". Physicists, by working with a mathematical model intensely, can often retrain their intuitions to be able to make pretty accurate intuitive guesses about what the model will predict; but no physicist claims that those intuitive guesses are the same as actual rigorous quantitative predictions based on the model. You get the latter by doing the math, not by intuition.

With the Kinetic Molecular theory (materials are composed of atoms in constant motion) you can logically deduce that gases should expand when heated, with no mathematics.

You can? How? Please show your work, as teachers like to say.

 

[PeterDonis]

Whereas with QM, there are no postulates that enable logical deduction without mathematics. This is a terrible situation.

No, it isn't, it's the same as for every other physical theory. As Feynman said, if you want to understand Nature, you must learn the language she speaks in.

 

[Nugatory]

From the replies so far, it seems like the answer to Question 1 is sort of "yes".

The answer to #1 is “No”. You’ve misunderstood our focus on why it is a bad idea to make up a new non-standard interpretation for high school students.

 

[charters]

Whether or not it's appropriate depends on if it's consistent with QM, isn't it? So is it? That's the question

Strictly speaking it is not consistent because no objective collapse approach is.

in this interpretation, collapse is happening all the time, with or without a detector, whenever wave packets interact, or they enter a field, like a magnetic field. So wave packets in condensed matter (like a star) get confined and collapse without a detector

This is too vague and ill defined to be taken seriously. Collapse cannot be happening all the time, in all interactions. For starters, beamsplitters do not collapse under any definition. Objective collapse models have to be extremely precise about the collapse triggers, as a huge class of these models are already constrained by experiment. Being not exactly quantum interpretations, they are vulnerable to experimental falsification.

 

[Idunno]

There's a problem with this: each of these orbitals can contain two electrons, not one. (Consider, for example, the 1s orbital of a helium atom in its ground state.) The two electrons have opposite spins. But there's no room in your "wave packet" description of electrons for them to have spin; how can a wave packet have spin? This is question I would expect a bright student to ask. How would you answer it?

The answer I came up with is to do with my ignorant reading of the Pauli Exclusion principle and the spin statistics theorem. The idea is that electrons in the same orbital are always 180 degrees out of phase. Which seems to be sort of what the spin statistics theorem says? (you probably won't like that, but I feel I should do my best to represent this interpretation) When one is cresting, the other is in the opposite trough, so to speak. That way they can coexist, I guess, as long as they are not occupying the same state. Notice that there is no room for more than two waves like this, if you try to fit a third one in, then the waves are intermingling, so that they occupy the same state, not allowed. Consistent with the exclusion principle.

Quantum state then, would be defined by timing? Not sure how to say it. The waves are 180 degrees out of phase, but there are also in perfect sync. In this interpretation (If you can call it that) being in sync makes them part of the same object.

Then an atom, with all its protons, neutrons and electrons, if all of them are in sync, the whole atom is one object. If you treat it gently, it reacts as one object. Same for molecules that are treated gently. So you can send molecules gently through a double slit and get a diffraction pattern.

Timing also explains entanglement in this interpretation (if I can call it that) two electrons in perfect sync are entangled, thus become part of the same object. It seems intuitively reasonable that measurement of one can affect the other with all I am saying.

There's another problem with it as well, one which is not obvious with electrons in atoms, but which is made evident by experiments run on free electrons. Schrodinger encountered this issue when he originally attempted to construct an interpretation of an electron's wave function similar to yours: he basically said the electron was a little packet of charge density, whose shape was described by its wave function. The problem with this was that when electrons are actually detected--for example, when they hit the screen of a cathode ray tube (which is unfortunately not as easy to give an everyday life example of now that TVs with picture tubes are no longer common )--they are always detected as little dots, which in general bear no resemblance to the wave function they had just before the detection.

Yeah, that's one of the main points. They are instantly reformable packets, all part of one object. When they hit the detector screen, they deposit all their energy into one spot. How big? depends on the mutual wavelength. They instantly become a small packet, or get absorbed, as in photons get absorbed (annihilated).

For example, electron diffraction experiments showed a wavelike pattern similar to that shown when light is diffracted, but with the intensity of the electron source turned down sufficiently, the pattern always resolved into individual dots, which only formed the complete pattern over time as the results of many runs were accumulated. (This also happens with light when the intensity of the source is turned down sufficiently, by the way.) But the wave function describing each electron has the shape of the diffraction pattern, not of a single dot. This was a key observation that made Schrodinger's interpretation untenable, and led to Born proposing the interpretation of the wave function as a probability amplitude.

Again, instantly reformable wave packets, all part of "one thing".

Just to be clear: I am not saying that there is some other QM interpretation that tells a consistent, intuitively satisfying story about all quantum experiments. There isn't; that's why there is no consensus among physicists about QM interpretations. For physicists doing active work in the field, they generally either remain agnostic about interpretations, or use whichever one seems most appropriate for the particular experiment they are doing or the particular theoretical model they are working on. But for high school students, I really think the best approach is to not adopt any particular interpretation, but to just tell students that there is no consensus about QM interpretations and leave it at that. If the students get really curious about interpretations, you could cover some of the most studied ones.

I agree with introducing multiple interpretations, I would just rather have one that tells an intuitive story. As you say, there isn't one (except possibly mine, hah!) so I thought I'd take a stab at it. No harm in that. :)

 

[PeterDonis]

The idea is that electrons in the same orbital are always 180 degrees out of phase.

No, that's not correct. They have opposite spins, but this has nothing whatever to do with the phase of their spatial wave functions, which is what the orbitals give you the shape of. The spins of the electrons are separate degrees of freedom from the configuration space (position-momentum) degrees of freedom.

In other words, the "intuitive story" you are trying to tell won't work.

I would just rather have one that tells an intuitive story. As you say, there isn't one

Which means you should not be trying to tell one. And, as we've said, you should definitely not be trying to make one up. You should be up front with your students that there is no intuitive story to be told.

No harm in that. :)

Yes, there is. If you try to make up an intuitive story to tell your students, instead of being up front with them about there not being any intuitive story to tell, you will be doing them a serious disservice.

 

[PeterDonis]

instantly reformable packets

This intuitive story doesn't work either. If you read up on Schrodinger's attempt to construct an interpretation of this sort (the one I referred to earlier, where he tried to interpret the electron as a packet of charge density with the shape of its wave function), you will find that he failed because, among other things, a wave packet can't instantaneously change its shape. The equations don't allow it. So "instantly reformable packets" are not consistent with QM.

 

[PeterDonis]

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