Happy New Year! 2025 is the centenary of some very important events in the development of quantum physics — the birth of new insights, of new mathematics, and of great misconceptions. For this reason, I’ve decided that this year I’ll devote more of this blog to quantum fundamentals, and take on some of the tricky issues that I carefully avoided in my recent book.
My focus will be on very basic questions, such as: How does quantum physics work, to the extent we humans understand it? Which of the widely-held and widely-promulgated ideas about quantum weirdness are true? And for those that aren’t, what is the right way to think about them?
I’ll frame some of this discussion in the context of the quantum two-slit experiment, because
- it’s famous,
- it’s often poorly explained
- it’s often poorly understood,
- it highlights (when properly understood) an extraordinarily strange aspect of quantum physics.
Not that I’ll cover this subject all in one post… far from it! It’s going to take quite some time.
The Visualization Problem
We humans often prefer to understand things visually. The problem with explaining quantum physics, aside from the fact that no one understands it 100%, is that all but the ultra-simplest problems are impossible to depict in an image or animation. This forces us to use words instead. Unfortunately, words are inherently misleading. Even when partial visual depictions are possible, they too are almost always misleading. (Math is helpful, but not as much as you’d think; it’s usually subtle and complicated, too.) So communication and clear thinking are big challenges throughout quantum physics.
These difficulties lead to many widespread misconceptions (some of which I myself suffered from when I was a student first learning the subject.) For instance, one of the most prevalent and problematic, common among undergraduates taking courses in chemistry or atomic physics, is the wrong idea that each elementary particle has its own wavefunction — a function which tells us the probability of where it might currently be located. This confusion arises, as much as anything else, from a visualization challenge.
Consider the quantum physics of the three electrons in a lithium atom. If you’ve read anything about quantum physics, you may have been led to believe that that each of the three electrons has a wave function, describing its behavior in three-dimensional space. In other words,
- naively the system would be described by three wave functions, each in three dimensions; each electron’s wave function tells us the probability that it is located at this point or that one;
- but in fact the three electrons are described by one wave function in nine dimensions, telling us simultaneously the overall probability that the first electron is t be found at this point, the second at that point, and the third at some other point.
Unfortunately, drawing something that exists in nine dimensions is impossible! Three wave functions in three dimensions is much easier to draw, and so, as a compromise/approximation that has some merits but is very confusing, that method of depiction is widely used in images of multiple electrons. Here, for instance, two of the lithium atom’s electrons are depicted as though they have wave functions sharing the yellow region (the “inner shell”), while the third is drawn as though it has a wave function occuping the [somewhat overlapping] blue region (the “next shell”). [The atomic nucleus is shown in red, but far larger than it actually is.] Something similar is done in this image of the electrons in oxygen from a chemistry class.)
Yet the meat of the quantum lithium atom lies in the fact that there’s actually only one wave function for the entire system, not three. Most notably, the Pauli exclusion principle, which is responsible for keeping the electrons from all doing the same things and leads to the shell-like structure, makes sense only because there’s only one wave function for the system. And so, the usual visual depictions of the three electrons in the atom are all inherently misleading.
Yet there’s no visual image that can replace them that is both correct and practical. And that’s a real problem.
That said, it is possible to use visual images for two objects traveling in one dimension, as I did in a recent article that explains what it means for a system of two particles to have only one wave function. But for today, we can set this particular issue aside.
What We Can’t Draw Can Hurt Our Brains
Like most interesting experiments, the underyling quantum physics of the quantum double slit experiment cannot be properly drawn. But depicting it somehow, or at least parts of it, will be crucial in understanding how it works. Most existing images that are made to try to explain it leave out important conceptual points. The challenge for me — not yet solved — is to find a better one.
In this post, I’ll start the process, opening a conversation with readers about what people do and don’t understand about this experiment, about what’s often said about it that is misleading or even wrong, and about why it’s so hard to draw anything that properly represents it. Over the year I expect to come back to the subject occasionally. With luck, I’ll find a way to describe this experiment to my satisfaction, and maybe yours, before the end of the year. I don’t know if I’ll succeed. Even if I do, the end product won’t be short, sweet and simple.
But let’s start at the beginning, with the conventional story of the quantum double-slit experiment. The goal here is not so much to explain the experiment — there are many descriptions of it on the internet — but rather to focus on exactly what we say and think about it. So I encourage you to read slowly and pay very close attention; in this business, every word can matter.
Observing the Two Slits and the Screen
We begin by throwing an ultra-microscopic object — perhaps a photon, or an electron, or a neutrino — toward a wall with two narrow, closely spaced slits cut in it. (The details of how we do this are not very important, although we do need to choose the slits and the distance to the screen with some care.) If the object manages to pass through the wall, then on the other side it continues onward until it hits a phosphorescent screen. Where it strikes the screen, the screen lights up. This is illustrated in Fig. 1, where several such objects are showing being sent outward from the left; a few pass through the slits and cause the screen to light up where they arrive.
If we do this many times and watch the screen, we’ll see flashes randomly around the screen, something like what is shown in Fig. 2:
But now let’s keep a record of where the flashes on the screen appear; that’s shown in Fig. 3, where new flashes are shown in orange and past flashes are shown in blue. When we do this, we’ll see a strange pattern emerge, seen not in each individual flash but over many flashes, growing clearer as the number of flashes increases. This pattern is not simply a copy of the shape of the two slits.
After a couple of thousand flashes, we’ll recognize that the pattern is characteristic of something known as interference (discussed further in Figs. 6-7 below):
By the way, there’s nothing hypothetical about this. Performing this experiment is not easy, because both the source of the objects and the screen are delicate and expensive. But I’ve seen it done, and I can confirm that what I’ve told you is exactly what one observes.
Trying to Interpret the Observations
The question is: given what is observed, what is actually happening as these microscopic objects proceed from source through slits to screen? and what can we infer about their basic properties?
We can conclude right away that the objects are not like bullets — not like “particles” in the traditional sense of a localized object that travels upon a definite path. If we fired bullets or threw tiny balls at the slitted wall, the bullets or balls would pass through the two slits and leave two slit-shaped images on the screen behind them, as in Fig. 5.
Nor are these objects ripples, meaning “waves” of some sort. Caution! Here I mean what scientists and recording engineers mean by “wave”: not a single wave crest such as you’d surf at a beach, but rather something that is typically a series of wave crests and troughs. (Sometimes we call this a “wave set” in ordinary English.)
If each object were like a wave, we’d see no dot-like flashes. Instead each object would leave the interference pattern seen in Fig. 4. This is illustrated in Fig. 6 and explained in Fig. 7. A wave (consisting of multiple crests and troughs) approaches the slits from the left in Fig. 6. After it passes through the slits, a striking pattern appears on the screen, with roughly equally spaced bright and dark regions, the brightest one in the center.
Where does the interference pattern come from? This is clearest if we look at the system from above, as in Fig. 7. The wave is coming in from the left, as a linear set of ripples, with crests in blue-green and troughs in red. The wall (represented in yellow) has two slits, from which emerge two sets of circular ripples. These ripples add and subtract from one another, making a complex, beautiful “interference” pattern. When this pattern reaches the screen at the opposite wall, it creates a pattern on the screen similar to that sketched in Fig. 6, with some areas that actively flicker separated by areas that are always dark.
It’s important to notice that the center of the phosphorescent screen is dark in Fig. 5 and bright in Fig. 6. The difference between particle-like bullets and wave-like ripples is stark.
And yet, whatever objects we’re dealing with in Figs. 2-4, they are clearly neither like the balls of Fig. 5 nor the waves of Fig. 6. Their arrival is marked with individual flashes, and the interference pattern builds up flash by flash; one object alone does not reveal the pattern. Strangely, each object seems to “know” about the pattern. After all, each one, independently, manages to avoid the dark zones and to aim for one of the bright zones.
How can these objects do this? What are they?
What Are These Objects?!
According to the conventional wisdom, Fig. 2 proves that the objects are somewhat like particles. When each object hits the wall, it instantaneously causes a single, tiny, localized flash on the screen, showing that it is itself a single, tiny, point-like object. It’s like a bullet leaving a bullet-hole: localized, sudden, and individual.
According to the conventional wisdom, Figs. 3-4 prove that the objects are somewhat like waves. They leave the same pattern that we would see if ocean swell were passing through two gaps in a harbor’s breakwater, as in Fig. 7. Interference patterns are characteristic only of waves. And because the interference pattern builds up over many independent flashes, occurring at different times, each object seems to “know,” independent of the others, what the interference pattern is. The logical conclusion is that each object interferes with itself, just as the waves of Figs. 6-7 do; otherwise how could each object “know” anything about the pattern? Interfering with oneself is something a wave can do, but a bullet or ball or anything else particle-like certainly cannot.
To review:
- A set of particles going through two slits wouldn’t leave an interference pattern; it would leave the pattern we’d expect of a set of bullets, as in Fig. 5.
- But waves going through two slits wouldn’t leave individual flashes on a screen; each wave would interfere with itself and leave activity all over the screen, with stronger and weaker effects in a predictable interference pattern, as in Figs. 6-7.
It’s as though the object is a wave when it goes through and past the slits, and turns into a particle before it hits the screen. (Note my careful use of the words “as though”; I did not say that’s what actually happens.)
And thus, according to the conventional wisdom, each object going through the slits is… well… depending on who you talk to or read…
- both a wave and a particle, or
- sometimes a wave and sometimes a particle, or
- equally wave and particle, or
- a thing with wave-like properties and with particle-like properties, or
- a particle-like thing described by a probability-wave (also known as a “wave function”), or
- a wave-like thing that can only be absorbed like a particle, or…
- ???
So… which is it?
Or is it any of the above?
Looking More Closely
We could try to explore this further. For instance, we could try to look more closely at what is going on, by asking whether our object is a particle that goes through one slit or is a wave that goes through both.
But the very process of looking at the object to see what slit it went through changes the interference pattern of Figs. 4 and 6 into the pattern in Fig. 5, shown in Fig. 9, that we’d expect for particles. We find two blobs, one for each slit, and no noticeable interference. It’s as though, by looking at an ocean wave, we turned it into a bullet, whereas when we don’t look at the ocean wave, it remains an ocean wave as it goes through the gaps, and only somehow coalesces into a bullet before it hits (or as it hits) the screen.
Said another way: it seems we cannot passively look at the objects. Looking at them is an active process, and it changes how they behave.
So this really doesn’t clarify anything. If anything, it muddies the waters further.
What sense can we make of this?
Before we even begin to try to make a coherent understanding out of this diverse set of observations, we’d better double-check that the logic of the conventional wisdom is accurate in the first place. To do that, each of us should read very carefully and think very hard about what has been observed and what has been written about it. For instance, in the list of possible interpretations given above, do the words “particle” and “wave” always mean what we think they do? They have multiple meanings even in English, so are we all thinking and meaning the same thing when we describe something as, say, “sometimes a wave and sometimes a particle”?
If we are very careful about what is observed and what is inferred from what is observed, as well as the details of language used to communicate that information, we may well worry about secret and perhaps unjustified assumptions lurking in the conventional wisdom.
For instance, does the object’s behavior at the screen, as in Fig. 2, really resemble a bullet hitting a wall? Is its interaction with the screen really instantaneous and tiny? Are its effects really localized and sudden?
Exactly how localized and sudden are they?
All we saw at the screen is a flash that is fast by human standards, and localized by human standards. But why would we apply human standards to something that might be smaller than an atom? Should we instead be judging speed and size using atomic standards? Perhaps even the standards of tiny atomic nuclei?
If our objects are among those things usually called “elementary particles” — such as photons, electrons, or neutrinos — then the very naming of these objects as “elementary particles” seems to imply that they are smaller than an atom, and even than an atom’s nucleus. But do the observations shown in Fig. 2 actually give some evidence that this is true? And if not… well, what do they show?
What do we precisely mean by “particle”? By “elementary particle”? By “subatomic particle”?
What actually happened at the slits? at the screen? between them? Can we even say, or know?
These are among the serious questions that face us. Something strange is going on, that’s for sure. But if we can’t first get our language, our logic, and our thinking straight — and as a writer, if I don’t choose and place every single word with great care — we haven’t a hope of collectively making sense of quantum physics. And that’s why this on-and-off discussion will take us all of 2025, at a minimum. Maybe it will take the rest of the decade. This is a challenge for the human mind, both for novices and for experts.
95 Responses
I recently read David Deutsch’s The Fabric of Reality quite an old book now.
His explanation of the Double Slit Exp I find quite satisfying. In that what we consider to be a single photon is actually a multiversal object, an infinite number of particles that are entangled, and so interact or interfere with themselves as they travel through the slits, but when we measure the particle at the screen we effectively only see one of these particles in our universe.
I may have misinterpreted but it seems so simple an explanation. Do you share this view or has it been superceded?
There are many interpretations out there, and I don’t know them all. Of those I know, each one moves the problem from one place to another, and does not resolve it. I don’t know Deutsch’s personal interpretation, but I’ve never heard another expert suggest that he has resolved the problem. (After all, each book on the subject explains the benefits of the author’s perspective but not the critique of that perspective, so it may sound better than it really is.)
In general, if you make one problem easy, you do it by adding in superstructure (such as multiversal objects) for which there is both conceptual baggage and no experimental evidence. The Everettian many-worlds interpretation is a great example of this.
My goal here is not to give you an interpretation but a clearer understanding of the problem. Right now the language you are using is potentially ambiguous; for instance, what is the object in the first place that is said to be multiversal?
Thanks for your reply.
I will endeavour to be less ambiguous!
I look forward to reading your take on the problem.
I’ve just read your latest book, and thought you succeeded admirably in clearly explaining particles, waves and wavicles!
Being less ambiguous with quantum physics is both necessary and difficult; I have my work cut out for me here!
Thanks for your kind thoughts on the book. I have supplemented some of that discussion with additional posts on this blog that you may find interesting, such as https://profmattstrassler.com/2024/07/09/particles-waves-and-wavicles/ , https://profmattstrassler.com/2024/07/11/a-particle-and-a-wavicle-fall-into-a-well/ , and https://profmattstrassler.com/2024/07/22/the-standard-model-more-deeply-how-the-proton-is-greater-than-the-sum-of-its-parts/ .
Many thanks.
I am an illustrator, and so its my job to illustrate a text as clearly as I can. To do this I initially visualise many versions of an illustration first in my mind, and then reject as many as I can. In order to end up with something which fulfills the brief.
It seems like you are in a similar situation. There are an infinity of ways of explaining a complex reality, and you must reject those that do not fit with the current theories, and also reject those that are not clear. So you end up with a better explanation.
My question for you is how do you judge unclear explanations? How do you reject them?
You may already do this, but perhaps having feedback somehow specifically on the clarity, by lay people would allow rejection of worse explanations.
One of the reasons I have this blog is for feedback about pedagogical clarity. Over the years, my pedagogical approaches to various notions have evolved both because of my own efforts to explain them here to a wide audience and because of the feedback I receive from readers of both book and blog. It’s been immensely useful to my teaching, and sometimes even to my own thinking about the universe. I’m sure the way I explain quantum physics will be different by the end of 2025 than it is right now, and maybe I’ll even think about it differently.
Explanations can fail for various reasons; clarity is just one of them. I’m always looking for linguistic ambiguity or a lack of precision, but there’s more to it. Fundamentally, I’m always guided by the underlying mathematics of quantum field theory, which is precise and which I know extremely well; that’s what gives me an advantage over most writers on this subject, because they’re always in danger of straying from the math, and from the knowledge about the cosmos that it encapsulates.
If the language of an explanation disagrees with the math, or could be seen to disagree with the math, then the language isn’t clear enough. And if an explanation requires some compromises and omissions for brevity, as many do, then any compromises/omissions that would cause the explanation to disagree with the math must be carefully evaluated. I always think carefully about whether they are misleading in important ways, ones that would be difficult to correct later in a more detailed article for those who want to learn more, including future physics students.
My guiding principle is that all explanations must be correct, in the sense that any compromises I make, and any language I use, should be defensible in front of a panel of theoretical physicists like myself. Even if they might disagree with my pedagogical choices, I expect the members of this imaginary panel to agree that my choices have been consistent and accurate at all times.
Matt, I think it’s quite simple. Art Hobson wrote about it, see https://arxiv.org/abs/1204.4616. The electron goes through both slits, but the act of detection performs something similar to the optical Fourier transform, so you see a dot on the screen. Then if you try to detect the electron at one slit, the act of detection performs something similar to the optical Fourier transform, so the electron goes through one slit only. Hence you lose the interference pattern.
If you read carefully, even in the abstract, you’ll see Hobson does not claim to have solved the problem. He only claims to address the simpler question: ” Are the fundamental constituents fields or particles? ”
He and I agree that the answer is “fields”, though I don’t agree with some of his methodology.
He and I also agree that knowing the answer does not resolve the conceptual puzzles of the double-slit experiment, and of many other quantum phenomena.
I read Art Hobson’s article carefully. That’s because I’d already looked into the issue and wrote about it, see https://physicsdefective.com/the-double-slit-experiment/. IMHO you can make sense of quantum physics. IMHO it’s simpler than you think.
John, be serious; your opinion, is never, never H.
Dr.Strassler:
As you stated, the reason why macroscopic objects only go thru one slit, is because any interaction with the environment, before it gets there, effectively determines its position.
What if we have a multiple atom object? Aren’t atoms, say in a molecule, continuously exchanging information / interacting with each other? Aren’t atoms in a molecule that is vibrating along is bonds, rotating along its axis, exchanging information? In other words, wouldn’t any kind of thermal motion, of the molecule itself, destroy the quantum effect?
The word “environment” is key, and so is the fact that the two slits are a macroscopic distance apart.
No matter how large an object, if it is strictly isolated from its environment, it can maintain its quantum state. That quantum state can defy classical (i.e. non-quantum, ordinary intuition.) See for instance https://www.scientificamerican.com/article/physicists-create-biggest-ever-schroedingers-cat/
But any realistic macroscopic object that is not being treated with extreme tender love and care in a laboratory has insanely many interactions with its environment — vastly more than those between the atoms within a molecule. A little ball of cross section 1 cm^2 in sunlight has 10^19 interactions per second with visible light photons from the Sun, each one of which helps to establish the shadow on the floor, where the floor is slightly cooler, with the effect that this temperature difference propagates outward and creates small stresses that cause billions of atoms to shift their positions — and so the fact that the object headed toward one slit and not the other is now stored in a gargantuan number of places with no hope of ever coming back to interact with the source that caused them. Some of the photons reflect off the ball and go flying out into space, carrying information about the ball’s position to the Moon and off to distant stars. This is an “open system”; information rapidly leaks out and is never recovered.
Only a “closed system”, isolated from its environment, can maintain quantum coherence and all of the information inherent in a quantum state. So the issue is not how big is your molecule; the issue is what else is it interacting with and how often and how strongly.
If the slits were microscopically close together, it would eventually become difficult for the environment to determine which slit the ball was headed for; but of course this would also require a microscopic ball, and so we have moved out of the range of my original point.
Dr.Stassler:
This leads to my second question, how come the slits themselves aren’t considered detectors? If one solitary atom in the slits records the passage, wouldn’t that be information? Or, when shooting single photons thru, does the slit indeed record the passage….sometimes…..but this is just blended into the interference pattern?
The interference pattern is caused by the photons that go through the slits without interacting with the wall in which they are cut. Other photons are mostly absorbed by the wall. Just a tiny, tiny fraction are affected by the edges of the slits; consider how little area the slit edges occupy. The slits — the gaps, I mean — occupy much more area.
Sometimes the atoms at the edge of a slit might absorb a photon, but then it isn’t observed at the screen. Or sometimes they might deflect a photon, which means they absorb the photon and emit another (or more than one) with somewhat lower energy. But that will be very rare and won’t observably affect the interference pattern.
Either way, this does not mean that a slit (or rather, the edges of the slit or the wall in which they are cut) are to be understood as detectors, at least not in any simple sense. They do cause loss of quantum coherence if they interact with the photon, but a detector is something more special than that. A detector records information in a semi-permament, readable sense. This is even an issue in classical physics; just because you create wind in the air as you run through it does not mean that your presence has been stored by the air in a form that can be read out a minute later.
Someone else asked the same question and we’ll have to look carefully at what detectors are soon. Your brain is one, so it’s particularly important to understand what makes it different from, say, a glass of water, or a wall with slits cut in it.
Dr.Strassler:
If a detector is placed, to determine which slit, the interference pattern vanishes, and the photons appear directly behind the slits, as one would expect for a photon passing thru the gap, without interacting with the edges, and not being deflected.
This leads to my third question:
Without the detector, the photons that pass thru the slits, WITHOUT INTERACTING with the edges of the slit, appear displaced off to the sides of the slit…..the interference pattern. How is momentum conserved?
Well, no, the first statement isn’t really true in general. I oversimplified (because I was reporting what the conventional wisdom says about the double-slit experiment.) What is actually seen depends how the photon detector behind the slit actually works. In fact what is seen may be a single-slit diffraction pattern, or something more complex.
As for your second question: let’s be precise. The photons are not dots that pass through the slits. They are wavicles, with a wave-like shape. They must gently interact with the wall even to “determine” or “find” where the slits are; after all, if the slits weren’t there, each photon would be absorbed or reflected with 100% probability. Even with the slits, each photon only has a finite probability of going through the slits. And so the wall as a whole, including the region between the two slits, can change the photon’s shape, absorbing momentum in the process. That is not the same as absorbing the photon and reemitting it, which would be an atomic-level event in which an atom would jump to a different atomic state.
You can see this in Figure 7 in this post. To the left, the waves have a definite right-ward momentum. As they pass through the slits, the fact that the wall blocks the wave everywhere except where the slits are present changes the shape of the wave, and the momentum now becomes indefinite, moving out in all directions (even if predominantly right-ward) from the slit. And so the photons have lost an indefinite amount of momentum to the wall, and no longer have definite momentum, allowing them to appear all over the screen.
To say it another way, it’s the standard uncertainty principle for waves. The waves initially have definite momentum and completely indefinite position. The slits then constrain the position along the wall, making it more definite; this automatically causes the momentum parallel to the wall to become less definite. So your assumption that a photon that goes through the slit maintains its momentum is a particle picture of a photon. That’s why I keep telling you that you need to understand it as a wavicle; it never behaves exactly like a particle, and this is a clear example of where that intuition will lead you astray.
Great question, though.
Dr.Strassler:
Ok, that makes sense. I realize the photons aren’t dot, but wavicles. Your use of the term “wavicle” gave me the best understanding of what is going on, and really helped me with the concept. I was just looking at it from the standpoint that when a single photon arrives at the wall, it appears as a dot…..not smeared out, and the interference pattern appears only after many many photons are shot at the wall. BTW, your book, which I have read cover to cover, sits on my shelf, right next to my Feynman lectures.
Good… but at the risk of telling you what you already know, note the imprecision in your words. (a) the photon creates a localized flash when it reaches the *screen* (I think that’s what you meant, but it’s important not to confuse the wall and the screen in this experiment) and (b) just because the photon creates a flash that is small on human scales does not mean that the photon is, at that moment, a little dot.
I’m under the impression that a photon entering a slit isn’t the same photon detected at the screen. Is this correct?
Also, does the weirdness of the double slit experiment disappear within QFT where the slits are viewed as fields interacting with the electromagnetic fields of the photons?
No.
You can send one photon at a time through the slits. One photon at a time arrives at the screen. Now, were they the same?
All photons are identical; you can’t put a flag on one and follow it around. The only way to say the one before the slit is different from the one at the screen would be to show that the one reaching the slit disappeared for a certain measurable amount of time, and a second one appeared at a substantially later time. But there’s no evidence of that; the photon travels at light speed from source to screen, without any delays involving disappearance and appearance. Indeed, the very act of trying to do a measurement to find out if the two photons are somehow different would ruin the interference pattern.
Quantum field theory says it’s a one particle problem, and there’s no need to invoke a second particle for this effect to occur. That, of course, is theory. But the theory works rather impressively well.
So there’s no experimental evidence that this is true, some evidence that it is false, and no way to prove it true without changing the problem. That said, I think that with the right device I could prove it false. If the source is a material that emits X-rays and the screen detects X-rays, but the slit is made of ordinary material that can’t emit X-rays, then how is an atom of this material going to absorb one X-ray and emit a second? And if not from an atom, where does this second X-ray come from? Doesn’t make much sense.
QFT does not eliminate the weirdness. It just changes the way you think about the problem by making it a lot harder to formulate precisely, and by forcing you to understand that photons (or electrons if you use them) are wavicles, never particles. We’re months off from getting to that issue.
I started making sense of this experiment thanks to the Feynman lectures, and I can’t wait to see the next episodes in this blog!
I hope I can get an answer to a question that puzzles me. Are not the slits a “detector”? Why the slit itself is not collapsing the wave function?
Thanks
Andrea
Ah, yes, this is a fantastic question! What makes something a detector?
This is a critical issue in understanding quantum physics. I’ll have to address it — but I’ll have to first figure out the simplest way to do so.
Is it possible to get a single wave function for an entire atom including the nucleus (with or without QCD)?
Thank you for your time prof!
Hmm… what do you mean by “get”? Do you mean “write down explicitly in math”? Or do you mean “have conceptually?”
Conceptually it’s no problem; if the atom is isolated from the rest of the world, then yes, it is described by one and only one wave function. If it isn’t isolated from the rest of the world, then, no, we have to include everything that interacts with it in order to have a wave function for the whole system.
Mathematically, the problem with trying to write something down explicitly is that we can’t even do that for a helium atom’s two electrons. Oh sure, in atomic physics classes and advanced chemistry classes, we might write down an approximation, where we try to write the wave function for the electrons using what is known as a Slater determinant over a product of single-particle states; perhaps you’ve seen that. But this is not what a real wave function actually looks like mathematically; it’s generally much more complicated, because the electrons interact with each other and they are not found in single-particle states.
Adding in the nucleus to the eletrons is no problem if we treat it as a single object. If we start to look inside it, first paying attention to the protons and neutrons and then to the fact that they’re made of quarks and gluons, the math gets worse and worse and worse — not only harder to calculate but harder even to write down.
Said another way: even in 1920s quantum theory, the wave function of an object that contains N particles is a complicated function of 3N variables. That means that an oxygen atom, with 8 electrons, 8 protons and 8 neutrons — even ignoring the quarks and gluons inside those protons and neutrons — is a function of 72 variables. That’s right, 72. Calculating this function precisely is supercomputer territory; writing down the answer in any human-useful form would be extraordinarily difficult; visualizing it properly is impossible. And this is for one, isolated, not particularly complex atom, described using 1920s methods without including the effects of quantum field theory.
Wave functions for field theory, where there a field variable at each location in space and thus N is gargantuan, are much worse. They are so awful to contemplate they they are almost never used. Different methodology proves essential.
It is well nigh impossible to visualize what is happening in ordinary classical pictures since the key non-classical concept in QM (and QFT too) is superposition. And superposition should not be interpreted like the addition of classical (electomagnetic, water, sound,…) waves but as the quantum particle (wavicle or quanton) becoming indefinite (with various amplitudes) between the definite eigen-states in the superposition. Any working (non-philosophical) quantum theorist who understands that a particle in a superposition state does not have a definite value prior to a “measurement” or state reduction–must at least implicitly imply that there is an quantum realm of indefiniteness (like the underwater part of an iceberg). Heisenberg, Shimony, and many others termed the “underwater” part as “potentiality” as opposed to definite actuality but it raises fewer metaphysical questions to just think of it in terms of indefinite actuality versus definite actuality. To better visualize what is happening in the double-slit experiment or in state reduction, it is better to use a pedagogical (or “toy”) model where the state vectors are replaced by just their support sets (set of eigenstates with non-zero coefficients in the superposition) and then to work with support sets as elements of a vector space over Z2 that still models the double-slit experiment and many other QM features (state reduction, unitary evolution, entanglement, Bell’s Theorem) all in a form that is much simplified but still “true enough” to the full Hilbert space math to make a good pedagogical model. For instance, the key mystery in the 2-slit experiment is how to answer the question of which slit did the particle go through in the no-detection case. Feynman points out that if the particle actually went through one slit or the other (even though undetected) then there would be no interference pattern so he states clearly that the particle does not go through one slit or the other (Character of Physical Law, pp. 139-40). All those statement are as if there was only the above-water part of the “iceberg” with everything is definite. What actually happens is that the superposition (slit 1 + slit 2) does not rise to the level of definiteness of going through one slit or the other, but stays as a superposition that unitarily evolves (all at the underwater level using that metaphor) yielding the interference pattern at the detection screen when it emerges (above water) as being definitely hitting one spot. This is all dealt with in my recent book “Partitions, Objective Indefiniteness, and Quantum Reality” but in much shorter and less mathy terms in a paper anyone can download at: https://ellerman.org/wp-content/uploads/2025/01/UnderstandingQM2.pdf,
Fantastic! Problem solved! It’s wonderful how my blog attracts so many people smarter than Feynman himself (and wildly smarter than me!) I can stop all my discussion at this point.
But hey, why don’t you (who have solved the problem) and Mr. Gantsevich a.k.a. Paulis Butlers (who has also solved the problem — his comments are below) — have a discussion about this (by email or Zoom or whatever, but *not* on my blog).
Of course, you have two completely different and incompatible solutions to the problem, so at least one of you is wrong. So have a chat, and when you have agreed which one of you is wrong and which of you is right, come back to me and tell me who it was.
Banishing of mysteries.
Dirac rigorously and logically introduces the ket-vectorsand the bra-vectors as well as the bracket: .Thisbracket describes the physically observable quantities. Itclearly shows that we need two quantities (bra and ket) fortheir adequate description. Unfortunately, Dirac concluded thatin interpreting QM one can use the vector bra or the vectorket. This wrong or instead of right and (much better together)was the fatal error. Generally accepted it prevented the rationalunderstanding of QM without mysteries since the adequatedescription of all observed QM phenomena only in the ket language is impossible in principle.It is the same as trying to march using only one leg. Belowwe show how the addition of the second leg makes marchingquite easy.We can imagine the potentially observed quantum object(wavicle) as a bra+ket pair in the bracket of any observablequantity. Being solutions of the Schrödinger equation braand ket have phases so the bracket also has the phase as thedifference between bra and ket phases. The wavicle interference with itself (the main QM secret according to Feynman) also reduces to triviality: no interference occurs when the wavicle bra and ket go the same way (andform the phase-independent constant background on the screen). When they go different ways then they acquire a phase difference and produce phase-dependent wavicle. The wavicles with phase contribute to positive or negative fluctuations over the constant background which participate in constructive and destructive interference.
Gantsevich SV (2022) Common sense and quantum mechanics. Ann Math Phys 5(2): 196-0198. DOI: 10.17352/amp.000066
These are very impressive declarations. Too bad they don’t make sense, at least not in English.
Mr Gantsevich, my website is not the forum for you to advertise your personal view of the universe and how it works. Maybe you’ll convince some other people some day; but you’ve made your claims, and that’s enough.
Thank you for clarifying some important details I hadn’t heard before – 1) there is only “one wave function for the entire system” under consideration; 2) “all the fields and their ripples are described by one and only one wave function”; 3) “As you make the slits further apart, the interference pattern becomes harder to observe. ‘It’s still there, though'”; 4) “The reason that macroscopic objects go through only one slit is that they interact with the air and the light in the room every tiny fraction of a second, which effectively measures where they are long before they even reach the two slits”.
It seems we’re always “inside” the wavefunction of a system in which we measure/interact; otherwise we couldn’t see the affects of the measurement/interaction. The two-slit experiment has this wall with two slits that is measuring/interacting-with the objects being sent toward a screen (which is also measuring/interacting).
Is it useful to think that the “two-slit” experiment is also like an “object with emptiness around it and then objects further out” experiment? Like an electron shot at a mass of atoms can be thought of as an electron shot at an atom (with an electron cloud) and there’s space on each side until it reaches the next atoms on each side? I.e. a two-slit experiment? This makes the two-slit experiment nothing unusual; in fact it’s happening all the time, isn’t it? If so, then it makes it not a special case, but the ordinary one. And the case that has to fit the math in even the most common interaction, like a photon hitting an electron.
I think what you’re asking about in your last paragraph is about keeping objects isolated and therefore quantum mechanically coherent. This is one of the key problems in a quantum computer; it must be highly isolated from its environment, because any interaction with the environment will potentially screw up the calculation. This fragility of quantum phenomena is precisely why they are so hard to observe outside of a laboratory.
And yes, you are correct: the two slit experiment is just a particularly famous but perfectly ordinary example of interference and correlation of a sort that we can’t visualize well or make logical sense of. Similarly, Schrodinger’s cat involves perfectly ordinary correlations, made both famous and macroscopic by careful engineering. These famous cases are useful in helping us highlight what is tricky and profoundly confusing (vs what seems tricky but actually isn’t) in quantum physics.
I am looking forward to your development.
Since I have generally thought about consecutive Stern-Gerlach experiment, I remain dumbfounded about two-slit experiments.
However, if we are “inside the wave” (the quantum field, I presume), the failure of “logical” reasoning lies with thinking of particles as “movable points” (discerning a cause of motion must requires a dichotomy between static and dynamic). We naturally associate a movable point with geometric points whose indivisibility is understood in metric terms. That is, we expect to speak of one point when visualizing zero-length displacements.
Even this is wrong, though. Singletons on a number line assume nested closed sets. A nesting of non-closed sets would be ambiguous in some way (actually, one may interpret Kolgomorov’s probability axiom for continuous probabilities in terms of nested non-closed sets).
But, if we are “inside the wave,” then part of our problem lies with how the mathematics we use for waves relates to the topology of our intuitive number lines.
What we learn for Fourier analysis is inadequate. The general theory of trigonometric series is a more expansive topic with several distinct conceptions of convergence. Fourier analysis is based upon recreating algebraic structure. No one has ever produced an algebraic proof of the fundamental theorem of algebra. Not all mathematics is algebra.
Most people have never heard of sets of uniqueness from the theory of trigonometric series. Cantor studied them. Cohen studied them. Apparently, when considered with topological notions like closed sets, the theory of distributions arises naturally,
https://en.m.wikipedia.org/wiki/Set_of_uniqueness#Singular_distributions
I cannot say whether or not a closed set of uniqueness ought to be the analogue of a closed singleton on a number line. Nor have I sorted through the all of the calculation techniques used by physicists — I hesitate to call it mathematics. So, I am unaware of direct relationship to the distributions significant to physics. But, sets of uniqueness do provide an immediate sense of how intuitive reasoning about particles fail when the mathematics is done in function spaces and the functions are described with trigonometric series.
No, I said we are “inside the wave function.” Wave functions and fields are completely different things: the former is a function on the space of all possibilities, and there is only one, while a field is a function of physical three-dimensional space, and there are many such fields. We are built out of ripples of the fields (that’s what “particles” [or “wavicles”, if you prefer] are), but all the fields and their ripples are described by one and only one wave function.
Thank you for the correction. I suppose my “inside the wave” ought to have been “inside the SMFs” (Standard Model Fields). I have written that in the plural because my recollection of the book discussion is that the “wavicle” designations are better understood as differentiating fields.
I would like to note two things, though. Maybe they are in error too.
Your post speaks of “objects.” Unfortunately, this is an ontological question, and, I think that your use of ‘wavicle’ ought to remain ambiguous in some manner. My remarks had been very specific about classical perspectives of ‘particle’ as an object in relation to the standard metric topology in a real space. I would hope that these deliberations on wavicles would lead to some differentiation from the classical view.
With regard to “the space of all possibilities” in your reply, I wonder if we do not need to be more careful. There are modal logics dealing with possibility and necessity. Moreover, the S4 logic is immediately related to topological spaces. By contrast, the first attempt at formulating a “quantum logic” had been done by Birkhoff and von Neumann. The lattice algebra underlying this logic is motivated by “the possible experimental outcomes” with which calculations in physics must accomodate. These are two very different ways of thinking about how to approach explanations for quantum phenomena.
Some time ago Peter Woit asked where probability enters quantum mechanics. Of course, he received various answers. But, one reason I can understand his consternation is that the “effective calculations” are understood by layering one algebraic structure upon another. Calculation and algebra go hand in hand. Meanwhile, probability might intrinsically enter into the situation via real numbers by a result called Richardson’s theorem.
What appears to be the case for physicists, however, is that the localization of (on shell) wavicle disturbances depends upon building a calculus on systems of test functions which, on their own, do not have a metric concept.
Anyway, you are the expert, not me. I am “all ears” so to speak. Thanks.
Well, again, the point is
a) we are *”inside” the wavefunction* [because the wave function describes everything in the universe.] The probabilities for everything that we are and do are given by asking questions of the wave function.
b) we are *made from wavicles of fields* [because that’s what the objects in the universe are all made from.]
The wave function describes the fields; the fields are inside the wave function, in this limited sense; the wavicles of the fields are also, therefore, inside the wave function, in that same limited sense; and we, made from the wavicles of the fields, are also therefore inside the wave function, in that limited sense of “inside”.
The “space of all possibilities” means “the space of all possible physical behaviors of the system in question”. That’s not the same as “possible experimental outcomes”, but is related to it.
As to the more sophisticated language of probability and logic that you are referring to, I’m not unfortunately familiar with this language. But I do not think that the “the localization of (on shell) wavicle disturbances depends upon building a calculus on systems of test functions which, on their own, do not have a metric concept.” This is a math way of looking at what localization means, not a physics way, and so I would shy away from notions such as “test functions” in favor of experimental procedure.
Let’s see how this develops over the year. Maybe the language you’re referring to is somehow useful.
Thank you for this additional clarification.
So, I watched your video with Dylan Curious. I greatly appreciated your statement of scientific agnosticism and your concern for finding ways of communicating where language has ambiguity.
At one point, Dylan began to speak about voxels. That is a bit of Newspeak for me. I would speak of volumes or volume elements. In either case, “voxels” appear to be an important aspect by which Newton distinguishes physics from mathematics in his Scholia.
I bring this up because of a principle called the unity of opposites and the intuitive reasoning about locality people learn in basic real analysis — namely, for the latter, the use of epsilon balls about a point.
When one describes light emanating from a point (in a flat 3-space), one imagines a snapshot in time with a spherical boundary. Intuitively, such a boundary has an interior and an exterior. By analogy with a circle in a 3-space, this intuition of an inside and an outside fails for a sphere in a 4-space.
Because of differential geometry, it is actually possible to visualize how “inside” and “outside” are meaningless for a sphere. It is called a sphere eversion,
https://m.youtube.com/watch?v=wO61D9x6lNY
The principle of the unity of opposites comes into play if one visualizes the sphere boundary as “gluing” the past time cone of the point of origin for light rays (the sphere interior) with the future time cone of the same point (the sphere exterior). To me, it is significant that sphere eversion is continuous in that what I visualize as a sphere ought to be thought of as a self-intersecting sphere.
It is not that I want to interject mathematics into your descriptions. I simply noticed the question about voxels. Sphere eversion is simply how I intuit the “hourglass conics” I see in all of the illustrations that accompany explanations intended to explain lightcones.
Perhaps the visualization might be useful to you in developing your own narratives.
Pixels are to a flat screen as voxels are to a three-dimensional cube. https://en.wikipedia.org/wiki/Voxel I’m afraid I don’t see the relation to Newtonian thinking.
I’ve never seen sphere eversion related to light cones, and I’m quite doubtful about it. The light cones are literally cones in 3+1 dimensions, and they satisfy a very simple equation: c^2 t^2 = x^2 + y^2 + z^2, where c is the cosmic speed limit, t is time, and x,y,z are spatial coordinates. At any fixed time, this equation says x^2 + y^2 + z^2 = R^2, where R=c|t| is a fixed constant. This is the equation for an ordinary sphere of radius R=c|t| ; note the absolute value sign. You get the same sphere at time t and at time -t, and the sphere disappears at t=0. So all that happens is that a sphere shrinks from finite size to zero size and then rebounds to finite size. The radius is continuous in time, while the derivative of the radius has a singularity at t=0, just like the function Abs[v].
Despite this discontinuity in the derivative of the radius, you can view this process as continuous by noting that the points (-c|t|,-|t|) for t<0 with the points (+x,+|t|) for t>0 form a continuous line x=ct. Therefore the light cone can be built out of a sphere of continuous lines. The sphere inverts in a much simpler way than a sphere inversion; it shrinks to a single point and comes out mirror-reversed. Nothing so complex and counterintuitive as a sphere eversion is required. So I’m afraid that you may be on the wrong track here.
I understand that perfectly well, Dr. Strassler. I have a degree in mathematics, although my skills in applied mathematics are deteriorated at this point.
I doubt you will appreciate the analogy which follows, but I will give it a try.
At the link,
https://www.pinterest.com/pin/427771664579274231/
you will find an image of how a mason thinks about an arch. The image has elements not found in a photograph of an arch,
https://www.pinterest.com/pin/403212972880739950/
Personally, I have no belief in time as an algebraic dimension, although it is necessary to our explanations. So, equations that are compatible with our measurements are, to me, much like the wooden frame used to build arches.
Although it is not your kind of mathematics, the link,
https://www.ams.org/journals/tran/1935-038-01/S0002-9947-1935-1501800-1/S0002-9947-1935-1501800-1.pdf
contains a comparison of types of orders. The order associated with the projective line is related to tetrahedral symmetries by virtue of 24 fixed ordered quadruples.
Likewise, sphere inversions relate to tetrahedra by virtue of their halfway model, the Morin surface,
https://en.m.wikipedia.org/wiki/Morin_surface#Structure_of_the_Morin_surface
I am not convinced that decorating 4-dimensional polytopes like the 24-cell with names of Dirac fermions ought really be considered physics, but, that is precisely what some research attempts in order to understand symmetries associated with physics. Even the 24-cell, itself, bears relation to tetrahedral symmetries. Thomas Banchoff has a paper explaining how its toroidal decomposition collapses to a 3-dimensional tetrahedron via the Hopf map.
I am extremely interested in, and grateful for, your point of view. You seem to be the only author attempting to explain our best theory without too much reliance on the historical views that do not conform with experiment.
I will try to minimize my comments as you continue your exposition this year. I expect that I have a lot to learn about “physical intuition” separate from mathematical elements.
Thanks.
I’ve never had much problem with self-interference or the fact that sensors change things. The waves going through the slit interact with it, a single slit produces an interference pattern, it doesn’t just perfectly cut out a segment of wavefront. Likewise if you add a sensor then the wave is going through a DIFFERENT slit. (If I recall the lectures of my youth correctly different sensors can have different effects on the outcome.) Adding a sensor and being surprised at the change is like making one slit star shaped and being shocked the pattern is altered.
What has always vexed me is that the resultant interaction with the screen is ‘localized’. (Again if I’m recalling right you can combine this with the photoelectric effect to eject single electrons from a metal screen.) Waves I can handle, in my experience most things make a lot more sense that way. But just how do such spread-out things have such localized results? Why is there enough particle-ness in the universe that waves alone won’t cut it?
It will be interesting to see where this leads.
I agree; that is indeed, when you think it through carefully, the only vexing part.
However, I wouldn’t say things in the way you did in your last question.
the problem of INTERPRETATION of the double-slit experiment is that we try to INTERPRET it with our macro world experience (“conventional anthropic wisdom”.
All physics is our homo sapience interpretation, our effort to explain in terms of our anthropic knowledge.
As to “according to the conventional wisdom, each object going through the slits is…” I am choosing “a thing with wave-like properties and with particle-like properties”. In nature there is no duality, it is just we humans don’t have single analogy for such events from our macro world experience.
Didn’t Feynman adequately reproduce all known behaviors of light with the theory of QED (Quantum Electrodynamics)? Does that theory somehow fall short, nowadays? Have new phenomena been observed which require a different explanation? Or are we trying to “peer behind the veil” and get at the deeper details of “how it can be that way”?
Assuming QED is sufficient for photons, as it was last I heard, how big a leap would it be to simply assume that something analogous operates in the case of _all_ objects (by which maybe it is meant, “all objects sufficiently small for the effects to be noticeable,” i.e. subatomic particles — but might also, for all we know or could tell, mean “all objects,” _period_)?
QED is indeed an extremely successful theory of light and charged objects (though Feynman is not the sole inventor; you are forgetting Dirac, Schwinger, Tomonaga, and others.)
However QED does not resolve any of the issues raised in the above article. As I will emphasize later, the perspective on this experiment that comes from quantum field theory is different, slightly but importantly, from the perspective which is implied by 1920s quantum theory. Nevertheless, the basic logical conundrum remains. You can learn this in many places, not the least of which is what Feynman himself said about this experiment; he had no proposed resolution for it.
There’s a quantitative difference between fig. 4 and fig. 9 that bugs me. I don’t have a background in physics, so maybe I’m missing something or taking the pictures too literally.
As I understand the phenomenon behind the experiment, fig. 4 comes from (I1 + I2)^2 and fig. 9 comes from I1^2 + I2^2, where I1 and I2 are values related to passing through each of the slots. But in that case, I wouldn’t expect to see the dots in fig. 4 stretching all the way to the end of the screen and not see anything in that area in fig. 9. In other words, I’d expect the striped pattern to disappear, but the average over slightly larger regions would be the same.
Is that correct? Am I missing something?
One of the problems is that the sensors affect Fig. 9, and so I’d have to be more specific about what they are and how they work in order to predict the details of Fig. 9. Also, there’s the single slit diffraction pattern, which I ignored in Fig. 9 (and 5). So yes, you are morally right: my illustrations are qualitative. It would be nice to redo them at some point with full quantitative details. But even then the answer is not sensor-independent, so there won’t be a unique answer. It’s potentially very complicated when you consider it seriously. My main focus really lies elsewhere, on basic conceptual points.
I’ve read that if you install The sensors, but don’t look at their output, you get the interference pattern. Only when you start paying attention to their output, which might distinguish which slit the particle went through, does the interference pattern disappear.
I even recall reading of an experiment which collected data regarding the strike locations of the particles on the screen, and the readings of the sensors, separately, and nobody looked at any of it until after the experiment was complete. As I recall reading, it was found that when one looked at the strike location data by itself, there was an interference pattern, but when one looked at the strike location and sensor data together (in whatever sense that expression is meaningful) the interference pattern disappeared — purely in the prices of analysis after the fact, long after the experiment was run. Unfortunately, that was a long time ago and I don’t recall where or when I read it.
I’ve since read hypotheses purporting to explain this, ranging from “the electron exists simultaneously at every point in time and space,” therefore has all the information. It needs to know which parts of the screen to avoid, and during which experiments or parts of experiments, to “causality operates backward in time,” so that our emplacing a sensor, or reading the sensor, or even analyzing the data taken from a sensor, is a cause which reaches backward in time to retroactively alter the behavior of the electron in the experimental apparatu — and others.
See also the “temporal double skit experiment,” explanation of the results which seems to require some of the particles to go faster than light, and others to travel backward in time.
You can make this experiment arbitrarily complicated, as though complicating it will somehow allow you a trick for resolving the basic conundrum, but you won’t get anywhere (and all the interpretations that are then laid on top of these complicated versions just add confusion; statements like “causality operating backward in time” are based on unjustified assumptions about how causality works.) This is fun stuff, in that it clarifies how quantum physics works, but no, no particles are going faster than light and none are traveling backward in time.
Fundamentally it remains the same as the original point about Schrodinger’s cat; the equations say clearly that the wave function branches, and we are *inside* the wave function. I’m not telling you to adopt Everett’s “many-worlds” interpretation of what that means, but the math is clear, and so far it correctly tells you what each of these experiments is going to reveal.
While in retrospect I like “foncusing”, it left me a bit foncused the first couple of times I read it.
A useful thing to observe in the double-slit is the slide from particle-like image on the screen when it’s a few wavelengths away from the plane of the slits to interference as the distance increases.
You also point at something that I wrestle with communicating. Whatever elementary particles are, they do not strongly conform to “waves” or “particles”. Of course the meanings of those two words are made up by people, so particles have no reason to conform to them. Unfortunately, there is so much historical communication in those terms, that the (unproductive) philosophical wrestling to classify elementary particles as waves or particles is pervasive in the public. I usually slip in an “Elementary particles are whatever they are, and there are times and places where the language of waves and particles will be useful and times and places where it will not.”
Dr. Strassler, out of curiosity, have you read Tim Maudlin’s “Philosophy of Physics: Quantum Theory” or Travis Norsen’s “Foundations of Quantum Mechanics”? Those are the two best books on quantum foundations that I have read, though unfortunately light on how these issues play out in QFT. (Maudlin’s “Philosophy of Physics: Space and Time” on relativity is also excellent.)
I know Maudlin personally and know his views; he’s very good, though we don’t always agree on what string theory does and doesn’t teach you (he hates it with a passion and I have a more nuanced view.) I don’t know Norsen. I think Maudlin and I are on the same page on quantum physics (not sure we are on Space and Time, though). But indeed I think you have to get into QFT to have any hope of making sense of things, as I’ll explain soon in this series of discussions….
According to S. V. Gantsevich single wavicle interference mechanism corresponds to the case in which the Dirac bracket components bra and ket pass through different slits. In this case, the phase difference of the bra and ket at the observation point is significant, and it is responsible for the occurrence of interference.
I find this interpretation very beautiful, logical and obvious. It would be very interesting to hear your opinion!
Gantsevich, S.V., Gurevich, V.L. Physics of Interference of Quantum Particles. Phys. Solid State 61, 2104–2109 (2019). https://doi.org/10.1134/S1063783419110155
https://link.springer.com/article/10.1134/S1063783419110155
pdf file: https://www.tvbjd.com/10.1134/S1063783419110155
Abstract—The bra + ket quantum language, introduced earlier by the authors to explain quantum correlation at macroscopic distances, makes it possible to understand the physical mechanism of interference of individual quantum particles without the idea of the transformation of a wave into a particle and vice versa, as well as to avoid claims of retrocausality, nonlocality, instantaneous interaction, and other similar phenomena supposedly inherent in quantum mechanics. Within the bra + ket approach, double- and triple-slit experiments, delayed choice experiments, and some more complex interference experiments with variable parameters were considered, the results of which has provoked a lively discussion over many years with opposite conclusions about particle trajectories in interferometers.
I’m glad you find it “obvious”. I don’t.
The literature is littered with wrong interpretations of quantum physics. I’m not going to weigh in any further than that.
Paulis Butlers. PhD
https://www.linkedin.com/in/paulis-butlers-phd-2622151a/
I’m sorry you don’t want to discuss different interpretations of quantum physics. It seems that without the Dirac bra+ket notation it is impossible to explain quantum effects in any simple and understandable way.
Dear Prof. Strassler,
could you show me some examples of mistakes in
Gantsevich, S.V., Gurevich, V.L. Physics of Interference of Quantum Particles. Phys. Solid State 61, 2104–2109 (2019). https://doi.org/10.1134/S1063783419110155 ?
Thank You!
No, I’m sorry. That’s a dark hole from which I will never emerge.
If you slowly degrade the effectiveness of the sensor does the wave slowly come back, or suddenly appear, or does that make no sense at all?
This is a very good but complicated question that depends on the details of how you degrade the sensor and how the particular sensor works. For instance: suppose that it was 50% effective, in that it works 50% of the time and completely fails to work 50% of the time; well, then 50% of the objects will show interference (in the sense that they’ll only show up in the patches that are bright when interference occurs) and 50% will not (in that they will show up in the two blotches in Figure 9.) Of course, object by object you will not be able to say what happens, because no matter what, each object just leads to one flash on the screen, so you can’t tell what happened to any given one of them.
If the sensor degrades in some more complex way, then the details really matter for figuring out what happens. But the important conceptual point is that what you would see in such cases is really measuring how the sensor works, and how it interacts with the objects; you’re not learning anything new about the objects on their own. This is the fundamental issue: measurement is not a passive process but rather an active one, and in quantum physics we discover this is centrally important.
My understanding was that if you use something like a semi silvered mirror as a beam splitter, then as you make the mirror light enough that you can detect the momentum change, you lose the interference pattern. Because you’re extracting information at that point.
Related aside: I always find the implications of the delayed-choice quantum-eraser tricky to grasp intuitively.
Your first point sounds correct, but again, I assume that the way the pattern is lost depends on the details of the mirror. As for the second point, the issue with such studies is that they never actually clarify what is true. Instead they just make clear that various naive viewpoints are false. The equations, meanwhile, always work; human interpretations, not so much.
I’ve been interested in Jacob Barandes’ work regarding non-Markovian stochastic systems, and how unistochastic matrices behave versus their underlying unitary matrices. I don’t think his work is presenting anything new per se, but I think he’s framing things in a way that might prove extremely helpful.
I agree. He and I haven’t had time to talk this year, thanks to my being fully distracted by the book; but yes, I think there is something interesting in his approach. I have asked him some basic questions that he couldn’t answer at the time (he hadn’t thought about them yet), and so he owes me some answers this year. Maybe at some point I’ll understand his approach well enough to learn something new from it, at least as far as new ways of thinking.
Barandes’ approach is quite novel and ingenious. He shows that the apparent wave behavior of a single particle, and its interference with itself is simply the result of a basic underlying indivisible stochastic process. Installing a sensor would make the process divisible.
The question I have not understood is how it works in quantum field theory. That’s the only place that matters, because quantum mechanics of a single particle disagrees with data, while quantum field theory does not.
To be clear: it *does* work, I just don’t understand what the implications are.
Barandes mentions in his papers and interviews that his scheme via indivisible processes yields interference for the double slit. Does anyone know if the actual calculation is available? Seeing how the concept (indivisible processes) rolls out in a calculation would do a lot to elucidate the machinery.
I don’t think this is done explicitly. One should start with simpler questions: how do you measure the location of one particle? That I think can be worked out.
I would like to know why you think the Barandes work is not new. Could you explain your thoughts please ?
I think the issue here is the difference between a new way to look at an old theory vs a new theory… i.e., a new way to get old equations and their predictions, as opposed to new equations with new predictions. It’s clearly the former. I think that is all that Jacob H. meant, but he can correct me if I am wrong.
thank you for the explanation. the indivisible time in the Barandes model is even more novel than concept of time used in QM — which is no different than classical physics.
Dr.Strassler:
Q1: in the double slit experiment, how close together do the slits have to be? I believe I had read somewhere that the distance between the slits is nanometers?
Q2: as you increase the distance between the slits, is there a distance, as the slits become more widely separated, where this experiment breaks down, and the “particles” can defiantly be determined as to which slit they go thru?
Q1: this depends, just as it does for any waves, on the wavelength of the object and on the width of each slit. (In quantum physics, the wavelength in turn depends both on the object’s momentum, which depends on its mass and on its energy.) So there’s no wordy answer; there are some formulas. I can try to dig them up.
Q2: As you make the slits further apart, the interference pattern becomes harder to observe. It’s still there, though. It’s complicated by the fact that there are also diffraction patterns from the individual slits, which I ignored in today’s discussion. So depending on the slit widths and separations you can get a lot of different behaviors. But no, particles are never things with definite paths; it just becomes harder and harder to see the effect.
Similarly, if the objects become less microscopic, it becomes harder and harder both to see the effect and to keep the objects from interacting with other things around them; Wikipedia describes a paper from 2019 as follows: “The experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were molecules that each comprised 2000 atoms (whose total mass was 25,000 atomic mass units.)” So there are no sudden changes, just gradually increasing difficulties.
The reason that macroscopic objects go through only one slit is that they interact with the air and the light in the room every tiny fraction of a second, which effectively measures where they are long before they even reach the two slits. To see the interference effect, you have to keep the objects from interacting with anything that effectively deetermines their position as they travel from where they are produced through the wall to the screen. That’s why the above-mentioned paper is so impressive; it’s not easy to make macroscopic objects, or even objects with a few hundred atoms in them, remain so perfectly isolated. Even thermal radiation from the object will kill the effect.
I believe Einstein tried to reconcile this by saying that a measurement of the recoil of the slit (momentum exchange) would determine which slit the electron went thru. However, Bohr had a counterargument I believe saying the exact position of the slit was indeterminate? is that correct?
I don’t remember the details of this historical discussions; we could look them up. But my interest is not in what the original confused physicists were thinking in the 1920s, trying to make sense of a crazy observation. My interest is what we should think now, with far more knowledge and also hindsight.
In any case, Einstein was not able to reconcile the issue using that approach or any other, and the experiment’s conceptual challenges have stood the test of time for a century.
When I think of this matter and try to explain it to others I’m always sticking to some mental visualizations I find good for that purpose. A key concept for me in all that is the probability field. That’s something invisible behind the real world, spreading in all directions.
Step 1. Imagine, I say, a fungus mycelium spreading in all directions from a tree. You don’t see it, it grows under the earth surface. Yet it grows and spreads, invisibly for you, and suddenly it produces a visible fruitbody.
Step 2. It is quite easy to imagine that a mycelium has enough energy to produce only one fruitbody. You can also imagine that a fruitbody can be provoked when mycelium is exposed to the sun. Then even though it spreads underground according to its own rules, you can take a shovel and make a couple of digs. If you’re lucky, yo can hit the mycelium, and as you expose it to the sun, it immediately produces a fruitbody.
Step 3. Imagine the mycelium spreads in a wave-like fashion, like butterfly-style swimming, diving deeper and returning closer to the surface each half a meter. With that, starting with a shovel from a tree, you would have higher luck in digging to the mycelium in certain places than in others. Thus an invisible law of mycelium spreading under the ground would govern your probability of striking the mushroom fruitbody. The fruitbody remains single and local, it is not a wave in any sense. But the mycelium spreads like a wave, and thus, the probability spreads like a wave.
Step 4. With all those concepts it is easy to imagine what would happen underground, if a mycelium hits an underground wall with two slits, and why it would naturally form an expected pattern of probability behind it.
So, the mental model for me is the oscillating probability field which travels the space and goes around the obstacles. You can always test it, but the moment you succeed and catch the particle, the probability is zeroes, as there were enough energy for only one.
The problem is (a) there is no probability field in physics, and (b) to the extent you view the wave function of a system as a “field” (which you shouldn’t, because it lacks many properties that fields have), it exists in the abstract space of possibilities for the system, not in the three-dimensional space that you and I live in.
In other words, you’re making the same common error that I highlighted in my discussion above of “The Visualization Problem.” You’re trying to visualize something in three-dimensional space which doesn’t exist in three-dimensional space… it exists in a space of much, much, much higher dimension that you (and I) cannot visualize.
Natural languages are not “designed” to convey crisply-defined concepts and ideas: they evolve in such a way that allow us to share, through speaking, concepts and ideas that are simple enough for us to be able to solve problems in a collaborative way.
Physics, on the other hand, uses math so as to define very precise and crisp concepts, ideas and processes that have to be both self-consistent (consistent within its own narrow field in Physics) and consistent across the board (consistent within the entire field of Physics), mainly because the models (theories) that describe these concepts, ideas and processes must be able to predict experiments and their data, both in a quantitative and qualitative way.
Having said that, it makes sense that languages do not have a proper way to describe a field like Quantum Mechanics.
Like for instance, superposition: we can perfectly describe what superposition is both as a physical concept, as well as a purely mathematical concept; the wave function, the solution to the Schodinger equation of a given quantum system is the linear combination of the entire fundamental set of the solutions to said differential equation, so, the system is in all of the states at once, each state being described by the set of eigenvalues (quantum numbers) of the given solution they belong to.
Being a wave functions, the solutions will have sines and cosines all over the place, so, integer numbers are at the heart of the eigenvalues of said equations, so, the “particle” nature of quantum systems is a natural consequence of said eigenvalues being expressions with integer numbers.
But then again, as it is a wave function, the “wavy” nature of said systems is inextricable from its its own “particly” nature.
All of this can be describe in non ambiguous ways with math, but is awkward to describe in plain language.
🙂 Well said — more precisely, as well said as can be said using language!
But honestly, if those were the only difficulties with language and quantum physics, I am confident I could solve them, and come up with analogies and pictures and concepts that would convey everything one needs to know.
The really big problem with quantum physics is the one you haven’t mentioned, the one that Einstein emphasized and the one that Everett tried to address: the equations of quantum physics do not tell us what happens in the universe in a way that corresponds to how you and I experience it.
As you have clearly said, it is all about those aspects of QM that worried many scientists (but not all), most notably Einstein and Everett as you point out, which has to do with the interpretation of QM, which does not have good press within the Physics community since way back in time. One way to put it is remembering the famous admonition “shut up and calculate”.
More recently it has gained some fresh traction, as some theoretical physicists are working on novel ideas pertaining to a broader view and understanding of QM.
I did describe the wave function as a mathematical object, as long as it stays pristine, that is, while nothing bumps into its state “as is”, but when anything bumps into its state, like for instance, a measurement, something that we neither know nor understand happens, something that, for lack of a better description, we describe as “wave function collapse”, when superposition transforms into one given state, just only one set of eigenvalues, the ones that corresponds to that particular state: that is what the measurement values show, said set of eigenvalues.
What is really going on, we just don’t get.
Clearly, Bohr’s interpretation of QM did not seat well with many physicists, and that is part of the problem.
What I think that happened is that QM had very fast an enormous success, with many scientists adding new ideas, concepts and theoretical solutions to hard problems, and early on in its evolution (of QM), scientists got involved in solving many other important problems of QM, so, the basis of QM was left unfinished, with no major incentives for young scientists to get into that line of research.
This kind of process has happened a few more times in modern times. We could argue that something similar happened with string theory: it became so relevant so fast, that it took the attention of most young scientists for some generations now, while some other problems in modern theoretical physics were laid to wait, for lack of enough human capital to handle it.
My comment does put a blame on only the fact that theoretical physicists are a very scarce kind of human beings, so, institutions have to deal with this as a fact of life, and do the best they can with the number of assets at hand, which are very, very few: tough luck.
Maybe now, with some very hard problems to solve that might or might not be related to having a fuller, broader basis of QM, the institutions around the world come to the realization that it makes sense to invest in solving said problem with the basis of QM.
You state this “wave function collapse” as though it is a fact. But it is an interpretation — an opinion.
In fact there have been, for quite some time, a lot of people working on the basics of quantum physics; one example is Wojciech Zurek
(https://public.lanl.gov/whz/ ) and of course before him was John Bell, and today there are many others. There was also Francis Everett, who pointed out there is a consistent alternative to wave-function collapse, though almost as unpleasant. Their progress does not clarify how to resolve the fundamental problem (which “wave function collapse” attempts, rather poorly and inconsistently, to address) but it does highlight many important facts about decoherence and measurement which have helped clarify what the problem is and is not.
I did not mean that the phrase “wave function collapse” were to be taken as a fact; my use of “for lack of a better description” was meant to imply that it is not a fact, is an interpretation, but it just happens that my writing in english sometimes gets kind of convoluted, for which I apologize.
I was talking about the problem of interpretation in QM, and the concept of the “wave function collapse” is at the very heart of the interpretation.
That is what I express with “What is really going on, we just don’t get.”
The “wave function collapse” is a way of describing what happens when the wave function is “bumped” by an external process (a measurement, or just a physical event when the system is affected by any external process or entity), but there is no experimental evidence that corresponds to what that expression actually describes.
That is what I meant to describe, that is an interpretation, and not a very good expression as regarded from Physics as a body of knowledge, but somehow, the expression stuck with the Physics community, and is still being used.
There are some experimental measurements that imply that the “collapse” is not instantaneous, even though is very fast for our senses.
Regarding decoherence and its relation to entanglement of a quantum system with external entities is more useful than the idea of “collapse”.
Quantum entanglement of simple systems does not necessarily give way to “collapse” or decoherence, as the new entangled system may remain quantum in nature.
It is when a quantum system entangles with a complex system with multiple interactions with the original quantum system, in such a way that the resulting system loses its quantum nature.
Maybe some institutions are already doing something in that line of research, like for instance, John Hopkins University hiring Dr Sean Carroll.
His research is on the intersection of Philosophy and Physics, as Homewood Professor of Natural Philosophy.
Sean is very keen on Everett’s approach to the basis of QM.
Then you have Jacob Barandes at Harvard, working on some other approach to the basis of QM.
There are many other examples of institutions doing some stuff in the area, the basis of QM; I just “shot” a couple of examples “from the hip” (the ones that I remember without checking).
So, there are some actions taken it that direction, so now, we have to wait and see what transpires from those efforts.
Hi Matt,
I’m glad that you chose the basics of quantum behavior as a topic. There is still so much to learn/unlearn here.
quote:
“But the very process of looking at the object to see what slit it went through changes the interference pattern of Figs. 4 and 6 into the pattern in Fig. 5, shown in Fig. 9, that we’d expect for particles.”
Q1: can sensors be added *behind* the slit, and be in an activated or inactivated state? I think about some sensitive magnetic detector (SQUID?) which should be ‘passive’ and not change circumstances at the slits. Would activating the detector destroy the pattern and de-activating it restore the pattern?
Even if that were so, would it matter if the information obtained from the measurement were either stored (=gained) or dumped (= no info gained). Not clear what the (backwards towards the slit) effect of measurement (behind the slit) is. I guess it must be the loss of phase coherence (between both beams) that destroys the interference pattern. But I’ll shut up and let YOU calculate. (grin).
Q2: a slit has a left edge and a right edge. Preferably sharp ones, where the density abruptly jumps from 0 to 1. (Am I the only one that dislikes infinite gradients?) I’ve never seen a good description of a wavicle going through just one single slit. Does interference also occur here (between disturbance by left and right edge?).
Wouter.
Q1 is actually very complex, because the details of the sensor and how it works starts to make a difference; exactly how much interaction is there between object and sensor, and can that interaction have significant effects even if the sensor is turned off. At some point I’ll have to address this properly, but I’m not prepared to do it yet.
Q2: You end up seeing wave-like behavior again, a more subtle form known as single slit diffraction. https://courses.lumenlearning.com/suny-physics/chapter/27-5-single-slit-diffraction/ You notice that sharp peak in the middle, but then a fainter pattern going outward, most easily visible if the slit is very narrow.
So indeed, as you’ve implicitly picked out, my characterization of the double-slit experiment, like those of most presenters, is too shallow. There are both single-slit and double-slit effects going on simultaneously — though which one is more important depends on the width of each slit and the spacing between the slits, and I’ve assumed the diffraction effect is small compared to the two-slit interference. Also, my Figure 9 is misleading, because if you looked really closely, you’d realize there’s actually more going on than in Figure 5, because there is diffraction for each slit, though that might be hard to detect.
You see already that we have many levels of issues to explore before we ever return to the double-slit experiment itself.
So, can the double-slit experiment be explained by the assumption that ALL matter is composed of quasiparticles which fluctuate between bosons and fermions depending on their flux energy densities, the higher the density the more massive it becomes.
Recently semi Dirac fermions were observed for the first time:
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.14.041057
– “in two dimensions, a peculiar class of fermions that are massless in one direction and massive in the perpendicular direction was predicted 16 years ago”
So, when placing the sensor(s) to observe (interfere) with the particles going through the sensors could be polarizing the wave function (state vectors through each slit) and turning it into a “massive” state.
If ALL matter is composed of quasiparticles, and you add the ZPE to it, then you could say we are back into the “aether” theory. The point is that if the fundamental fields like the Higgs have measurable values at each point is space then they are composed of fundamental energy states, the aether.
I recently came across this paper, “On the nature of electric charge” – Jafari Najafi, Mahdi (14 February, 2014)
“The present study provides an explicit description of the gravitational constant G
and the origin of electric charge will be inferred using generalized dimensional analysis.”
Conclusion: ” It was found that the origin of an electric charge (and electromagnetic field) is mass
change of particle(s) over time.”
This may not be too far out of the box, the quantum fluctuations could be semi Dirac fermions flipping from bosons to fermions and this could be the nature of an electric charge. This concept could be extended to “color charge” by scaling up the energy densities, the higher energy density fluctuations will produce color charge and quarks.
Could quasiparticles be the key to a unified theory?
Ref: https://www.researchgate.net/publication/269679115_On_the_nature_of_electric_charge
I’m afraid the idea in the paper you reference makes no sense.
What is the “best” theory for the nature of charge, how is it created?
Increasingly, I’ve switched to analyzing such problems in terms of direct interactions of mass-and-energy dependent information fields. Ignoring the testable information density seems a bad idea.
Could the analogy of a twist in a belt ( like a trouser belt ) be similar to what is happening. A belt can only be twisted in discrete amounts ( or anti-twisted ), and yet it has a non-local quality.
Why would that lead to the observed phenomena?
I observed as a child that a Mobius strip being force-fed through a slit would have to quote go around twice to get back to its starting point,” and was therefore a mechanically intuitive, understandable, explanation or analogy for spin-1/2 particles requiring 720° of spin to return to their original state. (And yes, I was reading, and thinking, about these things as a grade-school child.)
I have also since read and observed a very interesting video about the use of quaternions in modeling-and-computing rotation, and one of their inherent properties turns out also to be that while 360° of rotation returns a manipulated object to its original orientation, there is a “180° change of phase,” whatever that would mean in the physical world, and that a further 360° is required to correct the phase as well as the orientation. (There may be analogies here to the behavior of the Rubik’s cube, but that’s another discussion entirely.)
This is true, but not relevant to this experiment; after all, it works just as well with photons (bosons) as with electrons (fermions). Neither spin nor statistics plays a role.