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 foncusing, 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.
18 Responses
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.
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.
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.
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.
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?