The quantum double-slit experiment, in which objects are sent toward and through a pair of slits in a wall,and are recorded on a screen behind the slits, clearly shows an interference pattern. It’s natural to ask, “where does the interference occur?”
The problem is that there is a hidden assumption in this way of framing the question — a very natural assumption, based on our experience with waves in water or in sound. In those cases, we can explicitly see (Fig. 1) how interference builds up between the slits and the screen.
Figure 1: How water waves or sound waves interfere after passing through two slits.
But when we dig deep into quantum physics, this way of thinking runs into trouble. Asking “where” is not as straightforward as it seems. In the next post we’ll see why. Today we’ll lay the groundwork.
In my last post and the previous one, I put one or two particles in various sorts of quantum superpositions, and claimed that some cases display quantum interference and some do not. Today we’ll start looking at these examples in detail to see why interference does or does not occur. We’ll also encounter a difficulty asking where the interference occurs — a difficulty which will lead us eventually to deeper understanding.
First, a lightning review of interference for one particle. Take a single particle in a superposition that gives it equal probability of being right of center and moving to the left OR being left of center and moving to the right. Its wave function is given in Fig. 1.
Figure 1: The wave function of a single particle in a superposition of moving left from the right OR moving right from the left. The black curve represents the absolute-value-squared of the wave function, which gives the probability of finding the particle at that location. Red and blue curves show the wave function’s real and imaginary parts.
Then, at the moment and location where the two peaks in the wave function cross, a strong interference effect is observed, the same sort as is seen in the famous double slit-experiment.
Figure 2: A closeup of the interference pattern that occurs at the moment when the two peaks in Fig. 1 perfectly overlap. An animation is shown here.
The simplest way to analyze this is to approach it as a 19th century physicist might have done. In this pre-quantum version of the problem, shown in Fig. 3, the particle has a definite location and speed (and no wave function), with
a 50 percent chance of being left of center and moving right, and
a 50 percent chance of being right of center and moving left.
Figure 3: A pre-quantum view of Fig. 1, showing a single particle with equal probability of moving right or moving left. The particle will reach x=0 in both possibilities at the same time, but in pre-quantum physics, nothing special happens then.
Nothing interesting, in either possibility, happens when the particle reaches the center. Either it reaches the center from the left and keeps on going OR it reaches the center from the right and keeps on going. There is certainly no collision, and, in pre-quantum physics, there is also no interference effect.
Still, something abstractly interesting happens there. Before the particle reaches the center, the top and bottom of Fig. 3 are different. But just when the particle is at x=0, the two possibilities in the superposition describe the same object in the same place. In a sense, the two possibilities meet. In the corresponding quantum problem, this is the precise moment where the quantum interference effect is largest. That is a clue.
The pre-quantum version of this system, in which (like a 19th century scientist) I draw the particle as though it actually has a definite position and motion in each half of the superposition, looks like Fig. 1. The interference occurs when the particle in both halves of the superposition reaches the point at center, x=0.
Figure 1: A case where interference does occur.
Then I posed a puzzle. I put a system of two [distinguishable] particles into a superposition which, in pre-quantum language, looks like Fig. 2.
Figure 2: Two particles in a superposition of both particles moving right (starting from left of center) or both moving left (from right of center.) Their speeds are equal.
with all particles traveling at the same speed and passing each other without incident if they meet. And I pointed out three events that would happen in quick succession, shown in Figs. 2a-2c.
Figure 2.1: Event 1 at x=0.
Figure 2.2: Event 2a at x=+1 and event 2b at x=-1.
Figure 2.3: Event 3 at x=0.
And I asked the Big Question: in the quantum version of Fig. 2, when will we see quantum interference?
Will we see interference during events 1, 2a, 2b, and 3?
Will we see interference during events 1 and 3 only?
Will we see interference during events 2a and 2b only?
Will we see interference from the beginning of event 1 to the end of event 3?
Will we see interference during event 1 only?
Will we see no interference?
Will we see interference at some time other than events 1, 2a, 2b or 3?
A very curious thing about quantum physics, 1920’s style, is that it can create observable interference patterns that are characteristic of overlapping waves. It’s especially curious because 1920’s quantum physics (“quantum mechanics”) is not a quantum theory of waves. Instead it is a quantum theory of particles — of objects with position and motion (even though one can’t precisely know the position and the motion simultaneously.)
(This is in contrast to quantum field theory of the 1950s, which [in its simplest forms] really is a quantum theory of waves. This distinction is one I’ve touched on, and we’ll go into more depth soon — but not today.)
In 1920s quantum physics, the only wave in sight is the wave function, which is useful in one method for describing the quantum physics of these particles. But the wave function exists outside of physical space, and instead exists in the abstract space of possibilities. So how do we get interference effects that are observable in physical space from waves in a weird, abstract space?
However it works, the apparent similarity between interference in 1920s quantum physics and the interference observed in water waves is misleading. Conceptually speaking, they are quite different. And appreciating this point is essential for comprehending quantum physics, including the famous double slit experiment (which I reviewed here.)
But I don’t want to address the double-slit experiment yet, because it is far more complicated than necessary. The complications obscure what it is really going on. We can make things much easier with a simpler experimental design, one that allows us to visualize all the details, and to explore why and how and where interference occurs and what its impacts are in the real world.
Once we’ve understood this simpler experiment fully, we’ll be able to discard all sorts of misleading and wrong statements about the double-slit experiment, and return to it with much clearer heads. A puzzle will still remain, but its true nature will be far more transparent without the distracting cloud of misguided clutter.
A pause from my quantum series to announce a new interview on YouTube, this one on the Blackbird Physics channel, hosted by UMichigan graduate student and experimental particle physicist Ibrahim Chahrour. Unlike my recent interview with Alan Alda, which is for a general audience, this one is geared toward physics undergraduate students and graduate students. A lot of the topics are related to my book, but at a somewhat more advanced level. If you’ve had a first-year university physics class, or have done a lot of reading about the subject, give it a shot! Ibrahim asked great questions, and you may find many of the answers intriguing.
Here’s the list of the topics we covered, with timestamps.
What is really going on in the quantum double-slit experiment? The question raised in this post’s title seems to lie at the heart of the matter. In this experiment, which I recently reviewed here, particles of some sort are aimed, one at a time, at a wall with two slits, and their arrival is recorded on a screen behind the wall. As a parade of particles proceeds, one by one, past the wall, an interference pattern somehow appears, emerging gradually like a spectre on the screen.
Interference is a familiar effect, commonly seen in water waves and sound waves. If water waves passed through a pair of slits in a wall, interference would be observed and no one would be surprised. But here we have one particle passing through the wall at a time; it’s not at all the same thing. How can we explain the interference effect in this case?
It’s natural to imagine that somehow either
each particle acts like a wave, goes through both slits, and interferes with itself, or
the quantum wave function that describes each particle (or all the particles [?]) goes through both slits and interferes with itself.
So… which is it? Did the particle go through both slits, or did the wave function?
In 1920s quantum physics, there is a very simple answer to this question.
The answer is,…
“No.“
No — neither the particle nor the wave function [not its wavy pattern or its peak(s) or any other part of it] goes through the two slits.
