Of Particular Significance

Author: Matt Strassler

Quantum Interference 3: What Is Interfering?

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.

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POSTED BY Matt Strassler

ON March 26, 2025

Quantum Interference 2: When Does It Happen?

Last time, I showed you that a simple quantum system, consisting of a single particle in a superposition of traveling from the left OR from the right, leads to a striking quantum interference effect. It can then produce the same kind of result as the famous double-slit experiment.

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 2.2: *Event 2a at **x=+1** and* *event 2b at* **x=-1**.

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?
Something else altogether?

So? Well? What’s the correct answer?

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POSTED BY Matt Strassler

ON March 20, 2025

Quantum Interference 1: A Simple Example

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.

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POSTED BY Matt Strassler

ON March 18, 2025

A New Interview

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.

00:00 Intro
00:40 Why did you write “Waves in an Impossible Sea”?
03:50 What is mass?
09:03 What is Relativistic Mass? Is it a useful concept?
17:50 Why Quantum Field Theory (QFT) is necessary
23:50 Electromagnetic Field, Photons, and Quantum Electrodynamics (QED)
36:17 Particles are ripples in their Fields
38:47 Fields with zero-mass particles vs. ones whose particles have mass?
46:49 The Standard Model of Particle Physics
52:08 What was the motivation/history behind the Higgs field?
1:02:05 How the Higgs field works
1:05:33 The Higgs field’s “Vacuum Expectation Value”
1:12:02 The hierarchy problem
1:24:18 The current goals of the Large Hadron Collider

POSTED BY Matt Strassler

ON March 17, 2025

Did the Particle Go Through the Two Slits, or Did the Wave Function?

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.

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POSTED BY Matt Strassler

ON March 13, 2025

Do Quantum Wave Functions Collapse?

In the last post, I showed you how a projectile in a superposition of moving to the left or of moving to the right can only be measured to be doing one or the other. But what happens to the wave function of the system when the measurement is made? Does it… does it… COLLAPSE!?

Sounds scary. But it is only scary when it is badly explained.

Today I’ll show you what wave function collapse would mean, what it would require, and what a couple of the alternatives are. Among other things, I’ll show you that:

The standard way of explaining wave function collapse, which argues collapse is required to avoid a logical problem, is not legitimate;
If the Schrödinger wave equation is correct, then wave function collapse can never happen (and anything resembling “collapse” is viewed not as a physical effect but as a user’s choice);
Therefore, if wave function collapse really does occur, then the Schrödinger equation is wrong;
But if the Schrödinger wave equation is correct, an understanding of why quantum theory predicts only probabilities for multiple possibilities, rather than definite outcomes, is still lacking.

Today’s post uses several previous posts and their figures as a foundation, so I’ll start with a review of the most recent one, with links to others of relevance.

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POSTED BY Matt Strassler

ON March 10, 2025

Can a Quantum Particle Move in Two Directions at Once?

So far, in the context of 1920s quantum physics, I’ve given you a sense for what an ultra-microscopic measurement consists of, and how one can make a permanent record of it. [Modern (post-1950s) quantum field theory has a somewhat different picture; please keep that in mind. We’ll get to it later.] Along the way I’ve kept the object being measured very simple: just an incoming projectile with a fairly definite motion and moderately definite position, moving steadily in one direction. But now it’s time to consider objects in more interesting quantum situations, and what it means to measure them.

The question for today is: what is a quantum superposition?

I will show you that a quantum superposition of two possibilities, in which the wave function of a system contains one possibility AND another at the same time, does not mean that both possibilities occur; it means that one OR the other may occur.

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POSTED BY Matt Strassler

ON March 6, 2025

Making a Measurement Permanent

As part of my post last week about measurement and measurement devices, I provided a very simple example of a measuring device. It consists of a ball sitting in a dip on a hill (Fig. 1a), or, as a microscopic version of the same, a microsopic ball, made out of only a small number of atoms, in a magnetic trap (Fig. 1b). Either object, if struck hard by an incoming projectile, can escape and never return, and so the absence of the ball from the dip (or trap) serves to confirm that a projectile has come by. The measurement is crude — it only tells us whether there was a projectile or not — but it is reasonably definitive.

Fig. 1a: *A ball in a dimple on the side of the hill will be easily and permanently removed from its perch if struck by a passing object.*

Fig. 1b: *Similarly to Fig. 1a, a microscopic ball in a trap made from electric and/or magnetic field may easily escape the trap if struck.*

In fact, we could learn more about the projectile with a bit more work. If we measured the ball’s position and speed (approximately, to the degree allowed by the quantum uncertainty principle), we would get an estimate of the energy carried by the projectile and the time when the collision occurred. But how definitive would these measurements be?

With a macroscopic ball, we’d be pretty safe in drawing conclusions. However, if the objects being measured and the measurement device are ultra-microscopic — something approaching atomic size or even smaller — then the measurement evidence is fragile. Our efforts to learn something from the microscopic ball will be in vain if the ball suffers additional collisions before we get to study it. Indeed, if a tiny ball interacts with any other object, microscopic or macroscopic, there is a risk that the detailed information about its collision with the projectile will be lost, long before we are able to obtain it.

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POSTED BY Matt Strassler

ON March 3, 2025

What Is a Measurement?

Nature could be said to be constructed out an immense number of physical processes… indeed, that’s almost the definition of “physics”. But what makes a physical process a measurement? And once we understand that, what makes a measurement in quantum physics, a fraught topic, different from measurements that we typically perform as teenagers in a grade school science class?

We could have a long debate about this. But for now I prefer to just give examples that illustrate some key features of measurements, and to focus attention on perhaps the simplest intuitive measurement device… one that we’ll explore further and put to use in many interesting examples of quantum physics.

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POSTED BY Matt Strassler

ON February 27, 2025

The Particle and the “Particle” (Part 2)

In my last post, I looked at how 1920’s quantum physics (“Quantum Mechanics”, or QM) conceives of a particle with definite momentum and completely uncertain position. I also began the process of exploring how Quantum Field Theory (QFT) views the same object. I’m going to assume you’ve read that post, though I’ll quickly review some of its main points.

In that post, I invented a simple type of particle called a Bohron that moves around in a physical space in the shape of a one-dimensional line, the x-axis.

I discussed the wave function in QM corresponding to a Bohron of definite momentum P₁, and depicted that function Ψ(x₁) (where x₁ is the Bohron’s position) in last post’s Fig. 3.
In QFT, on the other hand, the Bohron is a ripple in the Bohron field, which is a function B(x) that gives a real number for each point x in physical space. That function has the form shown in last post’s Fig. 4.

We then looked at the broad implications of these differences between QM and QFT. But one thing is glaringly missing: we haven’t yet discussed the wave function in QFT for a Bohron of definite momentum P₁. That’s what we’ll do today.

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POSTED BY Matt Strassler

ON February 25, 2025

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