Of Particular Significance

Category: Quantum Basics

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

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

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

Why do I find the word particle so problematic that I keep harping on it, to the point that some may reasonably view me as obsessed with the issue? It has to do with the profound difference between the way an electron is viewed in 1920s quantum physics (“Quantum Mechanics”, or QM for short) as opposed to 1950s relativistic Quantum Field Theory (abbreviated as QFT). [The word “relativistic” means “incorporating Einstein’s special theory of relativity of 1905”.] My goal this week is to explain carefully this difference.

The overarching point:

I’ve discussed this to some degree already in my article about how the view of an electron has changed over time, but here I’m going to give you a fuller picture. To complete the story will take two or three posts, but today’s post will already convey one of the most important points.

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POSTED BY Matt Strassler

ON February 24, 2025

Yesterday I posted an animation of a quantum wave function, and as a brain teaser, I asked readers to see if they could interpret it. Here it is again:

Yesterday’s wave function, showing an interesting interference phenomenon.

Admittedly, it’s a classic trap — one I use as a teaching tool in every quantum physics class. The wave function definitely looks, intuitively, as though two particles are colliding. But no. . . the wave function describes only one particle.

And what is this particle doing? It’s actually in the midst of a disguised version of the famous double slit experiment! This version is much simpler than the usual one, and will be super-useful to us going forward. It will make it significantly easier to see how all the puzzles of the double-slit experiment play out, both from the old, outdated but better known perspective of 1920’s quantum physics and from the modern perspective of quantum field theory.

You can read the details about this wave function — why it can’t possibly describe two particles, why it shows interference despite there being only one particle, and why it gives us a simpler version of the double-slit experiment — in an addendum to yesterday’s post.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 21, 2025

A scientific brain teaser for readers: here’s a wave function evolving over time, presented in the three different representations that I described in a post earlier this week. [Each animation runs for a short time, goes blank, and then repeats.] Can you interpret what is happening here?

The explanation — and the reasons why this example is particularly useful, informative, and interesting (I promise!) — is coming soon [it will be posted here tomorrow morning Boston time, Friday Feb 21st.]

[Note added on Thursday: I give this example in every quantum mechanics class I teach. No matter how many times I have said, with examples, that a wave function exists in the space of possibilities, not in physical space, it happens every time that 90%-95% of the students think this shows two particles. It does not. And that’s why I always give this example.]

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 20, 2025

What is a wave function in quantum physics?

Such a question generates long and loud debates among philosophers of physics (and more limited debate among most physicists, who tend to prefer to make predictions using wave functions rather than wondering what they are.) I have a foot in both camps, even though I have no real credentials among the former set. But no matter; today I won’t try to answer my own question in any profound way. We can debate the deeper meaning of wave functions another time.

Instead I just want to address the question practically: what is this function for, in what sense does it wave, and how does it sit in the wider context of physics?

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POSTED BY Matt Strassler

ON February 19, 2025

Before we knew about quantum physics, humans thought that if we had a system of two small objects, we could always know where they were located — the first at some position x1, the second at some position x2. And after Isaac Newton’s breakthroughs in the late 17th century, we believed that by combining this information with knowledge of the objects’ motions and the forces acting upon them, we could calculate where they would be in the future.

But in our quantum world, this turns out not to be the case. Instead, in Erwin Schrödinger’s 1925 view of quantum physics, our system of two objects has a wave function which, for every possible x1 and x2 that the objects could have, gives us a complex number Ψ(x1, x2). The absolute-value-squared of that number, |Ψ(x1, x2)|2, is proportional to the probability for finding the first object at position x1 and the second at position x2 — if we actually choose to measure their positions right away. If instead we wait, the wave function will change over time, following Schrödinger’s wave equation. The updated wave function’s square will again tell us the probabilities, at that later time, for finding the objects at those particular positions.

The set of all possible object locations x1 and x2 is what I am calling the “space of possibilities” (also known as the “configuration space”), and the wave function Ψ(x1, x2) is a function on that space of possibilities. In fact, the wave function for any system is a function on the space of that system’s possibilities: for any possible arrangement X of the system, the wave function will give us a complex number Ψ(X).

Drawing a wave function can be tricky. I’ve done it in different ways in different contexts. Interpreting a drawing of a wave function can also be tricky. But it’s helpful to learn how to do it. So in today’s post, I’ll give you three different approaches to depicting the wave function for one of the simplest physical systems: a single object moving along a line. In coming weeks, I’ll give you more examples that you can try to interpret. Once you can read a wave function correctly, then you know your understanding of quantum physics has a good foundation.

For now, everything I’ll do today is in the language of 1920s quantum physics, Schrödinger style. But soon we’ll put this same strategy to work on quantum field theory, the modern language of particle physics — and then many things will change. Familiarity with the more commonly discussed 1920s methods will help you appreciate the differences.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 17, 2025

[An immediate continuation of Part 1, which you should definitely read first; today’s post is not stand-alone.]

The Asymmetry Between Location and Motion

We are in the middle of trying to figure out if the electron (or other similar object) could possibly be of infinitesimal size, to match the naive meaning of the words “elementary particle.” In the last post, I described how 1920’s quantum physics would envision an electron (or other object) in a state |P0> of definite momentum or a state |X0> of definite position (shown in Figs. 1 and 2 from last time.)

If it is meaningful to say that “an electron is really is an object whose diameter is zero”, we would naturally expect to be able to put it into a state in which its position is clearly defined and located at some specific point X0 — namely, we should be able to put it into the state |X0>. But do such states actually exist?

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 11, 2025

This is admittedly a provocative title coming from a particle physicist, and you might think it tongue-in-cheek. But it’s really not.

We live in a cosmos with quantum physics, relativity, gravity, and a bunch of elementary fields, whose ripples we call elementary particles. These elementary “particles” include objects like electrons, photons, quarks, Higgs bosons, etc. Now if, in ordinary conversation in English, we heard the words “elementary” and “particle” used together, we would probably first imagine that elementary particles are tiny balls, shrunk down to infinitesimal size, making them indivisible and thus elementary — i.e., they’re not made from anything smaller because they’re as small as could be. As mere points, they would be objects whose diameter is zero.

But that’s not what they are. They can’t be.

I’ll tell this story in stages. In my last post, I emphasized that after the Newtonian view of the world was overthrown in the early 1900s, there emerged the quantum physics of the 1920s, which did a very good job of explaining atomic physics and a variety of other phenomena. In atomic physics, the electron is indeed viewed as a particle, though with behavior that is quite unfamiliar. The particle no longer travels on a path through physical space, and instead its behavior — where it is, and where it is going — is described probabilistically, using a wave function that exists in the space of possibilities.

But as soon became clear, 1920s quantum physics forbids the very existence of elementary particles.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 10, 2025

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