I’ve been trying to get back to the blog recently. But every time I plan to write a blog post, something happens that requires my attention and adds to the list of items I should be writing about.
I’ve decided that the best I can do, for now, is to summarize some of the key stories that have been on my radar. The overarching news, aside from the 2026 physics Nobel Prize, is what you’ve heard: artificial intelligence (AI) is transforming mathematics and high-energy theoretical physics, no question. That said, what is reported in the media about this is usually wrong in key details, and almost always wildly overstates what’s been accomplished. Nevertheless, the advances in AI models in the last couple of months are historic and transformative, and there is every reason to expect this to accelerate. For people like me, 2027 will surely be very different from autumn 2026, which in turn barely resembles spring 2026.
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.
Pioneer Works is “an artist and scientist-led cultural center in Red Hook, Brooklyn that fosters innovative thinking through the visual and performing arts, technology, music, and science.” It’s a cool place: if you’re in the New York area, check them out! Among many other activities, they host a series called “Picture This,” in which scientists ruminate over scientific images that they particularly like. My own contribution to this series has just come out, in which I expound upon the importance and meaning of this graph from the CMS experimental collaboration at the Large Hadron Collider [LHC]. (The ATLAS experimental collaboration at the LHC has made essentially identical images.)
The point of the article is to emphasize the relation between the spikes seen in this graph and the images of musical frequencies that one might see in a recording studio (as in this image from this paper). The similarity is not an accident.
Each of the two biggest spikes is a sign of an elementary “particle”; the Z boson is the left-most spike, and the Higgs boson is the central spike. What is spiking is the probability of creating such a particle as a function of the energy of some sort of physical process (specifically, a collision of objects that are found inside protons), plotted along the horizontal axis. But energy E is related to the mass m of the “particle” (via E=mc2) and it is simultaneously related to the frequency f of the vibration of the “particle” (via the Planck-Einstein equation E = hf)… and so this really is a plot of frequencies, with spikes reflecting cosmic resonances analogous to the resonances of musical instruments. [If you find this interesting and would like more details, it was a major topic in my book.]
The title of the article refers to the fact that the Z boson and Higgs boson frequencies are out of tune, in the sense that if you slowed down their frequencies and turned them into sound, they’d be dissonant, and not very nice to listen to. The same goes for all the other frequencies of the elementary “particles”; they’re not at all in tune. We don’t know why, because we really have no idea where any of these frequencies come from. The Higgs field has a major role to play in this story, but so do other important aspects of the universe that remain completely mysterious. And so this image, which shows astonishingly good agreement between theoretical predictions (colored regions) and LHC data (black dots), also reveals how much we still don’t understand about the cosmos.
In a previous post, I showed you that the Standard Model, armed with its special angle θw of approximately 30 degrees, does a pretty good job of predicting a whole host of processes in the Standard Model. I focused attention on the decays of the Z boson, but there were many more processes mentioned in the bonus section of that post.
But the predictions aren’t perfect. They’re not enough to convince a scientist that the Standard Model might be the whole story. So today let’s bring these predictions into better focus.
This is my second post on the subject of why “the speed of light (in empty space)”, more accurately referred to as “the cosmic speed limit”, is so fast. This speed, denoted c, is about 186,000 miles (300,000 km) per second, which does indeed seem quick.
But as I pointed out in my first post on this subject, this isn’t really the right question, because it implicitly views humans as centrally important and asks why the cosmos as strange. That’s backward. We should instead ask why we ourselves are so slow. Not only does this honor the cosmos properly, making it clear that it is humans that are the oddballs here, this way of asking the question leads us to the answer.
And the answer is this: ordinary atomic material, from which we are made, is fragile. If a living creature were to move (relative to the objects around it) at speeds anywhere close to c, it couldn’t possibly survive its first slip and fall, or its first absent-minded collision with a door frame.
Today I’ll use a principled argument, founded on basic particle physics and its implications for atomic physics, to show that any living creature made from atoms will inevitably view the cosmic speed limit as extremely fast compared to the speeds that it ordinarily experiences.
One thing I emphasized is that while photons [“particles” of light] moving across empty space are always traveling waves moving at the speed of light c, electrons are different. When in motion they too are traveling waves, but unlike photons, they can slow down, and even be stationary. When stationary, they are standing waves, of a somewhat unfamiliar sort (as described here and here). All of this is discussed in detail in the book’s chapters 16 and 17.
Whiteson has sent me a couple of questions that listeners raised with him, and since I imagine some of you might have similar questions, I decided to answer them publicly here.
From the structure of the Standard Model of particle physics, one might wonder if the electron, muon and tau, so similar except for their masses, might really be the same object seen in three different guises. Last week, starting with a post for general readers, and then looking at the situation in more detail (Part 1 of this two-part series), I showed one way in which this idea fails to agree with experiment. Today I’ll give you another point of failure, focused on a property of particles known as “spin”.
Spin: The Idea In Brief
What is “spin” in physics? It’s related to the word “spin” in English, but with some adjustment. I’ll write a longer article about spin elsewhere, but here’s a brief introduction.
The Earth “spins”, both in the English sense and in the physics sense: it rotates. The same is true of a tennis ball. The rotation can be changed when the ball interacts with a tennis racket or with the ground. It can also be changed when it interacts with another tennis ball. In fact, if two balls strike each other, some of the spin of one ball can be transferred to the other, as in Fig. 1.
Figure 1: (Left) Two balls, the upper one spinning, approach and collide; (Right) The balls recoil from the collision, with some of the spin of the upper ball now transferred to the lower ball.
Elementary “particles” can have spin too, which can be (in part) changed by or transferred to other objects that they interact with. But this type of spin is somewhat different from ordinary rotation.
For example, an electron “spins”. Always. An interaction can change the direction of an electron’s spin, but it cannot change its overall amount. I’ll tell you what I mean by “amount” in a moment, but the quantity of the amount is a famous number:
h / 4π = ℏ / 2
where h, Planck’s constant, shows up whenever quantum physics matters. This amount of spin is tiny; if a tennis ball had this amount of spin, it wouldn’t have even rotated once since the universe was born. But for an electron, it’s quite a lot.
Usually, as shorthand, one takes the ℏ to be implicit, and just says that “the electron has spin 1/2”. I’ll do that in what follows.
How can we visualize this spinning? It’s not easy. It’s best not to visualize an electron as a small rotating ball; it’s the wrong picture. Quantum field theory, the modern theory of “particles”, gives a different picture. Just as we should think of light as a wave made of wave-like photons, we should think of the electron as a wave — specifically, a wave in the electron field. [This wave is not to be confused with a wave function, which is something else]. A wave in the electron field can rotate in ways that a little ball cannot. This, however, is hard to draw, and in any case is a story for another day.
The important point is that the spin of an elementary “particle” is not like the simple rotational spinning of a tennis ball, even though it is in the same category. An electron has spin intrinsically, by its very nature; there is no electron without its spin, just as there is no electron without its internal energy and rest mass (as emphasized in my recent book, Chapter 17). That’s certainly not true for a tennis ball, which can have any spin, including none.
These details won’t matter much in what follows, though, so let’s step away from these subtleties and move on.
Ways to Spin
So far, I’ve suggested two types of spinning:
the intrinsic spinning (or “intrinsic angular momentum”) of elementary particles
the ordinary spinning (or “ordinary angular momentum”) of objects that are rotating, or are in orbit around other objects.
Both contribute to the surprising way that physicists use the word “spin”.
Suppose we have an object that is made of multiple elementary particles. Its total angular momentum involves combining the intrinsic angular momentum of its elementary particles with the ordinary angular momentum that the particles may have as they move around each other. Physicists now do something unexpected: they refer to the object’s total angular momentum as its spin. They do this even though the object is not elementary, meaning that its spin may potentially combine both intrinsic spinning and ordinary spinning of the objects inside it.
So the real meaning of spin, as particle physicists use the term, is this: it is the total angular momentum of an isolated object — an object that may be elementary, or that may itself be formed from multiple elementary objects. That means that the spin of an object like an atom, made of electrons, protons and neutrons, or of a proton, made of quarks, antiquarks and gluons, may potentially arise from multiple sources.
Atoms, Protons and Strings
For example, let’s take a hydrogen atom, made from an electron and a proton. (For starters we’ll treat both of these subatomic particles as though they were elementary. We’ll return to their possible internal structure later.)
I’ll refer in the following to four atomic states, illustrated below in Fig. 2.
The ground state of a hydrogen atom (known as the “1s state”) has spin 0. Nevertheless, it is made of an electron with spin 1/2 surrounding a proton of spin 1/2. The two spin in opposite directions so that their angular momentum cancels.
There is a very slightly excited state, often neglected in first-year physics courses or in quick summaries of atomic physics, where the electron and proton spin in the same direction, and their spins add instead of cancelling. This state of the atom has spin 1; I’ll call it the “spin-flipped 1s state”. (The transition from this excited state to the ground state involves the emission of a radio wave photon with a wavelength of 21 cm, leading to the so-called “21 cm line” widely observed in astronomy. )
There are more dramatically excited states known as the “2s and 2p states”. The 2s state has spin 0, while the 2p state has spin 1. But even though the 2p state and the spin-flipped state both have spin 1, their spins have different origins. The total angular momentum of the 2p state does not come from the intrinsic angular momenta of the electron and proton; those cancel out, just as they do in the 1s and 2s states. Instead, the spin of the 2p state comes from a sort of rotational motion of the electron around the proton.
These four states are sketched in Figure 2. (Spin-flipped versions of the 2s and 2p states exist but are not shown.)
Figure 2: (Bottom left) In the ground state of hydrogen, the spin of the proton (central red dot) is opposite to that of the electron (surrounding blue cloud), so that the atom has spin 0. (Bottom right) If the electron spin is flipped, both the proton and electron spin in the same sense, giving the atom spin 1. (Top) While the 2s state is similar to the 1s state, the 2p state has the electron and proton spinning in opposite directions but has the electron moving around the proton (dashed black line), giving the atom spin 1.
The fact that the ground state has spin 0, and yet the 2p state has larger spin specifically due to the electron’s motion around the proton, illustrates the main point of this post. If an object is made from multiple constituent objects, nothing can prevent those constituents from moving around one another. That means they can have ordinary (or “orbital”) angular momentum, which then contributes, along with the constituents’ spin, to the combined object’s spin — i.e., to its total angular momentum.
Therefore, an object that is not elementary, and so contains multiple objects inside it, will inevitably have excited states with different amounts of spin. Indeed, the hydrogen atom has excited states of total angular momentum 0, 1, 2, 3, and so on. All atoms exhibit similar behavior.
The same applies for protons, which aren’t elementary either. The proton has spin 1/2, but its excited states have spin 1/2, 3/2, 5/2, 7/2, and so on. The first excited state of the proton, the Delta, has spin 3/2. This is most easily understood as a rearrangement of the spins of the quarks, gluons and anti-quarks that it contains (though the exact rearrangement is not obvious, due to the complexity of a proton; see also chapter 6 of the book.) The next excited state, the p(1440), has spin 1/2 like the proton. But many other excited states have been observed, with spin 3/2, 5/2, 7/2, 9/2, and perhaps even 11/2.
A string, such as one finds in string theory, is another object with internal constituents, which one might call bits-of-string. A string can always be spun faster. That’s why, in the superstring theory that is sometimes touted as a potential “theory-of-everything” (or in less grandiose language, a complete theory of space, fields and particles), there are states of all possible spin — any integer times 1/2. Unfortunately, were this really the theory of our universe, the higher-spin states of the string would probably have far too much mass for us to make them in near-term experiments, putting this prediction of the theory out of reach for now.
But string theory isn’t just useful in this rarified context. It can also be used to describe the physics of “hadrons” — objects made from quarks and gluons, including protons. All indications from experiments and numerical calculations do indeed suggest that hadrons come in all possible spins; this includes the excited states of the proton already mentioned above. (That said, the higher the spin, the harder it is to make the states, making it more and more challenging to observe them.)
Spin and the Electron, Muon and Tau
None of this is true for electrons, muons or taus, all of which have spin 1/2. No electron-like particle with spin 3/2 has ever been observed.
This argues strongly against the electron, muon and tau all being made from the same object. Atoms, protons and strings all have excited states with the same spin as the ground state, but at roughly the same mass, they also have excited states with more spin. If the muon were an excited state of the electron, we would expect to see an object with spin 3/2 that has a mass comparable to the muon, and certainly below the mass of the tau. Such a state would easily have been observed decades ago, so it doesn’t exist.
Are there loopholes to this logic? Yes. It is possible, in special circumstances, for the excited states with higher spin to have much larger masses than the excited states which share the same spin as the ground state. This is a long story which I won’t try to tell here, but examples arises in the context of extra dimensions, and others in the related context of exotic theories of quark-like and gluon-like objects (with buzzwords such as “AdS/CFT” or “gauge/string duality”).
However, it’s hard to apply the loophole to the muon and tau. In such a scenario, the electron should have many more cousins than just two, and some of the others should have observed by now.
Furthermore, data now confirms that both the tau and muon get their rest mass from the Higgs field; see Fig. 3. For such particles, the loopholes I just mentioned don’t apply.
Figure 3: The interaction strengths of various types of elementary particles with the Higgs field, plotted versus those particles’ rest masses. Any particle whose rest mass comes entirely or largely from the Higgs field should lie on or near the dashed line. The data shows this is true of both the tau τ and the muon μ, as well as of the bottom and top quarks b, t, and of the W and Z bosons.
We must also recall the arguments given in the first part of this series. If muons and taus are excited states of electrons, it should be possible for any sufficiently energetic collision to turn an electron into a muon or tau, and for decays via photons to do the reverse. But these processes are not observed.
In short, the properties of the electron, muon and tau disfavor the idea that they are somehow secretly the same object in three different quantum states. The explanation of their similarities must lie elsewhere.
[This is a follow-up to Monday’s post, going more into depth.]
Among the known elementary particles are three cousins: the electron, the muon and the tau. The three are identical in all known experiments — they have all the same electromagnetic and weak nuclear interactions, and no strong nuclear interactions — except for effects that arise from the fact that they have different rest masses:
[These differences arise from their different interactions with the Higgs field; to learn more about this, see Chapter 22 of my book.]
[Note added for clarity: these particles do exhibit slightly different magnetic moments, dramatically different lifetimes, and a number of other differences — but all of those variations can be traced back to the difference in their masses.]
Question: How sure are we that these three cousins aren’t actually the same object, seen in three different quantum states?
Within the Standard Model of particle physics, one finds three almost identical types of particles: the electron, the muon and the tau. Their interactions with the electromagnetic force, the weak nuclear force and the strong nuclear force are exactly the same. In particular, all three have electric charge -1 (which in first-year physics classes we would usually write as “-e”).
They’re not entirely identical, however. For instance, they have different masses.
Compare these to a hydrogen atom, which has mass 0.938783 GeV/c2 . (For the definition of “GeV”, which is an amount of energy, click here.) [Specifically, these are their “rest masses”. Rest mass is the type of mass that is intrinsic to objects and does not change with speed; see Chapter 5 of Waves in an Impossible Sea.]
Why does nature have these three similar particles, collectively called the “charged leptons“? We don’t know. But they’re not alone.
