Of Particular Significance

Category: Quantum Field Theory

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

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 17, 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

If you’re of a certain age, you know Alan Alda from his wonderful acting in television shows and in movies. But you may not know of his long-standing interest in science communication and his podcast Clear and Vivid (named for the characteristics that he feels all communication should have.)

Alda and I had a great conversation about the idea that we are made of waves, and what it means for our relationship to the universe. A slimmed-down version of that discussion is now available on his podcast. I hope you enjoy it!

Separately, as promised: to my last post, which covered various ways of depicting and interpreting wave functions, I’ve added explanations of the two quantum wave functions that I placed at the end. Tomorrow I’ll take a step back and consider wave functions from a larger point of view, taking a brief look at what they are (and aren’t), what’s “wavy” (and not) about them, and at their roles in contexts ranging from pre-quantum physics of the 19th century to quantum field theory of the 21st.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 18, 2025

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.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 13, 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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POSTED BY Matt Strassler

ON February 11, 2025

When the electron, the first subatomic particle to be identified, was discovered in 1897, it was thought to be a tiny speck with electric charge, moving around on a path governed by the forces of electricity, magnetism and gravity. This was just as one would expect for any small object, given the incredibly successful approach to physics that had been initiated by Galileo and Newton and carried onward into the 19th century.

But this view didn’t last long. Less than 15 years later, physicists learned that an atom has a tiny nucleus with positive electric charge and most of an atom’s mass. This made it clear that something was deeply wrong, because if Newton’s and Maxwell’s laws applied, then all the electrons in an atom should have spiraled into the nucleus in less than a second.

From 1913 to 1925, physicists struggled toward a new vision of the electron. They had great breakthroughs and initial successes in the late 1920s. But still, something was off. They did not really find what they were looking for until the end of the 1940s.

Most undergraduates in physics, philosophers who are interested in physics, and general readers mainly learn about quantum physics of the 1920s, that of Heisenberg, Born, Jordan and of Schrödinger. The methods developed at that time, often called “quantum mechanics” for historical reasons, represented the first attempt by physicists to make sense of the atomic, molecular, and subatomic world. Quantum mechanics is all you need to know if you just want to do chemistry, quantum computing, or most atomic physics. It forms the basis of many books about the applications of quantum physics, including those read by most non-experts. The strange puzzles of quantum physics, including the double-slit experiment that I reviewed recently, and many attempts to interpret or alter quantum physics, are often phrased using this 1920s-era approach.

What often seems to be forgotten is that 1920s quantum physics does not agree with data. It’s an approximation, and sometimes a very good one. But it is inconsistent with Einstein’s relativity principle, a cornerstone of the cosmos. This is in contrast to the math and concepts that replaced it, known as relativistic quantum field theory. Importantly, electrons in quantum field theory are very different from the electrons of the 1920s.

And so, when trying to make ultimate conceptual sense of the universe, we should always be careful to test our ideas using quantum field theory, not relying on the physics of the 1920s. Otherwise we risk developing an interpretation which is inconsistent with data, at a huge cost in wasted time. Meanwhile, when we do use the 1920s viewpoint, we should always remember its limitations, and question its implications.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON February 6, 2025

When it comes to the weak nuclear force and why it is weak, there’s a strange story which floats around. It starts with a true but somewhat misleading statement:

  • The weak nuclear force (which is weak because its effects only extend over a short range) has its short range because the particles which mediate the force, the W and Z bosons, have mass [specifically, they have “rest mass”.] This is in contrast to electromagnetic forces which can reach out over great distances; that’s because photons, the particles of light which mediate that force, have no rest mass.

This is misleading because fields mediate forces, not particles; it’s the W and Z fields that are the mediators for the weak nuclear force, just as the electromagnetic field is the mediator for the electromagnetic force. (When people speak of forces as due to exchange of “virtual particles” — which aren’t particles — they’re using fancy math language for a simple idea from first-year undergraduate physics.)

Then things get worse, because it is stated that

  • The connection between the W and Z bosons’ rest mass and the short range of the weak nuclear force is that
    • the force is created by the exchange of virtual W and Z bosons, and
    • due to the quantum uncertainty principle, these virtual particles with mass can’t live as long and/or travel as far as virtual photons can, shortening their range.

This is completely off-base. In fact, quantum physics plays no role in why the weak nuclear force is weak and short-range. (It plays a big role in why the strong nuclear force is strong and short-range, but that’s a tale for another day.)

I’ve explained the real story in a new webpage that I’ve added to my site; it has a non-technical explanation, and then some first-year college math for those who want to see it. It’s gotten some preliminary comments that have helped me improve it, but I’m sure it could be even better, and I’d be happy to get your comments, suggestions, questions and critiques if you have any.

[P.S. — if you try but are unable to leave a comment on that page, please leave one here and tell me what went wrong; and if you try but are unable to leave a comment here too for some reason, please send me a message to let me know.]

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 10, 2025

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.

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POSTED BY Matt Strassler

ON December 19, 2024

This week I’ll be at the University of Michigan in Ann Arbor, and I’ll be giving a public talk for a general audience at 4 pm on Thursday, December 5th. If you are in the area, please attend! And if you know someone at the University of Michigan or in the Ann Arbor area who might be interested, please let them know. (For physicists: I’ll also be giving an expert-level seminar at the Physics Department the following day.)

Here are the logistical details:

The Quantum Cosmos and Our Place Within It

Thursday, December 5, 2024, 4:00-5:00 PM ; Rackham Graduate School , 4th Floor Amphitheatre

Click to enlarge map

When we step outside to contemplate the night sky, we often imagine ourselves isolated and adrift in a vast cavern of empty space—but is it so? Modern physics views the universe as more full than empty. Over the past century, this unfamiliar idea has emerged from a surprising partnership of exotic concepts: quantum physics and Einstein’s relativity. In this talk I’ll illustrate how this partnership provides the foundation for every aspect of human experience, including the existence of subatomic particles (and the effect of the so-called “Higgs field”), the peaceful nature of our journey through the cosmos, and the solidity of the ground beneath our feet.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON December 2, 2024

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