One of the most challenging aspects of writing a book or blog about the universe (as physicists currently understand it) is that both writer and reader must confront the concept of fields. The problem isn’t that fields are intrinsically that complicated. It’s that they are an unfamiliar abstraction — and novel abstractions of any sort are always difficult both for a writer to describe and for a reader to grasp.
What I’ll do today is give an explanation of fields that is complementary to the one that appears in the book’s chapters 13 and 14. The book’s approach is slow, methodical, and detailed, but today’s will be more of an overview, brief and relatively shallow, and presented in a different order. You will likely come away with many unanswered questions, but the book should help with that. And if the book and today’s post combined are still not enough, you can ask a question in the comments below, or on the book question page.
After my post last week about familiar and unfamiliar standing waves — the former famous from musical instruments, the latter almost unknown except to physicists (see Chapter 17 of the book) — I got a number of questions. Quite a few took the form, “Surely you’re joking, Mr. Strassler! Obviously, if you have a standing wave in a box, and you remove the box, it will quickly disintegrate into traveling waves that move in opposite directions! There is no standing wave without a container.”
Well, I’m not joking. These waves are unfamiliar, sure, to the point that they violate what some readers may have learned elsewhere about standing waves. Today I’ll show you animations to prove it.
I have just submitted a book, entitled Waves in an Impossible Sea, to my publisher, Basic Books (a trade press well known for Gödel, Escher, Bach, as well as numerous other science and math titles.) If all goes smoothly, it will go on sale in March 2024 or thereabouts. Now that it is mostly done, I will have some more time for writing of other sorts, including posts on this blog.
In the book, I’ve tried to explain how modern physics intersects with human existence and experience. I hope it will bring a physicist’s perspective on the cosmos, and on humans’ place within it, to a wider range of people. Along the way, it explains clearly and correctly what the Higgs field’s role in nature is, and how it plays that role, to the extent we understand it.
The book is non-technical yet sophisticated; though a layperson with no science background can read it, it’s not a lightweight read. I’ve made the universe as comprehensible as I know how, but I haven’t oversimplified it. Of course I had to leave a lot out; otherwise the book would have been 3500 pages instead of 350. But whatever is covered in the book is covered as carefully as space allows.
Precisely because I’ve had to leave out so many interesting side-topics and technical details, I’ll be providing lots of supplementary material on this website. Some of it will be brief surveys of topics that couldn’t fit in the book; some of it will allow me to discuss subtle points that would have distracted from the flow of the book; and some of it will present some of the underlying math that didn’t belong in a non-technical book, but which I know will interest certain readers of this website. I’ll be writing much of that material in coming months, and as I finish parts of it, I’ll be posting them here. Your comments will be both welcome and essential in making sure that it is comprehensible and comprehensive.
Today I’m continuing the reader-requested explanation of the “triplet model,” (a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.) The math required is pre-university level, just algebra this time.
The third webpage, showing how to combine knowledge from the first page and second page of the series into a more complete cartoon of the triplet model, is ready. It illustrates, in rough form, how a small modification of the Higgs mechanism of the Standard Model can shift a “W” particle’s mass upward.
Future pages will seek to explain why the triplet model resembles this cartoon closely, and also to explore the implications for the Higgs boson.
I’m continuing the reader-requested explanation of the “triplet model,” a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.
The math required is pre-university level, mostly algebra and graphing.
Based on readers’ requests, I have started the process of explaining the “triplet model,” a classic variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.
The math required is pre-university level, so it should be broadly accessible to those who are interested.
Outside of physics, most people think of a vacuum as being the absence of air. For physicists thinking about the laws of nature, “vacuum” means space that has been emptied of everything — at least, emptied of everything that can actually be removed. That certainly means removing all particles from it. But even though vacuum implies emptiness, it turns out that empty space isn’t really that empty. There are always fields in that space, fields like the electric and magnetic fields, the electron field, the quark field, the Higgs field. And those fields are always up to something.
First, all of the fields are subject to “quantum fluctuations” — a sort of unstoppable jitter that nothing in our quantum world can avoid. [Sometimes these fluctuations are referred to as “virtual particles”; but despite the name, those aren’t particles. Real particles are well-behaved, long-lived ripples in those fields; fluctuations are much more random.] These fluctuations are always present, in any form of empty space.
Second, and more important for our current discussion, some of the fields may have average values that aren’t zero. [In our own familiar form of empty space, the Higgs field has a non-zero average value, one that causes many of the known elementary particles to acquire a mass (i.e. a rest mass).] And it’s because of this that the notion of vacuum can have a plural: forms of empty space can differ, even for a single universe, if the fields of that universe can take different possible average values in empty space. If a given universe can have more than one form of empty space, we say that “it has more than one vacuum”.
There are reasons to think our own universe might have more than one form of vacuum — more than just the one we’re familiar with. It is possible that the Standard Model (the equations used to describe all of the known elementary particles, and all the known forces except gravity) is a good description of our world, even up to much higher energies than our current particle physics experiments can probe. Physicists can predict, using those equations, how many forms of empty space our world would have. And their calculations show that our world would have (at least) two vacua: the one we know, along with a second, exotic one, with a much larger average value for the Higgs field. (Remember, this prediction is based on the assumption that the Standard Model’s equations apply in the first place.) An electron in empty space would have a much larger mass than the electrons we know and love (and need!)
The future of the universe, and our understanding of how the universe came to be, might crucially depend on this second, exotic vacuum. Today’s article sets the stage for future articles, which will provide an explanation of why the vacua of the universe play such a central role in our understanding of nature at its most elemental.
Familiar throughout our international culture, the “Big Bang” is well-known as the theory that scientists use to describe and explain the history of the universe. But the theory is not a single conceptual unit, and there are parts that are more reliable than others.
It’s important to understand that the theory — a set of equations describing how the universe (more precisely, the observable patch of our universe, which may be a tiny fraction of the universe) changes over time, and leading to sometimes precise predictions for what should, if the theory is right, be observed by humans in the sky — actually consists of different periods, some of which are far more speculative than others. In the more speculative early periods, we must use equations in which we have limited confidence at best; moreover, data relevant to these periods, from observations of the cosmos and from particle physics experiments, is slim to none. In more recent periods, our confidence is very, very strong.
History of the Universe, taken from my article with the same title, with added color-coded measures of how confident we can be in our understanding. In each colored zone, the degree of confidence and the observational/experimental source of that confidence is indicated. Three different possible starting points for the “Big Bang” are noted at the bottom; note that individual scientists may mean different things by the term. (Caution: there is a subtlety in the use of the words “Extremely Cold”; there are subtle quantum effects that I haven’t yet written about that complicate this notion.)
Notice that in the figure, I don’t measure time from the start of the universe. That’s because I don’t know how or when the universe started (and in particular, the notion that it started from a singularity, or worse, an exploding “cosmic egg”, is simply an over-extrapolation to the past and a misunderstanding of what the theory actually says.) Instead I measure time from the start of the Hot Big Bang in the observable patch of the universe. I also don’t even know precisely when the Hot Big Bang started, but the uncertainty on that initial time (relative to other events) is less than one second — so all the times I’ll mention, which are much longer than that, aren’t affected by this uncertainty.
I’ll now take you through the different confidence zones of the Big Bang, from the latest to the earliest, as indicated in the figure above.
Juan Maldacena, on his latest thinking on the relation between gravity, geometry and the entropy of quantum entanglement;
Igor Klebanov, on some fascinating work in which new relations have been found between some simple quantum field theories and a very poorly understood and exotic theory, known as Vassiliev theory (a theory that has more fields than a field theory but fewer than a string theory);
Raphael Bousso, on his recent attempts to prove the so-called “covariant entropy bound”, another relation between entropy and geometry, that Bousso conjectured over a decade ago;
Henrietta Elvang, on the resolution of a puzzle involving the relation between a supersymmetric field theory and a gravitational description of that same theory;
Nima Arkani-Hamed, about his work on the amplituhedron, a set of geometric objects that allow for the computation of particle scattering in various quantum field theories (and who related how one of Polchinski’s papers on quantum field theory was crucial in convincing him to stay in the field of high-energy physics);
Yours truly, in which I quickly reviewed my papers with Polchinski relating string theory and quantum field theory, emphasizing what an amazing experience it is to work with him; then I spoke briefly about my most recent Large Hadron Collider [LHC] research (#1,#2), and concluded with some provocative remarks about what it would mean if the LHC, having found the last missing particle of the Standard Model (i.e. the Higgs particle), finds nothing more.
The lectures have been recorded, so you will soon be able to find them at the KITP site and listen to any that interest you.
There were also two panel discussions. One was about the tremendous impact of Polchinski’s 1995 work on D-branes on quantum field theory (including particle physics, nuclear physics and condensed matter physics), on quantum gravity (especially through black hole physics), on several branches of mathematics, and on string theory. It’s worth noting that every talk listed above was directly or indirectly affected by D-branes, a trend which will continue in most of Friday’s talks. There was also a rather hilarious panel involving his former graduate students, who spoke about what it was like to have Polchinski as an advisor. (Sorry, but the very funny stories told at the evening banquet were not recorded. [And don’t ask me about them, because I’m not telling.])
Let me relate one thing that Eric Gimon, one of Polchinski’s former students, had to say during the student panel. Gimon, a former collaborator of mine, left academia some time ago and now works in the private sector. When it was his turn to speak, he asked, rhetorically, “So, how does calculating partition functions in K3 orientifolds” (which is part of what Gimon did as a graduate student) “prepare you for the real world?” How indeed, you may wonder. His answer: “A sense of pertinence.” In other words, an ability to recognize which aspects of a puzzle or problem are nothing but distracting details, and which ones really matter and deserve your attention. It struck me as an elegant expression of what it means to be a physicist.
