Carroll is a professor of theoretical physics and philosophy at Johns Hopkins University, while Whiteson is a professor of experimental particle physics — a member of the ATLAS experiment at the Large Hadron Collider — at the University of California, Irvine. Both are well-known authors and great communicators; check them out!
Stay tuned for far more book-related material; there will be a whole wing of this website devoted to answering readers’ questions and providing additional information for those who want to know more!
I have posted my fourth article discussing zero-point energy. (Here are the first, the second, and the third, which covered respectively the zero-point energy of a ball on a spring, a guitar string, and a bosonic field whose particles have zero mass, such as the electromagnetic field.) Today’s article looks at fields whose particles have non-zero mass, such as the Higgs field, and fermionic fields, such as the electron field and quark fields. It presents some simple formulas, and in its final section, shows how one can obtain them using math.
Along the way we’ll encounter the idea of “supersymmetry” and its failed role in the cosmological constant problem. This is a word which (for some good historical reasons) generates a lot of heat. But stay calm; I’m neither promoting it nor bashing it. Supersymmetry is an idea which proves useful as a conceptual tool, whether it is true in nature or not.
A central issue in discussions of particle physics’ present and future is known as the hierarchy puzzle. Although I discuss the hierarchy — its confusing nature and the debates that it generates — in my upcoming book, I do so rather briefly, and so, I’ll be putting up some new pages on this website with supplemental information. The same information is relevant for the cosmological constant problem. (Older pages already giving various perspectives on these issues can be found here, here and here.)
I have just posted the first new page, on “zero-point motion” and “zero-point energy.” It begins with a verbal, non-technical description of zero-point motion and zero-point energy. There follows a sketch of the details using pre-university math. Future pages will apply these ideas to quantum fields, addressing notions of “vacuum energy density” and the “cosmological constant”, and then turning to “Higgs feedback” and the core of the hierarchy puzzle.
A quick description of the hierarchy in question: it is a hierarchy of energy scales, or of mass scales. One way it can be described is in terms of particle masses:
This year marks a half-century since the discovery that a quantum field theory, now known as QCD (quantum chromodynamics), could be the underlying explanation for the strong nuclear force. That’s the force that holds quarks and gluons inside of protons and neutrons, and keeps protons and neutrons clumped together in atomic nuclei. This major step in theoretical physics occurred just a couple of years after it was discovered that a similar quantum field theory for the weak nuclear force (which includes W bosons, a Z boson and a Higgs boson) is mathematically consistent.
With these two breakthroughs came the sudden and unexpected triumph of quantum field theory, emerging as the basic mathematical and conceptual language for understanding the cosmos. It came after two decades in which most experts were convinced that quantum field theory was inconsistent, and only a stepping stone to something deeper.
This week I am in New York City attending two attached scientific meetings, both focused on QCD and other quantum field theories that share its key property, known as “confinement.” One meeting is hosted by New York University, and the other, the Annual Meeting of the Simons Collaboration on Confinement and QCD Strings, by the Simons Foundation. Many luminaries who have spent time on this subject are here together, ranging from David Gross, who co-invented the subject (and was a winner of the 2004 Nobel Prize), to brilliant graduate students who are hoping to reinvent it.
The press is full of excitement today at the news that anti-matter — hydrogen anti-atoms, specifically, made from positrons and anti-protons instead of electrons and protons — falls down rather than rising up. This has been shown in the ALPHA experiment at CERN. But no theoretical physicist is surprised. Today I’ll explain one of many reasons that no one in the halls of theoretical physics even blinked.
One basic point is that “anti-particle” is not a category but a relationship. We do not say “electrons are particles” and “positrons are anti-particles”, nor do we say “quarks are particles” and “anti-quarks are anti-particles.” Such statements would be inconsistent. Instead we say “quarks and anti-quarks are each others’ anti-particles.” (It’s like the term “opponent” in a football match.) That’s because some particles are their own anti-particles, including photons. If we tried to divide all the types of particles into two categories, it wouldn’t be clear where photons would go; we couldn’t say either that they are particles or that they are anti-particles.
“Anti-particle” is a relationship, exchanging electrons with positrons and leaving photons unchanged. It is not a category; there are no objects that can be said to be “antiparticles”. (If there were, would photons be particles or would they be anti-particles?)
Because of this, we can’t hope that all the types of particles separate into two groups, particles which fall and anti-particle which rise. At best, we would have to guess what would happen to particles that are their own anti-particles. Fortunately, this is easy. There is such a thing as a positronium atom, an exotic atom made from an electron and positron co-orbiting one other. A positronium atom is its own anti-particle; if we flip every particle for its anti-particle, the positronium atom’s electron and positron simply switch places. If indeed gravity pulls down on electrons and pushes up by the same amount on positrons, then gravity’s pull on a positronium atom would cancel. This atom would neither rise nor fall; it would float, feeling no net gravity.
This example would then lead us to expect that particles that are their own anti-particles will float. The logic would apply to photons; they would feel no gravity.
Electrons and quarks make up atoms and are known to fall. If the positrons and anti-quarks that make up anti-atoms were to rise instead, then positronium atoms would float. This would imply that photons float too. But experiments have shown for a century that photons fall.
This would be a consistent picture. But experimentally, it is false: photons do feel gravity. The Sun bends the path of light, a fact that made Einstein famous in 1919, and an object’s strong gravity can create a gravitational lens that completely distorts the appearances of objects behind it. Photons can even orbit black holes. So experiment would force us to accept the picture shown below, if we want positrons to rise. Unfortunately, it is logically inconsistent.
Since photons fall too, we would have to believe either that positronium floats even though photons fall, or that positrons rise even though positronium falls. Neither makes any sense either conceptually or mathematically.
The only consistent picture, then, is that everything falls. Are there any loopholes in this argument? Sure; perhaps the gravity of the Earth, made of atoms, causes electrons and quarks to fall rapidly and causes positrons and anti-quarks to rise slowly, so that positronium still falls, just more gently than ordinary atoms do. (The reverse would be true around a planet made of anti-atoms.) This gives us many more possibilities to consider, and we have to get into more complex questions of what experiment has and hasn’t excluded.
But we would still face another serious problem, because there are anti-quarks inside of protons. (One line of evidence for this is shown here.) If quarks and anti-quarks, which have the same inertial mass (the type of mass that determines how they change speed when pushed) had different gravitational mass (which determines how gravity affects them), then protons and neutrons, too, would not have equal inertial and gravitational mass. [The many gluons inside the protons and neutrons could make this even worse.] Since electrons do have equal inertial and gravitational mass, protons and neutrons would then fall at a different rate than electrons do. The consequence would be that different atoms would fall at slightly different rates. High precision experiments clearly say otherwise. This poses additional obstructions to the idea that anti-quarks (and the anti-protons and anti-neutrons that contain them) could rise in Earth’s gravity.
At best, when it comes to mass and gravity, existing experiments only allow for minor differences between atoms and anti-atoms. To look for subtle effects of any such differences is one of the real, long-term goals of the ALPHA experiment. What they’ve done so far is a neat experimental coup, but despite the headlines, it does not change our basic knowledge of anti-particles in general or of anti-atoms in particular. For that, we have a few years to wait.
Today a reader asked me “Out of the quantum fields which have mass, do any of them also have weight?” I thought other readers would be interested in my answer, so I’m putting it here. (Some of what is discussed below is covered in greater detail in my upcoming book.)
Before we start, we need to rephrase the question, because fields do not have mass.
Every book on science focuses attention on a little sliver of a vast, complex universe. In Waves in an Impossible Sea, I had intended to write mainly about the Higgs field, and the associated Higgs particle that was discovered in 2012 to great fanfare. I was planning to explain how the Higgs field does its job in the universe, and why it’s so important for the existence of life.
However, this plan had a problem. The Higgs field would be irrelevant were it not for quantum physics on the one hand and Einstein’s relativity on the other, and to comprehend the latter requires some understanding of Galileo’searlier concept of relativity. To show why the Higgs field can give mass (more precisely, rest mass) to certain types of particles requires combining all of these notions together. Each of these topics is daunting, worthy of multiple books, and I knew I couldn’t hope to cover them all in 100,000 words!
To my surprise, resolving this problem wasn’t as difficult as I expected, once I picked out a few crucial elements about each of these subjects that I felt everyone ought to know. Lining up those conceptual points carefully, I found I could give a non-technical yet accurate explanation of how elementary particles can get mass from a Higgs field. (A more mathematical explanation has been given previously on this website, in two series of articles here and here.)
Yet what surprised me even more was that the book’s main subject slowly changed as I wrote it. It became focused on the question of how ordinary life emerges from an extraordinary cosmos. Though a substantial section of the book is devoted to the Higgs field, it is situated in a much wider context than I originally imagined.
With a headline like that, you probably think this is a parody. But in fact, I’m dead serious. Not only that, the discovery was made in the 1960s. Due to an accident of history, the physicists involved just didn’t realize it back then.
That said, there are profound problems with this headline. But the headlines we’ve seen this week, along the lines that “Physicists create a baby wormhole in the laboratory”, are actually WORSE than this one.
It is more accurate to say that “string theory and extra dimensions were discovered experimentally in the 1960s” than to say that “a baby wormhole was created in a lab in the early 2020s.”
And now I’m going to show you why. As you’ll see in this post and the next, the two claims are related.
