Where Does The Mass Of A Proton Come From?
Frank Wilczek: The Origin of (most) Mass 2003
Quarks and gluons account for most of the mass of matter. The answer appears to be miraculous. Quarks and gluons—that are themselves massless. The equations of Quantum Chromodynamics output Mass without Mass, which sounds suspiciously like Something for Nothing. How did it happen? The key, again, is asymptotic freedom. Previously, I discussed this phenomenon in terms of hard and soft radiation. Hard radiation is rare, soft radiation is common. When quantum mechanics is taken into account a “bare”color charge, inserted into empty space, will start to surround itself with a cloud of virtual color gluons. These color gluons fields themselves carry color charge, so they are sources of additional soft radiation. The result is a self-catalyzing enhancement that leads to runaway growth. A small color charge, in isolation, builds up a big color thundercloud. All this structure costs energy, and theoretically the energy for a quark in isolation is infinite.
https://physics.mit.edu/wp-content/uploads/2021/01/physicsatmit_03_wilczek_originofmass.pdf
Martin B. van der Mark: Quantum mechanical probability current as electromagnetic 4-current from topological EM fields August 2015
The structure of stable matter is the result of a balance of forces working between some otherwise bound objects, particles, or granules. The final stage is a balance of forces on a continuous, circulating flow of energy, holding itself together. The proton’s internal dynamics must be essentially a light-speed knot of circulating energy. That energy is the “stuff” we were after, and it is continuous and takes part in the electromagnetic interaction.
https://www.researchgate.net/publication/281460952_Quantum_mechanical_probability_current_as_electromagnetic_4-current_from_topological_EM_fields
My comment: See the keywords here. The answer to the origin of mass seems to be miraculous. Its sounds suspiciously like Something from Nothing. And: The energy for a quark in isolation is infinite.
Could it be, that God holds an infinite power, instantiated energy/mass through his eternal power when he stretched out the universe, and all mass is just a manifestation of his eternal power?
David Tong: Particle Physics
What are we made of? What are the fundamental building blocks of the universe from which you, me, and everything else is constructed? Every experiment that we’ve ever performed can be explained in terms of a collection of particles interacting through a handful of forces. The description is given through the Standard Model. The language in which the Standard Model is written is known as quantum field theory. Matter is made of indivisible objects called atoms.The proton contains two up quarks and a down quark, while the neutron contains two down quarks and an up. Both quarks have fractional electric charge. In units in which the electron has charge −1, the up quark has charge +2/3 and the down quark charge − 1/3 . This then gives the familiar charges of the proton ( 2/3 + 2/3 − 1/3 = +1) and the neutron (- 1/3 − 1/3 + 2/3 = 0).
The Higgs Force: A force which role is dramatic: it allows all the elementary particles described in the table above to get a mass.
http://www.damtp.cam.ac.uk/user/tong/pp/pp.pdf
If you were to divide the particles that made up your body into smaller and smaller bits, you'd find that at every step along the way -- at least in terms of mass -- the whole was equal to the sum of its parts. If you broke your body down into its individual bones, fat and organs, they would add up to an entire human being. If you broke them down further, into cells, again, the cells would still add up to the same mass as you. Cells can be divided into organelles, organelles broken up into individual molecules, molecules into atoms, and atoms into protons, neutrons and electrons. At that level, there's a tiny but noticeable difference: the individual protons, neutrons and electrons are off by right around 1% from a human, thanks to nuclear binding energy.
The nucleus of a carbon atom has a mass that's approximately 0.8% lower than the individual protons and neutrons that compose it, thanks to nuclear binding energy.
A carbon atom, made up of six protons and six neutrons, is approximately 0.8% lighter than the individual component particles that make it up. The way carbon is formed is through the nuclear fusion of hydrogen into helium and then helium into carbon; the energy released is what powers most types of stars in both their normal and red giant phases, and the "lost mass" is where that energy comes from, thanks to Einstein's E = mc2. This is how most types of binding energy work: the reason it's harder to pull apart multiple things that are bound together is that they released energy when they were joined, and you have to put energy in to free them again.
This is why it's such a puzzling fact that when you take a look at the particles that make up the proton -- the three different quarks at the heart of them -- their combined masses are only 0.2% of the mass of the proton as a whole.
The particles of the standard model, with masses (in MeV) in the upper right. A proton, made up of two up quarks and one down quark, has a mass of ~938 MeV/c^2.
The way quarks bind into protons is fundamentally different from all the other forces and interactions we know of. Instead of the force getting stronger when objects get closer -- like the gravitational, electric or magnetic forces -- the attractive force goes down to zero when quarks get arbitrarily close. And instead of the force getting weaker when objects get farther away, the force pulling quarks back together gets stronger the farther away they get.
This property of the strong nuclear force is known as asymptotic freedom, and the particles that mediate this force are known as gluons. Somehow, the energy binding the proton together, the other 99.8% of the proton's mass, comes from these gluons.
Rather than three main, green (valence) quarks connected by (spring-like) gluons, the proton's structure is much more complicated, with additional (sea) quarks and gluons populating the proton's interior.
Because of how the strong nuclear force works, there are large uncertainties as to where these gluons are actually located at any point in time. We presently have a solid model of the average gluon density inside a proton, but if we want to know where the gluons are actually more likely to be located, that requires more experimental data, as well as better models to compare the data against. Recent advances by theorists Björn Schenke and Heikki Mäntysaari may be able to provide those much-needed models. As Mäntysaari detailed:
It is very accurately known how large the average gluon density is inside a proton. What is not known is exactly where the gluons are located inside the proton. We model the gluons as located around the three [valence] quarks. Then we control the amount of fluctuations represented in the model by setting how large the gluon clouds are, and how far apart they are from each other.
The internal structure of a proton, with quarks, gluons, and quark spin shown.
When you collide two particles like protons, a proton and a heavy ion, or two heavy ions together, you can't simply model them as proton-proton collisions. Instead, you see a distribution of three types of collisions: quark-quark collisions, quark-gluon collisions or gluon-gluon collisions. It's the components within these subatomic particles that actually collide, rather than the entire structures (the protons) themselves. While at lower energies, it's almost always quarks that collide, the higher energies reached by RHIC, the Relativistic Heavy Ion Collider, at Brookhaven and by the LHC at CERN have a very high probability of gluon-gluon interactions, with the potential to reveal the location of the gluons inside a proton itself. As Mäntysaari continued:
This process doesn't happen at all if the proton always looks the same. The more fluctuations we have, the more likely this process is to happen.
A better understanding of the internal structure of a proton, including how the "sea" quarks and gluons are distributed, has been achieved through both experimental improvements and new theoretical developments in tandem.
The combination of this new theoretical model and the ever-improving LHC data will better enable scientists to understand the internal, fundamental structure of protons, neutrons and nuclei in general, and hence to understand where the mass of the known objects in the Universe comes from. The biggest boon to this type of research, however, would be the development of an Electron-Ion Collider (EIC), a proposed collider by many collaborations across the world. Unlike RHIC or the LHC, which collide protons with ions -- resulting in a very messy final signal -- an EIC would be much more controlled, as there are no internal, uncontrollable motions inside an electron to confound the experimental results. If you want to study the internal structure of a proton or collection of nuclei, deep inelastic scattering is the only way to go. Considering that colliders began that journey less than a century ago, and that we're now achieving energies approximately a factor of 10,000 greater than when we first started, probing and understanding exactly how matter gets its mass may finally be within our reach. The quark-gluon plasma within the nucleus, and the attendant fluctuations, may finally be ready to reveal its secrets to us. And when it does, one of the longest-standing mysteries of physics, of where the mass of the known matter comes from (still a mystery even after discovery of the Higgs), may finally yield to humanity.
Diana Kwon: Where does mass come from? 05/12/16 2
The story of particle mass starts right after the big bang. During the very first moments of the universe, almost all particles were massless, traveling at the speed of light in a very hot “primordial soup.” At some point during this period, the Higgs field turned on, permeating the universe and giving mass to the elementary particles.
The Higgs field changed the environment when it was turned on, altering the way that particles behave. Some of the most common metaphors compare the Higgs field to a vat of molasses or thick syrup, which slows some particles as they travel through.
Others have envisioned the Higgs field as a crowd at a party or a horde of paparazzi. As famous scientists or A-list celebrities pass through, people surround them, slowing them down, but less-known faces travel through the crowds unnoticed. In these cases, popularity is synonymous with mass—the more popular you are, the more you will interact with the crowd, and the more “massive” you will be.
But why did the Higgs field turn on? Why do some particles interact more with the Higgs field than others? The short answer is: We don’t know.
“This is part of why finding the Higgs field is just the beginning—because we have a ton of questions,” says Matt Strassler, a theoretical physicist and associate of the Harvard University physics department.
The strong force and you
The Higgs field gives mass to fundamental particles—the electrons, quarks and other building blocks that cannot be broken into smaller parts. But these still only account for a tiny proportion of the universe’s mass.
The rest comes from protons and neutrons, which get almost all their mass from the strong nuclear force. These particles are each made up of three quarks moving at breakneck speeds that are bound together by gluons, the particles that carry the strong force. The energy of this interaction between quarks and gluons is what gives protons and neutrons their mass. Keep in mind Einstein’s famous E=mc2, which equates energy and mass. That makes mass a secret storage facility for energy.
“When you put three quarks together to create a proton, you end up binding up an enormous energy density in a small region in space,” says John Lajoie, a physicist at Iowa State University.
A proton is made of two up quarks and a down quark; a neutron is made of two down quarks and an up quark. Their similar composition makes the mass they acquire from the strong force nearly identical. However, neutrons are slightly more massive than protons—and this difference is crucial. The process of neutrons decaying into protons promotes chemistry, and thus, biology. If protons were heavier, they would instead decay into neutrons, and the universe as we know it would not exist.
“As it turns out, the down quarks interact more strongly with the Higgs [field], so they have a bit more mass,” says Andreas Kronfeld, a theoretical physicist at Fermilab. This is why the tiny difference between proton and neutron mass exists.
But what about neutrinos?
We’ve learned that the elementary particles get their mass from the Higgs field—but wait! There may be an exception: neutrinos. Neutrinos are in a class by themselves; they have extremely tiny masses (a million times smaller than the electron, the second lightest particle), are electrically neutral and rarely interact with matter.
Scientists are puzzled as to why neutrinos are so light. Theorists are currently considering multiple possibilities. It might be explained if neutrinos are their own antiparticles—that is, if the antimatter version is identical to the matter version. If physicists discover that this is the case, it would mean that neutrinos get their mass from somewhere other than the Higgs boson, which physicists discovered in 2012.
Neutrinos must get their mass from a Higgs-like field, which is electrically neutral and spans the entire universe. This could be the same Higgs that gives mass to the other elementary particles, or it could be a very distant cousin. In some theories, neutrino mass also comes from an additional, brand new source that could hold the answers to other lingering particle physics mysteries.
“People tend to get excited about this possibility because it can be interpreted as evidence for a brand new energy scale, naively unrelated to the Higgs phenomenon,” says André de Gouvêa, a theoretical particle physicist at Northwestern University.
This new mechanism may also be related to how dark matter, which physicists think is made up of yet undiscovered particles, gets its mass.
“Nature tends to be economical, so it's possible that the same new set of particles explains all of these weird phenomena that we haven't explained yet,” de Gouvêa says.
Frank Wilczek: The Origin of Mass 01/2021 3
Everyday work at the frontiers of modern physics usually involves complex concepts and extreme conditions. We speak of quantum fields, entanglement, or supersymmetry, and analyze the ridiculously small or conceptualize the incomprehensibly large. Just as Willie Sutton famously explained that he robbed banks because “that’s where the money is,” so we do these things because “that’s where the Unknown is.” It is an amazing and delightful fact, however, that occasionally this sophisticated work gives answers to childlike questions about familiar things. Here I’d like to describe how my own work on subnuclear forces, the world of quarks and gluons, casts brilliant new light on one such child-like question: What is the origin of mass?
Has Mass an Origin?
That a question makes grammatical sense does not guarantee that it is answerable, or even coherent. The concept of mass is one of the first things we discuss in my freshman mechanics class. Classical mechanics is, literally, unthinkable without it. Newton’s second law of motion says that the acceleration of a body is given by dividing the force acting upon it by its mass. So a body without mass wouldn’t know how to move, because you’d be dividing by zero. Also, in Newton’s law of gravity, the mass of an object governs the strength of the force it exerts. One cannot build up an object that gravitates, out of material that does not, so you can’t get rid of mass without getting rid of gravity. Finally, the most basic feature of mass in classical mechanics is that it is conserved. For example, when you bring together two bodies, the total mass is just the sum of the individual masses. This assumption is so deeply ingrained that it was not even explicitly formulated as a law. (Though I teach it as Newton’s Zeroth Law.) Altogether, in the Newtonian framework, it is difficult to imagine what would constitute an “origin of mass,’’ or even what this phrase could possibly mean. In that framework mass just is what it is—a primary concept. Later developments in physics make the concept of mass seem less irreducible. Einstein’s famous equation of special relativity theory, written in that way, betrays the prejudice that we should express energy in terms of mass. But we can write the same equation in the alternative form. When expressed in this form, it suggests the possibility of explaining mass in terms of energy. Einstein was aware of this possibility from the beginning. Indeed, his original 1905 paper is entitled, “Does the Inertia of a Body Depend on Its Energy Content?”
What Matters for Matter
Having convinced ourselves that the question of the origin of mass might make sense, let us now come to grips with it, in the very concrete form that it takes for ordinary matter. Ordinary matter is made from atoms. The mass of atoms is overwhelmingly concentrated in their nuclei. The surrounding electrons are of course crucial for discussing how atoms interact with each other—and thus for chemistry, biology, and electronics. But they provide less than a part in a thousand of the mass! Nuclei, which provide the lion’s share of mass, are assembled from protons and neutrons. All this is a familiar, well-established story, dating back seventy years or more. Newer and perhaps less familiar, but by now no less well-established is the next step: protons and neutrons are made from quarks and gluons. So most of the mass of matter can be traced, ultimately, back to quarks and gluons.
QCD: What It Is
The theory of quarks and gluons is called quantum chromodynamics, or QCD. QCD is a generalization of quantum electrodynamics (QED). For a nice description of quantum electrodynamics, written by an MIT grad who made good, I highly recommend QED: The Strange Theory of Electrons and Light, by Richard Feynman. The basic concept of QED is the response of photons to electric charge. Figure 1a shows a space-time picture of this core process. Figure 1b shows how it can be used to describe the effect of one electric charge on another, through the exchange of a “virtual” photon. [A virtual photon is simply one that gets emitted and absorbed without ever having a significant life of its own. So it is not a particle you can observe directly, but it can have effects on things you do observe.] In other words, Figure 1b describes electric and magnetic forces! Pictures like these, called Feynman diagrams, may look like childish scribbles, but their naïve appearance is misleading. Feynman diagrams are associated with definite mathematical rules that specify how likely it is for the process they depict to occur. The rules for complicated processes, perhaps involving many real and virtual charged particles and many real and virtual photons, are built up in a completely specific and definite way from the core process. It is like making constructions with TinkerToys . The particles are different kind of sticks you can use, and the core process provides the hubs that join them. Given these elements, the rules for construction are completely determined. In this way all the content of Maxwell’s equations for radio waves and light, Schrödinger’s equation for atoms and chemistry, and Dirac’s more refined version including spin—all this, and more, is faithfully encoded in the squiggle [Figure 1a].
At this most primitive level QCD is a lot like QED, but bigger. The diagrams look similar, and the rules for evaluating them are similar, but there are more kinds of sticks and hubs. More precisely, while there is just one kind of charge in QED—namely, electric charge—QCD has three different kinds of charge. They are called colors, for no good reason. We could label them red, white, and blue; or alternatively, if we want to make drawing easier, and to avoid the colors of the French flag, we can use red, green, and blue. Every quark has one unit of one of the color charges. In addition, quarks come in different “flavors.”The only ones that play a role in ordinary matter are two flavors called u and d, for up and down. [Of course, quark “flavors” have nothing to do with how anything tastes. And, these names for u and d don’t imply that there’s any real connection between flavors and directions. Don’t blame me; when I get the chance, I give particles dignified scientific-sounding names like axion and anyon.] There are u quarks with a unit of red charge, d quarks with a unit of green charge, and so forth, for six different possibilities altogether. And instead of one photon that responds to electric charge, QCD has eight color gluons that can either respond to different color charges or change one into another. So there is quite a large variety of sticks, and there are also many different kinds of hubs that connect them. It seems like things could get terribly complicated and messy. And so they would, were it not for the overwhelming symmetry of the theory. If you interchange red with blue everywhere, for example, you must still get the same rules. The more complete symmetry allows you to mix the colors continuously, forming blends, and the rules must come out the same for blends as for pure colors. I won’t be able to do justice to the mathematics here, of course. But the final result is noteworthy, and easy to convey: there is one and only one way to assign rules to all the possible hubs so that the theory comes out fully symmetric. Intricate it may be, but messy it is not! With these understandings, QCD is faithfully encoded in squiggles like Figure 1c, and the force between quarks emerges from squiggles like Figure 1d. We have definite rules to predict how quarks and gluons behave and interact. The calculations involved in describing specific processes, like the organization of quarks and gluons into protons, can be very difficult to carry through, but there is no ambiguity about the outcome. The theory is either right or wrong—there’s nowhere to hide.
How We Know It’s Right
Experiment is the ultimate arbiter of scientific truth. There are many experiments that test the basic principles of QCD. Most of them require rather sophisticated analysis, basically because we don’t get to see the underlying simple stuff, the individual quarks and gluons, directly. But there is one kind of experiment that comes very close to doing this, and that is what I’d like to explain to you now. I’ll be discussing what was observed at LEP. But before entering into details, I’d like to review a fundamental point about quantum mechanics, which is necessary background for making any sense at all of what happens. According to the principles of quantum mechanics, the result of an individual collision is unpredictable. We can, and do, control the energies and spins of the electrons and positrons precisely, so that precisely the same kind of collision occurs repeatedly; nevertheless, different results emerge. By making many repetitions, we can determine the probabilities for different outcomes. These probabilities encode basic information about the underlying fundamental interactions; according to quantum mechanics, they contain all the meaningful information.
When we examine the results of collisions at the Large Electron-Positron collider (LEP), we find there are two broad classes of outcomes. Each happens about half the time. In one class, the final state consists of a particle and its antiparticle moving rapidly in opposite directions. These could be an electron and an antielectron a muon and an antimuon or a tau and an antitau These particles, collectively called leptons, are all closely similar in their properties. Leptons do not carry color charges, so their main interactions are with photons, and thus their behavior should be governed by the rules of quantum electrodynamics QED. This is reflected, first of all, in the simplicity of their final states. Once produced, any of these particles could—in the language of Feynman diagrams—attach a photon using a QED hub, or alternatively, in physical terms, radiate a photon. The basic coupling of photons to a unit charge is fairly weak, however. Therefore each attachment is predicted to decrease the probability of the process being described, and so the most usual case is no attachment. In fact, the final state , including a photon, does occur, with about 1% of the rate of simply (and similarly for the other leptons). By studying the details of these 3-particle events, such as the probability for the photon to be emitted in different directions (the “antenna pattern”) and with different energy, we can check all aspects of our hypothesis for the underlying hub. This provides a wonderfully direct and incisive way to check the soundness of the basic conceptual building block from which we construct QED. We can then go on to address the extremely rare cases (.01%) where two photons get radiated, and so forth. For future reference, let’s call this first class of outcomes “QED events.” The other broad class of outcomes contains an entirely different class of particles, and is in manyways far more complicated. In these events the final state typically contains ten or more particles, selected from a menu of pions, rho mesons, protons and antiprotons, and many more. These are all particles that in other circumstances interact strongly with one another, and they are all constructed from quarks and gluons. Here, they make a smorgasbord of Greek and Latin alphabet soup. It’s such a mess that physicists have pretty much given up on trying to describe all the possibilities and their probabilities in detail. Fortunately, however, some simple patterns emerge if we change our focus from the individual particles to the overall flow of energy and momentum.
Most of the time—in about 90%of the cases—the particles emerge all moving in either one of two possible directions, opposite to one another. We say there are back-to-back jets. (Here, for once, the scientific jargon is both vivid and appropriate.) About 9% of the time, we find flows in three directions; about .9% of the time, four directions; and by then we’re left with a very small remainder of complicated events that are hard to analyze this way. I’ll call the second broad class of outcomes “QCD events.” Representative 2-jet and 3-jet QCD events, as they are actuallyobserved, are displayed in Figure 2. Now if you squint a little, you will find that the QED events and the QCD events begin to look quite similar. Indeed, the pattern of energy flow is qualitatively the same in both cases, that is, heavily concentrated in a few narrow jets. There are two main differences. One, relatively trivial, is that multiple jets are more common in QCD than in QED. The other is much more profound. It is that, of course, in the QED events the jets are just single particles, while in the quantum chromodynamics, QCD events the jets are sprays of several particles. In 1973, while I was a graduate student working with David Gross at Princeton, I discovered the explanation of these phenomena. We took the attitude that the deep similarities between the observed basic behaviors of leptons (based on QED) and the strongly interacting particles might indicate that the strongly interacting particles are also ultimately described by a simple, rule-based theory, with sticks and hubs. In other words, we squinted.
To bring our simplified picture of the QCD events into harmony with the observations, we relied on a theoretical discovery I’ll describe momentarily, which we christened asymptotic freedom. (Please notice that our term is not “cute.”) Actually, our discovery of asymptotic freedom preceded these specific experiments, so we were able to predict the results of these experiments before they were performed. As a historical matter, we discovered QCD and asymptotic freedom by trying to come to terms with the MIT-SLAC “scaling” experiments done at the Stanford Linear Collider in the late 1960s, for which Jerome Friedman, Henry Kendall, and Richard Taylor won the Nobel Prize in 1990. Since our analysis of the scaling experiments using QCD was (necessarily) more complicated and indirect, I’ve chosen to focus here on the later, but simpler to understand, experiments involving jets. The basic concept of asymptotic freedom is that the probability for a fastmoving quark or gluon to radiate away some of its energy in the form of other quarks and gluons depends on whether this radiation is “hard”or “soft”. Hard radiation is radiation that involves a substantial deflection of the particle doing the radiating, while soft radiation is radiation that does not cause such a deflection. Thus hard radiation changes the flow of energy and momentum, while soft radiation merely distributes it among additional particles, all moving together. Asymptotic freedom says that hard radiation is rare, but soft radiation is common. This distinction explains why on the one hand there are jets, and on the other hand why the jets are not single particles. A QCD event begins as the materialization of quark and antiquark, similar to how a QED event begins as the materialization of lepton-antilepton. They usually give us two jets, aligned along the original directions of the quark and antiquark, because only hard radiation can change the overall flow of energy and momentum significantly, and asymptotic freedom tells us hard radiation is rare. When a hard radiation does occur, we have an extra jet! But we don’t see the original quarks or antiquarks, individually, because they are always accompanied by their soft radiation, which is common.
By studying the antenna patterns of the multi-jet QCD events we can check all aspects of our hypotheses for the underlying hubs. Just as for QED, such antenna patterns provide a wonderfully direct and incisive way to check the soundness of the basic conceptual building blocks from which we construct QCD. Through analysis of this and many other applications, physicists have acquired complete confidence in the fundamental correctness of QCD. By now experimenters use it routinely to design experiments searching for new phenomena, and they refer to what they’re doing as “calculating backgrounds” rather than “testing QCD”! Many challenges remain, however, to make full use of the theory. The difficulty is always with the soft radiation. Such radiation is emitted very easily, and that makes it difficult to keep track of. You get a vast number of Feynman graphs, each with many attachments, and they get more and more difficult to enumerate, let alone calculate. That’s very unfortunate, because when we try to assemble a proton from quarks and gluons none of them can be moving very fast for very long (they’re supposed to be inside the proton, after all), so all their interactions involve soft radiation.
To meet this challenge, a radically different strategy is required. Instead of calculating the paths of quarks and gluons through space and time, using Feynman graphs, we let each segment of space-time keep track of how many quarks and gluons it contains. We then treat these segments as an assembly of interacting subsystems. Actually in this context “we” means a collection of hard-working CPUs. Skillfully orchestrated, and working full time at teraflop speeds, they manage to produce quite a good account of the masses of protons and other strongly interacting particles. The equations of QCD, which we discovered and proved from very different considerations, survive this extremely intense usage quite well. There’s a big worldwide effort, at the frontiers of computer technology and human ingenuity, to do calculations like this more accurately, and to calculate more things.
We find that 90% of the proton (and neutron) mass, and therefore 90% of the mass of ordinary matter, emerges from an idealized theory whose ingredients are entirely massless.
The Origin of (most) Mass
Now I’ve shown you the theory that describes quarks and gluons, and therefore has to account for most of the mass of matter. I’ve described some of the experiments that confirm the theory. And I’ve displayed successful calculations of hadron masses, including the masses of protons and neutrons, using this theory. In a sense, these calculations settle the question. They tell us the origin of (most) mass. But simply having a computer spit out the answer, after gigantic and totally opaque calculations, does not satisfy our hunger for understanding. It is particularly unsatisfactory in the present case, because the answer appears to be miraculous. The computers construct for us massive particles using building blocks—quarks and gluons—that are themselves massless. The equations of QCD Lite output Mass without Mass, which sounds suspiciously like Something for Nothing. How did it happen? The key, again, is asymptotic freedom. Previously, I discussed this phenomenon in terms of hard and soft radiation. Hard radiation is rare, soft radiation is common. There’s another way of looking at it, mathematically equivalent, that is useful here. From the classical equations of QCD, one would expect a force field between quarks that falls off as the square of the distance, as in ordinary electromagnetism (Coulomb’s law). It's enhanced coupling to soft radiation, however, means that when quantum mechanics is taken into account a “bare”color charge, inserted into empty space, will start to surround itself with a cloud of virtual color gluons. These color gluons fields themselves carry color charge, so they are sources of additional soft radiation. The result is a self-catalyzing enhancement that leads to runaway growth. A small color charge, in isolation, builds up a big color thundercloud.
All this structure costs energy, and theoretically the energy for a quark in isolation is infinite. That’s why we never see individual quarks. Having only a finite amount of energy to work with, Nature always finds a way to short-circuit the ultimate thundercloud. One way is to bring in an antiquark. If the antiquark could be placed right on top of the quark, their color charges would exactly cancel, and the thundercloud would never get started. There’s also another more subtle way to cancel the color charge by bringing together three quarks, one of each color. In practice, these exact cancellations can’t quite happen, however, because there’s a competing effect. Quarks obey the rules of quantum mechanics. It is wrong to think of them simply as tiny particles, rather they are quantum-mechanical wavicles. They are subject, in particular, to Heisenberg’s uncertainty principle, which implies that if you try to pin down their position too precisely, their momentum will be wildly uncertain. To support the possibility of large momentum, they must acquire large energy. In other words, it takes work to pin quarks down. Wavicles want to spread out. So there’s a competition between two effects. To cancel the color charge completely, we’d like to put the quark and antiquark at precisely the same place; but they resist localization, so it’s costly to do that.
This competition can result in a number of compromise solutions, where the quark and antiquark (or three quarks) are brought close together, but are not perfectly coincident. Their distribution is described by quantum mechanical wave functions. Many different stable wave-patterns are possible, and each corresponds to a different kind of particle that you can observe. There are patterns for protons, neutrons, and for each entry in the whole Greek and Latin smorgasbord. Each pattern has some characteristic energy, because the color fields are not entirely cancelled particles and because the wavicles are somewhat localized. And that, through is the origin of mass. A similar mechanism, though much simpler, works in atoms. Negatively charged electrons feel an attractive electric force from the positively charged nucleus, and from that point of view they’d like to snuggle right on top of it. Electrons are wavicles, though, and that inhibits them. The result, again, is a series of possible compromise solutions. These are what we observe as the energy levels of the atom. When I give the talk on which this article is based, at this point I use Dean Dauger’s marvelous “Atom in a Box” program to show the lovely, almost sensuous patterns of undulating waves that describe the possible states of that simplest of atoms, hydrogen. I hope you will explore “Atom in a Box”for yourself. You can link to it at http://www.dauger.com. In its absence, I will substitute a classic metaphor.
The wave patterns that describe protons, neutrons, and their relatives resemble the vibration patterns of musical instruments. In fact the mathematical equations that govern these superficially very different realms are quite similar. Musical analogies go back to the prehistory of science. Pythagoras, partly inspired by his discovery that harmonious notes are sounded by strings whose lengths are in simple numerical ratios, proposed that “All things are Number.”Kepler spoke of the music of the spheres, and his longing to find their hidden harmonies sustained him through years of tedious calculations and failed guesses before he identified the true patterns of planetary motions. Einstein, when he learned of Bohr’s atomic model, called it “the highest form of musicality in the sphere of thought.” Yet Bohr’s model, wonderful as it is, appears to us now as a very watered-down version of the true wave-mechanical atom; and the wave-mechanical proton is more intricate and symmetric by far! I hope that some artist/nerd will rise to the challenge, and construct a “Proton in a Box” for us to play with and admire.
The World as Concept, Algorithm, and Number
I will conclude with a few words concerning the broader significance of these developments for our picture of the world. A major goal of theoretical physics is to describe the world with the greatest possible economy of concepts. For that reason alone, it is an important result that we can largely eliminate mass as an independent property that we are forced to introduce in order to describe matter accurately. But there is more. The equations that describe the behavior of elementary particles become fundamentally simpler and more symmetric when the mass of the particles is zero. So eliminating mass enables us to bring more symmetry into the mathematical description of Nature. The understanding of the origin of mass that I’ve sketched for you here is the most perfect realization we have of Pythagoras’ inspiring vision that the world can be built up from concepts, algorithms, and numbers. Mass, a seemingly irreducible property of matter, and a byword for its resistance to change and sluggishness turn out to reflect a harmonious interplay of symmetry, uncertainty, and energy. Using these concepts, and the algorithms they suggest, pure computation outputs the numerical values of the masses of particles we observe. Still, as I’ve already mentioned, our understanding of the origin of mass is by no means complete. We have achieved a beautiful and profound understanding of the origin of most of the mass of ordinary matter, but not of all of it. The value of the electron mass, in particular, remains deeply mysterious even in our most advanced speculations about unification and string theory. And ordinary matter, we have recently learned, supplies only a small fraction of mass in the Universe as a whole. More beautiful and profound revelations surely await discovery. We continue to search for concepts and theories that will allow us to understand the origin of mass in all its forms, by unveiling more of Nature’s hidden symmetries.
1. https://www.forbes.com/sites/startswithabang/2016/08/03/where-does-the-mass-of-a-proton-come-from/?sh=783b43462e1d
2. https://www.symmetrymagazine.org/article/where-does-mass-come-from#:~:text=These%20particles%20are%20each%20made,protons%20and%20neutrons%20their%20mass.
3. https://physics.mit.edu/wp-content/uploads/2021/01/physicsatmit_03_wilczek_originofmass.pdf
Frank Wilczek: The Origin of (most) Mass 2003
Quarks and gluons account for most of the mass of matter. The answer appears to be miraculous. Quarks and gluons—that are themselves massless. The equations of Quantum Chromodynamics output Mass without Mass, which sounds suspiciously like Something for Nothing. How did it happen? The key, again, is asymptotic freedom. Previously, I discussed this phenomenon in terms of hard and soft radiation. Hard radiation is rare, soft radiation is common. When quantum mechanics is taken into account a “bare”color charge, inserted into empty space, will start to surround itself with a cloud of virtual color gluons. These color gluons fields themselves carry color charge, so they are sources of additional soft radiation. The result is a self-catalyzing enhancement that leads to runaway growth. A small color charge, in isolation, builds up a big color thundercloud. All this structure costs energy, and theoretically the energy for a quark in isolation is infinite.
https://physics.mit.edu/wp-content/uploads/2021/01/physicsatmit_03_wilczek_originofmass.pdf
Martin B. van der Mark: Quantum mechanical probability current as electromagnetic 4-current from topological EM fields August 2015
The structure of stable matter is the result of a balance of forces working between some otherwise bound objects, particles, or granules. The final stage is a balance of forces on a continuous, circulating flow of energy, holding itself together. The proton’s internal dynamics must be essentially a light-speed knot of circulating energy. That energy is the “stuff” we were after, and it is continuous and takes part in the electromagnetic interaction.
https://www.researchgate.net/publication/281460952_Quantum_mechanical_probability_current_as_electromagnetic_4-current_from_topological_EM_fields
My comment: See the keywords here. The answer to the origin of mass seems to be miraculous. Its sounds suspiciously like Something from Nothing. And: The energy for a quark in isolation is infinite.
Could it be, that God holds an infinite power, instantiated energy/mass through his eternal power when he stretched out the universe, and all mass is just a manifestation of his eternal power?
David Tong: Particle Physics
What are we made of? What are the fundamental building blocks of the universe from which you, me, and everything else is constructed? Every experiment that we’ve ever performed can be explained in terms of a collection of particles interacting through a handful of forces. The description is given through the Standard Model. The language in which the Standard Model is written is known as quantum field theory. Matter is made of indivisible objects called atoms.The proton contains two up quarks and a down quark, while the neutron contains two down quarks and an up. Both quarks have fractional electric charge. In units in which the electron has charge −1, the up quark has charge +2/3 and the down quark charge − 1/3 . This then gives the familiar charges of the proton ( 2/3 + 2/3 − 1/3 = +1) and the neutron (- 1/3 − 1/3 + 2/3 = 0).
The Higgs Force: A force which role is dramatic: it allows all the elementary particles described in the table above to get a mass.
http://www.damtp.cam.ac.uk/user/tong/pp/pp.pdf
If you were to divide the particles that made up your body into smaller and smaller bits, you'd find that at every step along the way -- at least in terms of mass -- the whole was equal to the sum of its parts. If you broke your body down into its individual bones, fat and organs, they would add up to an entire human being. If you broke them down further, into cells, again, the cells would still add up to the same mass as you. Cells can be divided into organelles, organelles broken up into individual molecules, molecules into atoms, and atoms into protons, neutrons and electrons. At that level, there's a tiny but noticeable difference: the individual protons, neutrons and electrons are off by right around 1% from a human, thanks to nuclear binding energy.
The nucleus of a carbon atom has a mass that's approximately 0.8% lower than the individual protons and neutrons that compose it, thanks to nuclear binding energy.
A carbon atom, made up of six protons and six neutrons, is approximately 0.8% lighter than the individual component particles that make it up. The way carbon is formed is through the nuclear fusion of hydrogen into helium and then helium into carbon; the energy released is what powers most types of stars in both their normal and red giant phases, and the "lost mass" is where that energy comes from, thanks to Einstein's E = mc2. This is how most types of binding energy work: the reason it's harder to pull apart multiple things that are bound together is that they released energy when they were joined, and you have to put energy in to free them again.
This is why it's such a puzzling fact that when you take a look at the particles that make up the proton -- the three different quarks at the heart of them -- their combined masses are only 0.2% of the mass of the proton as a whole.
The particles of the standard model, with masses (in MeV) in the upper right. A proton, made up of two up quarks and one down quark, has a mass of ~938 MeV/c^2.
The way quarks bind into protons is fundamentally different from all the other forces and interactions we know of. Instead of the force getting stronger when objects get closer -- like the gravitational, electric or magnetic forces -- the attractive force goes down to zero when quarks get arbitrarily close. And instead of the force getting weaker when objects get farther away, the force pulling quarks back together gets stronger the farther away they get.
This property of the strong nuclear force is known as asymptotic freedom, and the particles that mediate this force are known as gluons. Somehow, the energy binding the proton together, the other 99.8% of the proton's mass, comes from these gluons.
Rather than three main, green (valence) quarks connected by (spring-like) gluons, the proton's structure is much more complicated, with additional (sea) quarks and gluons populating the proton's interior.
Because of how the strong nuclear force works, there are large uncertainties as to where these gluons are actually located at any point in time. We presently have a solid model of the average gluon density inside a proton, but if we want to know where the gluons are actually more likely to be located, that requires more experimental data, as well as better models to compare the data against. Recent advances by theorists Björn Schenke and Heikki Mäntysaari may be able to provide those much-needed models. As Mäntysaari detailed:
It is very accurately known how large the average gluon density is inside a proton. What is not known is exactly where the gluons are located inside the proton. We model the gluons as located around the three [valence] quarks. Then we control the amount of fluctuations represented in the model by setting how large the gluon clouds are, and how far apart they are from each other.
The internal structure of a proton, with quarks, gluons, and quark spin shown.
When you collide two particles like protons, a proton and a heavy ion, or two heavy ions together, you can't simply model them as proton-proton collisions. Instead, you see a distribution of three types of collisions: quark-quark collisions, quark-gluon collisions or gluon-gluon collisions. It's the components within these subatomic particles that actually collide, rather than the entire structures (the protons) themselves. While at lower energies, it's almost always quarks that collide, the higher energies reached by RHIC, the Relativistic Heavy Ion Collider, at Brookhaven and by the LHC at CERN have a very high probability of gluon-gluon interactions, with the potential to reveal the location of the gluons inside a proton itself. As Mäntysaari continued:
This process doesn't happen at all if the proton always looks the same. The more fluctuations we have, the more likely this process is to happen.
A better understanding of the internal structure of a proton, including how the "sea" quarks and gluons are distributed, has been achieved through both experimental improvements and new theoretical developments in tandem.
The combination of this new theoretical model and the ever-improving LHC data will better enable scientists to understand the internal, fundamental structure of protons, neutrons and nuclei in general, and hence to understand where the mass of the known objects in the Universe comes from. The biggest boon to this type of research, however, would be the development of an Electron-Ion Collider (EIC), a proposed collider by many collaborations across the world. Unlike RHIC or the LHC, which collide protons with ions -- resulting in a very messy final signal -- an EIC would be much more controlled, as there are no internal, uncontrollable motions inside an electron to confound the experimental results. If you want to study the internal structure of a proton or collection of nuclei, deep inelastic scattering is the only way to go. Considering that colliders began that journey less than a century ago, and that we're now achieving energies approximately a factor of 10,000 greater than when we first started, probing and understanding exactly how matter gets its mass may finally be within our reach. The quark-gluon plasma within the nucleus, and the attendant fluctuations, may finally be ready to reveal its secrets to us. And when it does, one of the longest-standing mysteries of physics, of where the mass of the known matter comes from (still a mystery even after discovery of the Higgs), may finally yield to humanity.
Diana Kwon: Where does mass come from? 05/12/16 2
The story of particle mass starts right after the big bang. During the very first moments of the universe, almost all particles were massless, traveling at the speed of light in a very hot “primordial soup.” At some point during this period, the Higgs field turned on, permeating the universe and giving mass to the elementary particles.
The Higgs field changed the environment when it was turned on, altering the way that particles behave. Some of the most common metaphors compare the Higgs field to a vat of molasses or thick syrup, which slows some particles as they travel through.
Others have envisioned the Higgs field as a crowd at a party or a horde of paparazzi. As famous scientists or A-list celebrities pass through, people surround them, slowing them down, but less-known faces travel through the crowds unnoticed. In these cases, popularity is synonymous with mass—the more popular you are, the more you will interact with the crowd, and the more “massive” you will be.
But why did the Higgs field turn on? Why do some particles interact more with the Higgs field than others? The short answer is: We don’t know.
“This is part of why finding the Higgs field is just the beginning—because we have a ton of questions,” says Matt Strassler, a theoretical physicist and associate of the Harvard University physics department.
The strong force and you
The Higgs field gives mass to fundamental particles—the electrons, quarks and other building blocks that cannot be broken into smaller parts. But these still only account for a tiny proportion of the universe’s mass.
The rest comes from protons and neutrons, which get almost all their mass from the strong nuclear force. These particles are each made up of three quarks moving at breakneck speeds that are bound together by gluons, the particles that carry the strong force. The energy of this interaction between quarks and gluons is what gives protons and neutrons their mass. Keep in mind Einstein’s famous E=mc2, which equates energy and mass. That makes mass a secret storage facility for energy.
“When you put three quarks together to create a proton, you end up binding up an enormous energy density in a small region in space,” says John Lajoie, a physicist at Iowa State University.
A proton is made of two up quarks and a down quark; a neutron is made of two down quarks and an up quark. Their similar composition makes the mass they acquire from the strong force nearly identical. However, neutrons are slightly more massive than protons—and this difference is crucial. The process of neutrons decaying into protons promotes chemistry, and thus, biology. If protons were heavier, they would instead decay into neutrons, and the universe as we know it would not exist.
“As it turns out, the down quarks interact more strongly with the Higgs [field], so they have a bit more mass,” says Andreas Kronfeld, a theoretical physicist at Fermilab. This is why the tiny difference between proton and neutron mass exists.
But what about neutrinos?
We’ve learned that the elementary particles get their mass from the Higgs field—but wait! There may be an exception: neutrinos. Neutrinos are in a class by themselves; they have extremely tiny masses (a million times smaller than the electron, the second lightest particle), are electrically neutral and rarely interact with matter.
Scientists are puzzled as to why neutrinos are so light. Theorists are currently considering multiple possibilities. It might be explained if neutrinos are their own antiparticles—that is, if the antimatter version is identical to the matter version. If physicists discover that this is the case, it would mean that neutrinos get their mass from somewhere other than the Higgs boson, which physicists discovered in 2012.
Neutrinos must get their mass from a Higgs-like field, which is electrically neutral and spans the entire universe. This could be the same Higgs that gives mass to the other elementary particles, or it could be a very distant cousin. In some theories, neutrino mass also comes from an additional, brand new source that could hold the answers to other lingering particle physics mysteries.
“People tend to get excited about this possibility because it can be interpreted as evidence for a brand new energy scale, naively unrelated to the Higgs phenomenon,” says André de Gouvêa, a theoretical particle physicist at Northwestern University.
This new mechanism may also be related to how dark matter, which physicists think is made up of yet undiscovered particles, gets its mass.
“Nature tends to be economical, so it's possible that the same new set of particles explains all of these weird phenomena that we haven't explained yet,” de Gouvêa says.
Frank Wilczek: The Origin of Mass 01/2021 3
Everyday work at the frontiers of modern physics usually involves complex concepts and extreme conditions. We speak of quantum fields, entanglement, or supersymmetry, and analyze the ridiculously small or conceptualize the incomprehensibly large. Just as Willie Sutton famously explained that he robbed banks because “that’s where the money is,” so we do these things because “that’s where the Unknown is.” It is an amazing and delightful fact, however, that occasionally this sophisticated work gives answers to childlike questions about familiar things. Here I’d like to describe how my own work on subnuclear forces, the world of quarks and gluons, casts brilliant new light on one such child-like question: What is the origin of mass?
Has Mass an Origin?
That a question makes grammatical sense does not guarantee that it is answerable, or even coherent. The concept of mass is one of the first things we discuss in my freshman mechanics class. Classical mechanics is, literally, unthinkable without it. Newton’s second law of motion says that the acceleration of a body is given by dividing the force acting upon it by its mass. So a body without mass wouldn’t know how to move, because you’d be dividing by zero. Also, in Newton’s law of gravity, the mass of an object governs the strength of the force it exerts. One cannot build up an object that gravitates, out of material that does not, so you can’t get rid of mass without getting rid of gravity. Finally, the most basic feature of mass in classical mechanics is that it is conserved. For example, when you bring together two bodies, the total mass is just the sum of the individual masses. This assumption is so deeply ingrained that it was not even explicitly formulated as a law. (Though I teach it as Newton’s Zeroth Law.) Altogether, in the Newtonian framework, it is difficult to imagine what would constitute an “origin of mass,’’ or even what this phrase could possibly mean. In that framework mass just is what it is—a primary concept. Later developments in physics make the concept of mass seem less irreducible. Einstein’s famous equation of special relativity theory, written in that way, betrays the prejudice that we should express energy in terms of mass. But we can write the same equation in the alternative form. When expressed in this form, it suggests the possibility of explaining mass in terms of energy. Einstein was aware of this possibility from the beginning. Indeed, his original 1905 paper is entitled, “Does the Inertia of a Body Depend on Its Energy Content?”
What Matters for Matter
Having convinced ourselves that the question of the origin of mass might make sense, let us now come to grips with it, in the very concrete form that it takes for ordinary matter. Ordinary matter is made from atoms. The mass of atoms is overwhelmingly concentrated in their nuclei. The surrounding electrons are of course crucial for discussing how atoms interact with each other—and thus for chemistry, biology, and electronics. But they provide less than a part in a thousand of the mass! Nuclei, which provide the lion’s share of mass, are assembled from protons and neutrons. All this is a familiar, well-established story, dating back seventy years or more. Newer and perhaps less familiar, but by now no less well-established is the next step: protons and neutrons are made from quarks and gluons. So most of the mass of matter can be traced, ultimately, back to quarks and gluons.
QCD: What It Is
The theory of quarks and gluons is called quantum chromodynamics, or QCD. QCD is a generalization of quantum electrodynamics (QED). For a nice description of quantum electrodynamics, written by an MIT grad who made good, I highly recommend QED: The Strange Theory of Electrons and Light, by Richard Feynman. The basic concept of QED is the response of photons to electric charge. Figure 1a shows a space-time picture of this core process. Figure 1b shows how it can be used to describe the effect of one electric charge on another, through the exchange of a “virtual” photon. [A virtual photon is simply one that gets emitted and absorbed without ever having a significant life of its own. So it is not a particle you can observe directly, but it can have effects on things you do observe.] In other words, Figure 1b describes electric and magnetic forces! Pictures like these, called Feynman diagrams, may look like childish scribbles, but their naïve appearance is misleading. Feynman diagrams are associated with definite mathematical rules that specify how likely it is for the process they depict to occur. The rules for complicated processes, perhaps involving many real and virtual charged particles and many real and virtual photons, are built up in a completely specific and definite way from the core process. It is like making constructions with TinkerToys . The particles are different kind of sticks you can use, and the core process provides the hubs that join them. Given these elements, the rules for construction are completely determined. In this way all the content of Maxwell’s equations for radio waves and light, Schrödinger’s equation for atoms and chemistry, and Dirac’s more refined version including spin—all this, and more, is faithfully encoded in the squiggle [Figure 1a].
At this most primitive level QCD is a lot like QED, but bigger. The diagrams look similar, and the rules for evaluating them are similar, but there are more kinds of sticks and hubs. More precisely, while there is just one kind of charge in QED—namely, electric charge—QCD has three different kinds of charge. They are called colors, for no good reason. We could label them red, white, and blue; or alternatively, if we want to make drawing easier, and to avoid the colors of the French flag, we can use red, green, and blue. Every quark has one unit of one of the color charges. In addition, quarks come in different “flavors.”The only ones that play a role in ordinary matter are two flavors called u and d, for up and down. [Of course, quark “flavors” have nothing to do with how anything tastes. And, these names for u and d don’t imply that there’s any real connection between flavors and directions. Don’t blame me; when I get the chance, I give particles dignified scientific-sounding names like axion and anyon.] There are u quarks with a unit of red charge, d quarks with a unit of green charge, and so forth, for six different possibilities altogether. And instead of one photon that responds to electric charge, QCD has eight color gluons that can either respond to different color charges or change one into another. So there is quite a large variety of sticks, and there are also many different kinds of hubs that connect them. It seems like things could get terribly complicated and messy. And so they would, were it not for the overwhelming symmetry of the theory. If you interchange red with blue everywhere, for example, you must still get the same rules. The more complete symmetry allows you to mix the colors continuously, forming blends, and the rules must come out the same for blends as for pure colors. I won’t be able to do justice to the mathematics here, of course. But the final result is noteworthy, and easy to convey: there is one and only one way to assign rules to all the possible hubs so that the theory comes out fully symmetric. Intricate it may be, but messy it is not! With these understandings, QCD is faithfully encoded in squiggles like Figure 1c, and the force between quarks emerges from squiggles like Figure 1d. We have definite rules to predict how quarks and gluons behave and interact. The calculations involved in describing specific processes, like the organization of quarks and gluons into protons, can be very difficult to carry through, but there is no ambiguity about the outcome. The theory is either right or wrong—there’s nowhere to hide.
How We Know It’s Right
Experiment is the ultimate arbiter of scientific truth. There are many experiments that test the basic principles of QCD. Most of them require rather sophisticated analysis, basically because we don’t get to see the underlying simple stuff, the individual quarks and gluons, directly. But there is one kind of experiment that comes very close to doing this, and that is what I’d like to explain to you now. I’ll be discussing what was observed at LEP. But before entering into details, I’d like to review a fundamental point about quantum mechanics, which is necessary background for making any sense at all of what happens. According to the principles of quantum mechanics, the result of an individual collision is unpredictable. We can, and do, control the energies and spins of the electrons and positrons precisely, so that precisely the same kind of collision occurs repeatedly; nevertheless, different results emerge. By making many repetitions, we can determine the probabilities for different outcomes. These probabilities encode basic information about the underlying fundamental interactions; according to quantum mechanics, they contain all the meaningful information.
When we examine the results of collisions at the Large Electron-Positron collider (LEP), we find there are two broad classes of outcomes. Each happens about half the time. In one class, the final state consists of a particle and its antiparticle moving rapidly in opposite directions. These could be an electron and an antielectron a muon and an antimuon or a tau and an antitau These particles, collectively called leptons, are all closely similar in their properties. Leptons do not carry color charges, so their main interactions are with photons, and thus their behavior should be governed by the rules of quantum electrodynamics QED. This is reflected, first of all, in the simplicity of their final states. Once produced, any of these particles could—in the language of Feynman diagrams—attach a photon using a QED hub, or alternatively, in physical terms, radiate a photon. The basic coupling of photons to a unit charge is fairly weak, however. Therefore each attachment is predicted to decrease the probability of the process being described, and so the most usual case is no attachment. In fact, the final state , including a photon, does occur, with about 1% of the rate of simply (and similarly for the other leptons). By studying the details of these 3-particle events, such as the probability for the photon to be emitted in different directions (the “antenna pattern”) and with different energy, we can check all aspects of our hypothesis for the underlying hub. This provides a wonderfully direct and incisive way to check the soundness of the basic conceptual building block from which we construct QED. We can then go on to address the extremely rare cases (.01%) where two photons get radiated, and so forth. For future reference, let’s call this first class of outcomes “QED events.” The other broad class of outcomes contains an entirely different class of particles, and is in manyways far more complicated. In these events the final state typically contains ten or more particles, selected from a menu of pions, rho mesons, protons and antiprotons, and many more. These are all particles that in other circumstances interact strongly with one another, and they are all constructed from quarks and gluons. Here, they make a smorgasbord of Greek and Latin alphabet soup. It’s such a mess that physicists have pretty much given up on trying to describe all the possibilities and their probabilities in detail. Fortunately, however, some simple patterns emerge if we change our focus from the individual particles to the overall flow of energy and momentum.
Most of the time—in about 90%of the cases—the particles emerge all moving in either one of two possible directions, opposite to one another. We say there are back-to-back jets. (Here, for once, the scientific jargon is both vivid and appropriate.) About 9% of the time, we find flows in three directions; about .9% of the time, four directions; and by then we’re left with a very small remainder of complicated events that are hard to analyze this way. I’ll call the second broad class of outcomes “QCD events.” Representative 2-jet and 3-jet QCD events, as they are actuallyobserved, are displayed in Figure 2. Now if you squint a little, you will find that the QED events and the QCD events begin to look quite similar. Indeed, the pattern of energy flow is qualitatively the same in both cases, that is, heavily concentrated in a few narrow jets. There are two main differences. One, relatively trivial, is that multiple jets are more common in QCD than in QED. The other is much more profound. It is that, of course, in the QED events the jets are just single particles, while in the quantum chromodynamics, QCD events the jets are sprays of several particles. In 1973, while I was a graduate student working with David Gross at Princeton, I discovered the explanation of these phenomena. We took the attitude that the deep similarities between the observed basic behaviors of leptons (based on QED) and the strongly interacting particles might indicate that the strongly interacting particles are also ultimately described by a simple, rule-based theory, with sticks and hubs. In other words, we squinted.
To bring our simplified picture of the QCD events into harmony with the observations, we relied on a theoretical discovery I’ll describe momentarily, which we christened asymptotic freedom. (Please notice that our term is not “cute.”) Actually, our discovery of asymptotic freedom preceded these specific experiments, so we were able to predict the results of these experiments before they were performed. As a historical matter, we discovered QCD and asymptotic freedom by trying to come to terms with the MIT-SLAC “scaling” experiments done at the Stanford Linear Collider in the late 1960s, for which Jerome Friedman, Henry Kendall, and Richard Taylor won the Nobel Prize in 1990. Since our analysis of the scaling experiments using QCD was (necessarily) more complicated and indirect, I’ve chosen to focus here on the later, but simpler to understand, experiments involving jets. The basic concept of asymptotic freedom is that the probability for a fastmoving quark or gluon to radiate away some of its energy in the form of other quarks and gluons depends on whether this radiation is “hard”or “soft”. Hard radiation is radiation that involves a substantial deflection of the particle doing the radiating, while soft radiation is radiation that does not cause such a deflection. Thus hard radiation changes the flow of energy and momentum, while soft radiation merely distributes it among additional particles, all moving together. Asymptotic freedom says that hard radiation is rare, but soft radiation is common. This distinction explains why on the one hand there are jets, and on the other hand why the jets are not single particles. A QCD event begins as the materialization of quark and antiquark, similar to how a QED event begins as the materialization of lepton-antilepton. They usually give us two jets, aligned along the original directions of the quark and antiquark, because only hard radiation can change the overall flow of energy and momentum significantly, and asymptotic freedom tells us hard radiation is rare. When a hard radiation does occur, we have an extra jet! But we don’t see the original quarks or antiquarks, individually, because they are always accompanied by their soft radiation, which is common.
By studying the antenna patterns of the multi-jet QCD events we can check all aspects of our hypotheses for the underlying hubs. Just as for QED, such antenna patterns provide a wonderfully direct and incisive way to check the soundness of the basic conceptual building blocks from which we construct QCD. Through analysis of this and many other applications, physicists have acquired complete confidence in the fundamental correctness of QCD. By now experimenters use it routinely to design experiments searching for new phenomena, and they refer to what they’re doing as “calculating backgrounds” rather than “testing QCD”! Many challenges remain, however, to make full use of the theory. The difficulty is always with the soft radiation. Such radiation is emitted very easily, and that makes it difficult to keep track of. You get a vast number of Feynman graphs, each with many attachments, and they get more and more difficult to enumerate, let alone calculate. That’s very unfortunate, because when we try to assemble a proton from quarks and gluons none of them can be moving very fast for very long (they’re supposed to be inside the proton, after all), so all their interactions involve soft radiation.
To meet this challenge, a radically different strategy is required. Instead of calculating the paths of quarks and gluons through space and time, using Feynman graphs, we let each segment of space-time keep track of how many quarks and gluons it contains. We then treat these segments as an assembly of interacting subsystems. Actually in this context “we” means a collection of hard-working CPUs. Skillfully orchestrated, and working full time at teraflop speeds, they manage to produce quite a good account of the masses of protons and other strongly interacting particles. The equations of QCD, which we discovered and proved from very different considerations, survive this extremely intense usage quite well. There’s a big worldwide effort, at the frontiers of computer technology and human ingenuity, to do calculations like this more accurately, and to calculate more things.
We find that 90% of the proton (and neutron) mass, and therefore 90% of the mass of ordinary matter, emerges from an idealized theory whose ingredients are entirely massless.
The Origin of (most) Mass
Now I’ve shown you the theory that describes quarks and gluons, and therefore has to account for most of the mass of matter. I’ve described some of the experiments that confirm the theory. And I’ve displayed successful calculations of hadron masses, including the masses of protons and neutrons, using this theory. In a sense, these calculations settle the question. They tell us the origin of (most) mass. But simply having a computer spit out the answer, after gigantic and totally opaque calculations, does not satisfy our hunger for understanding. It is particularly unsatisfactory in the present case, because the answer appears to be miraculous. The computers construct for us massive particles using building blocks—quarks and gluons—that are themselves massless. The equations of QCD Lite output Mass without Mass, which sounds suspiciously like Something for Nothing. How did it happen? The key, again, is asymptotic freedom. Previously, I discussed this phenomenon in terms of hard and soft radiation. Hard radiation is rare, soft radiation is common. There’s another way of looking at it, mathematically equivalent, that is useful here. From the classical equations of QCD, one would expect a force field between quarks that falls off as the square of the distance, as in ordinary electromagnetism (Coulomb’s law). It's enhanced coupling to soft radiation, however, means that when quantum mechanics is taken into account a “bare”color charge, inserted into empty space, will start to surround itself with a cloud of virtual color gluons. These color gluons fields themselves carry color charge, so they are sources of additional soft radiation. The result is a self-catalyzing enhancement that leads to runaway growth. A small color charge, in isolation, builds up a big color thundercloud.
All this structure costs energy, and theoretically the energy for a quark in isolation is infinite. That’s why we never see individual quarks. Having only a finite amount of energy to work with, Nature always finds a way to short-circuit the ultimate thundercloud. One way is to bring in an antiquark. If the antiquark could be placed right on top of the quark, their color charges would exactly cancel, and the thundercloud would never get started. There’s also another more subtle way to cancel the color charge by bringing together three quarks, one of each color. In practice, these exact cancellations can’t quite happen, however, because there’s a competing effect. Quarks obey the rules of quantum mechanics. It is wrong to think of them simply as tiny particles, rather they are quantum-mechanical wavicles. They are subject, in particular, to Heisenberg’s uncertainty principle, which implies that if you try to pin down their position too precisely, their momentum will be wildly uncertain. To support the possibility of large momentum, they must acquire large energy. In other words, it takes work to pin quarks down. Wavicles want to spread out. So there’s a competition between two effects. To cancel the color charge completely, we’d like to put the quark and antiquark at precisely the same place; but they resist localization, so it’s costly to do that.
This competition can result in a number of compromise solutions, where the quark and antiquark (or three quarks) are brought close together, but are not perfectly coincident. Their distribution is described by quantum mechanical wave functions. Many different stable wave-patterns are possible, and each corresponds to a different kind of particle that you can observe. There are patterns for protons, neutrons, and for each entry in the whole Greek and Latin smorgasbord. Each pattern has some characteristic energy, because the color fields are not entirely cancelled particles and because the wavicles are somewhat localized. And that, through is the origin of mass. A similar mechanism, though much simpler, works in atoms. Negatively charged electrons feel an attractive electric force from the positively charged nucleus, and from that point of view they’d like to snuggle right on top of it. Electrons are wavicles, though, and that inhibits them. The result, again, is a series of possible compromise solutions. These are what we observe as the energy levels of the atom. When I give the talk on which this article is based, at this point I use Dean Dauger’s marvelous “Atom in a Box” program to show the lovely, almost sensuous patterns of undulating waves that describe the possible states of that simplest of atoms, hydrogen. I hope you will explore “Atom in a Box”for yourself. You can link to it at http://www.dauger.com. In its absence, I will substitute a classic metaphor.
The wave patterns that describe protons, neutrons, and their relatives resemble the vibration patterns of musical instruments. In fact the mathematical equations that govern these superficially very different realms are quite similar. Musical analogies go back to the prehistory of science. Pythagoras, partly inspired by his discovery that harmonious notes are sounded by strings whose lengths are in simple numerical ratios, proposed that “All things are Number.”Kepler spoke of the music of the spheres, and his longing to find their hidden harmonies sustained him through years of tedious calculations and failed guesses before he identified the true patterns of planetary motions. Einstein, when he learned of Bohr’s atomic model, called it “the highest form of musicality in the sphere of thought.” Yet Bohr’s model, wonderful as it is, appears to us now as a very watered-down version of the true wave-mechanical atom; and the wave-mechanical proton is more intricate and symmetric by far! I hope that some artist/nerd will rise to the challenge, and construct a “Proton in a Box” for us to play with and admire.
The World as Concept, Algorithm, and Number
I will conclude with a few words concerning the broader significance of these developments for our picture of the world. A major goal of theoretical physics is to describe the world with the greatest possible economy of concepts. For that reason alone, it is an important result that we can largely eliminate mass as an independent property that we are forced to introduce in order to describe matter accurately. But there is more. The equations that describe the behavior of elementary particles become fundamentally simpler and more symmetric when the mass of the particles is zero. So eliminating mass enables us to bring more symmetry into the mathematical description of Nature. The understanding of the origin of mass that I’ve sketched for you here is the most perfect realization we have of Pythagoras’ inspiring vision that the world can be built up from concepts, algorithms, and numbers. Mass, a seemingly irreducible property of matter, and a byword for its resistance to change and sluggishness turn out to reflect a harmonious interplay of symmetry, uncertainty, and energy. Using these concepts, and the algorithms they suggest, pure computation outputs the numerical values of the masses of particles we observe. Still, as I’ve already mentioned, our understanding of the origin of mass is by no means complete. We have achieved a beautiful and profound understanding of the origin of most of the mass of ordinary matter, but not of all of it. The value of the electron mass, in particular, remains deeply mysterious even in our most advanced speculations about unification and string theory. And ordinary matter, we have recently learned, supplies only a small fraction of mass in the Universe as a whole. More beautiful and profound revelations surely await discovery. We continue to search for concepts and theories that will allow us to understand the origin of mass in all its forms, by unveiling more of Nature’s hidden symmetries.
1. https://www.forbes.com/sites/startswithabang/2016/08/03/where-does-the-mass-of-a-proton-come-from/?sh=783b43462e1d
2. https://www.symmetrymagazine.org/article/where-does-mass-come-from#:~:text=These%20particles%20are%20each%20made,protons%20and%20neutrons%20their%20mass.
3. https://physics.mit.edu/wp-content/uploads/2021/01/physicsatmit_03_wilczek_originofmass.pdf
Last edited by Otangelo on Mon Jul 19, 2021 2:18 pm; edited 5 times in total
