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The Origin of Mass

Why is a bowling ball so heavy? You might answer that the bowling ball has a lot of material packed in its spherical shape. But suppose I were to ask what gives weight to that material. Here, you might go on to list the ingredients and respective weights for the material. Still, I’m not satisfied. What gives mass to these ingredients? How far do we need to go down this ladder to find the true origin of the bowling ball’s weight? Or will there always be another ingredient? In either case, the question remains: where does mass come from? As we will see, these are questions that lie at the cutting-edge of physics.

To explain why mass exists, it is prudent to first understand what mass is. Mass is commonly misunderstood as the weight of an object as measured on a balance. Weight is the result of gravitational attraction between two bodies, in this case between the bowling ball and the earth. While the bowling ball’s mass increases the strength of this attraction, the existence of mass is independent of gravity. Just imagine an astronaut walking on the surface of the moon; his weight has decreased, but his mass remains the same (Chown, 2007). However, there is another aspect of mass to consider. According to Isaac Newton, objects have inertia: the tendency to maintain a constant speed. It is mass that resists changes in such motion, otherwise known as acceleration. If I push a group of objects with equal force, those with smaller masses undergo larger acceleration than objects with larger masses (Chown, 2007). That is also why it is easier to catch a falling baseball than a falling bowling ball: the bowling ball’s larger mass makes it more resistant to stopping.

These two aspects of mass may seem completely different. On the one hand, we mentioned that mass is responsible for gravitational attraction. On the other hand, mass resists acceleration. These two forms of mass are respectively known as gravitational mass and inertial mass. Our first puzzle about mass is the following coincidence: gravitational and inertial mass are equal (Clark, 2013). Take Galileo’s celebrated Leaning tower of Pisa experiment: if we were to simultaneously drop a bowling ball and a baseball from a ledge, we would find that they reach the ground at the same time. Why? This can only occur if gravitational mass equals inertial mass (Clark, 2013). Current experiments show that inertial mass is equal to gravitational mass to within 0.0000000000001 (Clark, 2013).

How can there be this equivalence? The answer cannot be found with Newton or even Einstein, both of whom assume this equivalence in their theories of gravity (Clark, 2013). Experiments are planned and ongoing to further understand the relationship between inertial mass and gravitational mass (Clark, 2013). In the meantime, we will continue to look for the origin of “mass,” which can be taken to mean either inertial or gravitational mass.

“As hinted with the origin of the bowling ball’s weight, discovering the origin of mass requires us to climb down a ladder to the most basic ingredients we can find.”

Where should we start? As hinted with the origin of the bowling ball’s weight, discovering the origin of mass requires us to climb down a ladder to the most basic ingredients we can find. The first place to look, then, is atoms. Atoms are the ingredients of matter throughout the universe. They are composed of protons (positively charged) and neutrons in the center (the nucleus), with electrons (negatively charged) buzzing around the nucleus. The number of these particles depends on the particular atom, as can be seen in a periodic table. Why does an atom have mass?

Frank Wilczek, theoretical physicist and professor at MIT, knows a lot about this problem. His work on the subject as a graduate student ultimately earned him a Nobel Prize (Sample, 2010, p. 136). Central to the discussion is the relationship between mass and energy, which was originally formulated by Einstein. One of the most famous equations in all of science is E=mc^2, where m is the mass, E is the energy associated with an object at rest, and c is the speed of light. This equation says that 1 kilogram of mass has energy associated with 22 megatons of TNT, an idea that was put to use during World War II. Yet the equation also can be written m=E/c^2, which says that a given energy has an equivalent mass. This has important implications. Suppose, for example, that two particles collide at speeds near the speed of light. The “debris” after the impact will have more mass than the original particles because energy from the particles’ motion converts into mass1 (Sample, 2010, p. 7). Wilczek showed that at least 95 percent of all mass in the universe is a similar result of energy becoming mass (Wilczek, 2008).

Indeed, m=E/c^2 is the most significant contributor to an atom’s mass. Perhaps unsurprisingly, the mass of the atom comes from its ingredients—the proton, neutron, electron masses, which means that we want to know where those masses come from. But this time there’s a catch. The total electron mass is imperceptibly small compared to the nucleus (roughly a thousandth of the nucleus mass) (Wilczek, 2003). As a result, we will follow Wilczek and ignore the electron’s contribution to the atom’s mass and focus instead on the nucleus. At this point, it may not come as a surprise that protons and neutrons are composed of more basic ingredients. They each contain three subatomic particles called “quarks.” These quarks have some important properties to consider; with the help of massless “gluons”, they are responsible for holding the nucleus together (Kane, 2005). Without these particles, the positive charge of the proton would cause the nucleus to fly apart, something gravity is far too weak to counteract (Wilczek, 2008, p. 27).

The gluons mediate a whole new kind of force: the strong nuclear force. The strange behavior of this force is that it actually grows with distance.2 As a result, quarks exert the least force—and therefore have the least energy—when they are closest together (Wilczek, 2003). Under this scenario, we would expect the quarks to snuggle up as close as possible, creating zero energy. Now, quantum mechanics tells us that quarks (and for that matter all particles) are not really particles at all. Instead, they are really waves packed into a localized region: “Wavicles,” as Wilczek refers to them (Wilczek, 2003). These wavicles can’t quite be made to overlap, however. The famous Heisenberg Uncertainty Principle says that if they overlap (a precise position), a large range of possible momenta (the “umph” associated with a moving object), and hence energy, would result. “It takes work to pin quarks down. Wavicles want to spread out,” as Wilczek (2005) explains. Each particle, including protons and neutrons, acquires a unique energy from this strong force-quark interaction. From Einstein’s famous m=E/c^2, that energy goes into the mass of the object (Wilczek, 2003).

“So if we are willing to make approximations, we have found a way to account for the bowling ball’s mass: it comes from the finite energy of the quarks and gluons within the nucleus.”

This explanation did not require the quarks to have any mass. The motion of the quarks created the mass of the proton and neutron, and it turns out that 95 percent of the observed proton and neutron masses can be accounted for in this manner! The other 5 percent comes from taking the quark’s mass into account (Wilczek, 2003). So if we are willing to make approximations, we have found a way to account for the bowling ball’s mass: it comes from the finite energy of the quarks and gluons within the nucleus. And why stop with the bowling ball? As Ian Sample (2010) explains in his book Massive, “Any object you care to mention, from your pet dog to your cellphone, owes most of its mass to the intense energy it takes to keep it in one piece” (p. 7).

However, electrons and quarks are more fundamental particles than protons and neutrons. What if we want to know where all of the atom’s mass comes from? For the true answer, we face the unfortunate situation of climbing down the ladder3 to yet another set of ingredients that inhabit the subatomic realm, an area governed by “elementary particle physics.”

Notice that the word “elementary” seems to imply that these are the smallest ingredients possible. This may provoke skepticism, given our steady movement toward smaller and smaller bits. In his book Supersymmetry, Gordon Kane, a theoretical physicist at the University of Michigan, cites three reasons why these are indeed the smallest ingredients (Kane, 2000, p. 21). The first reason is experimental: many experiments have tried to analyze the structure of these particles at deeper levels (up to 10,000 times), but have failed in finding any new building blocks. The second reason is theoretical: within the accepted scientific theories, it is not mathematically possible to give structure to such particles. Finally, the unification of the fundamental forces4 is possible if, and only if, these particles have no internal structure (Kane, 2000, p. 21).

These fundamental particles are described in a framework known as the Standard Model of particle physics. There are three “families” of such fundamental particles, sorted by increasing mass. The first family contains stable particles such as the electron, the up quark, and the down quark (Kane, 2005). The other two families contain heavier versions of quarks and electrons, such as the charm, strange, top, and bottom quarks, muon, and tau electrons (Kane, 2005). These particles interact the same way as the ordinary particles, but have short lifetimes before decaying (Kane, 2005). Overall, the observed masses for these particles span eleven orders of magnitude (Kane, 2005), with the top quark the largest! Can we account for such a range of masses?

We begin our attempt to explain elementary particle mass with an important concept in physics: symmetry. A symmetry in physics means a property of nature that does not change under different circumstances (Lightman, 2013). Many examples of such symmetry can be found in nature. A sphere, for example, has rotational symmetry because it does not appear to change upon rotation.

There are aspects of the Standard Model that are symmetric, known as internal symmetries (Kane, 2000, p. 28). For example, the laws describing two seemingly different particles, such as an electron and a neutrino, are the same (Kane, 2000, p. 28). A similar symmetry exists between the electromagnetic and weak force; i.e., the laws describing these forces turn out to be the same. This may seem strange; the weak force is responsible for carrying out radioactive decay processes (Sample 2010, p. 6), yet the electromagnetic force is associated with bar magnets and Van de Graff Generators. Nevertheless, the two forces act the same upon swapping their respective mediating particles: the photon and W, Z bosons (Lightman, 2013).

However, there are problems here. The first internal symmetry mentioned (that associated with electrons and neutrinos) requires massless electrons and neutrinos (Kane, 2000, p. 29). The second symmetry (that between the electromagnetic and weak forces) is also inconsistent with observation; the photon has an infinite range, while the W and Z bosons’ range span just one percent of an atomic nucleus width (Sample, 2010, p. 59). Just as the gravitational field hides the symmetry of translation in our daily lives (going up is not the same as going down), some other kind of field must be present to hide these predicted symmetries—a field that gives mass to particles. Enter the Higgs field.

“Without the Higgs field, all particles would move at the speed of light.”

Without the Higgs field, all particles would move at the speed of light. In the 1960’s, theorists invented this field to grant mass to the W and Z bosons, while leaving the photon untouched; this effect explains the difference in the forces’ ranges (Sample, 2010, p. 60). Now, the Higgs field is naturally present throughout the universe. Since a natural state has the least amount of energy (a fundamental idea in physics), a nonzero Higgs field minimizes the field’s energy (Kane, 2005). This is quite unusual. A ball on top of a hill has a minimum energy when the gravitational field turns off. Not so for the Higgs; a finite field strength minimizes the energy. The natural, finite field is the fundamental aspect of the Higgs field, allowing it to provide the “mass-giving energy” (via m=E/c^2) to particles (Kane, 2000, p. 152; Lightman, 2013). The Higgs provides a mechanism for elementary particles to acquire mass, thus completing the Standard Model.

Evidence for the Higgs came in July 2012. Researchers working with the Large Hadron Collider (LHC) spent several years studying the collision products of particles accelerated close to the speed of light. It turns out that the Higgs Boson, the particle serving as the mediator of the Higgs mechanism, can show up in such products (Butterworth, 2013). The Higgs Boson was found as a 5-sigma result, meaning that there was a 1 in 3.2 million chance that the discovery was a statistical fluke (Butterworth, 2013). Most recently, the discovery prompted the 2013 physics Nobel Prize to be awarded to Peter Higgs and Francois Englert, the original formulators of the theory.

We have now come to understand much about the bowling ball’s mass. Most of it comes from the quarks’ inherent energy, while the rest is obtained from particle interactions with the Higgs field. The stronger the interaction of a particle with the field, the greater the mass.

“Supersymmetry requires us to climb the ladder down 17 orders of magnitude smaller than the atomic scale—to the Planck scale.”

But at this point, the Higgs field seems mysterious. In particular, why does the natural state of the Higgs field just happen to be nonzero? Why does the Higgs field leave the photon unaffected, but not the W, Z bosons? Such mechanisms were originally postulated, not derived, in order to preserve the symmetry of the Standard Model (Kane, 2000, p. 56). In addition, the Higgs mechanism only gives a qualitative glimpse of the origin of mass; unfortunately, it cannot be used to predict the masses of, say, the electron (Kane, 2003) or of the top quark. Furthermore, it is still unclear if the energy that creates this mass has the intrinsic property of inertia. This last point will have to wait for later, but we can look to the theory of Supersymmetry to provide a deeper understanding of the Higgs mechanism. Supersymmetry requires us to climb the ladder down 17 orders of magnitude smaller than the atomic scale—to the Planck scale.

At the Planck Scale, the electromagnetic force is predicted to merge with the weak force. This provides an intriguing clue; perhaps at this scale, the natural state of the Higgs field has zero energy. Supersymmetry shows that a natural Higgs field emerges as we go to Standard Model scales and beyond (Kane, 2000, p. 153). As a bonus, the rate at which the Higgs field emerges can be used to predict the unusually heavy top-quark mass (Kane, 2000, p. 154). This is getting somewhere. Supersymmetry shows promise for predicting many such values, especially when combined with String Theory5. This use of string theory, however, has yet to be accomplished in a convincing way (Kane, 2005).

We have climbed down as far as possible, and found promising possibilities for predicting many of the known masses. Will Supersymmetry and String Theory give the final answer for the bowling ball’s mass? Some physicists do not believe that this mass we have been describing—the “rest mass” resulting from the mass-energy equation m=E/c^2—explains mass’ property to resist acceleration, otherwise known as inertia. Why should, for example, the energy of the quarks’ motions lead to inertia?

One possible explanation for inertia relies on quantum fluctuations of empty space. We again turn to Heisenberg’s Uncertainty Principle, this time in a slightly different form. This principle says that nature may violate energy conservation, provided it does so in a short time interval (Chown, 2007). In other words, empty space isn’t really empty. It’s teeming with particles, otherwise known as “virtual particles”, popping in and out of existence. Researchers showed that when a free mass travels through empty space, virtual particles can exert a drag force that increases with the object’s acceleration (Haisch et al., 2001). To maintain that acceleration, a force proportional to that acceleration must be applied. This force-acceleration relationship has a strong resemblance to inertia, a property that resists acceleration (Chown, 2007). The authors claim that these findings do not conflict with the Higgs, since they explain different physical properties. “The Higgs mechanism explains the rest mass of subatomic particles while the vacuum interaction explains their inertial mass” (Chown, 2007).

Much progress has been made in understanding the origin of the bowling ball’s weight, but there is still much that is not known. The Higgs mechanism told us how the energy of interactions can produce mass, but the explanation of the quantum vacuum, described above, may be necessary to understand inertial mass. And since the equivalence of gravitational and inertial mass remains a mystery, it is unclear whether we have actually accounted for the origin of the bowling ball’s weight (a property of gravitational mass). Indeed, there may be questions that we will never understand about the origin of mass, but the pieces of understanding that we pick up in the process make it a worthwhile venture.

Notes

1Energy is conserved in this collision. The initial energy of the particles comes from kinetic energy. Upon colliding, that energy goes into the rest energy of the particles. As a result, the particles acquire more mass.

2(Source: Wilczek, 2008, p. 49). If the strong force grows with distance, why isn’t the strong force crunching everything together? For this to happen, we would need to create unfathomably large clouds of gluons to mediate this crunching effect, which takes more energy than exists in the universe. It turns out that the strong force only increases in strength over a range about the size of an atomic nucleus (“Fundamental Forces,” HyperPhysics)!

3Why should we climb further down the ladder? Wilczek gives one reason. Without quark and electron masses, drastic changes in matter would result. Suppose, for example, that we were to quadruple the mass of the electron. In this scenario, electrons would be able to merge with protons, forming neutrons. Since electrons are crucial for chemistry, life as we know it—which relies on a multitude of chemical reactions—would not be attainable (Wilczek, 2008, p. 200). Thus a deeper understanding of the origin of mass may shed light on anthropic questions (questions relating to human existence).

4These forces are electromagnetism, the strong force (holds the nucleus together), the weak force (radioactive decay), and gravity. As it turns out, a discrepancy between inertial and gravitational mass is necessary for gravity to be formulated under a similar framework as the other three fundamental forces of nature (Clark, 2013). Such a framework requires describing gravity in the language of quantum mechanics, which is one of the outstanding problems in theoretical physics (Clark, 2013).

5While an extensive discussion of Supersymmetry and String Theory is beyond the scope of this essay, the interested reader may refer to Brian Greene’s The Elegant Universe for an accessible explanation of the subject.

 

References

Ball, P. (2009). Quark statistics shed light on universe’s symmetry. Nature, 458, 559.

Butterworth, J. (2013, September 4). Higgs boson: What’s next? New Scientist, (2933).

Chown, M. (2007). Mass Medium. In M. Chown (Author), The never-ending days of being dead (pp. 166-192). London, England: Faber and Faber.

Clark, S. (2013, January 22). Sacrificing Einstein: Relativity’s keystone has to go. New Scientist, (2900).

Fundamental Forces. (n.d.). Retrieved November 1, 2013, from HyperPhysics
website: http://hyperphysics.phy-astr.gsu.edu/hbase/forces/funfor.html

Haisch, B., Rueda, A., & Dobyns, Y. (2001). Inertial mass and the quantum vacuum
fields. Annalen der Physik, 10(5), 393-414.

Kane, G. (2000). Supersymmetry: Squarks, photinos, and the unveiling of the ultimate laws of nature. Cambridge, MA: Perseus.

Kane, G. (2005, July). The mysteries of mass. Scientific American, 41-48.

Lightman, A. (2013, March/April). Symmetrical universe: Order and beauty at the core of creation. Orion, 26-35.

Sample, I. (2010). Massive: The missing particle that sparked the greatest hunt in science. New York, NY: Basic Books.

Wilczek, F. (2005). The origin of Mass. Frontline India. Volume 22, Issue 10.

Wilczek, F. (2003). The origin of Mass. MIT Physics Annual, 24-35.

Wilczek, F. (2008). The lightness of being. New York, NY: Basic Books.

Sam Moore Author’s Note

Class of 2016, transfer student from California
 Major: Physics
. Physics interests: condensed matter and many-particle systems, astrophysics. Hobbies: basketball, the outdoors, music composition. I find research essays to be one of the most rewarding writing styles. The process allows me to investigate and learn the material deeply. There are many aspects of high-energy physics that I don’t understand. Hence, this science essay provided the perfect opportunity to improve my knowledge. The timing was excellent; the Nobel Prize for the discovery of the Higgs was awarded while working on the piece, providing even more sources on the origin of mass.