13. See “Hideki Yukawa,” http://en.wikipedia.org/wiki/Hideki_Yukawa, “Pion,” http://en.wikipedia.org/wiki/Pion, “Strong force,” http://en.wikipedia.org/wiki/Strong_force (all sites last visited 3/10/13).
The pion, like all strongly interacting particles, is actually a composite particle, made of a light quark (either “up” or “down”) with a light anti-quark (either “anti-up” or “anti-down”).
14. See “Muon,” http://en.wikipedia.org/wiki/Muon (site last visited 3/10/13). Throughout this book we'll be placing emphasis on the muon because it is a truly point-like elementary particle (lepton) that has played a key role in unraveling the mystery of mass. It may also provide an avenue to the next generation of ultra-high-energy particle colliders, i.e., the Muon Collider. See http://en.wikipedia.org/wiki/Muon_collider (site last visited 3/10/13). Muons at rest live only about two millionths of a second (2 × 10-6 seconds). But because of a remarkable effect in relativity, as particles approach the speed of light, time slows down for them, and their lifetimes are extended; the muons are produced with energies that are hundreds of times their masses, and they can live hundreds of times longer, and this gets them down to the surface of the earth for detection.
15. See “Manhattan Project,” http://en.wikipedia.org/wiki/Manhatten_project, and “Atomic bombings of Hiroshima and Nagasaki,” http://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki (sites last visited 3/10/13).
CHAPTER 3. WHO ORDERED THAT?
1. See “Pion,” http://en.wikipedia.org/wiki/Pion (site last visited 3/10/13). The positively charged π+ is the “antiparticle” of the negatively charged π–. Antimatter was theoretically predicted by the young genius Paul Dirac in 1926, who merged quantum theory together with Einstein's theory of special relativity, as we discuss this in chapter 9. A few years after Dirac's prediction, the antielectron, dubbed the “positron,” was discovered in experiment. The theoretical prediction of antimatter is considered to be one of the greatest triumphs of twentieth-century physics. Each particle has a corresponding antiparticle species in nature. In some cases, like the photon and the neutral π0, a particle can be its own antiparticle (we call such a particle “self-conjugate”; only electrically neutral particles can be self-conjugate).
2. The Wikipedia article on the muon reads as though we wrote it: http://en.wikipedia.org/wiki/Muon (site last visited 3/13/13).
3. The Wikipedia article on I. I. Rabi (pronounced “Robby”), a Nobel laureate, mentor of Leon Lederman, and a great and influential scientist, is well worth taking time to read: http://en.wikipedia.org/wiki/Isidor_Isaac_Rabi (site last visited 3/13/13). We quote the moving last paragraph from this article: “Rabi died at his home in Riverside Drive, Manhattan, from cancer, on 11 January 1988. In his last days, he was reminded of his greatest achievement in a poignant fashion when his physicians examined him using magnetic resonance imaging, a technology that had been developed from his ground-breaking research on magnetic resonance. ‘I saw myself in that machine,’ he remarked, ‘I never thought my work would come to this.’”
4. See, e.g., the article on the Standard Model: http://en.wikipedia.org/wiki/Standard_model (site last visited 3/13/13). There are also many books and documentaries describing the history of particle physics and the Standard Model and beyond.
5. See “Muon-catalyzed fusion,” http://en.wikipedia.org/wiki/Muon_catalyzed_fusion (site last visited 3/13/13).
6. See the Fermilab site for the Muon Collider: http://www.fnal.gov/pub/muon_collider/. Searching online for “Muon Collider” pulls up stuff like: http://www.dvice.com/archives/2012/07/muon-collider-c.php (sites last visited 3/13/13).
7. See the “History” section of the “Muon” entry: http://en.wikipedia.org/wiki/Muon#History (site last visited 3/13/13).
8. So, in summary, the muons are not the primary cosmic rays, and they aren't even the secondary ones (the pions are secondaries) but rather they are the tertiary products of decaying pions produced in the high-up-in-the-atmosphere cosmic ray collisions! The muons are deeply penetrating because they don't have strong interactions and make it down to the surface of the earth where they could be detected, but the pions are reabsorbed in collisions with nuclei, and they have a shorter lifetime, so they don't make it to lower levels of the atmosphere.
9. What we usually quote as a particle “lifetime” is actually the “e-folding time,” which is slightly longer than the half-life. That is, the number of particles, at time t, is proportional to e–t/τ where τ is the e-folding time; this is equivalently to 2–t/τ’ where τ’ is the half-life, and τ = τ’/ln(2) = 1.44 τ’.
10. See the “History” section of the “Pion” entry: http://en.wikipedia.org/wiki/Pion#History. In 1948 the first “artificially produced” pions were created by the cyclotron at the University of California, Berkeley. The charged pions that are directly produced in the upper atmosphere decayed into the muons that were ultimately detected in 1937 at the surface of the earth. Since muons do not interact strongly with protons of neutrons they are able to penetrate matter very deeply and arrive at the surface of the earth (with some help from Einstein's time dilation). In fact, you must go rather deep into the earth to shield yourself from having any muons hit you, as they can penetrate to great depths through rock. The fact that all of this deep penetration through matter happens tells us that muons are not strongly interacting particles—i.e., they were not the pions predicted by Yukawa.
Muons do have electric charges, and when a particle that has an electric charge passes through matter, it gradually loses energy by virtue of the electromagnetic interaction. Typically, it slightly scatters off of an electron in an atom and is slightly accelerated, causing it to radiate a photon.
Photons are radiated from charged particles when they accelerate; that's how light is produced by a chemical reaction, such as burning. The reaction rapidly accelerates electrons as they collide with one another. This is also the principle of radio transmission. An antenna is a wire in which electrons are accelerated, causing them to emit the low-energy photons that are radio waves. This photon radiation has a fancy Germanic name: bremsstrahlung. An example of this is a dental X-ray machine, where accelerated electrons, like those in an old TV picture tube, collide with a metal target. In the target the electrons instantly decelerate, losing all of their energy by collisions with other electrons and atomic nuclei. Whenever the electron collides, it radiates a bremsstrahlung photon. If the initial electron energy is high, the resulting emitted photons will also be energetic, and this can make X-rays, or gamma rays, etc. We'll henceforth call this “brem radiation” or “brem photons” like our colleagues at the lunch table at Fermilab do. You can use this particle physics slang to impress your significant other.
The amount of brem radiation depends upon how much the charged particle is instantaneously accelerated in a collision. An electron is a very light particle, having a tiny mass of only 0.511 MeV. It can therefore get bumped around and jiggle and bounce, thus accelerating a lot in collisions. Think of box of Ping-Pong® balls rattling around in a truck on a bumpy road. The Ping-Pong ball is such a featherweight that it can't sit still in a bumpy environment. Electrons therefore produce a lot of brem photons when they pass through matter because they bounce around and recoil in collisions so much. Electrons therefore quickly lose all of their energy when they enter matter. If the muon were as light as an electron, it would never reach the surface of the earth after being produced by a primary collision ten miles up in the sky. A muon, on the other hand, is 200 times heavier than an electron. Muons are like bowling balls compared to electrons. They don't accelerate or recoil much as they pass through matter and collide with atoms and electrons. So, muons tend not to produce so many brem photons. The muons therefore don't lose energy very much when they pass through matter. This is one of the reasons muons can make it to the surface of the earth and go considerable distance down through rock once they're produced some ten miles up in the atmosphere from decaying pions.
11. The pions are composite particles, made of quarks, as are the proton and neutron. All quark containing particles have strong interactions with one another (see the Appendix). Muons, however, are leptons, and leptons do not experience this strong force. This may be, in a larger sense, the focus of the question “Who ordered that?”—it remains a mystery why we have these two particular classes of particles: quarks with their strong interactions that bind them eternally into protons and neutrons and other strongly interacting particles, and leptons that just don't experience these strong forces.
A neutral pion contains a quark and an antiquark, and this is just a particle annihilating (quark) with an antiparticle (antiquark) inside the pion. All of the everyday nuclear matter in our world is composed of combinations of the two quarks, up and down. These objects are distinguished by their electric charges and their masses. We always define the electron to have an electric charge of –1. In these units, the up quark (u) has an electric charge of +2/3, and the down quark (d) an electric charge of –1/3. The proton is therefore not an elementary particle but rather a composite particle built of three quarks in the pattern u + u + d. Adding up the electric charges of the constituent quarks, we see that the proton charge is +1. Similarly, the neutron is composed of u + d + d, and the corresponding electric charge combination is 0. See the Appendix for more details.
12. Lewis Carroll, Alice's Adventures in Wonderland and Through the Looking-Glass and What Alice Found There, illustrations by John Tenniel (London: Macmillan and Co., 1866 & 72, 1866), 2 volumes. The marvelous illustrations are cataloged here: https://sites.google.com/site/lewiscarrollillustratedalice/ (site last visited 3/7/13).
13. Ibid.
14. This account appears in Leon M. Lederman and Dick Teresi, The God Particle: If the Universe Is the Answer, What Is the Question? (Mariner Books, 2006) and in Leon M. Lederman and Christopher T. Hill, Symmetry and the Beautiful Universe by (Amherst, NY: Prometheus Books, 2008).
15. Note that Lederman et al. were using positive muons that are always right-handed (R) in positively charged pion decay; the positively charged muon is actually the antiparticle of the muon, which, like the electron, is negatively charged. If Leon did the experiment with negatively charged muons they would all be left-handed, or L, in the negative pion decay. The chirality of a particle is always the opposite of the chirality of the antiparticle (as discussed in chapter 9, the anti-L particle is the absence of a negative energy L particle, or a “hole” in the vacuum, so the hole would be R).
16. See “Parity” (physics), http://en.wikipedia.org/wiki/Parity_%28physics%29, “T.D. Lee,” http://en.wikipedia.org/wiki/T_D_Lee, “C. N. Yang,” http://en.wikipedia.org/wiki/C_N_Yang (sites last visited 3/13/13).
17. See “Chien-Shiung Wu,” http://en.wikipedia.org/wiki/Madame_Wu (site last visited 3/13/13).
CHAPTER 4. ALL ABOUT MASS
1. Neil DeGrasse Tyson quote: https://www.facebook.com/pages/Higgs-Boson/384970858230425.
2. “‘Yeah, the Higgs boson is getting a lot of attention, but there are a lot of lower-profile bosons that are worth checking out if you get the chance’—Tamara Farrar—Unemployed,” http://www.theonion.com/articles/2012-in-technology,30782/ (site last visited 3/8/2013).
3. Perhaps to draw some sympathy for the plight of providing a more precise and universal definition in the text, we provide here a list and discussion of other forms of energy from our book Symmetry and the Beautiful Universe (Amherst, NY: Prometheus Books, 2007), chap. 2:
Potential energy is energy that is stored in an object or system, which is ready upon its release to make other objects move. For example, a compressed spring has potential energy that can launch a toy dart from a child's rubber tipped dart gun, or help to hoist open a garage door, or to run an old fashioned wind-up watch for days. This energy in a spring is actually the energy of deformation of the lattice of iron alloy (steel) atoms within the material as they are twisted slightly away from their normal relaxed pose. There can be many forms of potential energy. For example, a bank of snow sitting atop a mountain has gravitational potential energy, ready at an instant to fall and convert to kinetic energy of motion. Gasoline, or other fuels, contains chemical potential energy waiting to be released by the chemical reaction of oxidation (burning).
Chemical energy is created (or consumed) as various substances can undergo a vast array of chemical reactions that produce or consume energy. The precise form that the chemical energy takes depends upon the reaction. One rather common example is the burning of coal, oil, wood, or other substances which have a high percentage of carbon. “Burning” is the act of combining carbon with oxygen (a gas that is conveniently and generously supplied by the atmosphere). The basic reaction is C + O2 → CO2 + Q. Here Q is a symbol for energy, which includes particles of light (known as photons, or equivalently, the particles that make up electromagnetic radiation), and the rapid motion (kinetic energy) of the resulting molecules after burning. In other words, carbon combines with oxygen to produce carbon-dioxide plus energy.
Thermal energy is the high speed random motion of atoms, molecules, or other particles in a gas or other material. In a wood fireplace, the rapidly moving molecules, products of the combustion, collide with other molecules, such as the surrounding air, giving them kinetic energy, which propagates the heat outward into the room in a process called convection. The photons stream out into the room, as well as thermal radiation, producing radiant heat. The pleasurable sensation of a warm fire in a fireplace is nothing more than a bath of faster moving air molecules and photons.
Electrical energy is yet another form. In its simplest form, this is just the kinetic energy of the flow of electrons (an electric current) through a wire, through certain liquids, or in free space as in a vacuum tube (such as a cathode ray tube, a TV picture tube) or in a particle accelerator of electrons. If the wire has a large electrical resistance, then the electrons collide with the atoms in the wire, losing their energy, causing the wire atoms to move. The wire thus becomes hot, as in a toaster or an electric oven broiler. This is called electrical resistance, and leads to the loss of electrical energy.
The tricky thing about the book-keeping of electrical energy, however, is that an electron can radiate, or emit, a photon, the particle of light, through the process: The electron, after the emission of the photon has less energy than the electron before the “emitted photon,” has been created, carrying off a certain amount of energy. This can also go in reverse where the initial electron absorbs the photon and the final electron has gained the photon's energy. This is the fundamental process in nature that defines electromagnetism. Photons can be stored in an “electromagnetic field,” as a kind of photon soup, which itself contains the energy of the photons. So, energy in the basic processes of electricity and magnetism is difficult to keep track of, involving continual swapping back and forth between electrons and photons. Chemical energy, when examined microscopically, is really electrical energy within atoms and molecules. As we have indicated, energy is a precisely defined concept in physics. It is a useful concept because it is conserved in all processes. If we have a large box inside of which all possible things can happen, such as springs that can compress and expand, various bodies can fall and bounce, water can flow, chemicals react, objects burn, atomic nuclei disintegrate, etc., and through all of this there is one number that stays the same—the total energy.
We living organisms are also engines. Our bodies are consuming energy to sustain our metabolism, ergo our lives. Here we measure energy in “food calories,” usually designated with the upper case “C” as in Calorie. A typical (lean) person in America eats about 2000 Calories per day. To convert this into joules we multiply by (approximately) 4,200, hence the average lean person is consuming about 8,400,000, or 8.4 million joules of food energy per day! In a day there are 24 hours and 60 minutes per hour, and 60 seconds per minute, that is, 86,400 seconds total in a day. Therefore, the average person consumes energy, and burns off the equivalent e
nergy, at an average rate of about 8,400,000/86,400 = 97 watts. Therefore, each of us, as living, functioning, metabolizing beings, is approximately equivalent to a 100 watt light bulb in our metabolic power consumption. For comparison, the sun produces at ground level, a power of about 100 watts per square meter, averaged over a sunny day. So, a 30 meter by 30 meter solar collector, about the size of a large roof, with an efficiency of 10%, would be required for every person in our society to obtain all the presently required power from the sun.
Power: The “time rate” at which energy is produced or consumed or converted is called power. One can think of power as a kind of speed, if one thinks of energy as a kind of distance. If you want to take a trip somewhere, you must travel a certain distance. How fast you do this depends upon your speed. The greater the speed, the shorter the time for the trip. Likewise, you may want to consume a certain amount of energy to perform a task, such as mowing the lawn. How fast you perform the task determines the power you require, the time rate at which you consume the energy. The more power you consume, the shorter the time the task will take. Note that the power is not a fixed or conserved quantity because we can speed up or slow down the rate at which we perform the task. The total energy, on the other hand, is fixed, like the total distance traveled for a given trip.
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