Warped Passages (83 page)

^*
The name refers to the electron, not to the character in Greek mythology.

^*
Quoted in Gerald Holton and Stephen J. Brush,
Physics, the Human Adventure, from Copernicus to Einstein and Beyond
(Piscataway, NJ: Rutgers University Press, 2001).

^*
Gerald Holton,
The Advancement of Science, and Its Burdens
(Cambridge, MA: Harvard University Press, 1998).

^*
Quoted in Gerald Holton and Stephen J. Brush,
Physics, the Human Adventure, from Copernicus to Einstein and Beyond
(Piscataway, NJ: Rutgers University Press, 2001).

^*
“Ultraviolet” means “high-frequency.”

^†
A blackbody is actually an idealization; real objects like coal aren’t perfect black-bodies.

^*
“…at any cost, that is, except for the inviolability of the two laws of thermodynamics.” Quoted in David Cassidy,
Einstein and Our World
, 2nd edn (Atlantic Highlands, NJ: Humanities Press, 2004).

^*
Abraham Pais,
Subtle Is the Lord: The Science and Life of Albert Einstein
(Philadelphia: American Philological Association, 1982).

^†
Gerald Holton,
Thematic Origins of Scientific Thought
, revised edn (Cambridge, MA: Harvard University Press, 1988).

^*
Quoted in Abraham Pais,
Inward Bound: Of Matter and Forces in the Physical World
(Oxford: Oxford University Press, 1986).

^*
Integers are the familiar whole numbers: 0, 1, 2, 3, and so on.

^†
We are focusing here on discrete spectra. When a free electron is absorbed by an ion, a continuous—not a discrete—spectrum of light is emitted.

^*
Wavelength is equal to Planck’s constant,
h
, divided by momentum.

^†
Although we need three coordinates to specify a point in space, we sometimes simplify and pretend that the wavefunction depends only on a single coordinate. This makes it easier to draw pictures of wavefunctions on a piece of paper.

^*
He even helped to decipher the Rosetta Stone.

^*
People are actually capable of detecting individual photons, but only in carefully prepared experiments. Usually, you see more standard light composed of many photons.

^*
Werner Heisenberg,
Physics and Beyond: Encounters and Conversations
, translated by Arnold Pomerans (New York: Harper & Row, 1971).

^†
Ibid. Owing to his German nationalism, he also participated in the German atomic bomb project.

^‡
Gerald Holton,
The Advancement of Science, and Its Burdens
(Cambridge, MA: Harvard University Press, 1998).

^*
The GeV is a unit of energy that I will soon explain.

^*
“Tap” for British readers. We are assuming in this example that the faucet drips nonuniformly, which is not always true of real faucets.

^*
I will not derive the precise number here.

^*
The above reasoning is not entirely sufficient to fully explain the true uncertainty principle because you can never be sure that you are measuring true frequency if you measure for only a finite interval of time. Will the faucet leak for ever? Or did it leak only while you were making your measurement? Although it’s somewhat more subtle to demonstrate, you will never do better than the true uncertainty principle, even if you have a more accurate stopwatch.

^*
This is the same quantity that I referred to simply as the “Planck length” in earlier chapters.

^*
For those who already know some physics, this is orbital angular momentum.

^*
Despite the name “Standard Model,” there is an ambiguity in convention. Some people also include the hypothetical Higgs particle as well. However, the name should refer to the known particles only, and that is the convention I use. We’ll discuss the Higgs particle in Chapter 10.

^*
They have a very flexible spine and no collarbone, so can twist their bodies while conserving angular momentum. Actually, this is still actively studied.

^†
Richard Feynman said, “From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the nineteenth century will be judged as Maxwell’s discovery of the laws of electrodynamics.” (
The Feynman Lectures on Physics
, Vol. II (Reading, MA: Addison-Wesley Longman, 1970).)

^*
This is through the measurement of a quantity known as the electron anomalous magnetic moment.

^*
In Chapter 11 we will see that these are also called
virtual particles
.

^*
QED is quantum field theory applied to electromagnetism.

^*
In particle physics, this means the fundamental forces other than gravity (i.e., the weak force, the strong force, and the electromagnetic force).

^*
This honor was given not only for his science, but for his opposition to Home Rule in Ireland.

^*
Rutherford presented his results, but knew that in doing so he was contradicting Kelvin. A.S. Eve’s biography of Rutherford quotes him: “I came into the room, which was half dark, and presently spotted Lord Kelvin in the audience and realized that I was in for trouble at the last part of my speech dealing with the age of the earth, where my views conflicted with his. To my relief, Kelvin fell fast asleep, but as I came to the important point, I saw the old bird sit up, open an eye and cock a baleful glance at me! Then a sudden inspiration came, and I said, ‘Lord Kelvin had limited the age of the earth, provided no new source was discovered. That prophetic utterance refers to what we are now considering tonight, radium!’ Behold! the old boy beamed upon me.” (Eve,
Rutherford: Being the Life and Letters of the Rt. Hon. Lord Rutherford, O.M.
(Cambridge: Cambridge University Press, 1939).)

^†
Weak interactions had, however, been observed earlier, and nuclear mechanisms inside the Sun were known to occur. But the connection to a weak force was understood only later.

^*
It is actually an antineutrino, but that is not important to us here.

^*
The exact words are known because they were contained in a 1934 letter sent to participants of an important scientific meeting, which Pauli missed in order to attend a ball.

^†
Neutrinos were finally detected at a nuclear reactor by Clyde Cowan and Fred Reines in 1956, eliminating any residual doubts.

^*
One way to see that quantum mechanics and special relativity are relevant to this relation is that Planck’s constant tells us that quantum mechanics is involved, and the speed of light tells us that special relativity is too. The distance would be zero if Planck’s constant were zero (and classical physics applied) or if the speed of light were infinite.

^*
And George Zweig, though his paper was never published.

^*
Quark is also a type of German cheese. The name would be doubly appropriate if it contained curds, which would be floating in the cheese like quarks in a hadron. However, my German friends tell me it does not.

^†
We now know that there are six.

^*
This is the origin of the name “quantum chromodynamics.”
Chromos
is Greek for “color.”

^†
Or “supergluons” in the UK.

^*
The neutrinos are named after the charged leptons with which they directly interact through the weak force.

^*
I am describing the symmetry in terms of the consequences of a transformation, but, as always, symmetry is a property of the static system. That is, the system possesses symmetry, even if I don’t actually make the transformation.

^*
A cookie consisting of a sandwich of two round wafers with “creme” in between.

^*
This runs counter to American marketing terminology, which calls small things big.

^*
Recall that quantum mechanics and special relativity make energies and distances interchangeable. For readability, I’ll talk in terms of energies now, but processes involving high energies are the same as processes involving short distances.

^*
This is a modified version of Murray Gell-Mann’s term, the “totalitarian principle,” but I think that “anarchic principle” is a closer approximation to the physics to which it’s applied.

^*
Remember that the uncertainty principle relates uncertainty in length to the inverse of the uncertainty in momentum.

^*
Howard Georgi and S.L. Glashow, “Unity of all elementary-particle forces,”
Physical Review Letters
, vol. 32, pp. 438–441 (1974).

^*
This is known as the
desert hypothesis
.

^*
Remember that virtual particles’ masses are not the same as the masses of true physical particles.

^*
Pierre Ramond, Julius Wess Bruno Zumino, Sergio Ferrara, and others in Europe; and, independently, Y.A. Gol’fand, E.P. Likhtman, D.V. Volkov, and V.P. Akulov in the Soviet Union.

^*
The universe contains dark energy (energy that is not carried by any matter), that constitutes 70 % of the total energy in the universe. Though it might explain dark matter, neither supersymmetry (nor any other theory) explains dark energy.

^*
Keep in mind that the quantum mechanical relations tell us that while the Planck scale length is minuscule, the Planck scale energy is enormous.

^*
In actuality it is a virtual photon—not a real physical photon—that is exchanged.

^*
In fact, compactification on a Calabi-Yau manifold preserved just the right amount of supersymmetry for the theory to reproduce features of the Standard Model. Too much supersymmetry, and you couldn’t have left-handed particles that had different interactions from right-handed ones.

^*
D. Gross, J. Harvey, E. Martinec, and R. Rohm, “Heterotic string theory (I): The free heterotic string,”
Nuclear Physics
B, vol. 256, pp. 253–84 (1985).