From Eternity to Here (72 page)

19
Fitzgerald (1922).

20
Carroll, L. (2000), 175.

21
Obviously.

22
Diedrick (1995) lists a number of stories that feature time reversals in one form or another, in addition to the ones mentioned here: Lewis Carroll’s
Sylvie and Bruno
, Jean Cocteau’s
Le Testament d’Orphee
, Brian Aldiss’s
An Age
, and Philip K. Dick’s
Counter-Clock World
. In T. H. White’s
The Once and Future King
, the character of Merlyn experiences time backward, although White doesn’t try very hard to consistently maintain the conceit. More recently, the technique has been used by Dan Simmons in
Hyperion
, and serves as a major theme in Andrew Sean Greer’s
The Confessions of Max Tivoli
and in Greg Egan’s short story “The Hundred-Year Diary.” Vonnegut’s
Slaughterhouse-Five
includes a brief description of the firebombing of Dresden in reversed order, which Amis credits in the Afterword to
Time’s Arrow
.

23
Stoppard (1999), 12.

24
In addition to the First Law of Thermodynamics (“the total energy remains constant in any physical process”) and the Second Law (“the entropy of a closed system never decreases”), there is also a Third Law: As the temperature of a system is lowered, there is a minimum value (absolute zero) for which the entropy is also a minimum. These three laws have been colorfully translated as: “You can’t win; you can’t break even; and you can’t even get out of the game.” There is also a Zeroth Law: If two systems are both in thermal equilibrium with a third system, they are in thermal equilibrium with each other. Feel free to invent your own whimsical sporting analogies.

25
Eddington (1927), 74.

26
Snow (1998), 15.

27
In fact, it would be fair to credit Sadi Carnot’s father, French mathematician and military officer Lazare Carnot, with the first glimmerings of this concept of entropy and the Second Law. In 1784, Lazare Carnot wrote a treatise on mechanics in which he argued that perpetual motion was impossible, because any realistic machine would dissipate useful energy through the rattling and shaking of its component parts. He later became a successful leader of the French Revolutionary Army.

28
Not strictly true, actually. Einstein’s general theory of relativity, which explains gravitation in terms of the curvature of spacetime, implies that what we ordinarily call “energy” is not really conserved, for example, in an expanding universe. We’ll talk about that in Chapter Five. But for the purposes of most combustion engines, the expansion of the universe can be neglected, and energy really is conserved.

29
Specifically, by “measures the number of ways we can rearrange the individual parts,” we mean “is proportional to the logarithm of the number of ways we can rearrange the individual parts.” See the Appendix for a discussion of logarithms, and Chapter Nine for a detailed discussion of the statistical definition of entropy.

30
The temperature of the surface of the Sun is approximately 5,800 Kelvin. (One Kelvin is the same as one degree Celsius, except that zero Kelvin corresponds to -273 degrees C—absolute zero, the lowest possible temperature.) Room temperature is approximately 300 Kelvin. Space—or, more properly, the cosmic background radiation that suffuses space—is at about 3 Kelvin. There is a nice discussion of the role of the Sun as a hot spot in a cold sky in Penrose (1989).

31
You will sometimes hear claims by creationists to the effect that evolution according to Darwinian natural selection is incompatible with the growth of entropy, since the history of life on Earth has involved increasingly complex organisms purportedly descending from less complex forms. This is crazy on several levels. The most basic level is simply: The Second Law refers to closed systems, and an organism (or a species, or the biosphere) is not a closed system. We’ll discuss this a bit more in Chapter Nine, but that’s basically all there is to it.

32
Thompson (1862).

33
Pynchon (1984), 88.

3. THE BEGINNING AND END OF TIME

34
In fact there was a literal debate—the “Great Debate” between astronomers Harlow Shapley and Heber Curtis was held in 1920 at the Smithsonian in Washington, D.C. Shapley defended the position that the Milky Way was the entirety of the universe, while Curtis argued that the nebulae (or at least some of them, and in particular the Andromeda nebula M31) were galaxies like our own. Although Shapley ended up on the losing side of the big question, he did correctly understand that the Sun was not at the center of the Milky Way.

35
That’s a bit of poetic license. As we will explain later, the cosmological redshift is conceptually distinct from the Doppler effect, despite their close similarity. The former arises from the expansion of space through which the light is traveling, while the latter arises from the motion of the sources through space.

36
After decades of heroic effort, modern astronomers have finally been able to pin down the actual value of this all-important cosmological parameter: 72 kilometers per second per Megaparsec (Freedman et al., 2001). That is, for every million parsecs of distance between us and some galaxy, we will observe an apparent recession velocity of 72 km/sec. For comparison, the current size of the observable universe is about 28 billion parsecs across. A parsec is about 3.26 light years, or 30 trillion kilometers.

37
Strictly speaking, we should say “every sufficiently distant galaxy . . .” Nearby galaxies could be bound into pairs or groups or clusters under the influence of their mutual gravitational attraction. Such groups, like any bound systems, do not expand along with the universe; we say that they have “broken away from the Hubble flow.”

38
Admittedly, it’s a bit subtle. Just two footnotes prior, we said the observable universe was “28 billion parsecs” across. It’s been 14 billion years since the Big Bang, so you might think there are 14 billion light-years from here to the edge of the observable universe, which we can multiply by two to get the total diameter—28 billion light years, or about 9 billion parsecs, right? Was there a typo, or how can these be reconciled? The point is that distances are complicated by the fact that the universe is expanding, and in particular because it is being accelerated by dark energy. The physical distance today to the most distant galaxies within our observable universe is actually larger than 14 billion light-years. If you go through the math, the farthest point that was ever within our observable patch of universe is now 46 billion light-years, or 14 billion parsecs, distant.

39
The idea that particles aren’t created out of empty space should be clearly labeled as an assumption, although it seems to be a pretty good one—at least, within the current universe. (Later we’ll see that particles can very rarely appear from the vacuum in an accelerating universe, in a process analogous to Hawking radiation around black holes.) The old Steady State theory explicitly assumed the opposite, but had to invoke new kinds of physical processes to make it work (and it never really did).

40
To be careful about it, the phrase
Big Bang
is used in two different ways. One way is as we’ve just defined it—the hypothetical moment of infinite density at the beginning of the universe, or at least conditions in the universe very, very close to that moment in time. But we also speak of the “Big Bang model,” which is simply the general framework of a universe that expands from a hot, dense state according to the rules of general relativity; and sometimes we drop the
model
. So you might read newspaper stories about cosmologists “testing the predictions of the Big Bang.” You can’t test the predictions of some moment in time; you can only test predictions of a model. Indeed, the two concepts are fairly independent—we will be arguing later in the book that a complete theory of the universe will have to replace the conventional Big Bang singularity by something better, but the Big Bang model of the evolution of the universe over the last 14 billion years is well established and not going anywhere.

41
The microwave background has a messy history. George Gamow, Ralph Alpher, and Robert Herman wrote a series of papers in the late 1940s and early 1950s that clearly predicted the existence of relic microwave radiation from the Big Bang, but their work was subsequently largely forgotten. In the 1960s, Robert Dicke at Princeton and A. G. Doroshkevich and Igor Novikov in the Soviet Union independently recognized the existence and detectability of the radiation. Dicke went so far as to assemble a talented group of young cosmologists (including David Wilkinson and P. J. E. Peebles, who would go on to become leaders in the field) to build an antenna and search for the microwave background themselves. They were scooped by Penzias and Wilson, just a few miles away, who were completely unaware of their work. Gamow passed away in 1968, but it remains mysterious why Alpher and Herman never won the Nobel Prize for their predictions. They told their side of the story in a book,
Genesis of the Big Bang
(Alpher and Herman, 2001). In 2006, John Mather and George Smoot were awarded the Prize for their measurements of the blackbody spectrum and temperature anisotropies in the microwave background, using NASA’s Cosmic Background Explorer (COBE) satellite.

42
The full story is told by Farrell (2006).

43
Bondi and Gold (1948); Hoyle (1948).

44
See for example Wright (2008).

45
Needless to say, that’s making a long story very short. Type Ia supernovae are believed to be the result of the catastrophic gravitational collapse of white dwarf stars. A white dwarf is a star that has used up all of its nuclear fuel and just sits there quietly, supported by the basic fact that electrons take up space. But some white dwarfs have companion stars, from which matter can slowly dribble onto the dwarf. Eventually the white dwarf hits a point—the Chandrasekhar Limit, named after Subrah manyan Chandrasekhar—where the outward pressure due to electrons cannot compete with the gravitational pull, and the star collapses into a neutron star, ejecting its outer layers as a supernova. Because the Chandrasekhar Limit is approximately the same for every white dwarf in the universe, the brightness of the resulting explosions is approximately the same for every Type Ia supernova. (There are other types of supernovae, which don’t involve white dwarfs at all.) But astronomers have learned how to correct for the differences in brightness by using the empirical fact that brighter supernovae take longer to decline in brightness after the peak luminosity. The story of how astronomers search for such supernovae, and how they eventually discovered the acceleration of the universe, is told in Goldsmith (2000), Kirshner (2004), and Gates (2009); the original papers are Riess et al. (1998) and Perlmutter et al. (1999).

46
Another subtle point needs to be explained. The expansion rate of the universe is measured by the Hubble constant, which relates distance to redshift. It’s not really a “constant”; in the early universe the expansion was much faster, and what we might call the Hubble “parameter” was a lot larger than our current Hubble constant. We might expect that the phrase
the universe is accelerating
means “the Hubble parameter is increasing,” but that’s not true—it just means “it’s not decreasing very fast.” The “acceleration” refers to an increase in the apparent velocity of any particular galaxy over time. But that velocity is equal to the Hubble parameter times the distance, and the distance is increasing as the universe expands. So an accelerating universe is not necessarily one in which the Hubble parameter is increasing, just one in which the product of the Hubble parameter with the distance to any particular galaxy is increasing. It turns out that, even with a cosmological constant, the Hubble parameter never actually increases; it decreases more slowly as the universe expands and dilutes, until it approaches a fixed constant value after all the matter has gone away and there’s nothing left but cosmological constant.

47
We’re being careful to distinguish between two forms of energy that are important for the evolution of the contemporary universe: “matter,” made of slowly moving particles that dilute away as the universe expands, and “dark energy,” some mysterious stuff that doesn’t dilute away at all, but maintains a constant energy density. But matter itself comes in different forms: “ordinary matter,” including all of the kinds of particles we have ever discovered in experiments here on Earth, and “dark matter,” some other kind of particle that can’t be anything we’ve yet directly seen. The mass (and therefore energy) in ordinary matter is mostly in the form of atomic nuclei—protons and neutrons—but electrons also contribute. So ordinary matter includes you, me, the Earth, the Sun, stars, and all the gas and dust and rocks in space. We know how much of that stuff there is, and it’s not nearly enough to account for the gravitational fields observed in galaxies and clusters. So there must be dark matter, and we’ve ruled out all known particles as candidates; theorists have invented an impressive menu of possibilities, including “axions” and “neutralinos” and “Kaluza-Klein particles.” All told, ordinary matter makes up about 4 percent of the energy in the universe, dark matter makes up about 22 percent, and dark energy makes up about 74 percent. Trying to create or detect dark matter directly is a major goal of modern experimental physics. See Hooper (2007), Carroll (2007), or Gates (2009) for more details.