From Eternity to Here (81 page)

289
This discussion assumes that the assumptions we previously made in discussing the entropy of our comoving patch remain valid—in particular, that it makes sense to think of the patch as an autonomous system. That is certainly not necessarily correct, but it is usually implicitly assumed by people who study these scenarios.

290
Aguirre and Gratton (2003). Hartle, Hawking, and Hertog (2008) also investigated universes with high entropy in the past and future and low entropy in the middle, in the context of Euclidean quantum gravity.

291
This is true even in ordinary nongravitational situations, where the total energy is strictly conserved. When a high-energy state decays into a lower-energy one, like a ball rolling down a hill, energy isn’t created or destroyed; it’s just transformed from a useful low-entropy form into a useless high-entropy form.

292
Farhi, Guth, and Guven (1990). See also Farhi and Guth (1987), and Fischler, Morgan, and Polchinski (1990a, 1990b). Guth writes about this work in his popular-level book (1997).

293
The most comprehensive recent work on this question was carried out by Anthony Aguirre and Matthew Johnson (2006). They catalogued all the different ways that baby universes might be created by quantum tunneling, but in the end were unable to make a definitive statement about what actually happens. (“The unfortunate bottom line, then, is that while the relation between the various nucleation processes is much clearer, the question of which ones actually occur remains open.”) From a completely different perspective, Freivogel et al. (2006) considered inflation in an anti-de Sitter background, using Maldacena’s correspondence. They concluded that baby universes were not created. But our interest is de Sitter backgrounds, not anti-de Sitter backgrounds; it’s unclear whether the results can be extended from one context to the other. For one more take on the evolution of de Sitter space, see Bousso (1998).

294
Carroll and Chen (2004).

295
One assumption here is that the de Sitter space is in a true vacuum state; in particular, that there is no other state of the theory where the vacuum energy vanishes, and spacetime could look like Minkowski space. To be honest, that is not necessarily a realistic assumption. In string theory, for example, we are pretty sure that 10-dimensional Minkowski space is a good solution of the theory. Unlike de Sitter, Minkowski space has zero temperature, so can plausibly avoid the creation of baby universes. To make the scenario described here work, we have to imagine either that there are no states with zero vacuum energy, or that the amount of spacetime that is actually in such a state is sufficiently small compared to the de Sitter regions.

16. EPILOGUE

296
And that’s despite the fact that, just as the manuscript was being completed, another book with exactly the same title appeared on the market! (Viola, 2009). His subtitle is quite different, however: “Rediscovering the Ageless Purpose of God.” I do hope nobody orders the wrong book by accident.

297
Feynman, Leighton, and Sands (1970), 46-8.

298
Popper (1959). Note that Popper went a bit further than the demarcation problem; he wanted to understand all of scientific progress as a series of falsified conjectures. Compared to how science is actually done, this is a fairly impoverished way of understanding the process; ruling out conjectures is important, but there’s a lot more that goes into the real workings of science.

299
See Deutsch (1997) for more on this point.

300
For one example among many, see Swinburne (2004).

301
Lemaître (1958).

302
Steven Weinberg put it more directly: “The more the universe seems comprehensible, the more it also seems pointless” (Weinberg 1977, 154).

303
I regret that this book has paid scant attention to current and upcoming new experiments in fundamental physics. The problem is that, as fascinating and important as those experiments are, it’s very hard to tell ahead of time what we are going to learn from them, especially about a subject as deep and all-encompassing as the arrow of time. We’re not going to build a telescope that will use tachyons to peer into other universes, unfortunately. What we might do is build particle accelerators that reveal something about supersymmetry, which in turn teaches us something about string theory, which we can use to understand more about quantum gravity. Or we might gather data from giant telescopes—collecting not only photons of light, but also cosmic rays, neutrinos, gravitational waves, or even particles of dark matter—that reveal something surprising about the evolution of the universe. The real world surprises us all the time: dark matter and dark energy are obvious examples. As a theoretical physicist, I’ve written this book from a rather theoretical perspective, but as a matter of history it’s often new experiments that end up awakening us from our dogmatic slumbers.

APPENDIX: MATH

304
These properties are behind the “magic of mathematics” appealed to above. For example, suppose we wanted to figure out what was meant by 10 to the power 0.5. I know that, whatever that number is, it has to have the property that 10
^0.5
• 10
^0.5
= 10
^{(0.5 + 0.5)}
= 10
¹
= 10.

In other words, the number 10
^0.5
times itself gives us 10; that means that 10
^0.5
must simply be the square root of 10. (And likewise for any other base raised to the power 0.5.) By similar tricks, we can figure out the exponential of any number we like.

BIBLIOGRAPHY

Note: Many of these bibliography entries are referenced explicitly in the text, but many are not. Some were influential in shaping the point of view presented here; others were foils to be argued against. Some are research articles that fill in technical details on the topics of this book, while others provide additional background reading at an accessible level. All of them are interesting.

My favorite modern books about the arrow of time include David Albert’s
Time and Chance
, Huw Price’s
Time’s Arrow and Archimedes’ Point
, Brian Greene’s
The Fabric of the Cosmos
, and Michael Lockwood’s
The Labyrinth of Time.
Any of those will give you a complementary viewpoint to that presented here. Etienne Klein’s
Chronos
, Craig Callender’s
Introducing Time
, and Paul Davies’s
About Time
all discuss the subject of time more broadly. For background in general relativity I suggest Kip Thorne’s
Black Holes and Time Warps
, and for black holes and information loss in particular Leonard Susskind’s
The Black Hole War
. For cosmology I recommend Dennis Overbye’s
Lonely Hearts of the Cosmos
or Alan Guth’s
The Inflationary Universe.
David Lindley’s
Boltzmann’s Atom
and Hans Christian von Baeyer’s
Warmth Disperses and Time Passes
provide fascinating historical background, as does Stephen Brush’s anthology of original papers on kinetic theory. Zeh’s
The Physical Basis of the Direction of Time
tackles the subject at a technical level.

Many of the modern (post-1992) research articles can be downloaded for free from the arXiv physics preprint server
http://arxiv.org/
.

More information and links to further resources can be found at the book’s Web site,
http://eternitytohere.com
.

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