From Eternity to Here: The Quest for the Ultimate Theory of Time

by Sean M. Carroll

  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 100.5 • 100.5 = 10(0.5 + 0.5) = 101 = 10.

  In other words, the number 100.5 times itself gives us 10; that means that 100.5 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.

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  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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