Текст книги "Теория струн и скрытые измерения вселенной"

Автор книги: Стив Надис

Соавторы: Яу Шинтан
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Текущая страница: 29 (всего у книги 29 страниц)

[123] Aspinwall, interview with author, June 23, 2008.

[124] Gross, interview with author, September 24, 2008.

[125] Avi Loeb (Harvard University), interview with author, September 25,2008.

[126] American Mathematical Society, “Interview with Heisuke Hironaka,” Notices of the AMS52, no. 9 (October 2005): 1,015.

[127] Steve Nadis, “Cosmic Inflation Comes of Age,” Astronomy(April 2002).

[128] Andrew Strominger, “String Theory, Black Holes, and the Fundamental Laws of Nature,” lecture, Harvard University, Cambridge, Mass., April 4, 2007.

[129] Ibid.

[130] Hirosi Ooguri (California Institute of Technology), interview with author, October 8, 2008.

[131] Strominger, lecture.

[132] Andrew Strominger and Cumrun Vafa, “Microscopic Origin of the Bekenstein‑Hawking Entropy,” Physics Letters В379 (June 27, 1996): 99‑104.

[133] Andrew Strominger, quoted in Gary Taubes, “Black Holes and Beyond,” Science Watch, May/June 1999, http://archive.sciencewatch.com/may‑june99/sw_may‑june99_page3.htm.

[134] Hirosi Ooguri, interview with author, October 8, 2008.

[135] Strominger, quoted in Taubes, “Black Holes and Beyond.”

[136] Xi Yin (Harvard University), interview with author, October 14, 2008.

[137] Ibid.

[138] Xi Yin, interview with author, October 22, 2008.

[139] Frederik Denef (Harvard University), interview with author, August 26, 2008.

[140] Xi Yin, interview with author, October 14, 2008.

[141] Aaron Simons, interview with author, February 9, 2007.

[142] Ibid.

[143] J. M. Maldacena, A. Strominger, and E. Witten, “Black Hole Entropy in M‑Theory” Journal of High Energy Physics9712 (1997), http://arxiv.org/PS_cache/hepth/pdf/9711/9711053vl.pdf.

[144] Juan Maldacena (IAS), interview with author, September 4, 2008.

[145] Hirosi Ooguri, Andrew Strominger, and Cumrun Vafa, “Black Hole Attractors and the Topological String,” Physical Review D70 (2004).

[146] Cumrun Vafa (Harvard University), interviewwith author, September 26, 2008.

[147] James Sparks (Harvard University), interview with author, February 6, 2007.

[148] Amanda Gefter, “The Elephant and the Event Horizon,” New Scientist(October 26,2006): 36–39.

[149] John Preskill, “On Hawking’s Concession,” July 24, 2004, http://www.theory.caltech.edu/~preskill/jp_24jul04.html.

[150] Andrew Strominger (Harvard University), interview with author, February 7, 2007.

[151] Juan Maldacena, “The Illusion of Gravity,” Scientific American, November 2005, pp. 57–58, 61.

[152] Davide Castelvecchi, “Shadow World,” Science News172 (November 17,2007).

[153] Taubes, “Black Holes and Beyond.”

[154] L. Frank Baum, The Wizard of Oz(Whitefish, Mont.: Kessinger, 2004), p. 111.

[155] Volker Braun (Dublin Institute for Advanced Studies), interview with author, November 4, 2008.

[156] Philip Candelas (Oxford University), interview with author, December 1, 2008.

[157] Ibid.

[158] Andrew Strominger (Harvard University), interview with author, February 7, 2007.

[159] Cumrun Vafa, “The Geometry of Grand Unified Theories,” lecture, Harvard University, Cambridge, Mass., August 29, 2008.

[160] Chris Beasley (Stony Brook University), interview with author, November 13, 2008.

[161] Burt Оvrut (University of Pennsylvania), interview with author, July 20, 2008.

[162] Ovrut, interview with author, February 2, 2007.

[163] Ron Donagi (University of Pennsylvania), interview with author, November 14, 2008.

[164] Donagi, interview with author, November 19, 2008.

[165] Candelas, interview with author, December 1, 2008.

[166] Donagi, interview with author, May 3, 2008

[167] Ovrut, interview with author, November 20, 2008.

[168] Donagi, interview with author, November 20, 2008.

[169] Ovrut, interview with author, November 20, 2008.

[170] Shamit Kachru (Stanford University), interview with author, November 4, 2008.

[171] Michael Douglas (Stony Brook University), interview with author, August 20, 2008.

[172] Candelas, interview with author, December 1, 2008.

[173] Simon Donaldson (Imperial College), interview with author, November 29, 2008.

[174] Ovrut, interview with author, November 19, 2008.

[175] Candelas, interview with author, December 1, 2008.

[176] Strominger, interview with author, February 7, 2007.

[177] Adrian Cho, “String Theory Gets Real – Sort Of,” Science306 (November 26, 2004): 1,461.

[178] Candelas, interview with author, December 1, 2008.

[179] Allan Adams (MIT), interview with author, November 15, 2008.

[180] Gary Shiu, quoted in Adrian Cho, “String Theory Gets Real – Sort Of” Science306 (November 26, 2004): 1,461.

[181] Shamit Kachru (Stanford University), e‑mail letter to author, December 6, 2008.

[182] Shamit Kachru, Renata Kallosh, Andrei Linde, and Sandip Trivedi, “De Sitter Vacua in String Theory,” Physical Review D68 (2003).

[183] Raman Sundrum (Johns Hopkins University), interview with author, February 22, 2007.

[184] Liam McAllister (Cornell University), interview with author, November 12, 2008.

[185] Kachru, interview with author, September 8, 2007.

[186] Liam McAllister (Princeton University), interview with author, February 20, 2007.

[187] Joe Polchinski (University of California, Santa Barbara), interview with author, February 6, 2006.

[188] David Gross, quoted in Dennis Overbye, “Zillions of Universes? Or Did Ours Get Lucky?” New York Times, October 28, 2003.

[189] Burton Richter, “Randall and Susskind,” letter to editor, New York Times, January 29, 2006.

[190] Leonard Susskind, The Cosmic Landscape(New York: Little Brown, 2006), pp. 354–355.

[191] Tristan Hubsch (Howard University), interview with author, November 7, 2008.

[192] Mark Gross (Stanford University), interview with author, October 31, 2008.

[193] Gross, interview with author, September 19, 2008.

[194] Miles Reid (University of Warwick), interview with author, August 12, 2007.

[195] Allan Adams (MIT), interview with author, October 31, 2008.

[196] Gross, interview with author, October 31, 2008.

[197] Adams, interview with author, October 31, 2008.

[198] Tristan Hubsch, e‑mail letter to author, December 15, 2008.

[199] Melanie Becker (Texas A&M University), interview with author, February 1, 2007.

[200] Andrew Strominger (Harvard University), interview with author, February 7, 2007.

[201] Li‑Sheng Tseng (Harvard University), interview with author, December 17, 2008.

[202] Becker, interview with author, February 1, 2007.

[203] Polchinski, interview with author, January 29, 2007.

[204] Strominger, interview with author, August 1, 2007.

[205] Burt Ovrut (University of Pennsylvania), interview with author, February 2, 2007.

[206] Geoffrey Landis, “Vacuum States,” Asimov's Science Fiction12 (July 1988): 73–79.

[207] Andrew R. Frey, Matthew Lippert, and Brook Williams, “The Fall of Stringy de Sitter,” Physical Review D. 68 (2003).

[208] Sidney Coleman, “Fate of the False Vacuum: Semi‑classical Theory,” Physical Review D. 15 (May 15, 1977): 2,929‑2,936.

[209] Steve Giddings (University of California, Santa Barbara), interview with author, September 24, 2007.

[210] Matthew Kleban (New York University), interview with author, January 17, 2008.

[211] Dennis Overbye, “One Cosmic Question, Too Many Answers,” New York Times, September 2, 2003.

[212] Andrei Linde (Stanford University), interview with author, December 27, 2007.

[213] Giddings, interview with author, October 17, 2007.

[214] Shamit Kachru (Stanford University), interview with author, September 18, 2007.

[215] Linde, interview with author, December 27, 2007.

[216] Henry Tye (Cornell University), interview with author, September 12, 2007.

[217] Linde, interview with author, January 10, 2008.

[218] S. W. Hawking, “The Cosmological Constant,” Philosophical Transactions of the Royal Society A. 310 (1983): 303–310.

[219] Kleban, interview with author, January 17, 2008.

[220] Steven B. Giddings, “The Fate of Four Dimensions,” Physical Review D. 68 (2003).

[221] Geoffrey Landis, “Vacuum States,” Asimov's Science Fiction12 (July 1988): 73–79.

[222] Andrew R. Frey, Matthew Lippert, and Brook Williams, “The Fall of Stringy de Sitter,” Physical Review D. 68(2003).

[223] Sidney Coleman, “Fate of the False Vacuum: Semi‑classical Theory,” Physical Review D. 15 (May 15, 1977): 2,929‑2,936.

[224] Steve Giddings (University of California, Santa Barbara), interview with author, September 24, 2007.

[225] Matthew Kleban (New York University), interview with author, January 17, 2008.

[226] Dennis Overbye, “One Cosmic Question, Too Many Answers,” New York Times, September 2, 2003.

[227] Andrei Linde (Stanford University), interview with author, December 27, 2007.

[228] Giddings, interview with author, October 17, 2007.

[229] Shamit Kachru (Stanford University), interview with author, September 18, 2007.

[230] Linde, interview with author, December 27, 2007.

[231] Henry Tye (Cornell University), interview with author, September 12, 2007.

[232] Linde, interview with author, January 10,2008.

[233] S. W. Hawking, “The Cosmological Constant,” Philosophical Transactions of the Royal Society A. 310 (1983): 303–310.

[234] Kleban, interview with author, January 17, 2008.

[235] Steven B. Giddings, “The Fate of Four Dimensions,” Physical Review D. 68 (2003).

[236] Текст этого и последующих комментариев до конца Главы 12 отсутствует в издании. Похоже, что и комментарии с начала этой главы неверны ( прим. Vadi)

[237] То же.

[238] То же.

[239] То же.

[240] То же.

[241] То же.

[242] То же.

[243] То же.

[244] То же.

[245] То же.

[246] То же.

[247] То же.

[248] То же.

[249] То же.

[250] То же.

[251] Peter Goddard, ed., Paul Dirac: The Man and His Work(New York: Cambridge University Press, 1998).

[252] Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” Communications in Pure and Applied Mathematics13 (February 1960).

[253] Chen Ning Yang, S. S. Chem: A Great Geometer of the 20th Century(Boston: International Press, 1998), p. 66.

[254] Robert Osserman, Poetry of the Universe(New York: Anchor Books, 1996), pp. 142–143.

[255] Richard P. Feynman, The Character of Physical Law(New York: Modern Library, 1994), p. 50.

[256] Michael Atiyah, quoted in Patricia Schwarz, “Sir Michael Atiyah on Math, Physics and Fun,” The Official String Theory Web site, http://www.superstringtheory.com/people/atiyah.html.

[257] Jim Holt, “Unstrung,” New Yorker, October 2, 2006, p. 86.

[258] Michael Atiyah, “Pulling the Strings,” Nature438 (December 22–29, 2005): 1,081.

[259] Robert Mills, “Beauty and Truth,” in Chen Ning Yang: A Great Physicist of the 20th Century, ed. Shing‑Tung Yau and C. S. Liu (Boston: International Press, 1995), p. 199.

[260] Henry Tye (Cornell University), e‑mail letter to author, December 19, 2008.

[261] Brian Greene, interview by Ira Flatow, “Big Questions in Cosmology,” Science Friday, NPR, April 3, 2009.

[262] К. C. Cole, “A Theory of Everything,” New York Times Magazine, October 18, 1987.

[263] Nicolai Reshetikhin (University of California, Berkeley), interview with author, June 5, 2008.

[264] Robbert Dijkgraaf (University of Amsterdam), interview with author, February 8, 2007.

[265] Brian Greene, The Elegant Universe(New York: Vintage Books, 2000), p. 210.

[266] Andrew Strominger (Harvard University), interview with author, August 1, 2007.

[267] S. Ramanujan, “On Certain Arithmetic Functions,” Transactions of the Cambridge Philosophical Society22 (1916): 159–184.

[268] Lothar Goettsche, “A Conjectural Generating Function for Numbers of Curves on Surfaces,” November II, 1997, arXiv.org, Cornell University archives, http://arxiv.org/PS_cache/alg‑geom/pdf/9711/9711012vl.pdf.

[269] Ai‑Ko Liu, “Family Blowup Formula, Admissible Graphs and the Enumeration of Singular Curves, I,” Journal of Differential Geometry56 (2000): 381–579.

[270] Bong Lian (Brandeis University), interview with author, December 12, 2007.

[271] Michael Atiyah, “Pulling the Strings,” Nature438 (December 22–29, 2005): 1,082.

[272] Glennda Chui, “Wisecracks Fly When Brian Greene and Lawrence Krauss Tangle Over String Theory,” Symmetry 4(May 2007): 17–21.

[273] Sean Carroll, “String Theory: Not Dead Yet,” Cosmic Variance blog, Discoveronline magazine, May 24,2007, http://cosmicvariance.com.

[274] Edward Witten, quoted in К. C. Cole, “A Theory of Everything,” New York Times Magazine, October 18, 1987.

[275] Ibid.

[276] Alan Guth (MIT), interview with author, September 13, 2007.

[277] Brian Greene, The Elegant Universe(New York: Vintage Books, 2000), p. 261.

[278] Max Tegmark (MIT), interview with author, October 23, 2007.

[279] Faye Flam, “Getting Comfortable in Four Dimensions,” Science266 (December 9, 1994): 1, 640.

[280] Cumrun Vafa (Harvard University), interview with author, January 19, 2007.

[281] Robbert Dijkgraaf (University of Amsterdam), interview with author, February 8, 2007.

[282] David Morrison (University of California, Santa Barbara), interview with author, May 27, 2008.

[283] Allan Adams (MIT), interview with author, May 23, 2008.

[284] Joe Polchinski (University of California, Santa Barbara), interview with author, August 31, 2007.

[285] Edward Witten (Institute for Advanced Study), e‑mail letter to author, January 30, 2007.

[286] Adams, interview with author, May 23, 2008.

[287] Turnbull WWW Server, “Quotations by Gauss,” School of Mathematical Sciences, University of St. Andrews, St. Andrews, Fife, Scotland, February 2006, http://wwwgroups.dcs.st‑and.ac.uk/‑history/Quotations/Gauss.html.

[288] Ibid.

[289] Brian Greene, “String Theory on Calabi‑Yau Manifolds,” lectures given at Theoretical Advanced Study Institute, 1996 session (TASI‑96), Boulder, June 1996.

[290] К. C. Cole, “Time, Space Obsolete in New View of Universe,” Los Angeles Times, November 16, 1999.

[291] Andrew Strominger (Harvard University), interview with author, August 1, 2007.

[292] Morrison, interview with author, May 29, 2008.

[293] Brian Greene, Elegant Universe(New York: Vintage Books, 2000), pp. 268, 273.

[294] Paul Aspinwall (Duke University), interview with author, June 6, 2008.

[295] Morrison, interview with author, May 27, 2008.

[296] Andrew Strominger (Harvard University), February 7, 2007.

[297] Chris Beasley, Jonathan Heckman, and Cumrun Vafa, “GUTs and Exceptional Branes in F‑Theory – I,” November 18, 2008, http://arxiv.org/abs/0802.3391; Chris Beasley, Jonathan Heckman, and Cumrun Vafa, “GUTs and Exceptional Branes in F‑Theory – II: Experimental Predictions,” June 12, 2008, http://arxiv.org/abs/arxiv:0806.0102; Ron Donagi and Martijn Wijnholt, “Model Building with F‑Theory,” March 3, 2008, http://lanl.arxiv.org/pdf/0802.2969v2; and Ron Donagi and Martijn Wijnholt, “Breaking GUT Groups in F‑Theory,” August 17, 2008, http://lanl.arxiv,org/pdf/0808.2223vl.

[298] Strominger, interview with author, July 23, 2007.

[299] Cumrun Vafa (Harvard University), interview with author, November 2, 2007.

[300] Leonard Mlodinow, Euclid's Mirror(New York: Simon & Schuster, 2002), p. 255.

[301] Edward Witten (Institute for Advanced Study), e‑mail letter to author, February 12, 2007.

[302] David Morrison (University of California, Santa Barbara), interview with author, May 27, 2008.

[303] Ravi Vakil (Stanford University), interview with author, May 28, 2008.

[304] Strominger, interview with author, August 1, 2007.

[305] Piers Bursill‑Hall, “Why Do We Study Geometry? Answers Through the Ages,” lecture, Faulkes Institute for Geometry, University of Cambridge, May 1, 2002.

[306] Donald Zeyl (University of Rhode Island), interview with author, October 18, 2007.