String theory landscape: Difference between revisions

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	The '''string theory landscape''' or '''anthropic landscape''' refers to the large number of different ] in ]. It arises from the idea that there are an extremely large number of ] ] (ground states) in ].{{ref\|largenumber}} The large number of possibilites arise from different choices of ]s and different values of generalized ]es over different ] cycles.{{ref\|fluxvacua}} This large number of ] ] (ground states) is thought by some physicists to be large enough that the known laws of physics, the ], occurs in at least one, although computing quantities such as masses of particles and ]s for even a single vacuum is a technically difficult problem.		The '''string theory landscape''' or '''anthropic landscape''' refers to the large number of different ] in ]. It arises from the idea that there are an extremely large number of ] ] (ground states) in ].{{ref\|largenumber}} The large number of possibilites arise from different choices of ]s and different values of generalized ]es over different ] cycles.{{ref\|fluxvacua}} This large number of ] ] (ground states) is thought by some physicists to be large enough that the known laws of physics, the ], occurs in at least one, although computing quantities such as masses of particles and ]s for even a single vacuum is a technically difficult problem.

	The idea of the string theory landscape has been used to propose a concrete implementation of the ], the idea that fundamental constants may have the values they have not for fundamental physical reasons, but rather because such values are necessary for life (and hence intelligent observers to measure the constants). In 1987, ] proposed that the observed value of the ] was so small because it is not possible for life to occur in a universe with a much larger cosmological constant.{{ref\|weinberg}} In order to implement this idea in a concrete physical theory, it is necessary to postulate that a ] in which fundamental physical parameters can take different values. This has been realized in the context of ]. Some physicists, starting with Weinberg. have proposed that ] can be used to compute probability distributions for fundamental physical parameters, where the probability <math>P(x)</math> of observing some fundamental parameters <math>x</math> is given by,		The idea of the string theory landscape has been used to propose a concrete implementation of the ], the idea that fundamental constants may have the values they have not for fundamental physical reasons, but rather because such values are necessary for life (and hence intelligent observers to measure the constants). In 1987, ] proposed that the observed value of the ] was so small because it is not possible for life to occur in a universe with a much larger cosmological constant.{{ref\|weinberg}} In order to implement this idea in a concrete physical theory, it is necessary to postulate that a ] in which fundamental physical parameters can take different values. This has been realized in the context of ]. Some physicists, starting with Weinberg, have proposed that ] can be used to compute probability distributions for fundamental physical parameters, where the probability <math>P(x)</math> of observing some fundamental parameters <math>x</math> is given by,
	:<math>P(x)=P_\mathrm{prior}(x)\times P_\mathrm{selection}(x),</math>		:<math>P(x)=P_\mathrm{prior}(x)\times P_\mathrm{selection}(x),</math>
	where <math>P_\mathrm{prior}</math> is the prior probability, from fundamental theory, of the parameters <math>x</math> and <math>P_\mathrm{selection}</math> is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters <math>x</math>. These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:		where <math>P_\mathrm{prior}</math> is the prior probability, from fundamental theory, of the parameters <math>x</math> and <math>P_\mathrm{selection}</math> is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters <math>x</math>. These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:

Revision as of 19:48, 4 March 2006

The string theory landscape or anthropic landscape refers to the large number of different false vacua in string theory. It arises from the idea that there are an extremely large number of metastable vacua (ground states) in string theory. The large number of possibilites arise from different choices of Calabi-Yau manifolds and different values of generalized magnetic fluxes over different homology cycles. This large number of metastable vacua (ground states) is thought by some physicists to be large enough that the known laws of physics, the Standard Model, occurs in at least one, although computing quantities such as masses of particles and Yukawa couplings for even a single vacuum is a technically difficult problem.

The idea of the string theory landscape has been used to propose a concrete implementation of the anthropic principle, the idea that fundamental constants may have the values they have not for fundamental physical reasons, but rather because such values are necessary for life (and hence intelligent observers to measure the constants). In 1987, Steven Weinberg proposed that the observed value of the cosmological constant was so small because it is not possible for life to occur in a universe with a much larger cosmological constant. In order to implement this idea in a concrete physical theory, it is necessary to postulate that a multiverse in which fundamental physical parameters can take different values. This has been realized in the context of eternal inflation. Some physicists, starting with Weinberg, have proposed that Bayesian probability can be used to compute probability distributions for fundamental physical parameters, where the probability $P(x)$ of observing some fundamental parameters $x$ is given by,

P(x)=P_{\mathrm {prior} }(x)\times P_{\mathrm {selection} }(x),

where $P_{\mathrm {prior} }$ is the prior probability, from fundamental theory, of the parameters $x$ and $P_{\mathrm {selection} }$ is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters $x$ . These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:

The function $P_{\mathrm {prior} }$ is completely unknown in string theory and may be impossible to define or interpret in any sensible probablistic way.
The function $P_{\mathrm {selection} }$ is completely unknown, since so little is known about the origin of life and criteria (such as the number of galaxies) must be used as a proxy for the number of observers. Moreover, it may never be possible to compute it for parameters radically different from those of the observable universe.
Interpreting probability in a context where it is only possible to draw one sample from a distribution is problematic.

Various physicists have tried to address these objections, but as yet there is no widespread agreement. These ideas have been reviewed by Carroll . Tegmark et al. have recently considered these objections and proposed a simplified anthropic scenario for axion dark matter in which they argue that the first two of these problems do not apply.

Although few dispute the idea that string theory appears to have an unimaginably large number of metastable vacua, the existence, meaning and scientific relevance of the anthropic landscape remain highly controversial. Prominent proponents of the idea include Michael Douglas, Andrei Linde, Joseph Polchinski, Sir Martin Rees and Leonard Susskind who advocate it as a solution to the cosmological constant problem. Opponents, such as David Gross, suggest that the idea is inherently unscientific, unfalsifiable or premature.

The term "landscape" comes from evolutionary biology (see Fitness landscape) and was first applied to cosmology by Lee Smolin in his book . It was first used in the context of string theory by Susskind. There are several popular books about the anthropic principle in cosmology. Two popular physics blogs are opposed to the anthropic principle.

References

The most commonly quoted number is of order 10. See M. Douglas, "The statistics of string / M theory vacua", JHEP 0305, 46 (2003). arXiv:hep-th/0303194; S. Ashok and M. Douglas, "Counting flux vacua", JHEP 0401, 060 (2004).
R. Bousso and J. Polchinski, "Quantization of four-form fluxes and dynamical neutralization of the cosmological constant", JHEP 06, 006 (2000). arXiv:hep-th/0004134 S. Kachru, R. Kallosh, A. Linde and S. Trivedi, "de Sitter vacua in string theory", Phys. Rev. D68, 046005 (2003). arXiv:hep-th/0301240
S. Weinberg, "Anthropic bound on the cosmological constant", Phys. Rev. Lett. 59, 2607 (1987).
S. M. Carroll, "Is our universe natural?", arXiv:hep-th/0512148.
M. Tegmark, A. Aguirre, M. Rees and F. Wilczek, "Dimensionless constants, cosmology and other dark matters", arXiv:astro-ph/0511774. F. Wilczek, "Enlightenment, knowledge, ignorance, temptation," arXiv:hep-ph/0512187. See also the discussion at .
L. Smolin, "Did the universe evolve?," Classical and Quantum Gravity 9, 173–191 (1992). L. Smolin, The Life of the Cosmos (Oxford, 1997)
L. Susskind, "The anthropic landscape of string theory", arXiv:hep-th/0302219.
L. Susskind, The cosmic landscape: string theory and the illusion of intelligent design (Little, Brown, 2005). M. J. Rees, Just six numbers: the deep forces that shape the universe (Basic Books, 2001). R. Bousso and J. Polchinski, "The string theory landscape", Sci. Am. 291, 60–69 (2004).
Lubos Motl's blog and Peter Woit's blog frequently attack the landscape.

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