The
string theory landscape or
anthropic landscape refers to the large number of possible
false vacuaIn quantum field theory, a false vacuum is a metastable sector of space that appears to be a perturbative vacuum, but is unstable due to instanton effects that may tunnel to a lower energy state. This tunneling can be caused by quantum fluctuations or the creation of high-energy particles...
in
string theoryString theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything , a manner of describing the known fundamental forces and matter in a mathematically complete system...
. The "landscape" includes so many possible configurations that some physicists think that the known laws of physics, the
standard modelThe Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong nuclear interactions, which mediate the dynamics of the known subatomic particles. Developed throughout the mid to late 20th century, the current formulation was finalized in the mid 1970s upon...
and
general relativityGeneral relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...
with a positive cosmological constant, occur in at least one of them. The
anthropic landscape refers to the collection of those portions of the landscape that are suitable for supporting human life, an application of the
anthropic principleIn astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...
that selects a subset of the theoretically possible configurations.
In string theory the number of false vacua is commonly quoted as 10
500. The large number of possibilities arises from different choices of
Calabi-Yau manifoldA Calabi-Yau manifold is a special type of manifold that shows up in certain branches of mathematics such as algebraic geometry, as well as in theoretical physics...
s and different values of generalized
magnetic fluxMagnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
es over different
homologyIn mathematics , homology is a certain general procedure to associate a sequence of abelian groups or modules with a given mathematical object such as a topological space or a group...
cycles. If one assumes that there is no structure in the space of vacua, the problem of finding one with a sufficiently small cosmological constant is NP complete, being a version of the
subset sum problem.
Anthropic principle
The idea of the string theory landscape has been used to propose a concrete implementation of the
anthropic principleIn astrophysics and cosmology, the anthropic principle is the philosophical argument that observations of the physical Universe must be compatible with the conscious life that observes it. Some proponents of the argument reason that it explains why the Universe has the age and the fundamental...
, 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 WeinbergSteven Weinberg is an American theoretical physicist and Nobel laureate in Physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interaction between elementary particles....
proposed that the observed value of the
cosmological constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
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 a
multiverseThe multiverse is the hypothetical set of multiple possible universes that together comprise everything that exists and can exist: the entirety of space, time, matter, and energy as well as the physical laws and constants that describe them...
in which fundamental physical parameters can take different values. This has been realized in the context of
eternal inflationIn physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized extremely rapid exponential expansion of the early universe by a factor of at least 1078 in volume, driven by a negative-pressure vacuum energy density. The inflationary epoch comprises the first part...
.
Bayesian probability
Some physicists, starting with Weinberg, have proposed that
Bayesian probabilityBayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...
can be used to compute probability distributions for fundamental physical parameters, where the probability
of observing some fundamental parameters
is given by,
where
is the prior probability, from fundamental theory, of the parameters
and
is the anthropic selection function, determined by the number of "observers" that would occur in the universe with parameters
. These probabilistic arguments are the most controversial aspect of the landscape. Technical criticisms of these proposals have pointed out that:
- The function
is completely unknown in string theory and may be impossible to define or interpret in any sensible probabilistic way.
- The function
is completely unknown, since so little is known about the origin of life. Simplified 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
Sample size determination is the act of choosing the number of observations to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample...
from a distributionIn probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....
is problematic.
Various physicists have tried to address these objections, and the ideas remain extremely controversial both within and outside the string theory community. These ideas have been reviewed by Carroll.
Simplified approaches
TegmarkMax Tegmark is a Swedish-American cosmologist. Tegmark is a professor at the Massachusetts Institute of Technology and belongs to the scientific directorate of the Foundational Questions Institute.-Early life:...
et al. have recently considered these objections and proposed a simplified anthropic scenario for
axionThe axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics...
dark matterIn astronomy and cosmology, dark matter is matter that neither emits nor scatters light or other electromagnetic radiation, and so cannot be directly detected via optical or radio astronomy...
in which they argue that the first two of these problems do not apply.
Vilenkin and collaborators have proposed a consistent way to define the probabilities for a given vacuum.
A problem with many of the simplified approaches people have tried is that they "predict" a cosmological constant that is too large by a factor of 10–1000 (depending on one's assumptions) and hence suggest that the cosmic acceleration should be much more rapid than is observed.
Criticism
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
Andrei LindeAndrei Dmitriyevich Linde is a Russian-American theoretical physicist and professor of Physics at Stanford University. Dr. Linde is best known for his work on the concept of the inflationary universe. He received his Bachelor of Science degree from Moscow State University. In 1975, Linde was...
, Sir Martin Rees and especially
Leonard SusskindLeonard Susskind is the Felix Bloch Professor of Theoretical Physics at Stanford University. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology...
, who advocate it as a solution to the
cosmological-constantIn physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...
problem. Opponents, such as
David GrossDavid Jonathan Gross is an American particle physicist and string theorist. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for their discovery of asymptotic freedom. He is currently the director and holder of the Frederick W...
, suggest that the idea is inherently unscientific, unfalsifiable or premature. A famous debate on the anthropic landscape of string theory is the Smolin-Susskind debate on the merits of the landscape.
The term "landscape" comes from evolutionary biology (see
Fitness landscapeIn evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes and reproductive success. It is assumed that every genotype has a well-defined replication rate . This fitness is the "height" of the landscape...
) and was first applied to cosmology by
Lee SmolinLee Smolin is an American theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo. He is married to Dina Graser, a communications lawyer in Toronto. His brother is David M...
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 this use of the anthropic principle.
External links