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String theory landscape
 
 
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The string theory landscape or anthropic landscape refers to the large number of possible false vacua
False vacuum

In quantum field theory, a false vacuum is a metastable sector of space which appears to be a vacuum state but is unstable to instanton effects which may quantum tunnelling to a lower energy state....
 in string theory
String theory

String theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum gravity. The String s of string theory are one-dimensional oscillating lines, but they are no longer considered fundamental to the theory, which can be formulated in terms of points or surfaces too....
. The "landscape" includes so many possible configurations that it is thought by some physicists that the known laws of physics, the Standard Model
Standard Model

The Standard Model of particle physics is a theory of three of the four known fundamental interactions and the elementary particles that take part in these interactions....
 and General relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
 with a positive cosmological constant, occurs 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 principle
Anthropic principle

In physics and cosmology, the anthropic principle is the collective name for several ways of asserting that physical and chemistry theories, especially astrophysics and cosmology, need to take into account that there is life on Earth, and that one form of that life, Homo sapiens, has attained sapience....
 that selects a subset of the theoretically possible configurations.

In string theory the number of false vacua is commonly quoted as 10500.






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The string theory landscape or anthropic landscape refers to the large number of possible false vacua
False vacuum

In quantum field theory, a false vacuum is a metastable sector of space which appears to be a vacuum state but is unstable to instanton effects which may quantum tunnelling to a lower energy state....
 in string theory
String theory

String theory is a developing branch of theoretical physics that combines quantum mechanics and general relativity into a quantum gravity. The String s of string theory are one-dimensional oscillating lines, but they are no longer considered fundamental to the theory, which can be formulated in terms of points or surfaces too....
. The "landscape" includes so many possible configurations that it is thought by some physicists that the known laws of physics, the Standard Model
Standard Model

The Standard Model of particle physics is a theory of three of the four known fundamental interactions and the elementary particles that take part in these interactions....
 and General relativity
General relativity

General relativity or the general theory of relativity is the Geometry Theoretical physics of gravitation published by Albert Einstein in 1916....
 with a positive cosmological constant, occurs 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 principle
Anthropic principle

In physics and cosmology, the anthropic principle is the collective name for several ways of asserting that physical and chemistry theories, especially astrophysics and cosmology, need to take into account that there is life on Earth, and that one form of that life, Homo sapiens, has attained sapience....
 that selects a subset of the theoretically possible configurations.

In string theory the number of false vacua is commonly quoted as 10500. The large number of possibilities arises from different choices of Calabi-Yau manifold
Calabi-Yau manifold

In mathematics, Calabi–Yau manifolds are sometimes defined as compact K?hler manifolds whose canonical bundle is trivial, though many other similar but inequivalent definitions are sometimes used....
s and different values of generalized magnetic flux
Magnetic flux

Magnetic flux, represented by the Greek letter F , is a measure of quantity of magnetism, taking into account the strength and the extent of a magnetic field....
es over different homology
Homology (mathematics)

In mathematics , homology is a certain general procedure to associate a sequence of abelian groups or module 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
Subset sum problem

In computer science, the subset sum problem is an important problem in computational complexity theory and cryptography. The problem is this: given a set of integers, does the sum of some non-empty subset equal exactly zero? For example, given the set , the answer is YES because the subset sums to zero....
.

Anthropic principle

The idea of the string theory landscape has been used to propose a concrete implementation of the anthropic principle
Anthropic principle

In physics and cosmology, the anthropic principle is the collective name for several ways of asserting that physical and chemistry theories, especially astrophysics and cosmology, need to take into account that there is life on Earth, and that one form of that life, Homo sapiens, has attained sapience....
, 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
Steven Weinberg

Steven Weinberg is an United States physicist and Nobel Prize in Physics for his contributions with Abdus Salam and Sheldon Lee Glashow to the Electroweak interaction of the weak force and electromagnetism interaction between elementary particles....
 proposed that the observed value of the cosmological constant
Cosmological constant

In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a Einstein's 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 multiverse
Multiverse (science)

The multiverse is the hypothetical set of multiple possible universes that together comprise all of reality. The different universes within the multiverse are sometimes called parallel universes....
 in which fundamental physical parameters can take different values. This has been realized in the context of eternal inflation
Cosmic inflation

In physical cosmology, cosmic inflation is the hypothesis that the wiktionary:nascent universe passed through a phase of exponential growth metric expansion of space was driven by a negative pressure vacuum energy density....
.

Bayesian probability

Some physicists, starting with Weinberg, have proposed that Bayesian probability
Bayesian probability

Bayesian probability interprets the concept of probability as 'a measure of a state of knowledge' , and not as a frequentist . Broadly speaking, there are two views on Bayesian probability that interpret the 'state of knowledge' concept in different ways....
 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

    The sample size of a statistical sample is the number of observations that constitute it. It is typically denoted n, a positive integer ....
     from a distribution
    Probability distribution

    In probability theory and statistics, a probability distribution identifies either the probability of each value of an unidentified random variable , or the probability of the value falling within a particular interval ....
     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

Tegmark
Max Tegmark

Max Tegmark is a Sweden-United States physical cosmology. Tegmark is an Associate Professor at the Massachusetts Institute of Technology where he belongs to the scientific directorate of the Foundational Questions Institute....
 et al. have recently considered these objections and proposed a simplified anthropic scenario for axion
Axion

The axion is a hypothetical elementary particle postulated by the Peccei-Quinn theory in 1977 to resolve the strong-CP problem in quantum chromodynamics ....
 dark matter
Dark matter

In astronomy and physical cosmology, dark matter is Hypothesis matter that is undetectable by its emitted electromagnetic radiation, but whose presence can be inferred from gravity effects on visible matter....
 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.

Proponents and opponents of the idea

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 Linde
Andrei Linde

Andrei 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 Cosmic inflation....
, Sir Martin Rees and especially Leonard Susskind
Leonard Susskind

Leonard Susskind is the Felix Bloch professor of theoretical physics at Stanford University in the field of string theory and quantum field theory....
 who advocate it as a solution to the cosmological constant
Cosmological constant

In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a Einstein's universe....
 problem. Opponents, such as David Gross
David Gross

David Jonathan Gross is an United States particle physics and string theory. Along with Frank Wilczek and David Politzer, he was awarded the 2004 Nobel Prize in Physics for his discovery of asymptotic freedom....
, suggest that the idea is inherently unscientific, unfalsifiable or premature.

The term "landscape" comes from evolutionary biology
Evolutionary biology

Evolutionary biology is a sub-field of biology concerned with the origin of species from a common descent and descent of species, as well as their evolution, multiplication and diversity over time....
 (see Fitness landscape
Fitness landscape

In evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes and reproductive success....
) and was first applied to cosmology by Lee Smolin
Lee Smolin

Lee Smolin is an United States theoretical physicist, a researcher at the Perimeter Institute for Theoretical Physics, and an adjunct professor of physics at the University of Waterloo....
 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.

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