Kodama state
Encyclopedia
In 1988, Hideo Kodama wrote down the equations of the Kodama state, but as it described a positive (de Sitter universe
) spacetime, which was believed to be inconsistent with observation, it was largely ignored.
In 2002, Lee Smolin
suggested that the Kodama state is a ground state
which has a good semiclassical limit which reproduces the dynamics of general relativity
with a positive (de Sitter) cosmological constant
, 4 dimensions, and gravitons. It is an exact solution to ordinary constraints on background independent quantum gravity, providing evidence that loop quantum gravity
is indeed a quantum gravity with the correct semiclassical description. In 2003, Edward Witten
published a paper in response to Lee Smolin's, arguing that the Kodama state is unphysical, due to an analogy to a state in Chern-Simons theory
wavefunction
s, resulting in negative energies. In 2006, Andrew Randono published two papers which address these objections, by generalizing the Kodama state. Randono concluded that the Immirzi parameter
, when generalized with a real value, fixed by matching with black hole entropy, describes parity violation in quantum gravity, and is CPT
invariant, and is normalizable, and chiral
, consistent with known observations of both gravity and quantum field theory. Randono claims that Witten's conclusions rest on the Immirzi parameter
taking on an imaginary number
, which simplifies the equation. The physical inner product may resemble the MacDowell-Mansouri action
formulation of gravity.
De Sitter universe
A de Sitter universe is a cosmological solution to Einstein's field equations of General Relativity which is named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to...
) spacetime, which was believed to be inconsistent with observation, it was largely ignored.
In 2002, Lee Smolin
Lee Smolin
Lee 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...
suggested that the Kodama state is a ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
which has a good semiclassical limit which reproduces the dynamics of general relativity
General relativity
General 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 (de Sitter) 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 stationary universe...
, 4 dimensions, and gravitons. It is an exact solution to ordinary constraints on background independent quantum gravity, providing evidence that loop quantum gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...
is indeed a quantum gravity with the correct semiclassical description. In 2003, Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
published a paper in response to Lee Smolin's, arguing that the Kodama state is unphysical, due to an analogy to a state in Chern-Simons theory
Chern-Simons theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type, introduced by Edward Witten. It is so named because its action is proportional to the integral of the Chern–Simons 3-form....
wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
s, resulting in negative energies. In 2006, Andrew Randono published two papers which address these objections, by generalizing the Kodama state. Randono concluded that the Immirzi parameter
Immirzi parameter
The Immirzi parameter is a numerical coefficient appearing in loop quantum gravity, a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units...
, when generalized with a real value, fixed by matching with black hole entropy, describes parity violation in quantum gravity, and is CPT
CPT symmetry
CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity, and time simultaneously.-History:...
invariant, and is normalizable, and chiral
Chirality (physics)
A chiral phenomenon is one that is not identical to its mirror image . The spin of a particle may be used to define a handedness for that particle. A symmetry transformation between the two is called parity...
, consistent with known observations of both gravity and quantum field theory. Randono claims that Witten's conclusions rest on the Immirzi parameter
Immirzi parameter
The Immirzi parameter is a numerical coefficient appearing in loop quantum gravity, a nonperturbative theory of quantum gravity. The Immirzi parameter measures the size of the quantum of area in Planck units...
taking on an imaginary number
Imaginary number
An imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
, which simplifies the equation. The physical inner product may resemble the MacDowell-Mansouri action
MacDowell-Mansouri action
The MacDowell–Mansouri action is a mathematical object that is used to derive Einstein's field equations of general relativity....
formulation of gravity.