Please comment if you have a suggestion for a post!
Thanks
Martin
Wednesday, 20 June 2012
On: Life and Negentropy
The negentropy, also negative entropy or syntropy or entaxy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life. The concept and phrase "negative entropy" were introduced by Erwin Schrödinger in his 1943 popular-science book What is Life? Later, Léon Brillouin shortened the phrase to negentropy, to express it in a more "positive" way: a living system imports negentropy and stores it. In 1974, Albert Szent-Györgyi proposed replacing the term negentropy with syntropy. That term may have originated in the 1940s with the Italian mathematician Luigi Fantappiè, who tried to construct a unified theory of biology and physics. Buckminster Fuller tried to popularize this usage, but negentropy remains common.
In a note to What is Life? Schrödinger explained his use of this phrase.
In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos. Thus, negentropy has units when defined based on specific entropy per unit mass, and when defined based on specific entropy per unit energy. This definition enabled: i) scale-invariant thermodynamic representation of dynamic order existence, ii) formulation of physical principles exclusively for dynamic order existence and evolution, and iii) mathematical interpretation of Schrödinger's negentropy debt.
Information theory
In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.
Negentropy is defined as
where S is the differential entropy of the Gaussian density with the same mean and variance as p_x and S is the differential entropy of p_x:
Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in Independent Component Analysis.
Correlation between statistical negentropy and Gibbs' free energy
There is a physical quantity closely linked to free energy, with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873 Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. The said quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal process and then Planck for the isothermal-isobaric process More recently, the Massieu-Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics, applied among the others in molecular biology and thermodynamic non-equilibrium processes.
In a note to What is Life? Schrödinger explained his use of this phrase.
In 2009, Mahulikar & Herwig redefined negentropy of a dynamically ordered sub-system as the specific entropy deficit of the ordered sub-system relative to its surrounding chaos. Thus, negentropy has units when defined based on specific entropy per unit mass, and when defined based on specific entropy per unit energy. This definition enabled: i) scale-invariant thermodynamic representation of dynamic order existence, ii) formulation of physical principles exclusively for dynamic order existence and evolution, and iii) mathematical interpretation of Schrödinger's negentropy debt.
Information theory
In information theory and statistics, negentropy is used as a measure of distance to normality. Out of all distributions with a given variance, the normal or Gaussian distribution is the one with the highest entropy. Negentropy measures the difference in entropy between a given distribution and the Gaussian distribution with the same variance. Thus, negentropy is always nonnegative, is invariant by any linear invertible change of coordinates, and vanishes if and only if the signal is Gaussian.
Negentropy is defined as
where S is the differential entropy of the Gaussian density with the same mean and variance as p_x and S is the differential entropy of p_x:
Negentropy is used in statistics and signal processing. It is related to network entropy, which is used in Independent Component Analysis.
Correlation between statistical negentropy and Gibbs' free energy
There is a physical quantity closely linked to free energy, with a unit of entropy and isomorphic to negentropy known in statistics and information theory. In 1873 Willard Gibbs created a diagram illustrating the concept of free energy corresponding to free enthalpy. On the diagram one can see the quantity called capacity for entropy. The said quantity is the amount of entropy that may be increased without changing an internal energy or increasing its volume. In other words, it is a difference between maximum possible, under assumed conditions, entropy and its actual entropy. It corresponds exactly to the definition of negentropy adopted in statistics and information theory. A similar physical quantity was introduced in 1869 by Massieu for the isothermal process and then Planck for the isothermal-isobaric process More recently, the Massieu-Planck thermodynamic potential, known also as free entropy, has been shown to play a great role in the so-called entropic formulation of statistical mechanics, applied among the others in molecular biology and thermodynamic non-equilibrium processes.
On: Heat Death
The heat death of the universe is a suggested ultimate fate of the universe, in which the universe has diminished to a state of no thermodynamic free energy and therefore can no longer sustain motion or life. Heat death does not imply any particular absolute temperature; it only requires that temperature differences or other process may no longer be exploited to perform work. In the language of physics, this is when the universe reaches the maximum entropy. The hypothesis of heat death stems from the 1850s ideas of William Thomson, 1st Baron Kelvin, who extrapolated the views of the theory of heat as mechanical energy loss in nature as embodied in the first two laws of thermodynamics to processes in the universe.
Origins of the idea
The idea of heat death stems from the second law of thermodynamics, which states that entropy tends to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, in nature there is a tendency to the dissipation of mechanical energy ; hence, by extrapolation, there exists the view that the mechanical movement of the universe will run down, as work is converted to heat, in time due to the second law. The idea of heat death was first proposed in loose terms beginning in 1851 by William Thomson, 1st Baron Kelvin, who theorized further on the mechanical energy loss views of Sadi Carnot, James Joule, and Rudolf Clausius . Thomson’s views were then elaborated on more definitively over the next decade by Hermann von Helmholtz and William Rankine.
History
The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851 William Thomson outlined the view, as based on recent experiments on the dynamical theory of heat, that "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."
In 1852, Thomson published his "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy" in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will tend to dissipate or run down, naturally. The ideas in this paper, in relation to their application to the age of the sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject. In 1862, Thomson published "On the age of the sun’s heat", an article in which he reiterated his fundamental beliefs in the indestructibility of energy and the universal dissipation of energy, leading to diffusion of heat, cessation of useful motion, and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. In a key paragraph, Thomson wrote:
The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.
In the years to follow both Thomson’s 1852 and the 1865 papers, Helmholtz and Rankine both credited Thomson with the idea, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a "heat death" which will be the "end of all physical phenomena" .
Current status
Inflationary cosmology suggests that in the early universe, before cosmic inflation, energy was uniformly distributed, and the universe was thus in a state superficially similar to heat death. However, these two states are actually very different: in the early universe, gravity was a very important force, and in a gravitational system, if energy is uniformly distributed, entropy is quite low, compared to a state in which most matter has collapsed into black holes. Thus, such a state is not in thermodynamic equilibrium, as it is thermodynamically unstable. However, in the heat death scenario, the energy density is so low that the system can be thought of as non-gravitational, such that a state in which energy is uniformly distributed is a thermal equilibrium state, i.e., the state of maximal entropy.
The final state of the universe depends on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a "closed" universe that undergoes recollapse, a heat death is expected to occur, with the universe approaching arbitrarily high temperature and maximal entropy as the end of the collapse approaches. In an "open" or "flat" universe that continues expanding indefinitely, a heat death is also expected to occur, with the universe cooling to approach absolute zero temperature and approaching a state of maximal entropy over a very long time period. There is dispute over whether or not an expanding universe can approach maximal entropy; it has been proposed that in an expanding universe, the value of maximum entropy increases faster than the universe gains entropy, causing the universe to move progressively further away from heat death.
There is also some uncertainty remaining on the exact value of the current entropy of the universe. A recent analysis of entropy suggests that the visible universe has more entropy than previously thought. This is because the research concludes that supermassive black holes are the largest contributor.
Time frame for heat death
From the Big Bang through the present day and well into the future, matter and dark matter in the universe are thought to be concentrated in stars, galaxies, and galaxy clusters. Therefore, the universe is not in thermodynamic equilibrium and objects can do physical work., §VID. The decay time for a supermassive black hole of roughly 1 galaxy-mass due to Hawking radiation is in the order of 10100 years, so entropy can be produced until at least that time. After that time, the universe enters the so-called dark era, and is expected to consist chiefly of a dilute gas of photons and leptons., §VIA. With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long time scales. Speculatively, it is possible that the universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state., §VE. It is also possible that entropy production will cease and the universe will achieve heat death.
Origins of the idea
The idea of heat death stems from the second law of thermodynamics, which states that entropy tends to increase in an isolated system. If the universe lasts for a sufficient time, it will asymptotically approach a state where all energy is evenly distributed. In other words, in nature there is a tendency to the dissipation of mechanical energy ; hence, by extrapolation, there exists the view that the mechanical movement of the universe will run down, as work is converted to heat, in time due to the second law. The idea of heat death was first proposed in loose terms beginning in 1851 by William Thomson, 1st Baron Kelvin, who theorized further on the mechanical energy loss views of Sadi Carnot, James Joule, and Rudolf Clausius . Thomson’s views were then elaborated on more definitively over the next decade by Hermann von Helmholtz and William Rankine.
History
The idea of heat death of the universe derives from discussion of the application of the first two laws of thermodynamics to universal processes. Specifically, in 1851 William Thomson outlined the view, as based on recent experiments on the dynamical theory of heat, that "heat is not a substance, but a dynamical form of mechanical effect, we perceive that there must be an equivalence between mechanical work and heat, as between cause and effect."
In 1852, Thomson published his "On a Universal Tendency in Nature to the Dissipation of Mechanical Energy" in which he outlined the rudiments of the second law of thermodynamics summarized by the view that mechanical motion and the energy used to create that motion will tend to dissipate or run down, naturally. The ideas in this paper, in relation to their application to the age of the sun and the dynamics of the universal operation, attracted the likes of William Rankine and Hermann von Helmholtz. The three of them were said to have exchanged ideas on this subject. In 1862, Thomson published "On the age of the sun’s heat", an article in which he reiterated his fundamental beliefs in the indestructibility of energy and the universal dissipation of energy, leading to diffusion of heat, cessation of useful motion, and exhaustion of potential energy through the material universe while clarifying his view of the consequences for the universe as a whole. In a key paragraph, Thomson wrote:
The result would inevitably be a state of universal rest and death, if the universe were finite and left to obey existing laws. But it is impossible to conceive a limit to the extent of matter in the universe; and therefore science points rather to an endless progress, through an endless space, of action involving the transformation of potential energy into palpable motion and hence into heat, than to a single finite mechanism, running down like a clock, and stopping for ever.
In the years to follow both Thomson’s 1852 and the 1865 papers, Helmholtz and Rankine both credited Thomson with the idea, but read further into his papers by publishing views stating that Thomson argued that the universe will end in a "heat death" which will be the "end of all physical phenomena" .
Current status
Inflationary cosmology suggests that in the early universe, before cosmic inflation, energy was uniformly distributed, and the universe was thus in a state superficially similar to heat death. However, these two states are actually very different: in the early universe, gravity was a very important force, and in a gravitational system, if energy is uniformly distributed, entropy is quite low, compared to a state in which most matter has collapsed into black holes. Thus, such a state is not in thermodynamic equilibrium, as it is thermodynamically unstable. However, in the heat death scenario, the energy density is so low that the system can be thought of as non-gravitational, such that a state in which energy is uniformly distributed is a thermal equilibrium state, i.e., the state of maximal entropy.
The final state of the universe depends on the assumptions made about its ultimate fate, and these assumptions have varied considerably over the late 20th century and early 21st century. In a "closed" universe that undergoes recollapse, a heat death is expected to occur, with the universe approaching arbitrarily high temperature and maximal entropy as the end of the collapse approaches. In an "open" or "flat" universe that continues expanding indefinitely, a heat death is also expected to occur, with the universe cooling to approach absolute zero temperature and approaching a state of maximal entropy over a very long time period. There is dispute over whether or not an expanding universe can approach maximal entropy; it has been proposed that in an expanding universe, the value of maximum entropy increases faster than the universe gains entropy, causing the universe to move progressively further away from heat death.
There is also some uncertainty remaining on the exact value of the current entropy of the universe. A recent analysis of entropy suggests that the visible universe has more entropy than previously thought. This is because the research concludes that supermassive black holes are the largest contributor.
Time frame for heat death
From the Big Bang through the present day and well into the future, matter and dark matter in the universe are thought to be concentrated in stars, galaxies, and galaxy clusters. Therefore, the universe is not in thermodynamic equilibrium and objects can do physical work., §VID. The decay time for a supermassive black hole of roughly 1 galaxy-mass due to Hawking radiation is in the order of 10100 years, so entropy can be produced until at least that time. After that time, the universe enters the so-called dark era, and is expected to consist chiefly of a dilute gas of photons and leptons., §VIA. With only very diffuse matter remaining, activity in the universe will have tailed off dramatically, with extremely low energy levels and extremely long time scales. Speculatively, it is possible that the universe may enter a second inflationary epoch, or, assuming that the current vacuum state is a false vacuum, the vacuum may decay into a lower-energy state., §VE. It is also possible that entropy production will cease and the universe will achieve heat death.
On: M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories . Though a full description of the theory is not known, the low-entropy dynamics are known to be supergravity interacting with 2- and 5-dimensional membranes.
This idea is the unique supersymmetric theory in eleven dimensions, with its low-entropy matter content and interactions fully determined, and can be obtained as the strong coupling limit of type IIA string theory because a new dimension of space emerges as the coupling constant increases.
Drawing on the work of a number of string theorists, Edward Witten of the Institute for Advanced Study suggested its existence at a conference at USC in 1995, and used M-theory to explain a number of previously observed dualities, initiating a flurry of new research in string theory called the second superstring revolution.
In the early 1990s, it was shown that the various superstring theories were related by dualities which allow the description of an object in one super string theory to be related to the description of a different object in another super string theory. These relationships imply that each of the super string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".
Originally the letter M in M-theory was taken from membrane, a construct designed to generalize the strings of string theory. However, as Witten was more skeptical about membranes than his colleagues, he opted for "M-theory" rather than "Membrane theory". Witten has since stated that the different interpretations of the M can be a matter of taste for the user, such as magic, mystery, and mother theory.
M-theory has been criticized for lacking predictive power or being untestable. Further work continues to find mathematical constructs that join various surrounding theories. However, the tangible success of M-theory can be questioned, given its current incompleteness and limited predictive power.
History and development
Prior to May 1995
Before 1995 there were five known consistent superstring theories, which were given the names Type I string theory, Type IIA string theory, Type IIB string theory, heterotic SO theory, and heterotic E8×E8 theory. The five theories all share essential features that relate them to the name of string theory. Each theory is fundamentally based on vibrating, one-dimensional strings at approximately the length of the Planck length. Calculations have also shown that each theory requires more than the normal four spacetime dimensions . When the theories are analyzed in detail, significant differences appear.
Type I string theory and supplements
The Type I string theory has vibrating strings like the rest of the string theories. These strings vibrate both in closed loops, so that the strings have no ends, and as open strings with two loose ends. The open loose strings are what separates the Type I string theory from the other four string theories. This was a feature that the other string theories did not contain.
String vibrational patterns
The calculations of the String Vibrational Patterns show that the list of string vibrational patterns and the way each pattern interacts and influences others vary from one theory to another. These and other differences hindered the development of the string theory as being the theory that united quantum mechanics and general relativity successfully. Attempts by the physics community to eliminate four of the theories, leaving only one string theory, have not been successful.
M-theory
M-theory attempts to unify the five string theories by examining certain identifications and dualities. Thus each of the five string theories become special cases of M-theory.
As the names suggest, some of these string theories were thought to be related to each other. In the early 1990s, string theorists discovered that some relations were so strong that they could be thought of as an identification.
Type IIA and Type IIB
The Type IIA string theory and the Type IIB string theory were known to be connected by T-duality; this essentially meant that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R, where distances are measured in units of the Planck length.
This was a profound result. First, this was an intrinsically quantum mechanical result; the identification did not hold in the realm of classical physics. Second, because it is possible to build up any space by gluing circles together in various ways, it would seem that any space described by the IIA string theory can also be seen as a different space described by the IIB theory. This implies that the IIA string theory can identify with the IIB string theory: any object which can be described with the IIA theory has an equivalent, although seemingly different, description in terms of the IIB theory. This suggests that the IIA string theory and the IIB string theory are really aspects of the same underlying theory.
Other dualities
There are other dualities between the other string theories. The heterotic SO and the heterotic E8×E8 theories are also related by T-duality; the heterotic SO description of a circle of radius R is exactly the same as the heterotic E8×E8 description of a circle of radius 1/R. This implies that there are really only three superstring theories, which might be called the Type I theory, the Type II theory, and the heterotic theory.
There are still more dualities, however. The Type I string theory is related to the heterotic SO theory by S-duality; this means that the Type I description of weakly interacting particles can also be seen as the heterotic SO description of very strongly interacting particles. This identification is somewhat more subtle, in that it identifies only extreme limits of the respective theories. String theorists have found strong evidence that the two theories are really the same, even away from the extremely strong and extremely weak limits, but they do not yet have a proof strong enough to satisfy mathematicians. However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.
Only two string theories
Given the above commonalities there appear to be only two string theories: the heterotic string theory and the type II theory. There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.
Last step
This last step is best explained first in a certain limit. In order to describe our world, strings must be extremely tiny objects. So when one studies string theory at low energies, it becomes difficult to see that strings are extended objects — they become effectively zero-dimensional . Consequently, the quantum theory describing the low energy limit is a theory that describes the dynamics of these points moving in spacetime, rather than strings. Such theories are called quantum field theories. However, since string theory also describes gravitational interactions, one expects the low-energy theory to describe particles moving in gravitational backgrounds. Finally, since superstring string theories are supersymmetric for supersymmetry is needed for consistency, one expects to see supersymmetry appearing in the low-energy approximation. These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory.
Supergravity theories
The possible supergravity theories were classified by Werner Nahm in the 1970s. In 10 dimensions, there are only two supergravity theories, which are denoted Type IIA and Type IIB. This similar denomination is not a coincidence; the Type IIA string theory has the Type IIA supergravity theory as its low-energy limit and the Type IIB string theory gives rise to Type IIB supergravity. The heterotic SO and heterotic E8×E8 string theories also reduce to Type IIA and Type IIB supergravity in the low-energy limit. This suggests that there may indeed be a relation between the heterotic/Type I theories and the Type II theories.
This idea is the unique supersymmetric theory in eleven dimensions, with its low-entropy matter content and interactions fully determined, and can be obtained as the strong coupling limit of type IIA string theory because a new dimension of space emerges as the coupling constant increases.
Drawing on the work of a number of string theorists, Edward Witten of the Institute for Advanced Study suggested its existence at a conference at USC in 1995, and used M-theory to explain a number of previously observed dualities, initiating a flurry of new research in string theory called the second superstring revolution.
In the early 1990s, it was shown that the various superstring theories were related by dualities which allow the description of an object in one super string theory to be related to the description of a different object in another super string theory. These relationships imply that each of the super string theories is a different aspect of a single underlying theory, proposed by Witten, and named "M-theory".
Originally the letter M in M-theory was taken from membrane, a construct designed to generalize the strings of string theory. However, as Witten was more skeptical about membranes than his colleagues, he opted for "M-theory" rather than "Membrane theory". Witten has since stated that the different interpretations of the M can be a matter of taste for the user, such as magic, mystery, and mother theory.
M-theory has been criticized for lacking predictive power or being untestable. Further work continues to find mathematical constructs that join various surrounding theories. However, the tangible success of M-theory can be questioned, given its current incompleteness and limited predictive power.
History and development
Prior to May 1995
Before 1995 there were five known consistent superstring theories, which were given the names Type I string theory, Type IIA string theory, Type IIB string theory, heterotic SO theory, and heterotic E8×E8 theory. The five theories all share essential features that relate them to the name of string theory. Each theory is fundamentally based on vibrating, one-dimensional strings at approximately the length of the Planck length. Calculations have also shown that each theory requires more than the normal four spacetime dimensions . When the theories are analyzed in detail, significant differences appear.
Type I string theory and supplements
The Type I string theory has vibrating strings like the rest of the string theories. These strings vibrate both in closed loops, so that the strings have no ends, and as open strings with two loose ends. The open loose strings are what separates the Type I string theory from the other four string theories. This was a feature that the other string theories did not contain.
String vibrational patterns
The calculations of the String Vibrational Patterns show that the list of string vibrational patterns and the way each pattern interacts and influences others vary from one theory to another. These and other differences hindered the development of the string theory as being the theory that united quantum mechanics and general relativity successfully. Attempts by the physics community to eliminate four of the theories, leaving only one string theory, have not been successful.
M-theory
M-theory attempts to unify the five string theories by examining certain identifications and dualities. Thus each of the five string theories become special cases of M-theory.
As the names suggest, some of these string theories were thought to be related to each other. In the early 1990s, string theorists discovered that some relations were so strong that they could be thought of as an identification.
Type IIA and Type IIB
The Type IIA string theory and the Type IIB string theory were known to be connected by T-duality; this essentially meant that the IIA string theory description of a circle of radius R is exactly the same as the IIB description of a circle of radius 1/R, where distances are measured in units of the Planck length.
This was a profound result. First, this was an intrinsically quantum mechanical result; the identification did not hold in the realm of classical physics. Second, because it is possible to build up any space by gluing circles together in various ways, it would seem that any space described by the IIA string theory can also be seen as a different space described by the IIB theory. This implies that the IIA string theory can identify with the IIB string theory: any object which can be described with the IIA theory has an equivalent, although seemingly different, description in terms of the IIB theory. This suggests that the IIA string theory and the IIB string theory are really aspects of the same underlying theory.
Other dualities
There are other dualities between the other string theories. The heterotic SO and the heterotic E8×E8 theories are also related by T-duality; the heterotic SO description of a circle of radius R is exactly the same as the heterotic E8×E8 description of a circle of radius 1/R. This implies that there are really only three superstring theories, which might be called the Type I theory, the Type II theory, and the heterotic theory.
There are still more dualities, however. The Type I string theory is related to the heterotic SO theory by S-duality; this means that the Type I description of weakly interacting particles can also be seen as the heterotic SO description of very strongly interacting particles. This identification is somewhat more subtle, in that it identifies only extreme limits of the respective theories. String theorists have found strong evidence that the two theories are really the same, even away from the extremely strong and extremely weak limits, but they do not yet have a proof strong enough to satisfy mathematicians. However, it has become clear that the two theories are related in some fashion; they appear as different limits of a single underlying theory.
Only two string theories
Given the above commonalities there appear to be only two string theories: the heterotic string theory and the type II theory. There are relations between these two theories as well, and these relations are in fact strong enough to allow them to be identified.
Last step
This last step is best explained first in a certain limit. In order to describe our world, strings must be extremely tiny objects. So when one studies string theory at low energies, it becomes difficult to see that strings are extended objects — they become effectively zero-dimensional . Consequently, the quantum theory describing the low energy limit is a theory that describes the dynamics of these points moving in spacetime, rather than strings. Such theories are called quantum field theories. However, since string theory also describes gravitational interactions, one expects the low-energy theory to describe particles moving in gravitational backgrounds. Finally, since superstring string theories are supersymmetric for supersymmetry is needed for consistency, one expects to see supersymmetry appearing in the low-energy approximation. These three facts imply that the low-energy approximation to a superstring theory is a supergravity theory.
Supergravity theories
The possible supergravity theories were classified by Werner Nahm in the 1970s. In 10 dimensions, there are only two supergravity theories, which are denoted Type IIA and Type IIB. This similar denomination is not a coincidence; the Type IIA string theory has the Type IIA supergravity theory as its low-energy limit and the Type IIB string theory gives rise to Type IIB supergravity. The heterotic SO and heterotic E8×E8 string theories also reduce to Type IIA and Type IIB supergravity in the low-energy limit. This suggests that there may indeed be a relation between the heterotic/Type I theories and the Type II theories.
Professional Brain Training
Check this out, i've been using it and its amazing...
http://www.lumosity.com
http://www.lumosity.com
Sunday, 17 June 2012
Ace on the River
Texas hold 'em is a variation of the standard card game of poker. The game consists of two cards being dealt face down to each player and then five community cards being placed face-up by the dealer—a series of three then two additional single cards, with players having the option to check, bet, raise or fold after each deal; i.e., betting may occur prior to the flop, "on the flop", "on the turn", and "on the river".
Texas Hold 'em is the "H" game featured in H.O.R.S.E and in H.O.S.E.
Objective
In Texas hold 'em, as in all variants of poker, individuals compete for an amount of money or chips contributed by the players themselves . Because the cards are dealt randomly and outside the control of the players, each player attempts to control the amount of money in the pot based either on the hand they are holding,
or on their prediction as to what their opponents may be holding.
The game is divided into a series of hands or deals; at the conclusion of each hand, the pot is typically awarded to one player . A hand may end at the showdown, in which case the remaining players compare their hands and the highest hand is awarded the pot; that highest hand is usually held by only one player, but can be held by more in the case of a tie. The other possibility for the conclusion of a hand occurs when all but one player has folded and have thereby abandoned any claim to the pot, in which case the pot is awarded to the player who has not folded.
After its invention and spread throughout Texas, hold 'em was introduced to Las Vegas in 1967 by a group of Texan gamblers and card players, including Crandell Addington, Doyle Brunson, and Amarillo Slim. Addington said the first time he saw the game was in 1959. "They didn't call it Texas hold 'em at the time, they just called it hold 'em.… I thought then that if it were to catch on, it would become the game. Draw poker, you bet only twice; hold 'em, you bet four times. That meant you could play strategically. This was more of a thinking man's game."
For several years the Golden Nugget Casino in Downtown Las Vegas was the only casino in Las Vegas to offer the game. At that time, the Golden Nugget's poker room was "truly a 'sawdust joint,' with…oiled sawdust covering the floors." Because of its location and decor, this poker room did not receive many rich drop-in clients, and as a result, professional players sought a more prominent location. In 1969, the Las Vegas professionals were invited to play Texas hold 'em at the entrance of the now-demolished Dunes Casino on the Las Vegas Strip. This prominent location, and the relative inexperience of poker players with Texas hold 'em, resulted in a very remunerative game for professional players.
During this time, B & G Publishing Co., Inc. published Doyle Brunson's revolutionary poker strategy guide, Super/System. In 1983, Al Alvarez published The Biggest Game in Town, a book detailing a 1981 World Series of Poker event. The first book of its kind, it described the world of professional poker players and the World Series of Poker. Alvarez's book is credited with beginning the genre of poker literature and with bringing Texas hold 'em to a wider audience.
Interest in hold 'em outside of Nevada began to grow in the 1980s as well. Although California had legal card rooms offering draw poker, Texas hold 'em was prohibited under a statute that made illegal the game "stud-horse". But in 1988 Texas hold 'em was declared legally distinct from stud-horse in Tibbetts v. Van De Kamp, 271 Cal. Rptr. 792 . Almost immediately card rooms across the state offered Texas hold 'em. After a trip to Las Vegas, bookmakers Terry Rogers and Liam Flood introduced the game to European card players in the early 1980s.
Popularity
Texas Hold 'Em is one of the most popular forms of poker. Texas Hold 'em's popularity surged in the 2000s due to exposure on television, the Internet and popular literature. During this time hold 'em replaced seven-card stud as the most common game in U.S. casinos. The no-limit betting form is used in the widely televised main event of the World Series of Poker and the World Poker Tour .
Hold 'em's simplicity and popularity have inspired a wide variety of strategy books which provide recommendations for proper play. Most of these books recommend a strategy that involves playing relatively few hands but betting and raising often with the hands one plays.
In the first decade of the twenty-first century, Texas hold 'em experienced a surge in popularity worldwide. the appearance of television commercials advertising online cardrooms, and the 2003 World Series of Poker championship victory by online qualifier Chris Moneymaker.
Television and film
Prior to poker becoming widely televised, the movie Rounders, starring Matt Damon and Edward Norton, gave moviegoers a romantic view of the game as a way of life. Texas hold 'em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the "Cadillac of Poker." A clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker was also incorporated into the film. More recently, a high-stakes Texas Hold'em game was central to the plot of the 2006 James Bond film Casino Royale, in place of baccarat, the casino game central to the novel on which the film was based. In 2008, an acclaimed short film called Shark Out of Water was released on DVD. This film is unique in that it deals with the darker, more addicting elements of the game and features Phil Hellmuth and Brad Booth.
Hold 'em tournaments had been televised since the late 1970s, but they did not become popular until 1999, when hidden lipstick cameras were first used to show players' private hole cards on the Late Night Poker TV show in the United Kingdom. Hold 'em exploded in popularity as a spectator sport in the United States and Canada in early 2003, when the World Poker Tour adopted the lipstick cameras idea. A few months later, ESPN's coverage of the 2003 World Series of Poker featured the unexpected victory of Internet player Chris Moneymaker, an amateur player who gained admission to the tournament by winning a series of online tournaments. Moneymaker's victory initiated a sudden surge of interest in the World Series, based on the egalitarian idea that anyone—even a rank novice—can become a world champion.
In 2003, there were 839 entrants in the WSOP Main Event, and triple that number in 2004. The crowning of the 2004 WSOP champion, Greg "Fossilman" Raymer, a patent attorney from Connecticut, further fueled the popularity of the event among amateur players. In the 2005 Main Event, an unprecedented 5,619 entrants vied for a first prize of $7,500,000. The winner, Joe Hachem of Australia, was a semi-professional player. This growth continued in 2006, with 8,773 entrants and a first place prize of $12,000,000 .
Beyond the World Series, other television shows—including the long running World Poker Tour—are credited with increasing the popularity of Texas hold 'em. In addition to its presence on network and general audience cable television, poker has now become a regular part of sports networks' programming in the United States.
Literature
Twenty years after the publication of Alvarez's groundbreaking book, James McManus
published a semi-autobiographical book, Positively Fifth Street, which simultaneously describes the trial surrounding the murder of Ted Binion and McManus' own entry into the 2000 World Series of Poker. McManus, a poker amateur, finished 5th in the No-Limit Texas Hold 'em main event, winning over $200,000. In the book McManus discusses events surrounding the World Series, the trial of Sandy Murphy and Rick Tabish, poker strategy, and some history of poker and the world series.
Michael Craig's 2005 book The Professor, the Banker, and the Suicide King details a series of high stakes Texas hold 'em one-on-one games between Texas banker Andy Beal and a rotating group of poker professionals. As of 2006, these games were the highest stakes ever played, reaching $100,000–$200,000 fixed limit.
Online poker
The ability to play cheaply and anonymously online has been credited as a cause of the increase in popularity of Texas hold 'em.
Although online poker grew from its inception in 1998 until 2003, Moneymaker's win and the appearance of televisions advertisements in 2003 contributed to a tripling of industry revenues in 2004.
Texas Hold 'em is the "H" game featured in H.O.R.S.E and in H.O.S.E.
Objective
In Texas hold 'em, as in all variants of poker, individuals compete for an amount of money or chips contributed by the players themselves . Because the cards are dealt randomly and outside the control of the players, each player attempts to control the amount of money in the pot based either on the hand they are holding,
or on their prediction as to what their opponents may be holding.
The game is divided into a series of hands or deals; at the conclusion of each hand, the pot is typically awarded to one player . A hand may end at the showdown, in which case the remaining players compare their hands and the highest hand is awarded the pot; that highest hand is usually held by only one player, but can be held by more in the case of a tie. The other possibility for the conclusion of a hand occurs when all but one player has folded and have thereby abandoned any claim to the pot, in which case the pot is awarded to the player who has not folded.
After its invention and spread throughout Texas, hold 'em was introduced to Las Vegas in 1967 by a group of Texan gamblers and card players, including Crandell Addington, Doyle Brunson, and Amarillo Slim. Addington said the first time he saw the game was in 1959. "They didn't call it Texas hold 'em at the time, they just called it hold 'em.… I thought then that if it were to catch on, it would become the game. Draw poker, you bet only twice; hold 'em, you bet four times. That meant you could play strategically. This was more of a thinking man's game."
For several years the Golden Nugget Casino in Downtown Las Vegas was the only casino in Las Vegas to offer the game. At that time, the Golden Nugget's poker room was "truly a 'sawdust joint,' with…oiled sawdust covering the floors." Because of its location and decor, this poker room did not receive many rich drop-in clients, and as a result, professional players sought a more prominent location. In 1969, the Las Vegas professionals were invited to play Texas hold 'em at the entrance of the now-demolished Dunes Casino on the Las Vegas Strip. This prominent location, and the relative inexperience of poker players with Texas hold 'em, resulted in a very remunerative game for professional players.
During this time, B & G Publishing Co., Inc. published Doyle Brunson's revolutionary poker strategy guide, Super/System. In 1983, Al Alvarez published The Biggest Game in Town, a book detailing a 1981 World Series of Poker event. The first book of its kind, it described the world of professional poker players and the World Series of Poker. Alvarez's book is credited with beginning the genre of poker literature and with bringing Texas hold 'em to a wider audience.
Interest in hold 'em outside of Nevada began to grow in the 1980s as well. Although California had legal card rooms offering draw poker, Texas hold 'em was prohibited under a statute that made illegal the game "stud-horse". But in 1988 Texas hold 'em was declared legally distinct from stud-horse in Tibbetts v. Van De Kamp, 271 Cal. Rptr. 792 . Almost immediately card rooms across the state offered Texas hold 'em. After a trip to Las Vegas, bookmakers Terry Rogers and Liam Flood introduced the game to European card players in the early 1980s.
Popularity
Texas Hold 'Em is one of the most popular forms of poker. Texas Hold 'em's popularity surged in the 2000s due to exposure on television, the Internet and popular literature. During this time hold 'em replaced seven-card stud as the most common game in U.S. casinos. The no-limit betting form is used in the widely televised main event of the World Series of Poker and the World Poker Tour .
Hold 'em's simplicity and popularity have inspired a wide variety of strategy books which provide recommendations for proper play. Most of these books recommend a strategy that involves playing relatively few hands but betting and raising often with the hands one plays.
In the first decade of the twenty-first century, Texas hold 'em experienced a surge in popularity worldwide. the appearance of television commercials advertising online cardrooms, and the 2003 World Series of Poker championship victory by online qualifier Chris Moneymaker.
Television and film
Prior to poker becoming widely televised, the movie Rounders, starring Matt Damon and Edward Norton, gave moviegoers a romantic view of the game as a way of life. Texas hold 'em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the "Cadillac of Poker." A clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker was also incorporated into the film. More recently, a high-stakes Texas Hold'em game was central to the plot of the 2006 James Bond film Casino Royale, in place of baccarat, the casino game central to the novel on which the film was based. In 2008, an acclaimed short film called Shark Out of Water was released on DVD. This film is unique in that it deals with the darker, more addicting elements of the game and features Phil Hellmuth and Brad Booth.
Hold 'em tournaments had been televised since the late 1970s, but they did not become popular until 1999, when hidden lipstick cameras were first used to show players' private hole cards on the Late Night Poker TV show in the United Kingdom. Hold 'em exploded in popularity as a spectator sport in the United States and Canada in early 2003, when the World Poker Tour adopted the lipstick cameras idea. A few months later, ESPN's coverage of the 2003 World Series of Poker featured the unexpected victory of Internet player Chris Moneymaker, an amateur player who gained admission to the tournament by winning a series of online tournaments. Moneymaker's victory initiated a sudden surge of interest in the World Series, based on the egalitarian idea that anyone—even a rank novice—can become a world champion.
In 2003, there were 839 entrants in the WSOP Main Event, and triple that number in 2004. The crowning of the 2004 WSOP champion, Greg "Fossilman" Raymer, a patent attorney from Connecticut, further fueled the popularity of the event among amateur players. In the 2005 Main Event, an unprecedented 5,619 entrants vied for a first prize of $7,500,000. The winner, Joe Hachem of Australia, was a semi-professional player. This growth continued in 2006, with 8,773 entrants and a first place prize of $12,000,000 .
Beyond the World Series, other television shows—including the long running World Poker Tour—are credited with increasing the popularity of Texas hold 'em. In addition to its presence on network and general audience cable television, poker has now become a regular part of sports networks' programming in the United States.
Literature
Twenty years after the publication of Alvarez's groundbreaking book, James McManus
published a semi-autobiographical book, Positively Fifth Street, which simultaneously describes the trial surrounding the murder of Ted Binion and McManus' own entry into the 2000 World Series of Poker. McManus, a poker amateur, finished 5th in the No-Limit Texas Hold 'em main event, winning over $200,000. In the book McManus discusses events surrounding the World Series, the trial of Sandy Murphy and Rick Tabish, poker strategy, and some history of poker and the world series.
Michael Craig's 2005 book The Professor, the Banker, and the Suicide King details a series of high stakes Texas hold 'em one-on-one games between Texas banker Andy Beal and a rotating group of poker professionals. As of 2006, these games were the highest stakes ever played, reaching $100,000–$200,000 fixed limit.
Online poker
The ability to play cheaply and anonymously online has been credited as a cause of the increase in popularity of Texas hold 'em.
Although online poker grew from its inception in 1998 until 2003, Moneymaker's win and the appearance of televisions advertisements in 2003 contributed to a tripling of industry revenues in 2004.
On: Quantum Geometry
In theoretical physics, quantum geometry is the set of new mathematical concepts generalizing the concepts of geometry whose understanding is necessary to describe the physical phenomena at very short distance scales . At these distances, quantum mechanics has a profound effect on physics.
Quantum gravity
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge our usual geometrical intuition. More technically, quantum geometry refers to the shape of the spacetime manifold as seen by D-branes which includes the quantum corrections to the metric tensor, such as the worldsheet instantons. For example, the quantum volume of a cycle is computed from the mass of a brane wrapped on this cycle. As another example, a distance between two quantum mechanics particles can be expressed in terms of the Lukaszyk–Karmowski metric.
In an alternative approach to quantum gravity called loop quantum gravity, the phrase "quantum geometry" usually refers to the formalism within LQG where the observables that capture the information about the geometry are now well defined operators on a Hilbert space. In particular, certain physical observables, such as the area, have a discrete spectrum. It has also been shown that the loop quantum geometry is non-commutative.
It is possible that this strictly quantized understanding of geometry will be consistent with the quantum picture of geometry arising from string theory.
Quantum gravity
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge our usual geometrical intuition. More technically, quantum geometry refers to the shape of the spacetime manifold as seen by D-branes which includes the quantum corrections to the metric tensor, such as the worldsheet instantons. For example, the quantum volume of a cycle is computed from the mass of a brane wrapped on this cycle. As another example, a distance between two quantum mechanics particles can be expressed in terms of the Lukaszyk–Karmowski metric.
In an alternative approach to quantum gravity called loop quantum gravity, the phrase "quantum geometry" usually refers to the formalism within LQG where the observables that capture the information about the geometry are now well defined operators on a Hilbert space. In particular, certain physical observables, such as the area, have a discrete spectrum. It has also been shown that the loop quantum geometry is non-commutative.
It is possible that this strictly quantized understanding of geometry will be consistent with the quantum picture of geometry arising from string theory.
Subscribe to:
Posts (Atom)