title: Nova (Richard Rider)

text: Rider learns that Worldmind has been recruiting for the Corps without telling him. When he learns that Ego the Living Planet is among the new recruits, he becomes enraged and tries to battle Worldmind. As a result, he is stripped of his rank and ejected from the Nova Corps. Because his body has become dependent on the Nova Force, Rider will die if he is without it for too long. As a temporary measure, he borrows the quantum bands from Wendell Vaughn and becomes Quasar. Using his new abilities, Rider rescues the Corps from the War of Kings. Ego is removed as a Centurion and Rider regains his Nova Prime status, but not before most of the new recruits are slaughtered by the Shi'ar Imperial Guard. Nova agrees to train the remaining new Centurions, including his younger brother Robert.


title: Nova (Richard Rider)

text: Nova is recruited for the Secret Avengers by Steve Rogers and sent to Mars to investigate Roxxon's operations on that planet. While there, Rider discovers a second Serpent Crown secreted there, only to fall under its influence until rescued by Rogers and his team of Avengers. Shortly after this mission, Nova is called away to deal with the events of "The Thanos Imperative" and Steve Rogers confirms he has left the team.


title: Nova (Richard Rider)

text: A lost Nova Corps ship appears from a tear in space-time known as the Fault. Onboard is Zan Philo, a long-missing Nova centurion who is assigned to train the new recruits. Later, Rider and Darkhawk find themselves inside the Fault, where they are called to do battle for the Sphinx against his younger self. Because of the unstable timestream inside the Fault, Nova is able to return with Namorita, his old girlfriend who had died a few years earlier. Rider returns to Project Pegasus, where he confronts an alternate Quasar who originates from the Cancerverse, a universe within the Fault.


title: Nova (Richard Rider)

text: Catching up to the alternate Quasar, Rider returns to the Fault to see the Universal Church of Truth rip it wide open. Assisted by others, he confronts Lord Mar-Vell, the evil alternate version of Captain Marvel, but cannot stop him. Entering the Fault to assist the Guardians of the Galaxy, Rider and the Guardians watch Thanos destroy Mar-Vell. Now facing an enraged Thanos, Rider pulls the Nova Force from the rest of the Corps for extra strength. He and Star-Lord are able to hold Thanos back for the few minutes it takes for the Fault to close, trapping all three of them in the Cancerverse. The two heroes continue to fight Thanos for a Cosmic Cube which has the power to send them home. Rider charges the Cube with the Nova Force to create a doorway for Star-Lord, intending to remain behind and keep Thanos from escaping too. Star-Lord escapes, but Rider is unable to prevent Thanos from escaping as well. Because no one is immediately aware Star-Lord survived, Nova and Star-Lord receive a statue in their honor on Hala.


title: Nova (Richard Rider)

text: The latest Nova, Sam Alexander, locates the Xandarian Worldmind. Rider's consciousness awakens within the Worldmind during the encounter. It is later revealed that Rider and the Worldmind survived the closure of the Fault and remain trapped in the Cancerverse. Using the Nova Force, Rider manages to escape the Cancerverse, returns to Earth to visit his mother, and learns that his father has died. He encounters Alexander and they begin working together. However, in his escape, Rider has become a portal to the Cancerverse, which repeatedly attempts to invade Earth through him. Rider returns to the Cancerverse in hopes of closing the portal and thus saving his own universe. Despite his resistance, he is co-opted by the Cancerverse, but is freed by Alexander, who has followed him. The two escape the Cancerverse once more, using the Cosmic Cube carried by Thanos' Cancerverse doppelganger. Rider and Alexander resume their lives and relationships on Earth while continuing as Nova Corpsmen.


title: Nova (Richard Rider)

text: In the aftermath of "Empyre," Nova represents the Nova Corps during a Galactic Council meeting held by Super-Skrull. When Emperor Stote of the Zn'rx was found dead in the restroom and Noh-Varr becomes a suspect after attacking the Skrull subaltern Val-Korr, Nova calls in the Guardians of the Galaxy to investigate Emperor Stote's murder.


title: Nova (Richard Rider)

text: During the "Judgment Day" storyline, Nova appears at Port Prometheus to protect the evacuees from the attackers at the time when Uranos the Undying was attacking.


title: Nova (Richard Rider)

text: Nova derives his powers from an energy source called the Nova Force which all Nova Corps Centurions wield. This energy was transferred to Rider by the Nova-Centurion Rhomann Dey. The Nova Force affords Rider superhuman powers including flight, superhuman strength, speed, and durability, as well as the power to absorb energy directed against him and release it as gravimetric pulses and beams, either from specific parts of his body or from his entire body. Nova is a good hand-to-hand combatant, and has been coached by Chord.


title: Nova (Richard Rider)

text: Nova wears a standard Xandarian StarCorps uniform, designed to accommodate his powers without being damaged by them. The uniform is highly resistant to damage, including outer space conditions, and is airtight. In addition, the uniform has a built-in life support function that can sustain Rider under the most extreme environmental conditions, including acting as a life-support suit by locking off the mouth and eyes of the helmet. The helmet contains a radio, telescopic sights, night vision sensors, and heat imaging sensors, as well as a visual heads-up display for tracking energy signatures. Nova's helmet has a rigid construction and shape when worn, but becomes as malleable as cloth when it is not, allowing Rider to hide it in his civilian clothes when desired. Nova's uniform is not only extremely malleable, but contains specific functions to aid Rider in his role as a Nova Corps Centurion. Among these features are an electromagnetic discharge that can nullify gravity and an interface to stargates that allow him to enter hyperspace, where he can move at velocities exceeding the speed of light. Rider can also alter the appearance and nature of his uniform to suit his needs. However, as Rider learns the hard way, the Nova Corps keeps a strict dress code. When he makes major cosmetic changes to his uniform after rejoining the New Warriors, Nova is summarily ordered to conform to standard.


title: Nova (Richard Rider)

text: During Annihilation, Rider's uniform is altered and enhanced to house the Xandarian Worldmind as well as the entire Nova Force, which was previously used by all members of the Nova Corps. With the Worldmind and the Nova Force, Rider possesses tremendously augmented strength and durability as well as nearly limitless quantities of energy. The Worldmind consists of the entire culture and history of Xandar as well as the individual minds of thousands of years of dead Xandarians. The consensus voice of the Worldmind can speak directly to Rider, helping him to control the Nova Force, fight enemies, sense energy, interface with electronics, and protect against psionic abilities. The Worldmind can also assume direct control of Rider's body when he is asleep.


title: Nova (Richard Rider)

text: In 1997, on the eve of the impending release of the "Blade" motion picture, Marv Wolfman sued Marvel Characters Inc. over ownership of all characters he had created for Marvel Comics, including Nova and Blade. A ruling in Marvel's favor was handed down on November 6, 2000. Wolfman's stance was that he had not signed work-for-hire contracts when he created characters including Blade and Nova. In a nonjury trial, the judge ruled that Marvel's later use of the characters was sufficiently different to protect it from Wolfman's claim of copyright ownership.


title: Nova (Richard Rider)

text: In the alternate future of Earth X, Nova resides in the afterlife. He and two other deceased heroes, Ms. Marvel and Star-Lord, lead an initial charge against Mephisto but are swiftly defeated.


title: Nova (Richard Rider)

text: Nova is featured in "". Unable to overcome his fear and horror of the slaughter occurring around him, Nova fails to act in his own defense when Spider-Man attacks him. Daredevil intervenes but is bitten when Nova is too shocked to assist. He and Thor are rescued by the Fantastic Four and united with the other surviving heroes on the S.H.I.E.L.D. Helicarrier. Nova panics further when Nick Fury formulates a desperate last stand defense, citing that this was nothing like previous global threats; and that the world was as good as dead. Regardless, Nova helps in the battle until he is bitten by Ms. Marvel. As a zombie, he participates in a failed attack on Doctor Doom's castle, in an effort to get at the humans inside. A zombie version of Nova can be seen in the "Marvel Zombies" limited series, being shredded by a hail of metal fragments hurled by Magneto.


title: Nova (Richard Rider)

text: He is still mobile, as a zombie, when a swarm of zombies attack and attempt to consume the Silver Surfer. During the incident, Zombie Hulk crushes Zombie Hercules when the latter attempts to steal the Silver Surfer's head. Nova backs away, saying "On second thought, you keep that, big guy". He is later killed by the cosmic zombies.


title: Nova (Richard Rider)

text: Richard Rider appears frequently in the "Spider-Girl" series, which is set in an alternate future. The MC2 Nova (co-created by Tom DeFalco and Ron Frenz) first appeared in Spider-Girl #7 and wrongly believed Spider-Girl was a supervillain since she was fighting Darkdevil at the time. After a brief battle Nova later realizes his mistake.


title: Nova (Richard Rider)

text: Over time, the MC2 Nova attempts to tutor Spider-Girl on the importance of being a superhero. His arrogance and lack of patience with younger heroes causes his lessons to be largely ignored. However, the fact that Nova was a founding member of the New Warriors gave Spider-Girl the inspiration to form a new MC2 version of the Warriors.


title: Nova (Richard Rider)

text: By the time of the series, Nova has served as a temporary Avenger. He also appears in the "Last Hero Standing" and "Avengers Next" limited series. Nova also assisted in the battle against Galactus in "Last Planet Standing". The Nova in the MC2/Spider-Girl future is eventually confirmed to be Richard Rider in "Avengers Next" #2. His attitude toward Spider-Girl is often arrogant and dismissive, bordering on the contemptuous; but later he becomes impressed by her, after her surviving a battle against the Avengers' enemy Seth.


title: Nova (Richard Rider)

text: Nova appears as the sole Caucasian member of a team of Avengers from a parallel reality where the Middle East is the dominant superpower. He serves the ruler of this alternate Earth, the tyrannical female Sphinx. He is shown the truth of how the female Sphinx used the energy of the Ka Stone to reshape reality by the original Sphinx's former advisor Sayge. Nova betrays the Sphinx to join Marvel Man (Vance Astrovik) and Firestar of that world's Mutant Liberation Front as well as Night Thrasher whose parents were murdered in this reality on the orders of the Sphinx. When Nova threatens to murder the Sphinx's cat, she restores reality.


title: Nova (Richard Rider)

text: The second Nova series Nova deals with Nova 0:0, who is much more adept at using his powers than Richard Rider. He often fights Nova in order to test him and to push Nova into using his powers in new ways. It is revealed that this Nova is in fact the alternate reality version of Richard's younger brother Robert. In that reality Robert gained the Nova Force powers instead of Richard and stayed behind to lead the Nova Corps and help Xandar rebuild after the war with the Skrulls. Robert's earth had been destroyed by the Deathstorm while he was off in space. Nova 0:0 would later sacrifice his life preventing the Deathstorm from destroying the 616-version of Earth. He died and was buried on Mars. In the fourth Nova series the Robert Rider of the 616-version of Earth also becomes a member of the Nova Corps (alongside various other humans and non-humans) and again proves capable of using his powers in ways his brother Richard had not.


title: Nova (Richard Rider)

text: Issue #15 of "What If?" contained four stories in which a young widow, a homeless man, Peter Parker, and a criminal became Nova instead of Richard.


title: Nova (Richard Rider)

text: In "What If? Annihilation", the Annihilation Wave reaches Earth in the climactic battle of the super hero Civil War. Nova, Captain America, and Iron Man work together and sacrifice themselves while using a weapon to destroy the wave and save Earth.


title: Nova (Richard Rider)

text: In March 2022, Marvel Studios was revealed to be developing a project featuring Richard Rider / Nova, with Sabir Pirzada writing. It will be a Special Presentation released on Disney+.


title: Minkowski space

text: In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Although initially developed by mathematician Hermann Minkowski for Maxwell's equations of electromagnetism, the mathematical structure of Minkowski spacetime was shown to be implied by the postulates of special relativity.


title: Minkowski space

text: Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure on which special relativity is formulated. While the individual components in Euclidean space and time may differ due to length contraction and time dilation, in Minkowski spacetime, all frames of reference will agree on the total distance in spacetime between events. Because it treats time differently than it treats the 3 spatial dimensions, Minkowski space differs from four-dimensional Euclidean space.


title: Minkowski space

text: In 3-dimensional Euclidean space (e.g., simply "space" in Galilean relativity), the isometry group (the maps preserving the regular Euclidean distance) is the Euclidean group. It is generated by rotations, reflections and translations. When time is appended as a fourth dimension, the further transformations of translations in time and Galilean boosts are added, and the group of all these transformations is called the Galilean group. All Galilean transformations preserve the 3-dimensional Euclidean distance. This distance is purely spatial. Time differences are "separately" preserved as well. This changes in the spacetime of special relativity, where space and time are interwoven.


title: Minkowski space

text: Spacetime is equipped with an indefinite non-degenerate bilinear form, variously called the "Minkowski metric", the "Minkowski norm squared" or "Minkowski inner product" depending on the context. The Minkowski inner product is defined so as to yield the spacetime interval between two events when given their coordinate difference vector as argument. Equipped with this inner product, the mathematical model of spacetime is called Minkowski space. The analogue of the Galilean group for Minkowski space, preserving the spacetime interval (as opposed to the spatial Euclidean distance) is the Poincaré group.


title: Minkowski space

text: As manifolds, Galilean spacetime and Minkowski spacetime are "the same". They differ in what further structures are defined "on" them. The former has the Euclidean distance function and time interval (separately) together with inertial frames whose coordinates are related by Galilean transformations, while the latter has the Minkowski metric together with inertial frames whose coordinates are related by Poincaré transformations.


title: Minkowski space

text: In his second relativity paper in 1905–06 Henri Poincaré showed how, by taking time to be an imaginary fourth spacetime coordinate , where is the speed of light and is the imaginary unit, Lorentz transformations can be visualized as ordinary rotations of the four dimensional Euclidean sphere


title: Minkowski space

text: Poincaré set for convenience. Rotations in planes spanned by two space unit vectors appear in coordinate space as well as in physical spacetime as Euclidean rotations and are interpreted in the ordinary sense. The "rotation" in a plane spanned by a space unit vector and a time unit vector, while formally still a rotation in coordinate space, is a Lorentz boost in physical spacetime with "real" inertial coordinates. The analogy with Euclidean rotations is only partial since the radius of the sphere is actually imaginary which turns rotations into rotations in hyperbolic space


title: Minkowski space

text: This idea, which was mentioned only briefly by Poincaré, was elaborated by Minkowski in a paper in German published in 1908 called "The Fundamental Equations for Electromagnetic Processes in Moving Bodies". Minkowski, using this formulation, restated the then-recent theory of relativity of Einstein. In particular, by restating the Maxwell equations as a symmetrical set of equations in the four variables combined with redefined vector variables for electromagnetic quantities, he was able to show directly and very simply their invariance under Lorentz transformation. He also made other important contributions and used matrix notation for the first time in this context.


title: Minkowski space

text: From his reformulation he concluded that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional spacetime continuum.


title: Minkowski space

text: In a further development in his 1908 "Space and Time" lecture, Minkowski gave an alternative formulation of this idea that used a real time coordinate instead of an imaginary one, representing the four variables of space and time in coordinate form in a four dimensional real vector space. Points in this space correspond to events in spacetime. In this space, there is a defined light-cone associated with each point, and events not on the light-cone are classified by their relation to the apex as "spacelike" or "timelike". It is principally this view of spacetime that is current nowadays, although the older view involving imaginary time has also influenced special relativity.


title: Minkowski space

text: In the English translation of Minkowski's paper, the Minkowski metric as defined below is referred to as the "line element". The Minkowski inner product of below appears unnamed when referring to orthogonality (which he calls "normality") of certain vectors, and the Minkowski norm squared is referred to (somewhat cryptically, perhaps this is translation dependent) as "sum".


title: Minkowski space

text: Minkowski's principal tool is the Minkowski diagram, and he uses it to define concepts and demonstrate properties of Lorentz transformations (e.g. proper time and length contraction) and to provide geometrical interpretation to the generalization of Newtonian mechanics to relativistic mechanics. For these special topics, see the referenced articles, as the presentation below will be principally confined to the mathematical structure (Minkowski metric and from it derived quantities and the Poincaré group as symmetry group of spacetime) "following" from the invariance of the spacetime interval on the spacetime manifold as consequences of the postulates of special relativity, not to specific application or "derivation" of the invariance of the spacetime interval. This structure provides the background setting of all present relativistic theories, barring general relativity for which flat Minkowski spacetime still provides a springboard as curved spacetime is locally Lorentzian.


title: Minkowski space

text: Where is velocity, and , , and are Cartesian coordinates in 3-dimensional space, and is the constant representing the universal speed limit, and is time, the four-dimensional vector is classified according to the sign of . A vector is timelike if , spacelike if , and null or lightlike if . This can be expressed in terms of the sign of as well, which depends on the signature. The classification of any vector will be the same in all frames of reference that are related by a Lorentz transformation (but not by a general Poincaré transformation because the origin may then be displaced) because of the invariance of the interval.


title: Minkowski space

text: The set of all null vectors at an event of Minkowski space constitutes the light cone of that event. Given a timelike vector , there is a worldline of constant velocity associated with it, represented by a straight line in a Minkowski diagram.


title: Minkowski space

text: Once a direction of time is chosen, timelike and null vectors can be further decomposed into various classes. For timelike vectors one has


title: Minkowski space

text: An orthonormal basis for Minkowski space necessarily consists of one timelike and three spacelike unit vectors. If one wishes to work with non-orthonormal bases it is possible to have other combinations of vectors. For example, one can easily construct a (non-orthonormal) basis consisting entirely of null vectors, called a null basis.


title: Minkowski space

text: Vector fields are called timelike, spacelike or null if the associated vectors are timelike, spacelike or null at each point where the field is defined.


title: Minkowski space

text: Time-like vectors have special importance in the theory of relativity as they correspond to events which are accessible to the observer at (0, 0, 0, 0) with a speed less than that of light. Of most interest are time-like vectors which are "similarly directed" i.e. all either in the forward or in the backward cones. Such vectors have several properties not shared by space-like vectors. These arise because both forward and backward cones are convex whereas the space-like region is not convex.


title: Minkowski space

text: "Positivity of scalar product": An important property is that the scalar product of two similarly directed time-like vectors is always positive. This can be seen from the reversed Cauchy–Schwarz inequality below. It follows that if the scalar product of two vectors is zero then one of these at least, must be space-like. The scalar product of two space-like vectors can be positive or negative as can be seen by considering the product of two space-like vectors having orthogonal spatial components and times either of different or the same signs.


title: Minkowski space

text: Using the positivity property of time-like vectors it is easy to verify that a linear sum with positive coefficients of similarly directed time-like vectors is also similarly directed time-like (the sum remains within the light-cone because of convexity).


title: Minkowski space

text: "The reversed Cauchy inequality" is another consequence of the convexity of either light-cone. For two distinct similarly directed time-like vectors and this inequality is


title: Minkowski space

text: It is assumed below that spacetime is endowed with a coordinate system corresponding to an inertial frame. This provides an "origin", which is necessary in order to be able to refer to spacetime as being modeled as a vector space. This is not really "physically" motivated in that a canonical origin ("central" event in spacetime) should exist. One can get away with less structure, that of an affine space, but this would needlessly complicate the discussion and would not reflect how flat spacetime is normally treated mathematically in modern introductory literature.


title: Minkowski space

text: For an overview, Minkowski space is a -dimensional real vector space equipped with a nondegenerate, symmetric bilinear form on the tangent space at each point in spacetime, here simply called the "Minkowski inner product", with metric signature either or . The tangent space at each event is a vector space of the same dimension as spacetime, .


title: Minkowski space

text: In practice, one need not be concerned with the tangent spaces. The vector space nature of Minkowski space allows for the canonical identification of vectors in tangent spaces at points (events) with vectors (points, events) in Minkowski space itself. See e.g. or These identifications are routinely done in mathematics. They can be expressed formally in Cartesian coordinates as


title: Minkowski space

text: Here and are any two events and the second basis vector identification is referred to as parallel transport. The first identification is the canonical identification of vectors in the tangent space at any point with vectors in the space itself. The appearance of basis vectors in tangent spaces as first order differential operators is due to this identification. It is motivated by the observation that a geometrical tangent vector can be associated in a one-to-one manner with a directional derivative operator on the set of smooth functions. This is promoted to a "definition" of tangent vectors in manifolds "not" necessarily being embedded in . This definition of tangent vectors is not the only possible one as ordinary "n"-tuples can be used as well.


title: Minkowski space

text: A tangent vector at a point may be defined, here specialized to Cartesian coordinates in Lorentz frames, as column vectors associated to "each" Lorentz frame related by Lorentz transformation such that the vector in a frame related to some frame by transforms according to . This is the "same" way in which the coordinates transform. Explicitly,


title: Minkowski space

text: For some purposes it is desirable to identify tangent vectors at a point with "displacement vectors" at , which is, of course, admissible by essentially the same canonical identification. The identifications of vectors referred to above in the mathematical setting can correspondingly be found in a more physical and explicitly geometrical setting in . They offer various degree of sophistication (and rigor) depending on which part of the material one chooses to read.


title: Minkowski space

text: The metric signature refers to which sign the Minkowski inner product yields when given space ("spacelike" to be specific, defined further down) and time basis vectors ("timelike") as arguments. Further discussion about this theoretically inconsequential, but practically necessary, choice for purposes of internal consistency and convenience is deferred to the hide box below.


title: Minkowski space

text: In general, but with several exceptions, mathematicians and general relativists prefer spacelike vectors to yield a positive sign, , while particle physicists tend to prefer timelike vectors to yield a positive sign, . Authors covering several areas of physics, e.g. Steven Weinberg and Landau and Lifshitz ( and respectively) stick to one choice regardless of topic. Arguments for the former convention include "continuity" from the Euclidean case corresponding to the non-relativistic limit . Arguments for the latter include that minus signs, otherwise ubiquitous in particle physics, go away. Yet other authors, especially of introductory texts, e.g. , do "not" choose a signature at all, but instead opt to coordinatize spacetime such that the time "coordinate" (but not time itself!) is imaginary. This removes the need of the "explicit" introduction of a metric tensor (which may seem as an extra burden in an introductory course), and one needs "not" be concerned with covariant vectors and contravariant vectors (or raising and lowering indices) to be described below. The inner product is instead effected by a straightforward extension of the dot product in to . This works in the flat spacetime of special relativity, but not in the curved spacetime of general relativity, see (who, by the way use ). MTW also argues that it hides the true "indefinite" nature of the metric and the true nature of Lorentz boosts, which aren't rotations. It also needlessly complicates the use of tools of differential geometry that are otherwise immediately available and useful for geometrical description and calculation – even in the flat spacetime of special relativity, e.g. of the electromagnetic field.


title: Minkowski space

text: Mathematically associated to the bilinear form is a tensor of type at each point in spacetime, called the "Minkowski metric". The Minkowski metric, the bilinear form, and the Minkowski inner product are all the same object; it is a bilinear function that accepts two (contravariant) vectors and returns a real number. In coordinates, this is the matrix representing the bilinear form.


title: Minkowski space

text: For comparison, in general relativity, a Lorentzian manifold is likewise equipped with a metric tensor , which is a nondegenerate symmetric bilinear form on the tangent space at each point of . In coordinates, it may be represented by a matrix "depending on spacetime position". Minkowski space is thus a comparatively simple special case of a Lorentzian manifold. Its metric tensor is in coordinates the same symmetric matrix at every point of , and its arguments can, per above, be taken as vectors in spacetime itself.


title: Minkowski space

text: Introducing more terminology (but not more structure), Minkowski space is thus a pseudo-Euclidean space with total dimension and signature or . Elements of Minkowski space are called events. Minkowski space is often denoted or to emphasize the chosen signature, or just . It is perhaps the simplest example of a pseudo-Riemannian manifold.


title: Minkowski space

text: Then mathematically, the metric is a bilinear form on an abstract four-dimensional real vector space formula_11, that is,


title: Minkowski space

text: where formula_13 has signature formula_14, and signature is a coordinate-invariant property of formula_13. The space of bilinear maps forms a vector space which can be identified with formula_16, and formula_13 may be equivalently viewed as an element of this space. By making a choice of orthonormal basis formula_18, we can identify formula_19 with the space formula_20. The notation is meant to emphasise the fact that formula_21 and formula_22 are not just vector spaces but have added structure. formula_23.


title: Minkowski space

text: An interesting example of non-inertial coordinates for (part of) Minkowski spacetime are the Born coordinates. Another useful set of coordinates are the light-cone coordinates.


title: Minkowski space

text: The Minkowski inner product is not an inner product, since it is not positive-definite, i.e. the quadratic form need not be positive for nonzero . The positive-definite condition has been replaced by the weaker condition of non-degeneracy. The bilinear form is said to be "indefinite".


title: Minkowski space

text: The Minkowski metric is the metric tensor of Minkowski space. It is a pseudo-Euclidean metric, or more generally a "constant" pseudo-Riemannian metric in Cartesian coordinates. As such it is a nondegenerate symmetric bilinear form, a type tensor. It accepts two arguments , vectors in , the tangent space at in . Due to the above-mentioned canonical identification of with itself, it accepts arguments with both and in .


title: Minkowski space

text: As a notational convention, vectors in , called 4-vectors, are denoted in italics, and not, as is common in the Euclidean setting, with boldface . The latter is generally reserved for the -vector part (to be introduced below) of a -vector.


title: Minkowski space

text: yields an inner product-like structure on , previously and also henceforth, called the "Minkowski inner product", similar to the Euclidean inner product, but it describes a different geometry. It is also called the "relativistic dot product". If the two arguments are the same,


title: Minkowski space

text: the resulting quantity will be called the "Minkowski norm squared". The Minkowski inner product satisfies the following properties.


title: Minkowski space

text: The first two conditions imply bilinearity. The defining "difference" between a pseudo-inner product and an inner product proper is that the former is "not" required to be positive definite, that is, is allowed.


title: Minkowski space

text: The most important feature of the inner product and norm squared is that "these are quantities unaffected by Lorentz transformations". In fact, it can be taken as the defining property of a Lorentz transformation that it preserves the inner product (i.e. the value of the corresponding bilinear form on two vectors). This approach is taken more generally for "all" classical groups definable this way in classical group. There, the matrix is identical in the case (the Lorentz group) to the matrix to be displayed below.


title: Minkowski space

text: Two vectors and are said to be orthogonal if . For a geometric interpretation of orthogonality in the special case when and (or vice versa), see hyperbolic orthogonality.


title: Minkowski space

text: A vector is called a unit vector if . A basis for consisting of mutually orthogonal unit vectors is called an orthonormal basis.


title: Minkowski space

text: For a given inertial frame, an orthonormal basis in space, combined with the unit time vector, forms an orthonormal basis in Minkowski space. The number of positive and negative unit vectors in any such basis is a fixed pair of numbers, equal to the signature of the bilinear form associated with the inner product. This is Sylvester's law of inertia.


title: Minkowski space

text: More terminology (but not more structure): The Minkowski metric is a pseudo-Riemannian metric, more specifically, a Lorentzian metric, even more specifically, "the" Lorentz metric, reserved for -dimensional flat spacetime with the remaining ambiguity only being the signature convention.


title: Minkowski space

text: From the second postulate of special relativity, together with homogeneity of spacetime and isotropy of space, it follows that the spacetime interval between two arbitrary events called and is:


title: Minkowski space

text: This quantity is not consistently named in the literature. The interval is sometimes referred to as the square root of the interval as defined here.


title: Minkowski space

text: The invariance of the interval under coordinate transformations between inertial frames follows from the invariance of


title: Minkowski space

text: Where is a formula_33 matrix associated with . While possibly confusing, it is common practice to denote with just . The matrix is read off from the explicit bilinear form as


title: Minkowski space

text: For definiteness and shorter presentation, the signature is adopted below. This choice (or the other possible choice) has no (known) physical implications. The symmetry group preserving the bilinear form with one choice of signature is isomorphic (under the map given here) with the symmetry group preserving the other choice of signature. This means that both choices are in accord with the two postulates of relativity. Switching between the two conventions is straightforward. If the metric tensor has been used in a derivation, go back to the earliest point where it was used, substitute for , and retrace forward to the desired formula with the desired metric signature.


title: Minkowski space

text: A standard or orthonormal basis for Minkowski space is a set of four mutually orthogonal vectors such that


title: Minkowski space

text: Relative to a standard basis, the components of a vector are written where the Einstein notation is used to write . The component is called the timelike component of while the other three components are called the spatial components. The spatial components of a -vector may be identified with a -vector .


title: Minkowski space

text: There are many possible choices of standard basis obeying the condition formula_40 Any two such bases are related in some sense by a Lorentz transformation, either by a change-of-basis matrix formula_41, a real formula_33 matrix satisfying


title: Minkowski space

text: or formula_44 a linear map on the abstract vector space satisfying, for any pair of vectors formula_45


title: Minkowski space

text: Then if we have two different bases formula_47 and formula_48, we can write formula_49 or formula_50. While it might be tempting to think of formula_41 and formula_52 as the same thing, mathematically they are elements of different spaces, and act on the space of standard bases from different sides.


title: Minkowski space

text: Technically, a non-degenerate bilinear form provides a map between a vector space and its dual; in this context, the map is between the tangent spaces of and the cotangent spaces of . At a point in , the tangent and cotangent spaces are dual vector spaces (so the dimension of the cotangent space at an event is also ). Just as an authentic inner product on a vector space with one argument fixed, by Riesz representation theorem, may be expressed as the action of a linear functional on the vector space, the same holds for the Minkowski inner product of Minkowski space.


title: Minkowski space

text: Thus if are the components of a vector in a tangent space, then are the components of a vector in the cotangent space (a linear functional). Due to the identification of vectors in tangent spaces with vectors in itself, this is mostly ignored, and vectors with lower indices are referred to as covariant vectors. In this latter interpretation, the covariant vectors are (almost always implicitly) identified with vectors (linear functionals) in the dual of Minkowski space. The ones with upper indices are contravariant vectors. In the same fashion, the inverse of the map from tangent to cotangent spaces, explicitly given by the inverse of in matrix representation, can be used to define raising of an index. The components of this inverse are denoted . It happens that . These maps between a vector space and its dual can be denoted (eta-flat) and (eta-sharp) by the musical analogy.


title: Minkowski space

text: Contravariant and covariant vectors are geometrically very different objects. The first can and should be thought of as arrows. A linear functional can be characterized by two objects: its kernel, which is a hyperplane passing through the origin, and its norm. Geometrically thus, covariant vectors should be viewed as a set of hyperplanes, with spacing depending on the norm (bigger = smaller spacing), with one of them (the kernel) passing through the origin. The mathematical term for a covariant vector is 1-covector or 1-form (though the latter is usually reserved for covector "fields").


title: Minkowski space

text: The electromagnetic field tensor is a differential 2-form, which geometrical description can as well be found in MTW.


title: Minkowski space

text: One may, of course, ignore geometrical views all together (as is the style in e.g. and ) and proceed algebraically in a purely formal fashion. The time-proven robustness of the formalism itself, sometimes referred to as index gymnastics, ensures that moving vectors around and changing from contravariant to covariant vectors and vice versa (as well as higher order tensors) is mathematically sound. Incorrect expressions tend to reveal themselves quickly.


title: Minkowski space

text: Given a bilinear form formula_53, the lowered version of a vector can be thought of as the partial evaluation of formula_13, that is, there is an associated partial evaluation map


title: Minkowski space

text: The lowered vector formula_56 is then the dual map formula_57. Note it does not matter which argument is partially evaluated due to symmetry of formula_13.


title: Minkowski space

text: Non-degeneracy is then equivalent to injectivity of the partial evaluation map, or equivalently non-degeneracy tells us the kernel of the map is trivial. In finite dimension, as we have here, and noting that the dimension of a finite dimensional space is equal to the dimension of the dual, this is enough to conclude the partial evaluation map is a linear isomorphism from formula_21 to formula_60. This then allows definition of the inverse partial evaluation map,


title: Minkowski space

text: where the two different usages of formula_63 can be told apart by the argument each is evaluated on. This can then be used to raise indices. If we work in a coordinate basis, we find that the metric formula_63 is indeed the matrix inverse to formula_65


title: Minkowski space

text: The present purpose is to show semi-rigorously how "formally" one may apply the Minkowski metric to two vectors and obtain a real number, i.e. to display the role of the differentials, and how they disappear in a calculation. The setting is that of smooth manifold theory, and concepts such as convector fields and exterior derivatives are introduced.


title: Minkowski space

text: A full-blown version of the Minkowski metric in coordinates as a tensor field on spacetime has the appearance


title: Minkowski space

text: Explanation: The coordinate differentials are 1-form fields. They are defined as the exterior derivative of the coordinate functions . These quantities evaluated at a point provide a basis for the cotangent space at . The tensor product (denoted by the symbol ) yields a tensor field of type , i.e. the type that expects two contravariant vectors as arguments. On the right hand side, the symmetric product (denoted by the symbol or by juxtaposition) has been taken. The equality holds since, by definition, the Minkowski metric is symmetric. The notation on the far right is also sometimes used for the related, but different, line element. It is "not" a tensor. For elaboration on the differences and similarities, see


title: Minkowski space

text: "Tangent" vectors are, in this formalism, given in terms of a basis of differential operators of the first order,


title: Minkowski space

text: where is an event. This operator applied to a function gives the directional derivative of at in the direction of increasing with fixed. They provide a basis for the tangent space at .


title: Minkowski space

text: The exterior derivative of a function is a covector field, i.e. an assignment of a cotangent vector to each point , by definition such that


title: Minkowski space

text: for each vector field . A vector field is an assignment of a tangent vector to each point . In coordinates can be expanded at each point in the basis given by the . Applying this with , the coordinate function itself, and , called a "coordinate vector field", one obtains


title: Minkowski space

text: Since this relation holds at each point , the provide a basis for the cotangent space at each and the bases and are dual to each other,


title: Minkowski space

text: for general one-forms on a tangent space and general tangent vectors . (This can be taken as a definition, but may also be proved in a more general setting.)


title: Minkowski space

text: Thus when the metric tensor is fed two vectors fields , both expanded in terms of the basis coordinate vector fields, the result is


title: Minkowski space

text: where , are the "component functions" of the vector fields. The above equation holds at each point , and the relation may as well be interpreted as the Minkowski metric at applied to two tangent vectors at .


title: Minkowski space

text: As mentioned, in a vector space, such as that modelling the spacetime of special relativity, tangent vectors can be canonically identified with vectors in the space itself, and vice versa. This means that the tangent spaces at each point are canonically identified with each other and with the vector space itself. This explains how the right hand side of the above equation can be employed directly, without regard to spacetime point the metric is to be evaluated and from where (which tangent space) the vectors come from.


title: Minkowski space

text: where now , i.e., is still a metric tensor but now depending on spacetime and is a solution of Einstein's field equations. Moreover, "must" be tangent vectors at spacetime point and can no longer be moved around freely.


title: Minkowski space

text: Suppose "x" ∈ "M" is timelike. Then the simultaneous hyperplane for x is formula_74 Since this hyperplane varies as "x" varies, there is a relativity of simultaneity in Minkowski space.


title: Minkowski space

text: A Lorentzian manifold is a generalization of Minkowski space in two ways. The total number of spacetime dimensions is not restricted to be ( or more) and a Lorentzian manifold need not be flat, i.e. it allows for curvature.


title: Minkowski space

text: Complexified Minkowski space is defined as . Its real part is the Minkowski space of four-vectors, such as the four-velocity and the four-momentum, which are independent of the choice of orientation of the space. The imaginary part, on the other hand, may consist of four-pseudovectors, such as angular velocity and magnetic moment, which change their direction with a change of orientation. We introduce a pseudoscalar which also changes sign with a change of orientation. Thus, elements of are independent of the choice of the orientation.


title: Minkowski space

text: The inner product-like structure on is defined as for any . A relativistic pure spin of an electron or any half spin particle is described by as , where is the four-velocity of the particle, satisfying and is the 4D spin vector, which is also the Pauli–Lubanski pseudovector satisfying and .


title: Minkowski space

text: Minkowski space refers to a mathematical formulation in four dimensions. However, the mathematics can easily be extended or simplified to create an analogous generalized Minkowski space in any number of dimensions. If , -dimensional Minkowski space is a vector space of real dimension on which there is a constant Minkowski metric of signature or . These generalizations are used in theories where spacetime is assumed to have more or less than dimensions. String theory and M-theory are two examples where . In string theory, there appears conformal field theories with spacetime dimensions.


title: Minkowski space

text: de Sitter space can be formulated as a submanifold of generalized Minkowski space as can the model spaces of hyperbolic geometry (see below).


title: Minkowski space

text: As a "flat spacetime", the three spatial components of Minkowski spacetime always obey the Pythagorean Theorem. Minkowski space is a suitable basis for special relativity, a good description of physical systems over finite distances in systems without significant gravitation. However, in order to take gravity into account, physicists use the theory of general relativity, which is formulated in the mathematics of a non-Euclidean geometry. When this geometry is used as a model of physical space, it is known as curved space.


title: Minkowski space

text: Even in curved space, Minkowski space is still a good description in an infinitesimal region surrounding any point (barring gravitational singularities). More abstractly, we say that in the presence of gravity spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Thus, the structure of Minkowski space is still essential in the description of general relativity.


title: Minkowski space

text: The meaning of the term "geometry" for the Minkowski space depends heavily on the context. Minkowski space is not endowed with a Euclidean geometry, and not with any of the generalized Riemannian geometries with intrinsic curvature, those exposed by the "model spaces" in hyperbolic geometry (negative curvature) and the geometry modeled by the sphere (positive curvature). The reason is the indefiniteness of the Minkowski metric. Minkowski space is, in particular, not a metric space and not a Riemannian manifold with a Riemannian metric. However, Minkowski space contains submanifolds endowed with a Riemannian metric yielding hyperbolic geometry.


title: Minkowski space

text: Model spaces of hyperbolic geometry of low dimension, say or , "cannot" be isometrically embedded in Euclidean space with one more dimension, i.e. or respectively, with the Euclidean metric , disallowing easy visualization. By comparison, model spaces with positive curvature are just spheres in Euclidean space of one higher dimension. Hyperbolic spaces "can" be isometrically embedded in spaces of one more dimension when the embedding space is endowed with the Minkowski metric .


title: Minkowski space

text: in generalized Minkowski space of spacetime dimension . This is one of the surfaces of transitivity of the generalized Lorentz group. The induced metric on this submanifold,


title: Minkowski space

text: the pullback of the Minkowski metric under inclusion, is a Riemannian metric. With this metric is a Riemannian manifold. It is one of the model spaces of Riemannian geometry, the hyperboloid model of hyperbolic space. It is a space of constant negative curvature . The in the upper index refers to an enumeration of the different model spaces of hyperbolic geometry, and the for its dimension. A corresponds to the Poincaré disk model, while corresponds to the Poincaré half-space model of dimension .


title: Minkowski space

text: In the definition above is the inclusion map and the superscript star denotes the pullback. The present purpose is to describe this and similar operations as a preparation for the actual demonstration that actually is a hyperbolic space.


title: Minkowski space

text: In order to exhibit the metric it is necessary to pull it back via a suitable "parametrization". A parametrization of a submanifold of is a map whose range is an open subset of . If has the same dimension as , a parametrization is just the inverse of a coordinate map . The parametrization to be used is the inverse of "hyperbolic stereographic projection". This is illustrated in the figure to the left for . It is instructive to compare to stereographic projection for spheres.


title: Minkowski space

text: One computes according to the standard rules for computing differentials (though one is really computing the rigorously defined exterior derivatives),


title: Minkowski space

text: This last equation shows that the metric on the ball is identical to the Riemannian metric in the Poincaré ball model, another standard model of hyperbolic geometry.


title: Presidency of George W. Bush

text: George W. Bush's tenure as the 43rd president of the United States began with his first inauguration on January 20, 2001, and ended on January 20, 2009. Bush, a Republican from Texas, took office following a narrow victory over Democratic incumbent vice president Al Gore in the 2000 presidential election. Four years later, in the 2004 presidential election, he defeated Democrat nominee John Kerry to win re-election. Bush was succeeded by Democrat Barack Obama, who won the 2008 presidential election. Bush, the 43rd president, is the eldest son of the 41st president, George H. W. Bush.


title: Presidency of George W. Bush

text: A decisive event reshaping his administration was the terrorist attacks on September 11, 2001. In its aftermath, Congress created the United States Department of Homeland Security and Bush declared a global war on terrorism. He ordered an invasion of Afghanistan to overthrow the Taliban, destroy the terrorist group al-Qaeda, and capture Osama bin Laden. He also signed the controversial Patriot Act in order to authorize surveillance of suspected terrorists. In 2003, Bush ordered an invasion of Iraq, alleging that the Saddam Hussein regime possessed weapons of mass destruction. Intense criticism came when neither WMD stockpiles nor evidence of an operational relationship with al-Qaeda were found. Before 9/11, Bush had pushed through a $1.3 trillion tax cut program and the No Child Left Behind Act, a major education bill. He also pushed for socially conservative efforts, such as the Partial-Birth Abortion Ban Act and faith-based welfare initiatives. Also in 2003, he signed the Medicare Prescription Drug, Improvement, and Modernization Act, which created Medicare Part D.


title: Presidency of George W. Bush

text: During his second term, Bush reached multiple free trade agreements and successfully nominated John Roberts and Samuel Alito to the Supreme Court. He sought major changes to Social Security and immigration laws, but both efforts failed. The wars in Afghanistan and Iraq continued, and in 2007 he launched a surge of troops in Iraq. The Bush administration's response to Hurricane Katrina and the dismissal of U.S. attorneys controversy came under attack, with a drop in his approval ratings. A global meltdown in financial markets dominated his last days in office as policymakers looked to avert a major economic disaster, and he established the Troubled Asset Relief Program (TARP) to buy toxic assets from financial institutions.


title: Presidency of George W. Bush

text: At various points in his presidency, Bush was among both the most popular and unpopular presidents in U.S. history. He received the highest recorded approval ratings in the wake of the September 11 attacks, but also one of the lowest such ratings during the 2007–2008 financial crisis. Although public favorability of Bush has improved since he left office, his presidency has generally been rated as below-average by scholars.


title: Presidency of George W. Bush

text: The oldest son of George H. W. Bush, the 41st president of the United States, George W. Bush emerged as a presidential contender in his own right with his victory in the 1994 Texas gubernatorial election. After winning re-election by a decisive margin in the 1998 Texas gubernatorial election, Bush became the widely acknowledged front-runner in the race for the Republican nomination in the 2000 presidential election. In the years preceding the 2000 election, Bush established a stable of advisers, including supply-side economics advocate Lawrence B. Lindsey and foreign policy expert Condoleezza Rice. With a financial team led by Karl Rove and Ken Mehlman, Bush built up a commanding financial advantage over other prospective Republican candidates. Though several prominent Republicans declined to challenge Bush, Arizona senator John McCain launched a spirited challenge that was supported by many moderates and foreign policy hawks. McCain's loss in the South Carolina primary effectively ended the 2000 Republican primaries, and Bush was officially nominated for president at the 2000 Republican National Convention. Bush selected former secretary of defense Dick Cheney as his running mate; though Cheney offered little electoral appeal and had health problems, Bush believed that Cheney's extensive experience would make him a valuable governing partner.


title: Presidency of George W. Bush

text: With President Bill Clinton term-limited, the Democrats nominated Vice President Al Gore for president. Bush's campaign emphasized their own candidate's character in contrast with that of Clinton, who had been embroiled in the Lewinsky scandal. Bush held a substantial lead in several polls taken after the final debate in October, but the unearthing of Bush's 1976 DUI arrest appeared to sap his campaign's momentum. By the end of election night, Florida emerged as the key state in the election, as whichever candidate won the state would win the presidency. Bush held an extremely narrow lead in the vote by the end of election night, triggering an automatic recount. The Florida Supreme Court ordered a partial manual recount, but the Supreme Court of the United States effectively ordered an end to this process, on equal protection grounds, in the case of "Bush v. Gore", leaving Bush with a victory in both the state and the election. Though Gore narrowly won a plurality of the nationwide popular vote, Bush won the presidential election with 271 electoral votes compared to Gore's 266. In the concurrent congressional elections, Republicans retained a narrow majority in the House, but lost five seats in the Senate, leaving the partisan balance in the Senate at fifty Republicans and fifty Democrats.


title: Presidency of George W. Bush

text: Rejecting the idea of a powerful White House chief of staff, Bush had high-level officials report directly to him rather than Chief of Staff Andrew Card. Vice President Cheney emerged as the most powerful individual in the White House aside from Bush himself. Bush brought to the White House several individuals who had worked under him in Texas, including Senior Counselor Karen Hughes, Senior Adviser Karl Rove, legal counsel Alberto Gonzales, and Staff Secretary Harriet Miers. Other important White House staff appointees included Margaret Spellings as a domestic policy adviser, Michael Gerson as chief speechwriter, and Joshua Bolten and Joe Hagin as White House deputy chiefs of staff. Paul H. O'Neill, who had served as deputy director of the OMB under Gerald Ford, was appointed secretary of the treasury, while former Missouri senator John Ashcroft was appointed attorney general.


title: Presidency of George W. Bush

text: As Bush had little foreign policy experience, his appointments would serve an important role in shaping U.S. foreign policy during his tenure. Several of his initial top foreign policy appointees had served in his father's administration; Vice President Cheney had been secretary of defense, National Security Adviser Condoleezza Rice had served on the National Security Council, and deputy secretaries Paul Wolfowitz and Richard Armitage had also served in important roles. Secretary of State Colin Powell had served as chairman of the Joint Chiefs of Staff under the first president Bush. Bush had long admired Powell, and the former general was Bush's first choice for the position. Secretary of Defense Donald Rumsfeld, who had served in the same position during the Ford administration, rounded out the key figures in the national security team. Rumsfeld and Cheney, who had served together in the Ford administration, emerged as the leading foreign policy figures during Bush's first term.


title: Presidency of George W. Bush

text: O'Neill, who opposed the Iraq War and feared that the Bush tax cuts would lead to deficits, was replaced by John W. Snow in February 2003. Frustrated by the decisions of the Bush administration, particularly the launching of the Iraq War, Powell resigned following the 2004 elections. He was replaced by Rice, while then-deputy national security adviser Stephen Hadley took Rice's former position. Most of Bush's top staffers stayed on after the 2004 election, although Spellings joined the Cabinet as secretary of education and Gonzales replaced Ashcroft as attorney general. In early 2006, Card left the White House in the wake of the Dubai Ports World controversy and several botched White House initiatives, and he was replaced by Joshua Bolten. Bolten stripped Rove of some of his responsibilities and convinced Henry Paulson, the head of Goldman Sachs, to replace Snow as secretary of the treasury.


title: Presidency of George W. Bush

text: After the 2006 elections, Rumsfeld was replaced by former CIA director Robert Gates. The personnel shake-ups left Rice as one of the most prominent individuals in the administration, and she played a strong role in directing Bush's second term foreign policy. Gonzales and Rove both left in 2007 after controversy regarding the dismissal of U.S. attorneys, and Gonzales was replaced by Michael Mukasey, a former federal judge.


title: Presidency of George W. Bush

text: After the 2004 election, many expected that the aging Chief Justice William Rehnquist would step down from the United States Supreme Court. Cheney and White House Counsel Harriet Miers selected two widely respected conservatives, D.C. Circuit Court of Appeals judge John Roberts and Fourth Circuit judge Michael Luttig, as the two finalists. In June 2005, Justice Sandra Day O'Connor unexpectedly announced that she would retire from the court, and Bush nominated Roberts for her position the following month. After Rehnquist died in September, Bush briefly considered elevating Associate Justice Antonin Scalia to the position of chief justice, but instead chose to nominate Roberts for the position. Roberts won confirmation from the Senate in a 78–22 vote, with all Republicans and a narrow majority of Democrats voting to confirm Roberts.


title: Presidency of George W. Bush

text: To replace O'Connor, the Bush administration wanted to find a female nominee, but was unsatisfied with the conventional options available. Bush settled on Miers, who had never served as a judge, but who had worked as a corporate lawyer and White House staffer. Her nomination immediately faced opposition from conservatives (and liberals) who were wary of her unproven ideology and lack of judicial experience. After Senate Majority Leader Bill Frist informed Bush that Miers did not have the votes necessary to win confirmation, Miers withdrew from consideration. Bush then nominated Samuel Alito, who received strong support from conservatives but faced opposition from Democrats. Alito won confirmation in a 58–42 vote in January 2006. In the years immediately after Roberts and Alito took office, the Roberts Court was generally more conservative than the preceding Rehnquist Court, largely because Alito tended to be more conservative than O'Connor had been.


title: Presidency of George W. Bush

text: Bush also appointed 62 judges to the United States Courts of Appeals, 261 judges to the United States district courts, and 2 judges to the United States Court of International Trade. Among them were two future Supreme Court associate justices: Neil Gorsuch to a seat on the Court of Appeals for the Tenth Circuit in 2006, and Brett Kavanaugh to the Court of Appeals District of Columbia Circuit in 2006.


title: Presidency of George W. Bush

text: Bush's promise to cut taxes was the centerpiece of his 2000 presidential campaign, and upon taking office, he made tax cuts his first major legislative priority. A budget surplus had developed during the Bill Clinton administration, and with the Federal Reserve chairman Alan Greenspan's support, Bush argued that the best use of the surplus was to lower taxes. By the time Bush took office, reduced economic growth had led to less robust federal budgetary projections, but Bush maintained that tax cuts were necessary to boost economic growth. After Treasury secretary Paul O'Neill expressed concerns over the tax cut's size and the possibility of future deficits, Vice President Cheney took charge of writing the bill, which the administration proposed to Congress in March 2001.


title: Presidency of George W. Bush

text: Bush initially sought a $1.6 trillion tax cut over a ten-year period, but ultimately settled for a $1.35 trillion tax cut. The administration rejected the idea of "triggers" that would phase out the tax reductions should the government again run deficits. The Economic Growth and Tax Relief Reconciliation Act of 2001 won the support of congressional Republicans and a minority of congressional Democrats, and Bush signed it into law in June 2001. The act lowered the top income tax rate from 39 percent to 35 percent, and it also reduced the estate tax. The narrow Republican majority in the Senate necessitated the use of the reconciliation, which in turn necessitated that the tax cuts would phase out in 2011 barring further legislative action.


title: Presidency of George W. Bush

text: After the tax bill was passed, Senator Jim Jeffords left the Republican Party and began caucusing with the Democrats, giving them control of the Senate. After Republicans re-took control of the Senate during the 2002 mid-term elections, Bush proposed further tax cuts. With little support among Democrats, Congress passed the Jobs and Growth Tax Relief Reconciliation Act of 2003, which cut taxes by another $350 billion over 10 years. That law also lowered the capital gains tax and taxes on dividends. Collectively, the Bush tax cuts reduced federal individual tax rates to their lowest level since World War II, and government revenue as a share of gross domestic product declined from 20.9% in 2000 to 16.3% in 2004. Most of the Bush tax cuts were later made permanent by the American Taxpayer Relief Act of 2012, though that act rolled back the tax cuts on top earners.


title: Presidency of George W. Bush

text: Contrary to the rhetoric of the Bush administration and Republicans, the budget deficit increased, leaving many to believe the tax cuts were at fault. Statements by President Bush, Vice President Dick Cheney, and Senate Majority Leader Bill Frist that these tax cuts effectively "paid for themselves" were disputed by the CBPP, the U.S. Treasury Department and the CBO.


title: Presidency of George W. Bush

text: Aside from tax cuts, Bush's other major policy initiative upon taking office was education reform. Bush had a strong personal interest in reforming education, especially regarding the education of low-income and minority groups. He often derided the "soft bigotry of low expectations" for allowing low-income and minority groups to fall behind. Although many conservatives were reluctant to increase federal involvement in education, Bush's success in campaigning on education reform in the 2000 election convinced many Republicans, including Congressman John Boehner of Ohio, to accept an education reform bill that increased federal funding. Seeking to craft a bipartisan bill, Bush courted Democratic senator Ted Kennedy, a leading liberal senator who served as the ranking member on the Senate Committee on Health, Education, and Pensions.


title: Presidency of George W. Bush

text: Bush favored extensive testing to ensure that schools met uniform standards for skills such as reading and math. Bush hoped that testing would make schools more accountable for their performances and provide parents with more information in choosing which schools to send their children. Kennedy shared Bush's concern for the education of impoverished children, but he strongly opposed the president's proposed school vouchers, which would allow parents to use federal funding to pay for private schools. Both men cooperated to pass the No Child Left Behind Act, which dropped the concept of school vouchers but included Bush's idea of nationwide testing. Both houses of Congress registered overwhelming approval for the bill's final version, which Bush signed into law in January 2002. However, Kennedy would later criticize the implementation of the act, arguing that Bush had promised greater federal funding for education.


title: Presidency of George W. Bush

text: Shortly after the September 11 attacks, Bush announced the creation of the Office of Homeland Security and appointed former governor of Pennsylvania Tom Ridge its director. After Congress passed the Homeland Security Act to create the Department of Homeland Security (DHS), Ridge became the first director of the newly created department. The department was charged with overseeing immigration, border control, customs, and the newly established Transportation Security Administration (TSA), which focused on airport security. Though the FBI and CIA remained independent agencies, the DHS was assigned jurisdiction over the Coast Guard, the Immigration and Naturalization Service (which was divided into three agencies), the United States Customs Service (which was also divided into separate agencies), and the Federal Emergency Management Agency. The Homeland Security Act represented the most significant departmental reorganization since the National Security Act of 1947.


title: Presidency of George W. Bush

text: On October 26, 2001, Bush signed into law the Patriot Act. Passed on the president's request, the act permitted increased sharing of intelligence among the U.S. Intelligence Community and expanded the government's domestic authority to conduct surveillance of suspected terrorists. The Patriot Act also authorized the use of roving wiretaps on suspected terrorists and expanded the government's authority to conduct surveillance of suspected "lone wolf" terrorists. Bush also secretly authorized the National Security Agency to conduct warrantless surveillance of communications in and out of the United States.


title: Presidency of George W. Bush

text: McCain's 2000 presidential campaign brought the issue of campaign finance reform to the fore of public consciousness in 2001. McCain and Russ Feingold pushed a bipartisan campaign finance bill in the Senate, while Chris Shays (R-CT) and Marty Meehan (D-MA) led the effort of passing it in the House. In just the second successful use of the discharge petition since the 1980s, a mixture of Democrats and Republicans defied Speaker Dennis Hastert and passed a campaign finance reform bill. The House approved the bill with a 240–189 vote, while the bill passed the Senate in a 60–40 vote, the bare minimum required to overcome the filibuster. Throughout the congressional battle on the bill, Bush declined to take a strong position. However, in March 2002, Bush signed into law the Bipartisan Campaign Reform Act, stating that he thought the law would improve the financing system for elections but was "far from perfect." The law placed several limits on political donations and expenditures, and closed loopholes on contribution limits on donations to political candidates by banning the use of so-called "soft money." Portions of the law restricting independent expenditures would later be struck down by the Supreme Court in the 2010 case of "Citizens United v. FEC".


title: Presidency of George W. Bush

text: After the passage of the Bush tax cuts and the No Child Left Behind Act, Bush turned his domestic focus to healthcare. He sought to expand Medicare so it would also cover the cost of prescription drugs, a program that became known as Medicare Part D. Many congressional Democrats opposed the bill because it did not allow Medicare to negotiate the prices of drugs, while many conservative Republicans opposed the expansion of the government's involvement in healthcare. Assisted by Speaker of the House Dennis Hastert and Senate majority leader Bill Frist, Bush overcame strong opposition and won passage of his Medicare bill. In December 2003, Bush signed the Medicare Prescription Drug, Improvement, and Modernization Act, the largest expansion of Medicare since the program's creation in 1965.


title: Presidency of George W. Bush

text: After winning re-election in 2004, Bush made the partial privatization of Social Security his top domestic priority. He proposed restructuring the program so that citizens could invest some of the money they paid in payroll taxes, which fund the Social Security program. The president argued that Social Security faced an imminent funding crisis and that reform was necessary to ensure its continuing solvency. Bush expected a difficult congressional battle over his proposal, but, as he put it, "I've got political capital, and I intend to spend it." Groups like the AARP strongly opposed the plan, as did moderate Democrats like Max Baucus, who had supported the Bush tax cuts. Ultimately, Bush failed to win the backing of a single congressional Democrat for his plan, and even moderate Republicans like Olympia Snowe and Lincoln Chafee refused to back privatization. In the face of unified opposition, Republicans abandoned Bush's Social Security proposal in mid-2005.


title: Presidency of George W. Bush

text: Hurricane Katrina, one of the largest and most powerful hurricanes ever to strike the United States, ravaged several states along the Gulf of Mexico in August 2005. On a working vacation at his ranch in Texas, Bush initially allowed state and local authorities to respond to the natural disaster. The hurricane made landfall on August 29, devastating the city of New Orleans after the failure of that city's levees. Over eighteen hundred people died in the hurricane, and Bush was widely criticized for his slow response to the disaster. Stung by the public response, Bush removed Federal Emergency Management Agency director Michael D. Brown from office and stated publicly that "Katrina exposed serious problems in our response capability at all levels of government." After Hurricane Katrina, Bush's approval rating fell below 40 percent, where it would remain for the rest of his tenure in office.


title: Presidency of George W. Bush

text: Although he concentrated on other domestic policies during his first term, Bush supported immigration reform throughout his administration. In May 2006, he proposed a five-point plan that would increase border security, establish a guest worker program, and create a path to citizenship for the twelve million illegal immigrants living in the United States. The Senate passed the Comprehensive Immigration Reform Act of 2006, which included many of the president's proposals, but the bill did not pass the House of Representatives. After Democrats took control of Congress in the 2006 mid-term elections, Bush worked with Ted Kennedy to re-introduce the bill as the Comprehensive Immigration Reform Act of 2007. The bill received intense criticism from many conservatives, who had become more skeptical of immigration reform, and it failed to pass the Senate.


title: Presidency of George W. Bush

text: After years of financial deregulation accelerating under the Bush administration, banks lent subprime mortgages to more and more home buyers, causing a housing bubble. Many of these banks also invested in credit default swaps and derivatives that were essentially bets on the soundness of these loans. In response to declining housing prices and fears of an impending recession, the Bush administration arranged passage of the Economic Stimulus Act of 2008. Falling home prices started threatening the financial viability of many institutions, leaving Bear Stearns, a prominent U.S.-based investment bank, on the brink of failure in March 2008. Recognizing the growing threat of a financial crisis, Bush allowed Treasury secretary Paulson to arrange for another bank, JPMorgan Chase, to take over most Bear Stearn's assets. Out of concern that Fannie Mae and Freddie Mac might also fail, the Bush administration put both institutions into conservatorship. Shortly afterwards, the administration learned that Lehman Brothers was on the verge of bankruptcy, but the administration ultimately declined to intervene on behalf of Lehman Brothers.


title: Presidency of George W. Bush

text: Paulson hoped that the financial industry had shored itself up after the failure of Bear Stearns and that the failure of Lehman Brothers would not strongly impact the economy, but news of the failure caused stock prices to tumble and froze credit. Fearing a total financial collapse, Paulson and the Federal Reserve took control of American International Group (AIG), another major financial institution that teetered on the brink of failure. Hoping to shore up the other banks, Bush and Paulson proposed the Emergency Economic Stabilization Act of 2008, which would create the $700 billion Troubled Asset Relief Program (TARP) to buy toxic assets. The House rejected TARP in a 228–205 vote; although support and opposition crossed party lines, only about one-third of the Republican caucus supported the bill. After the Dow Jones Industrial Average dropped 778 points on the day of the House vote, the House and Senate both passed TARP. Bush later extended TARP loans to U.S. automobile companies, which faced their own crisis due to the weak economy. Though TARP helped end the financial crisis, it did not prevent the onset of the Great Recession, which would continue after Bush left office.


title: Presidency of George W. Bush

text: On his first day in office, President Bush reinstated the Mexico City policy, thereby blocking federal aid to foreign groups that offered assistance to women in obtaining abortions. Days later, he announced his commitment to channeling more federal aid to faith-based service organizations, despite the fears of critics that this would dissolve the traditional separation of church and state in the United States. To further this commitment, he created the White House Office of Faith-Based and Community Initiatives to assist faith-based service organizations. In 2003, Bush signed the Partial-Birth Abortion Ban Act, which banned intact dilation and extraction, an abortion procedure.


title: Presidency of George W. Bush

text: Early in his administration, President Bush became personally interested in the issue of stem cell research. The Clinton administration had issued guidelines allowing the federal funding of research utilizing stem cells, and Bush decided to study the situation's ethics before issuing his own executive order on the issue. Evangelical religious groups argued that the research was immoral as it destroyed human embryos, while various advocacy groups touted the potential scientific advances afforded by stem cell research. In August 2001, Bush issued an executive order banning federal funding for research on new stem cell lines; the order allowed research on existing stem cell lines to continue. In July 2006, Bush used his first presidential veto on the Stem Cell Research Enhancement Act, which would have expanded federal funding of embryonic stem cell research. A similar bill was passed in both the House of Representatives and the Senate early in mid-2007 as part of House Speaker Nancy Pelosi's 100-Hour Plan, but was vetoed by Bush.


title: Presidency of George W. Bush

text: After the Supreme Court struck down a state sodomy law in the 2003 case of "Lawrence v. Texas", conservatives began pushing for the Federal Marriage Amendment, which would define marriage as a union between a man and a woman. Bush endorsed this proposal and made it part of his campaign during the 2004 and 2006 election cycles. However, President Bush did break from his party in his tolerance of civil unions for homosexual couples.


title: Presidency of George W. Bush

text: Bush was staunchly opposed to euthanasia and supported Attorney General John Ashcroft's ultimately unsuccessful suit against the Oregon Death with Dignity Act. However, while he was governor of Texas, Bush had signed a law giving hospitals the authority to remove life support from terminally ill patients against the wishes of spouses or parents, if the doctors deemed it as medically appropriate. This perceived inconsistency in policy became an issue in 2005, when Bush signed controversial legislation to initiate federal intervention in the court battle of Terri Schiavo, a comatose Florida woman who ultimately died.


title: Presidency of George W. Bush

text: In March 2001, the Bush administration announced that it would not implement the Kyoto Protocol, an international treaty signed in 1997 that required nations to reduce their greenhouse gas emissions. The administration argued that ratifying the treaty would unduly restrict U.S. growth while failing to adequately limit emissions from developing nations. The administration questioned the scientific consensus on climate change. Bush stated that he believed global warming is real and a serious problem, although he asserted that there existed a "debate over whether it's man-made or naturally caused". The Bush administration's stance on global warming remained controversial in the scientific and environmental communities. Critics alleged that the administration misinformed the public and did not do enough to reduce carbon emissions and deter global warming.


title: Presidency of George W. Bush

text: On January 6, 2009, President Bush designated the world's largest protected marine area. The Pacific Ocean habitat includes the Mariana Trench and the waters and corals surrounding three uninhabited islands in the Northern Mariana Islands, Rose Atoll in American Samoa, and seven islands along the equator.


title: Presidency of George W. Bush

text: In July 2002, following several accounting scandals such as the Enron scandal, Bush signed the Sarbanes–Oxley Act into law. The act expanded reporting requirements for public companies Shortly after the start of his second term, Bush signed the Class Action Fairness Act of 2005, which had been a priority of his administration and part of his broader goal of instituting tort reform. The act was designed to remove most class action lawsuits from state courts to federal courts, which were regarded as less sympathetic to plaintiffs in class action suits.


title: Presidency of George W. Bush

text: Upon taking office, Bush had little experience with foreign policy, and his decisions were guided by his advisers. Bush embraced the views of Cheney and other neoconservatives, who de-emphasized the importance of multilateralism; neoconservatives believed that because the United States was the world's lone superpower, it could act unilaterally if necessary. At the same time, Bush sought to enact the less interventionist foreign policy he had promised during the 2000 campaign. Though the first several months of his presidency focused on domestic issues, the Bush administration pulled the U.S. out of several existing or proposed multilateral agreements, including the Kyoto Protocol, the Anti-Ballistic Missile Treaty, and the International Criminal Court.


title: Presidency of George W. Bush

text: Terrorism had emerged as an important national security issue in the Clinton administration, and it became one of the dominant issues of the Bush administration. In the late 1980s, Osama bin Laden had established al-Qaeda, a militant Sunni Islamist multi-national organization that sought to overthrow Western-backed governments in Saudi Arabia, Jordan, Egypt, and Pakistan. In response to Saudi Arabia's decision to begin hosting U.S. soldiers in 1991, al-Qaeda had begun a terrorist campaign against U.S. targets, orchestrating attacks such as the 1998 USS Cole bombing. During Bush's first months in office, U.S. intelligence organizations intercepted communications indicating that al-Qaeda was planning another attack on the United States, but foreign policy officials were unprepared for a major attack on the United States. Bush was briefed on al-Qaeda's activities, but focused on other foreign policy issues during his first months in office.


title: Presidency of George W. Bush

text: On September 11, 2001, al-Qaeda terrorists hijacked four airliners and flew two of them into the twin towers of the World Trade Center in New York City, destroying both 110-story skyscrapers. Another plane crashed into Pentagon, and a fourth plane was brought down in Pennsylvania following a struggle between the terrorists and the aircraft's passengers. The attacks had a profound effect on many Americans, who felt vulnerable to international attacks for the first time since the end of the Cold War. Appearing on national television on the night of the attacks, Bush promised to punish those who had aided the attacks, stating, "we will make no distinction between the terrorists who committed these acts and those who harbor them." In the following days, Bush urged the public to renounce hate crimes and discrimination against Muslim-Americans and Arab-Americans. He also declared a "War on Terror", instituting new domestic and foreign policies in an effort to prevent future terrorist attacks.


title: Presidency of George W. Bush

text: As Bush's top foreign policy advisers were in agreement that merely launching strikes against al-Qaeda bases would not stop future attacks, the administration decided to overthrow Afghanistan's conservative Taliban government, which harbored the leaders of al-Qaeda. Powell took the lead in assembling allied nations in a coalition that would launch attacks on multiple fronts. The Bush administration focused especially on courting Pakistani leader Pervez Musharraf, who agreed to join the coalition. On September 14, Congress passed a resolution called the Authorization for Use of Military Force Against Terrorists, authorizing the president to use the military against those responsible for the attacks. On October 7, 2001, Bush ordered the invasion of Afghanistan.


title: Presidency of George W. Bush

text: General Tommy Franks, the commander of the United States Central Command (CENTCOM), drew up a four-phase invasion plan. In the first phase, the U.S. built up forces in the surrounding area and inserted CIA and special forces operatives who linked up with the Northern Alliance, an Afghan resistance group opposed to the Taliban. The second phase consisted of a major air campaign against Taliban and al-Qaeda targets, while the third phase involved the defeat of the remaining Taliban and al-Qaeda forces. The fourth and final phase consisted of the stabilization of Afghanistan, which Franks projected would take three to five years. The war in Afghanistan began on October 7 with several air and missile strikes, and the Northern Alliance began its offensive on October 19. The capital of Kabul was captured on November 13, and Hamid Karzai was inaugurated as the new president of Afghanistan. However, the senior leadership of the Taliban and al-Qaeda, including bin Laden, avoided capture. Karzai would remain in power for the duration of Bush's presidency, but his effective control was limited to the area around Kabul, as various warlords took control of much of the rest of the country. While the Karzai's government struggled to control the countryside, the Taliban regrouped in neighboring Pakistan. As Bush left office, he considered sending additional troops to bolster Afghanistan against the Taliban, but decided to leave the issue for the next administration.


title: Presidency of George W. Bush

text: After the September 11 attacks, Bush's approval ratings increased tremendously. Inspired in part by the Truman administration, Bush decided to use his newfound political capital to fundamentally change U.S. foreign policy. He became increasingly focused on the possibility of a hostile country providing weapons of mass destruction (WMDs) to terrorist organizations. During his early 2002 State of the Union Address, Bush set forth what has become known as the Bush Doctrine, which held that the United States would implement a policy of preemptive military strikes against nations known to be harboring or aiding a terrorist organization hostile to the United States. Bush outlined what he called the "Axis of Evil," consisting of three nations that, he argued, posed the greatest threat to world peace due to their pursuit of weapons of mass destruction and potential to aid terrorists. The axis consisted of Iraq, North Korea and Iran. Bush also began emphasizing the importance of spreading democracy worldwide, stating in 2005 that "the survival of liberty in our land depends on the success of liberty in other land." Pursuant to this newly-interventionist policy, the Bush administration boosted foreign aid and increased defense expenditures. Defense spending rose from $304 billion in fiscal year 2001 to $616 billion in fiscal year 2008.


title: Presidency of George W. Bush

text: During the presidency of his father, the United States had launched the Gulf War against Iraq after the latter invaded Kuwait. Though the U.S. forced Iraq's withdrawal from Kuwait, it left Saddam Hussein's administration in place, partly to serve as a counterweight to Iran. After the war, the Project for the New American Century, consisting of influential neoconservatives like Paul Wolfowitz and Cheney, advocated for the overthrow of Hussein. Iraq had developed nuclear and chemical weapons prior to the Gulf War; after the war, it had submitted to WMD inspections conducted by the United Nations Special Commission until 1998, when Hussein demanded that all UN inspectors leave Iraq. The administration believed that, by 2001, Iraq was developing weapons of mass destruction, and could possibly provide those weapons to terrorists. Some within the administration also believed that Iraq shared some responsibility for the September 11 attacks, and hoped that the fall of Hussein's regime would help spread democracy in the Middle East, deter the recruitment of terrorists, and increase the security of Israel.


title: Presidency of George W. Bush

text: In the days following the September 11 attacks, hawks in the Bush administration such as Wolfowitz argued for immediate military action against Iraq, but the issue was temporarily set aside in favor of planning the invasion of Afghanistan. Beginning in September 2002, the Bush administration mounted a campaign designed to win popular and congressional support for the invasion of Iraq. In October 2002, Congress approved the Iraq Resolution, authorizing the use of force against Iraq. While congressional Republicans almost unanimously supported the measure, congressional Democrats were split in roughly equal numbers between support and opposition to the resolution. Bowing to domestic and foreign pressure, Bush sought to win the approval of the United Nations before launching an attack on Iraq. Led by Powell, the administration won the November 2002 passage of United Nations Security Council Resolution 1441, which called on Iraq to dismantle its WMD program. Meanwhile, senior administration officials became increasingly convinced that Iraq did indeed possess WMDs and was likely to furnish those WMDs to al-Qaeda; CIA Director George Tenet assured Bush that it was a "slam dunk" that Iraq possessed a stockpile of WMDs.


title: Presidency of George W. Bush

text: After a U.N. weapons inspections team led by Hans Blix, as well as another team led by Mohamed ElBaradei, failed to find evidence of an ongoing Iraqi WMD program, Bush's proposed regime change in Iraq faced mounting international opposition. Germany, China, France, and Russia all expressed skepticism about the need for regime change, and the latter three countries each possessed veto power on the United Nations Security Council. At the behest of British prime minister Tony Blair, who supported Bush but hoped for more international cooperation, Bush dispatched Powell to the U.N. to make the case to the Security Council that Iraq maintained an active WMD program. Though Powell's presentation preceded a shift in U.S. public opinion towards support of the war, it failed to convince the French, Russians, or Germans. Contrary to the findings of Blix and ElBaradei, Bush asserted in a March 17 public address that there was "no doubt" that the Iraqi regime possessed weapons of mass destruction. Two days later, Bush authorized Operation Iraqi Freedom, and the Iraq War began on March 20, 2003.


title: Presidency of George W. Bush

text: U.S.-led coalition forces, led by General Franks, launched a simultaneous air and land attack on Iraq on March 20, 2003, in what the American media called "shock and awe." With 145,000 soldiers, the ground force quickly overcame most Iraqi resistance, and thousands of Iraqi soldiers deserted. The U.S. captured the Iraqi capital of Baghdad on April 9, but Hussein escaped and went into hiding. While the U.S. and its allies quickly achieved military success, the invasion was strongly criticized by many countries; UN secretary-general Kofi Annan argued that the invasion was a violation of international law and the U.N. Charter.


title: Presidency of George W. Bush

text: On May 1, 2003, Bush delivered the "Mission Accomplished speech," in which he declared the end of "major combat operations" in Iraq. Despite the failure to find evidence of an ongoing WMD program or an operational relationship between Hussein and al-Qaeda, Bush declared that the toppling of Hussein "removed an ally of al-Qaeda" and ended the threat that Iraq would supply weapons of mass destruction to terrorist organizations. Believing that only a minimal residual American force would be required after the success of the invasion, Bush and Franks planned for a drawdown to 30,000 U.S. troops in Iraq by August 2003. Meanwhile, Iraqis began looting their own capital, presenting one of the first of many challenges the U.S. would face in keeping the peace in Iraq.


title: Presidency of George W. Bush

text: Bush appointed Paul Bremer to lead the Coalition Provisional Authority (CPA), which was charged with overseeing the transition to self-government in Iraq. In his first major order, Bremer announced a policy of de-Ba'athification, which denied government and military jobs to members of Hussein's Ba'ath Party. This policy angered many of Iraq's Sunnis, many of whom had joined the Ba'ath Party merely as a career move. Bremer's second major order disbanded the Iraqi military and police services, leaving over 600,000 Iraqi soldiers and government employees without jobs. Bremer also insisted that the CPA remain in control of Iraq until the country held elections, reversing an earlier plan to set up a transition government led by Iraqis. These decisions contributed to the beginning of the Iraqi insurgency opposed to the continuing U.S. presence. Fearing the further deterioration of Iraq's security situation, General John Abizaid ordered the end of the planned drawdown of soldiers, leaving over 130,000 U.S. soldiers in Iraq. The U.S captured Hussein on December 13, 2003, but the occupation force continued to suffer casualties. Between the start of the invasion and the end of 2003, 580 U.S. soldiers died, with two thirds of those casualties occurring after Bush's "Mission Accomplished" speech.


title: Presidency of George W. Bush

text: After 2003, more and more Iraqis began to see the U.S. as an occupying force. The fierce fighting of the First Battle of Fallujah alienated many in Iraq, while cleric Muqtada al-Sadr encouraged Shia Muslims to oppose the CPA. Sunni and Shia insurgents engaged in a campaign of guerrilla warfare against the United States, blunting the technological and organizational advantages of the U.S. military. While fighting in Iraq continued, Americans increasingly came to disapprove of Bush's handling of the Iraq War, contributing to a decline in Bush's approval ratings.


title: Presidency of George W. Bush

text: Bremer left Iraq in June 2004, transferring power to the Iraqi Interim Government, which was led by Ayad Allawi. In January 2005, the Iraqi people voted on representatives for the Iraqi National Assembly, and the Shia United Iraqi Alliance formed a governing coalition led by Ibrahim al-Jaafari. In October 2005, the Iraqis ratified a new constitution that created a decentralized governmental structure dividing Iraq into communities of Sunni Arabs, Shia Arabs, and Kurds. After a December 2005 election, Jafari was succeeded as prime minister by another Shia, Nouri al-Maliki. The elections failed to quell the insurgency, and hundreds of U.S. soldiers stationed in Iraq died during 2005 and 2006. Sectarian violence between Sunnis and Shias also intensified following the 2006 al-Askari mosque bombing. In a December 2006 report, the bipartisan Iraq Study Group described the situation in Iraq as "grave and deteriorating," and the report called for the U.S. to gradually withdraw soldiers from Iraq.


title: Presidency of George W. Bush

text: As the violence mounted in 2006, Rumsfeld and military leaders such as Abizaid and George Casey, the commander of the coalition forces in Iraq, called for a drawdown of forces in Iraq, but many within in the administration argued that the U.S. should maintain its troop levels. Still intent on establishing a democratic government in Iraq, the Bush administration rejected a drawdown and began planning for a change in strategy and leadership following the 2006 elections. After the elections, Bush replaced Rumsfeld with Gates, while David Petraeus replaced Casey and William J. Fallon replaced Abizaid. Bush and his National Security Council formed a plan to "double down" in Iraq, increasing the number of U.S. soldiers in hopes of establishing a stable democracy. After Maliki indicated his support for an increase of U.S. soldiers, Bush announced in January 2007 that the U.S. would send an additional 20,000 soldiers to Iraq as part of a "surge" of forces. Though Senator McCain and a few other hawks supported Bush's new strategy, many other members of Congress from both parties expressed doubt or outright opposition to it.


title: Presidency of George W. Bush

text: In April 2007, Congress, now controlled by Democrats, passed a bill that called for a total withdrawal of all U.S. troops by April 2008, but Bush vetoed the bill. Without the votes to override the veto, Congress passed a bill that continued to fund the war but also included the Fair Minimum Wage Act of 2007, which increased the federal minimum wage. U.S. and Iraqi casualties continuously declined after May 2007, and Bush declared that the surge had been a success in September 2007. He subsequently ordered a drawdown of troops, and the number of U.S. soldiers in Iraq declined from 168,000 in September 2007 to 145,000 when Bush left office. The decline in casualties following the surge coincided with several other favorable trends, including the Anbar Awakening and Muqtada al-Sadr's decision to order his followers to cooperate with the Iraqi government. In 2008, at the insistence of Maliki, Bush signed the U.S.–Iraq Status of Forces Agreement, which promised complete withdrawal of U.S. troops by the end of 2011. The U.S. would withdraw its forces from Iraq in December 2011, though it later re-deployed soldiers to Iraq to assist government forces in the Iraqi Civil War.


title: Presidency of George W. Bush

text: During and after the invasion of Afghanistan, the U.S. captured numerous members of al-Qaeda and the Taliban. Rather than bringing the prisoners before domestic or international courts, Bush decided to set up a new system of military tribunals to try the prisoners. In order to avoid the restrictions of the United States Constitution, Bush held the prisoners at secret CIA prisons in various countries as well as at the Guantanamo Bay detention camp. Because the Guantanamo Bay camp is on territory that the U.S. technically leases from Cuba, individuals within the camp are not accorded the same constitutional protections that they would have on U.S. territory. Bush also decided that these "enemy combatants" were not entitled to all of the protections of the Geneva Conventions as they were not affiliated with sovereign states. In hopes of obtaining information from the prisoners, Bush allowed the use of "enhanced interrogation techniques" such as waterboarding. The treatment of prisoners at Abu Ghraib, a U.S. prison in Iraq, elicited widespread outrage after photos of prisoner abuse were made public.