title: De Broglie–Bohm theory

text: In de Broglie–Bohm theory, the wavefunction is defined at both slits, but each particle has a well-defined trajectory that passes through exactly one of the slits. The final position of the particle on the detector screen and the slit through which the particle passes is determined by the initial position of the particle. Such initial position is not knowable or controllable by the experimenter, so there is an appearance of randomness in the pattern of detection. In Bohm's 1952 papers he used the wavefunction to construct a quantum potential that, when included in Newton's equations, gave the trajectories of the particles streaming through the two slits. In effect the wavefunction interferes with itself and guides the particles by the quantum potential in such a way that the particles avoid the regions in which the interference is destructive and are attracted to the regions in which the interference is constructive, resulting in the interference pattern on the detector screen.


title: De Broglie–Bohm theory

text: To explain the behavior when the particle is detected to go through one slit, one needs to appreciate the role of the conditional wavefunction and how it results in the collapse of the wavefunction; this is explained below. The basic idea is that the environment registering the detection effectively separates the two wave packets in configuration space.


title: De Broglie–Bohm theory

text: The ontology of de Broglie–Bohm theory consists of a configuration formula_15 of the universe and a pilot wave formula_16. The configuration space formula_3 can be chosen differently, as in classical mechanics and standard quantum mechanics.


title: De Broglie–Bohm theory

text: Thus, the ontology of pilot-wave theory contains as the trajectory formula_15 we know from classical mechanics, as the wavefunction formula_16 of quantum theory. So, at every moment of time there exists not only a wavefunction, but also a well-defined configuration of the whole universe (i.e., the system as defined by the boundary conditions used in solving the Schrödinger equation). The correspondence to our experiences is made by the identification of the configuration of our brain with some part of the configuration of the whole universe formula_15, as in classical mechanics.


title: De Broglie–Bohm theory

text: While the ontology of classical mechanics is part of the ontology of de Broglie–Bohm theory, the dynamics are very different. In classical mechanics, the accelerations of the particles are imparted directly by forces, which exist in physical three-dimensional space. In de Broglie–Bohm theory, the velocities of the particles are given by the wavefunction, which exists in a 3"N"-dimensional configuration space, where "N" corresponds to the number of particles in the system; Bohm hypothesized that each particle has a "complex and subtle inner structure" that provides the capacity to react to the information provided by the wavefunction by the quantum potential. Also, unlike in classical mechanics, physical properties (e.g., mass, charge) are spread out over the wavefunction in de Broglie–Bohm theory, not localized at the position of the particle.


title: De Broglie–Bohm theory

text: The wavefunction itself, and not the particles, determines the dynamical evolution of the system: the particles do not act back onto the wave function. As Bohm and Hiley worded it, "the Schrödinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the condition of the particles [...] the quantum theory can be understood completely in terms of the assumption that the quantum field has no sources or other forms of dependence on the particles". P. Holland considers this lack of reciprocal action of particles and wave function to be one "[a]mong the many nonclassical properties exhibited by this theory". It should be noted, however, that Holland has later called this a merely "apparent" lack of back reaction, due to the incompleteness of the description.


title: De Broglie–Bohm theory

text: In what follows below, we will give the setup for one particle moving in formula_21 followed by the setup for "N" particles moving in 3 dimensions. In the first instance, configuration space and real space are the same, while in the second, real space is still formula_21, but configuration space becomes formula_23. While the particle positions themselves are in real space, the velocity field and wavefunction are on configuration space, which is how particles are entangled with each other in this theory.


title: De Broglie–Bohm theory

text: We use variations of formula_24 for particle positions, while formula_25 represents the complex-valued wavefunction on configuration space.


title: De Broglie–Bohm theory

text: For many particles, we label them as formula_4 for the formula_29-th particle, and their velocities are given by


title: De Broglie–Bohm theory

text: The main fact to notice is that this velocity field depends on the actual positions of all of the formula_5 particles in the universe. As explained below, in most experimental situations, the influence of all of those particles can be encapsulated into an effective wavefunction for a subsystem of the universe.


title: De Broglie–Bohm theory

text: The one-particle Schrödinger equation governs the time evolution of a complex-valued wavefunction on formula_21. The equation represents a quantized version of the total energy of a classical system evolving under a real-valued potential function formula_33 on formula_21:


title: De Broglie–Bohm theory

text: For many particles, the equation is the same except that formula_25 and formula_33 are now on configuration space, formula_23:


title: De Broglie–Bohm theory

text: In Bohm's original papers [Bohm 1952], he discusses how de Broglie–Bohm theory results in the usual measurement results of quantum mechanics. The main idea is that this is true if the positions of the particles satisfy the statistical distribution given by formula_40. And that distribution is guaranteed to be true for all time by the guiding equation if the initial distribution of the particles satisfies formula_40.


title: De Broglie–Bohm theory

text: For a given experiment, one can postulate this as being true and verify it experimentally. But, as argued in Dürr et al., one needs to argue that this distribution for subsystems is typical. The authors argue that formula_40, by virtue of its equivariance under the dynamical evolution of the system, is the appropriate measure of typicality for initial conditions of the positions of the particles. The authors then prove that the vast majority of possible initial configurations will give rise to statistics obeying the Born rule (i.e., formula_40) for measurement outcomes. In summary, in a universe governed by the de Broglie–Bohm dynamics, Born rule behavior is typical.


title: De Broglie–Bohm theory

text: The situation is thus analogous to the situation in classical statistical physics. A low-entropy initial condition will, with overwhelmingly high probability, evolve into a higher-entropy state: behavior consistent with the second law of thermodynamics is typical. There are anomalous initial conditions that would give rise to violations of the second law; however in the absence of some very detailed evidence supporting the realization of one of those conditions, it would be quite unreasonable to expect anything but the actually observed uniform increase of entropy. Similarly in the de Broglie–Bohm theory, there are anomalous initial conditions that would produce measurement statistics in violation of the Born rule (conflicting the predictions of standard quantum theory), but the typicality theorem shows that absent some specific reason to believe one of those special initial conditions was in fact realized, the Born rule behavior is what one should expect.


title: De Broglie–Bohm theory

text: It is in this qualified sense that the Born rule is, for the de Broglie–Bohm theory, a theorem rather than (as in ordinary quantum theory) an additional postulate.


title: De Broglie–Bohm theory

text: It can also be shown that a distribution of particles which is "not" distributed according to the Born rule (that is, a distribution "out of quantum equilibrium") and evolving under the de Broglie–Bohm dynamics is overwhelmingly likely to evolve dynamically into a state distributed as formula_40.


title: De Broglie–Bohm theory

text: In the formulation of the de Broglie–Bohm theory, there is only a wavefunction for the entire universe (which always evolves by the Schrödinger equation). It should, however, be noted that the "universe" is simply the system limited by the same boundary conditions used to solve the Schrödinger equation. However, once the theory is formulated, it is convenient to introduce a notion of wavefunction also for subsystems of the universe. Let us write the wavefunction of the universe as formula_45, where formula_46 denotes the configuration variables associated to some subsystem (I) of the universe, and formula_47 denotes the remaining configuration variables. Denote respectively by formula_48 and formula_49 the actual configuration of subsystem (I) and of the rest of the universe. For simplicity, we consider here only the spinless case. The "conditional wavefunction" of subsystem (I) is defined by


title: De Broglie–Bohm theory

text: It follows immediately from the fact that formula_51 satisfies the guiding equation that also the configuration formula_48 satisfies a guiding equation identical to the one presented in the formulation of the theory, with the universal wavefunction formula_25 replaced with the conditional wavefunction formula_54. Also, the fact that formula_55 is random with probability density given by the square modulus of formula_56 implies that the conditional probability density of formula_48 given formula_49 is given by the square modulus of the (normalized) conditional wavefunction formula_59 (in the terminology of Dürr et al. this fact is called the "fundamental conditional probability formula").


title: De Broglie–Bohm theory

text: Unlike the universal wavefunction, the conditional wavefunction of a subsystem does not always evolve by the Schrödinger equation, but in many situations it does. For instance, if the universal wavefunction factors as


title: De Broglie–Bohm theory

text: then the conditional wavefunction of subsystem (I) is (up to an irrelevant scalar factor) equal to formula_54 (this is what standard quantum theory would regard as the wavefunction of subsystem (I)). If, in addition, the Hamiltonian does not contain an interaction term between subsystems (I) and (II), then formula_54 does satisfy a Schrödinger equation. More generally, assume that the universal wave function formula_25 can be written in the form


title: De Broglie–Bohm theory

text: where formula_65 solves Schrödinger equation and, formula_66 for all formula_14 and formula_46. Then, again, the conditional wavefunction of subsystem (I) is (up to an irrelevant scalar factor) equal to formula_54, and if the Hamiltonian does not contain an interaction term between subsystems (I) and (II), then formula_54 satisfies a Schrödinger equation.


title: De Broglie–Bohm theory

text: The fact that the conditional wavefunction of a subsystem does not always evolve by the Schrödinger equation is related to the fact that the usual collapse rule of standard quantum theory emerges from the Bohmian formalism when one considers conditional wavefunctions of subsystems.


title: De Broglie–Bohm theory

text: Pilot-wave theory is explicitly nonlocal, which is in ostensible conflict with special relativity. Various extensions of "Bohm-like" mechanics exist that attempt to resolve this problem. Bohm himself in 1953 presented an extension of the theory satisfying the Dirac equation for a single particle. However, this was not extensible to the many-particle case because it used an absolute time.


title: De Broglie–Bohm theory

text: A renewed interest in constructing Lorentz-invariant extensions of Bohmian theory arose in the 1990s; see "Bohm and Hiley: The Undivided Universe" and references therein. Another approach is given in the work of Dürr et al., in which they use Bohm–Dirac models and a Lorentz-invariant foliation of space-time.


title: De Broglie–Bohm theory

text: Thus, Dürr et al. (1999) showed that it is possible to formally restore Lorentz invariance for the Bohm–Dirac theory by introducing additional structure. This approach still requires a foliation of space-time. While this is in conflict with the standard interpretation of relativity, the preferred foliation, if unobservable, does not lead to any empirical conflicts with relativity. In 2013, Dürr et al. suggested that the required foliation could be covariantly determined by the wavefunction.


title: De Broglie–Bohm theory

text: The relation between nonlocality and preferred foliation can be better understood as follows. In de Broglie–Bohm theory, nonlocality manifests as the fact that the velocity and acceleration of one particle depends on the instantaneous positions of all other particles. On the other hand, in the theory of relativity the concept of instantaneousness does not have an invariant meaning. Thus, to define particle trajectories, one needs an additional rule that defines which space-time points should be considered instantaneous. The simplest way to achieve this is to introduce a preferred foliation of space-time by hand, such that each hypersurface of the foliation defines a hypersurface of equal time.


title: De Broglie–Bohm theory

text: Initially, it had been considered impossible to set out a description of photon trajectories in the de Broglie–Bohm theory in view of the difficulties of describing bosons relativistically. In 1996, Partha Ghose had presented a relativistic quantum-mechanical description of spin-0 and spin-1 bosons starting from the Duffin–Kemmer–Petiau equation, setting out Bohmian trajectories for massive bosons and for massless bosons (and therefore photons). In 2001, Jean-Pierre Vigier emphasized the importance of deriving a well-defined description of light in terms of particle trajectories in the framework of either the Bohmian mechanics or the Nelson stochastic mechanics. The same year, Ghose worked out Bohmian photon trajectories for specific cases. Subsequent weak-measurement experiments yielded trajectories that coincide with the predicted trajectories. The significance of these experimental findings has been discussed controversially.


title: De Broglie–Bohm theory

text: Chris Dewdney and G. Horton have proposed a relativistically covariant, wave-functional formulation of Bohm's quantum field theory and have extended it to a form that allows the inclusion of gravity.


title: De Broglie–Bohm theory

text: Nikolić has proposed a Lorentz-covariant formulation of the Bohmian interpretation of many-particle wavefunctions. He has developed a generalized relativistic-invariant probabilistic interpretation of quantum theory, in which formula_40 is no longer a probability density in space, but a probability density in space-time. He uses this generalized probabilistic interpretation to formulate a relativistic-covariant version of de Broglie–Bohm theory without introducing a preferred foliation of space-time. His work also covers the extension of the Bohmian interpretation to a quantization of fields and strings.


title: De Broglie–Bohm theory

text: Roderick I. Sutherland at the University in Sydney has a Lagrangian formalism for the pilot wave and its beables. It draws on Yakir Aharonov's retrocasual weak measurements to explain many-particle entanglement in a special relativistic way without the need for configuration space. The basic idea was already published by Costa de Beauregard in the 1950s and is also used by John Cramer in his transactional interpretation except the beables that exist between the von Neumann strong projection operator measurements. Sutherland's Lagrangian includes two-way action-reaction between pilot wave and beables. Therefore, it is a post-quantum non-statistical theory with final boundary conditions that violate the no-signal theorems of quantum theory. Just as special relativity is a limiting case of general relativity when the spacetime curvature vanishes, so, too is statistical no-entanglement signaling quantum theory with the Born rule a limiting case of the post-quantum action-reaction Lagrangian when the reaction is set to zero and the final boundary condition is integrated out.


title: De Broglie–Bohm theory

text: To incorporate spin, the wavefunction becomes complex-vector-valued. The value space is called spin space; for a spin-½ particle, spin space can be taken to be formula_72. The guiding equation is modified by taking inner products in spin space to reduce the complex vectors to complex numbers. The Schrödinger equation is modified by adding a Pauli spin term:


title: De Broglie–Bohm theory

text: In Dürr et al., the authors describe an extension of de Broglie–Bohm theory for handling creation and annihilation operators, which they refer to as "Bell-type quantum field theories". The basic idea is that configuration space becomes the (disjoint) space of all possible configurations of any number of particles. For part of the time, the system evolves deterministically under the guiding equation with a fixed number of particles. But under a stochastic process, particles may be created and annihilated. The distribution of creation events is dictated by the wavefunction. The wavefunction itself is evolving at all times over the full multi-particle configuration space.


title: De Broglie–Bohm theory

text: Hrvoje Nikolić introduces a purely deterministic de Broglie–Bohm theory of particle creation and destruction, according to which particle trajectories are continuous, but particle detectors behave as if particles have been created or destroyed even when a true creation or destruction of particles does not take place.


title: De Broglie–Bohm theory

text: To extend de Broglie–Bohm theory to curved space (Riemannian manifolds in mathematical parlance), one simply notes that all of the elements of these equations make sense, such as gradients and Laplacians. Thus, we use equations that have the same form as above. Topological and boundary conditions may apply in supplementing the evolution of Schrödinger's equation.


title: De Broglie–Bohm theory

text: For a de Broglie–Bohm theory on curved space with spin, the spin space becomes a vector bundle over configuration space, and the potential in Schrödinger's equation becomes a local self-adjoint operator acting on that space.


title: De Broglie–Bohm theory

text: De Broglie and Bohm's causal interpretation of quantum mechanics was later extended by Bohm, Vigier, Hiley, Valentini and others to include stochastic properties. Bohm and other physicists, including Valentini, view the Born rule linking formula_93 to the probability density function formula_94 as representing not a basic law, but a result of a system having reached "quantum equilibrium" during the course of the time development under the Schrödinger equation. It can be shown that, once an equilibrium has been reached, the system remains in such equilibrium over the course of its further evolution: this follows from the continuity equation associated with the Schrödinger evolution of formula_25. It is less straightforward to demonstrate whether and how such an equilibrium is reached in the first place.


title: De Broglie–Bohm theory

text: Antony Valentini has extended de Broglie–Bohm theory to include signal nonlocality that would allow entanglement to be used as a stand-alone communication channel without a secondary classical "key" signal to "unlock" the message encoded in the entanglement. This violates orthodox quantum theory but has the virtue of making the parallel universes of the chaotic inflation theory observable in principle.


title: De Broglie–Bohm theory

text: Unlike de Broglie–Bohm theory, on Valentini's theory the wavefunction evolution also depends on the ontological variables. This introduces an instability, a feedback loop that pushes the hidden variables out of "sub-quantal heat death". The resulting theory becomes nonlinear and non-unitary. Valentini argues that the laws of quantum mechanics are emergent and form a "quantum equilibrium" that is analogous to thermal equilibrium in classical dynamics, such that other "quantum non-equilibrium" distributions may in principle be observed and exploited, for which the statistical predictions of quantum theory are violated. It is controversially argued that quantum theory is merely a special case of a much wider nonlinear physics, a physics in which non-local (superluminal) signalling is possible, and in which the uncertainty principle can be violated.


title: De Broglie–Bohm theory

text: Below are some highlights of the results that arise out of an analysis of de Broglie–Bohm theory. Experimental results agree with all of quantum mechanics' standard predictions insofar as it has them. But while standard quantum mechanics is limited to discussing the results of "measurements", de Broglie–Bohm theory governs the dynamics of a system without the intervention of outside observers (p. 117 in Bell).


title: De Broglie–Bohm theory

text: The basis for agreement with standard quantum mechanics is that the particles are distributed according to formula_40. This is a statement of observer ignorance, but it can be proven that for a universe governed by this theory, this will typically be the case. There is apparent collapse of the wave function governing subsystems of the universe, but there is no collapse of the universal wavefunction.


title: De Broglie–Bohm theory

text: According to ordinary quantum theory, it is not possible to measure the spin or polarization of a particle directly; instead, the component in one direction is measured; the outcome from a single particle may be 1, meaning that the particle is aligned with the measuring apparatus, or −1, meaning that it is aligned the opposite way. For an ensemble of particles, if we expect the particles to be aligned, the results are all 1. If we expect them to be aligned oppositely, the results are all −1. For other alignments, we expect some results to be 1 and some to be −1 with a probability that depends on the expected alignment. For a full explanation of this, see the Stern–Gerlach experiment.


title: De Broglie–Bohm theory

text: In de Broglie–Bohm theory, the results of a spin experiment cannot be analyzed without some knowledge of the experimental setup. It is possible to modify the setup so that the trajectory of the particle is unaffected, but that the particle with one setup registers as spin-up, while in the other setup it registers as spin-down. Thus, for the de Broglie–Bohm theory, the particle's spin is not an intrinsic property of the particle; instead spin is, so to speak, in the wavefunction of the particle in relation to the particular device being used to measure the spin. This is an illustration of what is sometimes referred to as contextuality and is related to naive realism about operators. Interpretationally, measurement results are a deterministic property of the system and its environment, which includes information about the experimental setup including the context of co-measured observables; in no sense does the system itself possess the property being measured, as would have been the case in classical physics.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory gives the same results as quantum mechanics. It treats the wavefunction as a fundamental object in the theory, as the wavefunction describes how the particles move. This means that no experiment can distinguish between the two theories. This section outlines the ideas as to how the standard quantum formalism arises out of quantum mechanics. References include Bohm's original 1952 paper and Dürr et al.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory is a theory that applies primarily to the whole universe. That is, there is a single wavefunction governing the motion of all of the particles in the universe according to the guiding equation. Theoretically, the motion of one particle depends on the positions of all of the other particles in the universe. In some situations, such as in experimental systems, we can represent the system itself in terms of a de Broglie–Bohm theory in which the wavefunction of the system is obtained by conditioning on the environment of the system. Thus, the system can be analyzed with Schrödinger's equation and the guiding equation, with an initial formula_40 distribution for the particles in the system (see the section on the conditional wavefunction of a subsystem for details).


title: De Broglie–Bohm theory

text: It requires a special setup for the conditional wavefunction of a system to obey a quantum evolution. When a system interacts with its environment, such as through a measurement, the conditional wavefunction of the system evolves in a different way. The evolution of the universal wavefunction can become such that the wavefunction of the system appears to be in a superposition of distinct states. But if the environment has recorded the results of the experiment, then using the actual Bohmian configuration of the environment to condition on, the conditional wavefunction collapses to just one alternative, the one corresponding with the measurement results.


title: De Broglie–Bohm theory

text: Collapse of the universal wavefunction never occurs in de Broglie–Bohm theory. Its entire evolution is governed by Schrödinger's equation, and the particles' evolutions are governed by the guiding equation. Collapse only occurs in a phenomenological way for systems that seem to follow their own Schrödinger's equation. As this is an effective description of the system, it is a matter of choice as to what to define the experimental system to include, and this will affect when "collapse" occurs.


title: De Broglie–Bohm theory

text: In the standard quantum formalism, measuring observables is generally thought of as measuring operators on the Hilbert space. For example, measuring position is considered to be a measurement of the position operator. This relationship between physical measurements and Hilbert space operators is, for standard quantum mechanics, an additional axiom of the theory. The de Broglie–Bohm theory, by contrast, requires no such measurement axioms (and measurement as such is not a dynamically distinct or special sub-category of physical processes in the theory). In particular, the usual operators-as-observables formalism is, for de Broglie–Bohm theory, a theorem. A major point of the analysis is that many of the measurements of the observables do not correspond to properties of the particles; they are (as in the case of spin discussed above) measurements of the wavefunction.


title: De Broglie–Bohm theory

text: In the history of de Broglie–Bohm theory, the proponents have often had to deal with claims that this theory is impossible. Such arguments are generally based on inappropriate analysis of operators as observables. If one believes that spin measurements are indeed measuring the spin of a particle that existed prior to the measurement, then one does reach contradictions. De Broglie–Bohm theory deals with this by noting that spin is not a feature of the particle, but rather that of the wavefunction. As such, it only has a definite outcome once the experimental apparatus is chosen. Once that is taken into account, the impossibility theorems become irrelevant.


title: De Broglie–Bohm theory

text: There have also been claims that experiments reject the Bohm trajectories in favor of the standard QM lines. But as shown in other work, such experiments cited above only disprove a misinterpretation of the de Broglie–Bohm theory, not the theory itself.


title: De Broglie–Bohm theory

text: There are also objections to this theory based on what it says about particular situations usually involving eigenstates of an operator. For example, the ground state of hydrogen is a real wavefunction. According to the guiding equation, this means that the electron is at rest when in this state. Nevertheless, it is distributed according to formula_40, and no contradiction to experimental results is possible to detect.


title: De Broglie–Bohm theory

text: Operators as observables leads many to believe that many operators are equivalent. De Broglie–Bohm theory, from this perspective, chooses the position observable as a favored observable rather than, say, the momentum observable. Again, the link to the position observable is a consequence of the dynamics. The motivation for de Broglie–Bohm theory is to describe a system of particles. This implies that the goal of the theory is to describe the positions of those particles at all times. Other observables do not have this compelling ontological status. Having definite positions explains having definite results such as flashes on a detector screen. Other observables would not lead to that conclusion, but there need not be any problem in defining a mathematical theory for other observables; see Hyman et al. for an exploration of the fact that a probability density and probability current can be defined for any set of commuting operators.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory is often referred to as a "hidden-variable" theory. Bohm used this description in his original papers on the subject, writing: "From the point of view of the usual interpretation, these additional elements or parameters [permitting a detailed causal and continuous description of all processes] could be called 'hidden' variables." Bohm and Hiley later stated that they found Bohm's choice of the term "hidden variables" to be too restrictive. In particular, they argued that a particle is not actually hidden but rather "is what is most directly manifested in an observation [though] its properties cannot be observed with arbitrary precision (within the limits set by uncertainty principle)". However, others nevertheless treat the term "hidden variable" as a suitable description.


title: De Broglie–Bohm theory

text: Generalized particle trajectories can be extrapolated from numerous weak measurements on an ensemble of equally prepared systems, and such trajectories coincide with the de Broglie–Bohm trajectories. In particular, an experiment with two entangled photons, in which a set of Bohmian trajectories for one of the photons was determined using weak measurements and postselection, can be understood in terms of a nonlocal connection between that photon's trajectory and the other photon's polarization. However, not only the De Broglie–Bohm interpretation, but also many other interpretations of quantum mechanics that do not include such trajectories are consistent with such experimental evidence.


title: De Broglie–Bohm theory

text: The Heisenberg's uncertainty principle states that when two complementary measurements are made, there is a limit to the product of their accuracy. As an example, if one measures the position with an accuracy of formula_99 and the momentum with an accuracy of formula_100, then formula_101


title: De Broglie–Bohm theory

text: In de Broglie–Bohm theory, there is always a matter of fact about the position and momentum of a particle. Each particle has a well-defined trajectory, as well as a wavefunction. Observers have limited knowledge as to what this trajectory is (and thus of the position and momentum). It is the lack of knowledge of the particle's trajectory that accounts for the uncertainty relation. What one can know about a particle at any given time is described by the wavefunction. Since the uncertainty relation can be derived from the wavefunction in other interpretations of quantum mechanics, it can be likewise derived (in the epistemic sense mentioned above) on the de Broglie–Bohm theory.


title: De Broglie–Bohm theory

text: To put the statement differently, the particles' positions are only known statistically. As in classical mechanics, successive observations of the particles' positions refine the experimenter's knowledge of the particles' initial conditions. Thus, with succeeding observations, the initial conditions become more and more restricted. This formalism is consistent with the normal use of the Schrödinger equation.


title: De Broglie–Bohm theory

text: For the derivation of the uncertainty relation, see Heisenberg uncertainty principle, noting that this article describes the principle from the viewpoint of the Copenhagen interpretation.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory highlighted the issue of nonlocality: it inspired John Stewart Bell to prove his now-famous theorem, which in turn led to the Bell test experiments.


title: De Broglie–Bohm theory

text: In the Einstein–Podolsky–Rosen paradox, the authors describe a thought experiment that one could perform on a pair of particles that have interacted, the results of which they interpreted as indicating that quantum mechanics is an incomplete theory.


title: De Broglie–Bohm theory

text: Decades later John Bell proved Bell's theorem (see p. 14 in Bell), in which he showed that, if they are to agree with the empirical predictions of quantum mechanics, all such "hidden-variable" completions of quantum mechanics must either be nonlocal (as the Bohm interpretation is) or give up the assumption that experiments produce unique results (see counterfactual definiteness and many-worlds interpretation). In particular, Bell proved that any local theory with unique results must make empirical predictions satisfying a statistical constraint called "Bell's inequality".


title: De Broglie–Bohm theory

text: Alain Aspect performed a series of Bell test experiments that test Bell's inequality using an EPR-type setup. Aspect's results show experimentally that Bell's inequality is in fact violated, meaning that the relevant quantum-mechanical predictions are correct. In these Bell test experiments, entangled pairs of particles are created; the particles are separated, traveling to remote measuring apparatus. The orientation of the measuring apparatus can be changed while the particles are in flight, demonstrating the apparent nonlocality of the effect.


title: De Broglie–Bohm theory

text: The de Broglie–Bohm theory makes the same (empirically correct) predictions for the Bell test experiments as ordinary quantum mechanics. It is able to do this because it is manifestly nonlocal. It is often criticized or rejected based on this; Bell's attitude was: "It is a merit of the de Broglie–Bohm version to bring this [nonlocality] out so explicitly that it cannot be ignored."


title: De Broglie–Bohm theory

text: The de Broglie–Bohm theory describes the physics in the Bell test experiments as follows: to understand the evolution of the particles, we need to set up a wave equation for both particles; the orientation of the apparatus affects the wavefunction. The particles in the experiment follow the guidance of the wavefunction. It is the wavefunction that carries the faster-than-light effect of changing the orientation of the apparatus. An analysis of exactly what kind of nonlocality is present and how it is compatible with relativity can be found in Maudlin. Note that in Bell's work, and in more detail in Maudlin's work, it is shown that the nonlocality does not allow signaling at speeds faster than light.


title: De Broglie–Bohm theory

text: Bohm's formulation of de Broglie–Bohm theory in terms of a classically looking version has the merits that the emergence of classical behavior seems to follow immediately for any situation in which the quantum potential is negligible, as noted by Bohm in 1952. Modern methods of decoherence are relevant to an analysis of this limit. See Allori et al. for steps towards a rigorous analysis.


title: De Broglie–Bohm theory

text: Work by Robert E. Wyatt in the early 2000s attempted to use the Bohm "particles" as an adaptive mesh that follows the actual trajectory of a quantum state in time and space. In the "quantum trajectory" method, one samples the quantum wavefunction with a mesh of quadrature points. One then evolves the quadrature points in time according to the Bohm equations of motion. At each time step, one then re-synthesizes the wavefunction from the points, recomputes the quantum forces, and continues the calculation. (QuickTime movies of this for H + H reactive scattering can be found on the Wyatt group web-site at UT Austin.)


title: De Broglie–Bohm theory

text: This approach has been adapted, extended, and used by a number of researchers in the chemical physics community as a way to compute semi-classical and quasi-classical molecular dynamics. A recent (2007) issue of the Journal of Physical Chemistry A was dedicated to Prof. Wyatt and his work on "computational Bohmian dynamics".


title: De Broglie–Bohm theory

text: Eric R. Bittner's group at the University of Houston has advanced a statistical variant of this approach that uses Bayesian sampling technique to sample the quantum density and compute the quantum potential on a structureless mesh of points. This technique was recently used to estimate quantum effects in the heat capacity of small clusters Ne for "n" ≈ 100.


title: De Broglie–Bohm theory

text: There remain difficulties using the Bohmian approach, mostly associated with the formation of singularities in the quantum potential due to nodes in the quantum wavefunction. In general, nodes forming due to interference effects lead to the case where formula_102 This results in an infinite force on the sample particles forcing them to move away from the node and often crossing the path of other sample points (which violates single-valuedness). Various schemes have been developed to overcome this; however, no general solution has yet emerged.


title: De Broglie–Bohm theory

text: These methods, as does Bohm's Hamilton–Jacobi formulation, do not apply to situations in which the full dynamics of spin need to be taken into account.


title: De Broglie–Bohm theory

text: The properties of trajectories in the de Broglie–Bohm theory differ significantly from the Moyal quantum trajectories as well as the quantum trajectories from the unraveling of an open quantum system.


title: De Broglie–Bohm theory

text: Kim Joris Boström has proposed a non-relativistic quantum mechanical theory that combines elements of de Broglie-Bohm mechanics and Everett's many-worlds. In particular, the unreal many-worlds interpretation of Hawking and Weinberg is similar to the Bohmian concept of unreal empty branch worlds:


title: De Broglie–Bohm theory

text: Many authors have expressed critical views of de Broglie–Bohm theory by comparing it to Everett's many-worlds approach. Many (but not all) proponents of de Broglie–Bohm theory (such as Bohm and Bell) interpret the universal wavefunction as physically real. According to some supporters of Everett's theory, if the (never collapsing) wavefunction is taken to be physically real, then it is natural to interpret the theory as having the same many worlds as Everett's theory. In the Everettian view the role of the Bohmian particle is to act as a "pointer", tagging, or selecting, just one branch of the universal wavefunction (the assumption that this branch indicates which "wave packet" determines the observed result of a given experiment is called the "result assumption"); the other branches are designated "empty" and implicitly assumed by Bohm to be devoid of conscious observers. H. Dieter Zeh comments on these "empty" branches:


title: De Broglie–Bohm theory

text: Both Hugh Everett III and Bohm treated the wavefunction as a physically real field. Everett's many-worlds interpretation is an attempt to demonstrate that the wavefunction alone is sufficient to account for all our observations. When we see the particle detectors flash or hear the click of a Geiger counter, Everett's theory interprets this as our "wavefunction" responding to changes in the detector's "wavefunction", which is responding in turn to the passage of another "wavefunction" (which we think of as a "particle", but is actually just another wave packet). No particle (in the Bohm sense of having a defined position and velocity) exists according to that theory. For this reason Everett sometimes referred to his own many-worlds approach as the "pure wave theory". Of Bohm's 1952 approach, Everett said:


title: De Broglie–Bohm theory

text: In the Everettian view, then, the Bohm particles are superfluous entities, similar to, and equally as unnecessary as, for example, the luminiferous ether, which was found to be unnecessary in special relativity. This argument is sometimes called the "redundancy argument", since the superfluous particles are redundant in the sense of Occam's razor.


title: De Broglie–Bohm theory

text: According to Brown & Wallace, the de Broglie–Bohm particles play no role in the solution of the measurement problem. These authors claim that the "result assumption" (see above) is inconsistent with the view that there is no measurement problem in the predictable outcome (i.e. single-outcome) case. They also claim that a standard tacit assumption of de Broglie–Bohm theory (that an observer becomes aware of configurations of particles of ordinary objects by means of correlations between such configurations and the configuration of the particles in the observer's brain) is unreasonable. This conclusion has been challenged by Valentini, who argues that the entirety of such objections arises from a failure to interpret de Broglie–Bohm theory on its own terms.


title: De Broglie–Bohm theory

text: According to Peter R. Holland, in a wider Hamiltonian framework, theories can be formulated in which particles "do" act back on the wave function.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory has been derived many times and in many ways. Below are six derivations, all of which are very different and lead to different ways of understanding and extending this theory.


title: De Broglie–Bohm theory

text: De Broglie–Bohm theory has a history of different formulations and names. In this section, each stage is given a name and a main reference.


title: De Broglie–Bohm theory

text: Louis de Broglie presented his pilot wave theory at the 1927 Solvay Conference, after close collaboration with Schrödinger, who developed his wave equation for de Broglie's theory. At the end of the presentation, Wolfgang Pauli pointed out that it was not compatible with a semi-classical technique Fermi had previously adopted in the case of inelastic scattering. Contrary to a popular legend, de Broglie actually gave the correct rebuttal that the particular technique could not be generalized for Pauli's purpose, although the audience might have been lost in the technical details and de Broglie's mild manner left the impression that Pauli's objection was valid. He was eventually persuaded to abandon this theory nonetheless because he was "discouraged by criticisms which [it] roused". De Broglie's theory already applies to multiple spin-less particles, but lacks an adequate theory of measurement as no one understood quantum decoherence at the time. An analysis of de Broglie's presentation is given in Bacciagaluppi et al. Also, in 1932 John von Neumann published a paper, that was widely (and erroneously, as shown by Jeffrey Bub) believed to prove that all hidden-variable theories are impossible. This sealed the fate of de Broglie's theory for the next two decades.


title: De Broglie–Bohm theory

text: In 1926, Erwin Madelung had developed a hydrodynamic version of Schrödinger's equation, which is incorrectly considered as a basis for the density current derivation of the de Broglie–Bohm theory. The Madelung equations, being quantum Euler equations (fluid dynamics), differ philosophically from the de Broglie–Bohm mechanics and are the basis of the stochastic interpretation of quantum mechanics.


title: De Broglie–Bohm theory

text: Peter R. Holland has pointed out that, earlier in 1927, Einstein had actually submitted a preprint with a similar proposal but, not convinced, had withdrawn it before publication. According to Holland, failure to appreciate key points of the de Broglie–Bohm theory has led to confusion, the key point being "that the trajectories of a many-body quantum system are correlated not because the particles exert a direct force on one another ("à la" Coulomb) but because all are acted upon by an entity – mathematically described by the wavefunction or functions of it – that lies beyond them". This entity is the quantum potential.


title: De Broglie–Bohm theory

text: After publishing a popular textbook on Quantum Mechanics that adhered entirely to the Copenhagen orthodoxy, Bohm was persuaded by Einstein to take a critical look at von Neumann's theorem. The result was 'A Suggested Interpretation of the Quantum Theory in Terms of "Hidden Variables" I and II' [Bohm 1952]. It was an independent origination of the pilot wave theory, and extended it to incorporate a consistent theory of measurement, and to address a criticism of Pauli that de Broglie did not properly respond to; it is taken to be deterministic (though Bohm hinted in the original papers that there should be disturbances to this, in the way Brownian motion disturbs Newtonian mechanics). This stage is known as the "de Broglie–Bohm Theory" in Bell's work [Bell 1987] and is the basis for 'The Quantum Theory of Motion' [Holland 1993].


title: De Broglie–Bohm theory

text: The de Broglie–Bohm theory is an example of a hidden-variables theory. Bohm originally hoped that hidden variables could provide a local, causal, objective description that would resolve or eliminate many of the paradoxes of quantum mechanics, such as Schrödinger's cat, the measurement problem and the collapse of the wavefunction. However, Bell's theorem complicates this hope, as it demonstrates that there can be no local hidden-variable theory that is compatible with the predictions of quantum mechanics. The Bohmian interpretation is causal but not local.


title: De Broglie–Bohm theory

text: Bohm's paper was largely ignored or panned by other physicists. Albert Einstein, who had suggested that Bohm search for a realist alternative to the prevailing Copenhagen approach, did not consider Bohm's interpretation to be a satisfactory answer to the quantum nonlocality question, calling it "too cheap", while Werner Heisenberg considered it a "superfluous 'ideological superstructure' ". Wolfgang Pauli, who had been unconvinced by de Broglie in 1927, conceded to Bohm as follows:


title: De Broglie–Bohm theory

text: I just received your long letter of 20th November, and I also have studied more thoroughly the details of your paper. I do not see any longer the possibility of any logical contradiction as long as your results agree completely with those of the usual wave mechanics and as long as no means is given to measure the values of your hidden parameters both in the measuring apparatus and in the observe [sic] system. As far as the whole matter stands now, your 'extra wave-mechanical predictions' are still a check, which cannot be cashed.


title: De Broglie–Bohm theory

text: According to physicist Max Dresden, when Bohm's theory was presented at the Institute for Advanced Study in Princeton, many of the objections were ad hominem, focusing on Bohm's sympathy with communists as exemplified by his refusal to give testimony to the House Un-American Activities Committee.


title: De Broglie–Bohm theory

text: In 1979, Chris Philippidis, Chris Dewdney and Basil Hiley were the first to perform numeric computations on the basis of the quantum potential to deduce ensembles of particle trajectories. Their work renewed the interests of physicists in the Bohm interpretation of quantum physics.


title: De Broglie–Bohm theory

text: Eventually John Bell began to defend the theory. In "Speakable and Unspeakable in Quantum Mechanics" [Bell 1987], several of the papers refer to hidden-variables theories (which include Bohm's).


title: De Broglie–Bohm theory

text: The trajectories of the Bohm model that would result for particular experimental arrangements were termed "surreal" by some. Still in 2016, mathematical physicist Sheldon Goldstein said of Bohm's theory: "There was a time when you couldn't even talk about it because it was heretical. It probably still is the kiss of death for a physics career to be actually working on Bohm, but maybe that's changing."


title: De Broglie–Bohm theory

text: Bohmian mechanics is the same theory, but with an emphasis on the notion of current flow, which is determined on the basis of the quantum equilibrium hypothesis that the probability follows the Born rule. The term "Bohmian mechanics" is also often used to include most of the further extensions past the spin-less version of Bohm. While de Broglie–Bohm theory has Lagrangians and Hamilton-Jacobi equations as a primary focus and backdrop, with the icon of the quantum potential, Bohmian mechanics considers the continuity equation as primary and has the guiding equation as its icon. They are mathematically equivalent in so far as the Hamilton-Jacobi formulation applies, i.e., spin-less particles.


title: De Broglie–Bohm theory

text: All of non-relativistic quantum mechanics can be fully accounted for in this theory. Recent studies have used this formalism to compute the evolution of many-body quantum systems, with a considerable increase in speed as compared to other quantum-based methods.


title: De Broglie–Bohm theory

text: Bohm developed his original ideas, calling them the "Causal Interpretation". Later he felt that "causal" sounded too much like "deterministic" and preferred to call his theory the "Ontological Interpretation". The main reference is "The Undivided Universe" (Bohm, Hiley 1993).


title: De Broglie–Bohm theory

text: This stage covers work by Bohm and in collaboration with Jean-Pierre Vigier and Basil Hiley. Bohm is clear that this theory is non-deterministic (the work with Hiley includes a stochastic theory). As such, this theory is not strictly speaking a formulation of de Broglie–Bohm theory, but it deserves mention here because the term "Bohm Interpretation" is ambiguous between this theory and de Broglie–Bohm theory.


title: De Broglie–Bohm theory

text: In 1996 philosopher of science Arthur Fine gave an in-depth analysis of possible interpretations of Bohm's model of 1952.


title: De Broglie–Bohm theory

text: William Simpson has suggested a hylomorphic interpretation of Bohmian mechanics, in which the cosmos is an Aristotelian substance composed of material particles and a substantial form. The wave function is assigned a dispositional role in choreographing the trajectories of the particles.


title: De Broglie–Bohm theory

text: Pioneering experiments on hydrodynamical analogs of quantum mechanics beginning with the work of Couder and Fort (2006) have shown that macroscopic classical pilot-waves can exhibit characteristics previously thought to be restricted to the quantum realm. Hydrodynamic pilot-wave analogs have been able to duplicate the double slit experiment, tunneling, quantized orbits, and numerous other quantum phenomena which have led to a resurgence in interest in pilot wave theories. Coulder and Fort note in their 2006 paper that pilot-waves are nonlinear dissipative systems sustained by external forces. A dissipative system is characterized by the spontaneous appearance of symmetry breaking (anisotropy) and the formation of complex, sometimes chaotic or emergent, dynamics where interacting fields can exhibit long range correlations. Stochastic electrodynamics (SED) is an extension of the de Broglie–Bohm interpretation of quantum mechanics, with the electromagnetic zero-point field (ZPF) playing a central role as the guiding pilot-wave. Modern approaches to SED, like those proposed by the group around late Gerhard Grössing, among others, consider wave and particle-like quantum effects as well-coordinated emergent systems. These emergent systems are the result of speculated and calculated sub-quantum interactions with the zero-point field.


title: De Broglie–Bohm theory

text: Researchers performed the ESSW experiment. They found that the photon trajectories seem surrealistic only if one fails to take into account the nonlocality inherent in Bohm's theory.


title: De Broglie–Bohm theory

text: An experiment was conducted in 2016 which demonstrated the potential validity of the de-Broglie-Bohm theory via use of silicone oil droplets. In this experiment a drop of silicone oil is placed into a vibrating fluid bath, it then bounces across the bath propelled by waves produced by its own collisions, mimicking an electron's statistical behavior with remarkable accuracy.


title: Leonardo Campana

text: Leonardo Campana Romero (born 24 July 2000) is an Ecuadorian professional footballer who plays as a forward for Major League Soccer club Inter Miami, on loan from Premier League club Wolverhampton Wanderers, and the Ecuador national team.


title: Leonardo Campana

text: He began his career with Barcelona SC in 2016. He scored his first professional goal on 21 April 2019 against Delfín de Manta.


title: Leonardo Campana

text: On 21 January 2020 he moved to English Premier League club Wolverhampton Wanderers in a three-and-a-half-year deal.


title: Leonardo Campana

text: On 19 September, he joined Primeira Liga side, Famalicão, on a season long loan. Campana made his debut for Famalicão on 28 September 2020, being substituted for Rubén del Campo in a 2–1 victory over Belenenses SAD. Campana scored his first goal for Famalicão on 22 April 2021, during a 3–0 victory versus Gil Vicente F.C.


title: Leonardo Campana

text: On 16 July 2021, Campana joined Swiss Super League side Grasshopper on a season-long loan deal. His first appearance for the Swiss side came in a 2–0 defeat against Basel, where he conceded an own goal.


title: Leonardo Campana

text: On 20 January 2022, it was announced that Campana would join Major League Soccer club Inter Miami on a season-long loan. Campana made his debut for Inter Miami on 26 February 2022, starting in a 0–0 draw versus Chicago Fire FC. Campana scored his first goal for Inter Miami on 6 March 2022, their only goal in a 5–1 loss to Austin FC. Campana was named MLS Player of the Week for Week 6 of the 2022 season on 11 April 2022, for his hat trick against the New England Revolution.


title: Leonardo Campana

text: Campana started to gather attention at the 2019 South American U-20 Championship where he scored six goals in nine games as Ecuador were crowned champions.


title: Leonardo Campana

text: Campana is the son of former professional tennis player turned politician Pablo Campana, who after representing Ecuador at the 1996 Olympics is now Minister for commerce in the Ecuadorean government. His great-grandfather, Gabriel, won six Ecuadorian league winners’ medals in the 1920s, and his grandfather, Isidro Romero, was the president of Barcelona Sporting Club for 15 years and the team's stadium in Guayaquil, where Campana used to play, is named after him. Campana is also a United States citizen.


title: Shuri Castle

text: The date of construction is uncertain, but it was clearly in use as a castle during the Sanzan period (1322–1429). It is thought that it was probably built during the Gusuku period, like many other castles of Okinawa. When King Shō Hashi unified the three principalities of Okinawa and established the Ryukyu Kingdom, he used Shuri as a residence. At the same time, Shuri flourished as the capital and continued to do so during the Second Shō dynasty.


title: Shuri Castle

text: For 450 years from 1429, it was the royal court and administrative center of the Ryukyu Kingdom. It was the focal point of foreign trade, as well as the political, economic, and cultural heart of the Ryukyu Islands. According to records, the castle burned down several times, and rebuilt each time. During the reign of Shō Nei, samurai forces from the Japanese feudal domain of Satsuma seized Shuri on 6 May 1609. The Japanese withdrew soon afterwards, returning Shō Nei to his throne two years later, and the castle and city to the Ryukyuans, though the kingdom was now a vassal state under Satsuma's suzerainty and would remain so for roughly 250 years.


title: Shuri Castle

text: In the 1850s, Commodore Perry, twice forced his way into Shuri Castle, but was denied an audience with the king both times. In 1879, the kingdom was annexed by the Empire of Japan and the last king, Shō Tai, was compelled to move to Tokyo, and in 1884, he was “elevated” to the rank of marquess in the Japanese aristocracy. Subsequently, the castle was used as a barracks by the Imperial Japanese Army. The Japanese garrison withdrew in 1896, but not before having created a series of tunnels and caverns below it.


title: Shuri Castle

text: In 1908, Shuri City bought the castle from the Japanese government; however, it did not have funding to renovate it. In 1923, thanks to Japanese architect Ito Chuta, "Seiden" survived demolition after being re-designated a prefectural Shinto shrine known as Okinawa Shrine. In 1925, it was designated as a national treasure. Despite its decline, historian George H. Kerr described the castle as "one of the most magnificent castle sites to be found anywhere in the world, for it commands the countryside below for miles around and looks toward distant sea horizons on every side."


title: Shuri Castle

text: During World War II, the Imperial Japanese Army had set up its headquarters in the castle underground, and by early 1945 had established complex lines of defense and communications in the regions around Shuri, and across the southern part of the island as a whole. The Japanese defenses, centered on Shuri Castle, held off the massive American assault from 1 April through the month of May 1945. Beginning on 25 May, and as the final part of the Okinawa campaign, the American battleship "Mississippi" shelled it for three days and by 27 May it was ablaze. But the Japanese had conducted a skillful retreat days before, abandoning Shuri, and forcing the Americans to start a new battle again in the south. US Marine and Army units secured the castle against little resistance. On 29 May, Maj. Gen. Pedro del Valle—commanding the 1st Marine Division—ordered Captain Julian D Dusenbury of Company A, 1st Battalion, 5th Marines to capture the castle, which represented both strategic and psychological blows for the Japanese and was a milestone in the campaign.


title: Shuri Castle

text: After the war, the University of the Ryukyus was established in 1950 on the castle site, where it remained until 1975. In 1958, "Shureimon" was reconstructed and, starting from 1992, the 20th anniversary of reversion, the main buildings and surrounding walls of the central castle were reconstructed. At present, the entire area around the castle has been established as "Shuri Castle Park". In 2000, along with other "gusuku" and related sites, it was designated as a UNESCO World Heritage Site. However, only remnants such as stone walls and building foundations extant before 1950 are officially designated as World Heritage. In addition, 2000 saw the Shureimon gate at Shuri Castle featured on the new 2000 yen note, which entered circulation to commemorate the new millennium and the 26th G8 summit, which was held in Okinawa.


title: Shuri Castle

text: In the morning of 31 October 2019, a large fire broke out and burned down the "Seiden", the main hall, and also the "Hokuden" and "Nanden", adjacent buildings to the north and south. A security alarm went off around 2:30 a.m., and a call to emergency services was placed around 10 minutes later. The "Seiden", "Hokuden", "Nanden" and "Bandokoro" were completely destroyed. According to domestic news sources, "Six castle buildings occupying some in total were gutted." The fire was put out around 1:30 p.m.


title: Shuri Castle

text: Okinawa Police later told domestic broadcaster NHK that a security guard who checked on the alarm found that the main entrance doors to the "Seiden" were closed. When the guard unlocked the shutter and went inside, the interior was already filled with smoke. After police initially ruled out arson, authorities said that the fire was likely caused by an electrical fault after a burned electrical distribution board was found in the northeast side of where the "Seiden" had stood. Police investigations later revealed that the lighting panel had no signs of short circuiting, though a surveillance camera did capture flashing light in the "Seiden" main hall shortly before and after the fire.


title: Shuri Castle

text: The fire was the fifth time that Shuri Castle has been destroyed following previous incidents in 1453, 1660, 1709 and 1945. Okinawa Governor Denny Tamaki said after the fire that Shuri Castle is "a symbol of the Ryukyu Kingdom, an expression of its history and culture", and has vowed to rebuild it. Japan's Chief Cabinet Secretary Yoshihide Suga said that Shuri Castle is "an extremely important symbol of Okinawa". The Japanese Government is considering supplemental appropriations to support restoration work. UNESCO also said it would be ready to assist with Shuri Castle's reconstruction. A crowdfunding campaign set up by Naha City officials for the rebuilding of Shuri Castle had received over $3.2 million in donations as of 6 November 2019.


title: Shuri Castle

text: As of 10 February 2020, rebuilding efforts to restore the destroyed sections of Shuri Castle were underway. In May 2021, a scale replica of the castle measuring one twenty fifth of the size of the actual structure was recreated at the Tobu World Square theme park in Kinugawa Onsen.


title: Shuri Castle

text: Unlike Japanese castles, Shuri Castle was greatly influenced by Chinese architecture, with functional and decorative elements similar to that seen primarily in the Forbidden City. The gates and various buildings were painted in red with lacquer, walls and eaves colorfully decorated, and roof tiles made of Goryeo and later red Ryukyuan tiles, and the decoration of each part heavily using the king's dragon. Given that the "Nanden" and "Bandokoro" were both used for reception and entertainment of the Satsuma clan, a Japanese style design was used here only.


title: Shuri Castle

text: Ryukyuan elements also dominate. Like other "gusuku", the castle was built using Ryukyuan limestone, being surrounded by an outer shell which was built during the Second Shō dynasty from the second half of the 15th century to the first half of the 16th century. Similarly, "Okushoin-en" is the only surviving garden in a "gusuku" in the Ryukyu Islands, which made use of the limestone bedrock and arranged using local cycads.


title: Shuri Castle

text: The current renovation is designed with a focus on the castle's role as a cultural or administrative/political center, rather than one for military purposes. The buildings that had been restored as original wooden buildings (and subsequently destroyed in the 2019 fire) were only in the main citadel. The "Seiden" was rebuilt using wood from Taiwan and elsewhere after rituals blessing the removal of large trees from mountains in the Yanbaru region of Okinawa took place. Other buildings, such as the "Nanden" or "Hokuden" were only restored as facades, with interiors made using modern materials such as steel and concrete. Old walls remain in part, and were excavated and incorporated during the construction of the new castle wall, forming the only surviving external remains of the original castle.


title: Shuri Castle

text: Due to its central role in Ryukyuan political and religious life, Shuri is composed of and surrounded by various sites of historical interest. The castle complex itself can be divided into three main zones, namely a central administrative area (including the "Seidan" and "Ura"), an eastern living and ceremonial space (behind the "Seidan") called the "Ouchibara" (literally "inside field"), and a southwestern ceremonial area including the "Kyo-no-uchi" (literally "inside capital").


title: Shuri Castle

text: All of the buildings located at Shurijo are modern reconstructions, the originals being lost in 1945.


title: Shuri Castle

text: Shurijo operated not only as a base of political and military control, it was also regarded as a central religious sanctuary of the Ryukyuan people. Formerly there were 10 "utaki" (shrines) within the castle and the large area on the south-western side of the citadel was occupied by a sanctuary called "Kyo-no-uchi". This was a place where natural elements, such as trees and natural limestone rocks were utilized. Although "Noro" (priestesses) carried out a number of nature rituals (as also sometimes occurs in Shinto), the contents of the rituals and the layout of the inner part of the sacred areas remain unclear. After the war, limited religious observance continued on the site, mostly with the placement of incense sticks on places formerly considered sacred. However, restoration of the castle stopped general access to these sites, and for this reason, "Shuri Castle was resurrected, but it was destroyed as a place of worship".


title: Shuri Castle

text: Contacts between the Ryukyu Islands and China began in 1372 and lasted five centuries until the establishment of Okinawa Prefecture in 1879. When a new king commenced, the Emperor of China sent officials to attend the investiture ceremony at the castle. Through this ceremony, the kingdom reiterated its ties with China, both politically, commercially, and culturally. This custom also granted the new monarch official international recognition within east Asia.


title: Shuri Castle

text: The Chinese delegation included about 500 people, including a "Sapposhi" (ambassador) and a representative, both appointed by senior officials of the emperor. The envoys departed from Beijing and proceeded by land to Fuzhou in Fujian Province, where they sailed to the Ryukyu Islands, sometimes via Kumejima, on "Ukanshin" ("Crown Ships").


title: Shuri Castle

text: Among the first tasks of the Chinese delegation was a "Yusa" (religious ceremony) in memory of the late king. Words of condolence from the emperor were spoken in "Sōgen-ji" in Naha, and (after 1799) envoys were then received in "Shikina-en". Then the investiture ceremony took place in the "Una", where two platforms were erected between the "Nanden" and "Seiden", called "Kettei", reserved for the envoys, and "Sendokudai". The imperial official recited the formula for the appointment of the new king and bowed deeply.


title: Shuri Castle

text: Later, inside the castle, there was a "Feast of Investiture," followed by a "Mid-autumn Banquet", accompanied by songs and dances. This banquet was held on a temporary platform opposite the "Hokuden", a platform on which the Imperial envoys stood. On the shore of "Ryutan" and in the castle, the "Choyo Banquet", during which a boat race and musical performances took place, was also held in the presence of the delegation. Two successive farewell banquets were then held opposite "Hokuden", and finally a banquet at "Tenshikan", where the king gave the Chinese delegation gold presents as an august sign for their return.


title: Shuri Castle

text: In the 2002 computer game, "", the last mission takes place while assaulting Shurijo. In the 2008 video game, "", the last American mission ("Breaking Point") also takes place in the castle, where US Marines make their final push to take Okinawa. In the game, main characters in the plot die alongside several US forces as the player proceeds upwards under mortar and small arms fire to "Ura", the courtyard of the ruined castle, which was targeted by US airstrikes to soften Japanese forces entrenched there. Also the Call of Duty World at War multiplayer map ("Courtyard") takes place at Shuri Castle.


title: ZPU

text: The ZPU (, meaning "anti-aircraft machine gun mount") is a family of towed anti-aircraft gun based on the Soviet 14.5×114mm KPV heavy machine gun. It entered service with the Soviet Union in 1949 and is used by over 50 countries worldwide.


title: ZPU

text: Quadruple (ZPU-4), double- (ZPU-2 and ZU-2) and single-barreled (ZPU-1) versions of the weapon exist.


title: ZPU

text: The first dedicated Soviet mount for anti-aircraft machine guns was developed around 1928 by Fedor Tokarev and was adopted for service in 1931. It was a base for mounting up to four 7.62 mm PM M1910 (Russian Maxim) guns. This was also called a ZPU, although the name М-4 was also assigned to it. It served the Soviet armed forces in all major conflicts until 1945. 12.7 mm DShK 1938 was used an anti-aircraft weapon it was mounted on pintle and tripod mounts, and on a triple mount on the GAZ-AA truck. Late in the war, it was mounted on the cupolas of IS-2 tanks and ISU-152 self-propelled guns. As an infantry heavy support weapon it used a two-wheeled trolley which unfolded into a tripod for anti-aircraft use.


title: ZPU

text: Development of the ZPU-2 and ZPU-4 began in 1945, with development of the ZPU-1 starting in 1947. All three were accepted into service in 1949. Improved optical predicting gunsights were developed for the system in the 1950s.


title: ZPU

text: All weapons in the ZPU series have air-cooled quick-change barrels and can fire a variety of ammunition including API (B32), API (BS41), API-T (BZT) and I-T (ZP) projectiles. Each barrel has a maximum rate of fire of around 600 rounds per minute, though this is practically limited to about 150 rounds per minute.


title: ZPU

text: The quad-barrel ZPU-4 uses a four-wheel carriage similar to that once used by the obsolete 25 mm automatic anti-aircraft gun M1940. In firing position, the weapon is lowered onto firing jacks. It can be brought in and out of action in about 15 to 20 seconds, and can be fired with the wheels in the traveling position if needed.


title: ZPU

text: The double-barrel ZPU-2 was built in two different versions; the early model has large mud guards and two wheels that are removed in the firing position, and the late model has wheels that fold and are raised from the ground in the firing position.


title: ZPU

text: ZPU-2 turned out to be too heavy for the Airborne Troops, so a new UZPU-2 (later redesignated as ZU-2) was developed from ZPU-1.


title: ZPU

text: The single-barrel ZPU-1 is carried on a two-wheeled carriage and can be broken down into several 80-kilogram pieces for transport over rough ground.


title: ZPU

text: The series was used during the Korean War by Chinese and North Korean forces, and was later considered to be the most dangerous opposition to U.S. helicopters in Vietnam. Later it was used by Morocco and the Polisario Front in the Western Sahara War. It was also used by Iraqi forces during Operation Desert Storm and again in Operation Iraqi Freedom. In 1974 the Cyprus National Guard artillery batteries used their ZPU-2s against the Turkish air force.


title: ZPU

text: In the Russian military, it was replaced by the newer and more powerful ZU-23 23 mm twin automatic anti-aircraft gun.


title: ZPU

text: During the Lebanese Civil War, the Lebanese militias mounted the ZPU-2 and ZPU-4 on various vehicles, such as M113 armored personnel carriers, to create self-propelled support vehicles.


title: ZPU

text: The ZPU has seen widespread use by both sides in the Libyan Civil War, Syrian Civil War, and Yemeni Civil War, being often mounted on technical pickup trucks. The weapon is credited for bringing down several Syrian Air Force helicopters.


title: ZPU

text: In North Korea, ZPU systems have been modified to be able to be directed by a MR-104 "Drum Tilt", where the guns are shown to be fired without personnel manning them.


title: Tom Robinson

text: Thomas Giles Robinson (born 1 June 1950) is a British singer, bassist, radio presenter and long-time LGBT rights activist, best known for the hits "Glad to Be Gay", "2-4-6-8 Motorway", and "Don't Take No for an Answer", with his Tom Robinson Band. He later peaked at No. 6 in the UK Singles Chart with his solo single "War Baby".


title: Tom Robinson

text: Tom Robinson was born into a middle-class family in Cambridge on 1 June 1950. He attended Friends' School, Saffron Walden, a co-ed privately funded Quaker school, between 1961 and 1967. He played guitar in a trio at school called The Inquisition. Robinson has two brothers, Matthew (a former BBC executive producer) and George, and a sister, Sophy.


title: Tom Robinson

text: At the age of 13, Robinson realised that he was gay when he fell in love with another boy at school. Until 1967, male homosexual activity was a crime in England, punishable by prison. He had a nervous breakdown and attempted suicide at 16. A head teacher got him transferred to Finchden Manor, a therapeutic community, in Kent, for teenagers with emotional difficulties, where he spent his following six years. At the community, Robinson was inspired by John Peel's "The Perfumed Garden" on pirate Radio London, and by a visit from Alexis Korner. The legendary bluesman and broadcaster transfixed a roomful of people, using nothing but his voice and an acoustic guitar. The whole direction of Robinson's life and career became suddenly clear to him.


title: Tom Robinson

text: In 1973, Robinson moved to London and joined the acoustic trio Café Society. They impressed Ray Davies, of The Kinks, enough for him to sign them to his Konk label and produce their debut album. According to Robinson, Davies's other commitments made the recording a lengthy process and, after it sold only 600 copies, he left the band. Subsequently, when the Tom Robinson Band were playing at the Nashville Rooms in London, Robinson saw Davies enter and sarcastically performed The Kinks' hit "Tired of Waiting for You". Davies retaliated with the less-than-complimentary Kinks single "Prince of the Punks", about Robinson.


title: Tom Robinson

text: In London, Robinson became involved in the emerging gay scene and embraced the politics of gay liberation, which linked gay rights to wider issues of social justice. Inspired by an early Sex Pistols gig, he founded the more political Tom Robinson Band in 1976. The following year the group released the single "2-4-6-8 Motorway", which peaked at No. 5 in the UK Singles Chart for two weeks. The song alludes obliquely to a gay truck driver. In February 1978, the band released the live extended play "Rising Free", which peaked at No. 18 in the UK Singles Chart and included his anthemic song "Glad to Be Gay", originally written for a 1976 London gay pride parade. The song was banned by the BBC. In May 1978, the band released its debut album, "Power in the Darkness", which was very well received, peaking at No. 4 in the UK Albums Chart, and receiving a gold certification by the BPI. Their second album, "TRB Two" (1979), however, was a commercial and critical failure, and the band broke up four months after its release.


title: Tom Robinson

text: In 1979, Robinson co-wrote several songs with Elton John, including his minor hit "Sartorial Eloquence (Don't Ya Wanna Play This Game No More?)", which peaked at No. 39 in the U.S. "Billboard" Hot 100 and a song about a young boy in boarding school who has a crush on an older student called "Elton's Song". It was recorded, but not released until 1981 on the album "The Fox". He played two songs live— "Glad to Be Gay" and "1967 (So Long Ago)" — during June of that year at The Secret Policeman's Ball (1979).


title: Tom Robinson

text: In 1980, Robinson organised Sector 27, a less political rock band that released a critically acclaimed but unsuccessful album, "Sector 27", produced by Steve Lillywhite. The band nevertheless received an enthusiastic reception at a Madison Square Garden concert with The Police. However, their management company went bankrupt, the band disintegrated, and Robinson suffered another nervous breakdown. Desolate, in debt, and sorrowing from a breakup with a beau, Robinson fled to Hamburg, Germany, much like his idol David Bowie . Living in a friend's spare room, he began writing again and ended up working in East Berlin with local band NO55.


title: Tom Robinson

text: In 1982, Robinson penned the song "War Baby" about divisions between East and West Germany, and recorded his first solo album "North by Northwest" with producer Richard Mazda. "War Baby" peaked at No. 6 in the UK Singles Chart and at No. 1 in the UK Indie Chart for three weeks, reviving his career. His following single, "Listen to the Radio: Atmospherics", co-written with Peter Gabriel, peaked at No. 39 in the UK Singles Chart, and provided him further income when it was covered by Pukka Orchestra in 1984. The Pukkas' version was a top 20 hit in Canada under the title "Listen to the Radio".


title: Tom Robinson

text: Robinson's return to Britain led to late-night performances in cabarets at the Edinburgh Fringe, some of which later surfaced on the live album "Midnight at the Fringe" (1988). His career enjoyed a resurgence in the mid-1990s with a trio of albums for the respected folk/roots label Cooking Vinyl and a Glastonbury performance in 1994.


title: Tom Robinson

text: In 1986, a BBC producer offered him his own radio show on the BBC World Service. Since then Robinson has, unusually, presented programmes on all the BBC's national stations: Radio 1, Radio 2, Radio 3, Radio 4, 5 Live and 6 Music. He presented "The Locker Room", a long-running series about men and masculinity, for Radio 4 in the early 1990s, and later hosted the "Home Truths" tribute to John Peel a year after his death in 2004.


title: Tom Robinson

text: In 1997, he won a Sony Academy Award for "You've Got to Hide Your Love Away", a radio documentary about gay music, produced by Benjamin Mepsted. He currently presents his own show on 6 Music, on Saturdays between 9pm and midnight, and on Sundays between 6pm and 8pm as "Now Playing @6Music", a show that plays songs based on a certain theme and listeners' input. He also has a show broadcast at 2am on Monday mornings, which is focused on music by local bands from "BBC Introducing". In 1994 he wrote and presented "Surviving Suicide", about his suicide attempt.


title: Tom Robinson

text: Currently, Robinson rarely performs live, apart from two annual free concerts, known as the Castaway Parties, for members of his mailing list. These take place in South London and Belgium every January. In the Belgian Castaway shows, he introduces many songs in Dutch. The Castaway Parties invariably feature a wide variety of established and unknown artists and groups who have included Show of Hands, Philip Jeays, Jan Allain, Jakko Jakszyk, Stoney, Roddy Frame, Martyn Joseph, The Bewley Brothers and Paleday alongside personal friends such as Lee Griffiths and T. V. Smith.


title: Tom Robinson

text: In 2009, Robinson founded "Fresh on the Net", a showcase website for upcoming bands and artists whose aim is "to help independent musicians find new listeners, and independent listeners find new music".


title: Tom Robinson

text: Robinson played "2-4-6-8 Motorway" and "Glad to Be Gay" at the BBC introducing stage on the Friday afternoon of the 2011 Glastonbury Festival, after announcing that The Coral would not be showing as they were 'stuck in the mud'. In July 2013, at the Tabernacle on Powis Square in Notting Hill, a new line-up of TRB performed the entire "Power in the Darkness" album to launch its release on CD. The title track featured a guest appearance by T. V. Smith.


title: Tom Robinson

text: In 2014, he was one of the performers at the opening ceremonies of WorldPride in Toronto, Ontario, Canada, alongside Melissa Etheridge, Deborah Cox and Steve Grand.


title: Tom Robinson

text: In October 2015 he released his first new album in 20 years, "Only The Now". It included contributions from Billy Bragg, Ian McKellen and Lee Forsyth Griffiths. It was made with award-winning producer and multi-instrumentalist Gerry Diver and released on his own Castaway Northwest Recordings. Tom supported the album by playing many festivals that summer including Glastonbury, Latitude, Wickham and Green Man. He also played a showcase at London's Queen Elizabeth Hall in September and a 15-date tour throughout October and November. Robinson also received a BASCA Gold Badge award in the same month. This was for his exceptional contribution to British music.


title: Tom Robinson

text: In late 2018 and early 2019 Robinson deputised for Radio 2 DJ Johnnie Walker on his Sunday show "Sounds of the 70s".


title: Tom Robinson

text: In 2020, Robinson embarked on a four-night solo acoustic tour prior to beginning a 22-date UK "70th Birthday Tour" featuring a 5-piece band.


title: Tom Robinson

text: Robinson does not identify exclusively as gay. He has had past experiences with women and has asserted that he has always made it clear that he liked both men and women. He now identifies as bisexual, but in the past he used the phrase 'gay', synonymous with 'queer', to encompass the entire LGBT community. He felt the term 'bisexual' was a cop-out.


title: Tom Robinson

text: A longtime supporter and former volunteer of London's Gay Switchboard help-line, it was at a 1982 benefit party for the organisation that Robinson met Sue Brearley, the woman with whom he would eventually live and have two children, and later marry.


title: Tom Robinson

text: In the mid-1990s, when Robinson became a father, the tabloids ran stories about what they deemed as a sexual orientation change, running headlines such as "Britain's Number One Gay in Love with Girl Biker!" ("The Sunday People)". Robinson continued to identify as a gay man, telling an interviewer for "The Guardian": "I have much more sympathy with bisexuals now, but I am absolutely not one." He added, "Our enemies do not draw the distinction between gay and bisexual."


title: Tom Robinson

text: In a 1994 interview for "The Boston Globe" newspaper, Robinson asserted: "We've been fighting for tolerance for the last 20 years, and I've campaigned for people to be able to love whoever the hell they want. That's what we're talking about: tolerance and freedom and liberty—life, liberty, and the pursuit of happiness. So if somebody won't grant me the same tolerance I've been fighting for them, hey, they've got a problem, not me."


title: Tom Robinson

text: In 1996 Robinson released an album "Having It Both Ways". On it, he added a verse to "Glad to Be Gay", in which he sings: "Well if gay liberation means freedom for all, a label is no liberation at all. I'm here and I'm queer and do what I do, I'm not going to wear a straitjacket for you." In 1998, his epic about bisexuality, "Blood Brother", won three awards at the Gay & Lesbian American Music Awards in New York. In the same year, he also performed at the fifth International Conference on Bisexuality at Harvard University in Cambridge, Massachusetts.


title: Tom Robinson

text: Peter Tatchell criticised "Glad Not to Be Gay", an article written by Vanessa Thorpe about Robinson in "The Independent" newspaper, for suggesting the LGBT community would be "shocked and angered" that a gay man would "go straight". Tatchell stated: "Tom Robinson has behaved rather commendably, in my view. Ever since the beginning of his relationship with Sue, he has continued to describe himself as 'a gay man who happens to be in love with a woman'. Who could quarrel with that? I can't."


title: Tom Robinson

text: Robinson is a supporter of Amnesty International and Peter Tatchell's OutRage! human rights organisation and was a leader of the Rock Against Racism campaign.


title: Tom Robinson

text: A fictionalised version of Tom Robinson, portrayed by Mathew Baynton, appears in the last episode of the first series of the BBC One television drama "Ashes to Ashes", as leader at a Gay Liberation Front protest in London. The character is later incarcerated with other protestors by the time-travelling protagonist, Detective Inspector Alex Drake (played by Keeley Hawes) and dismisses her claims that he will one day marry a woman. The scene supposedly takes place on 9 October 1981, precisely fourteen months before the real Tom Robinson met his future bride. The character then leads other protestors in singing a round of "Glad to Be Gay" in the confinement facility, much to Sergeant Viv James' annoyance. "2-4-6-8 Motorway" is also used in the soundtrack during the protest after Detective Sergeant Ray Carling sings a few bars to Alex, who then proceeds to drive a pink tank over a parked Ford Escort, which she believes would otherwise have later been used in a car bombing. Robinson's song "War Baby" (which he premiered the night he met his wife) is used in the soundtrack of the third series.


title: Tom Robinson

text: Over his career, Robinson has released more than twenty albums either as a solo performer or as a member of a group. He has also released fanclub-only bootlegs known as the "Castaway Club" series.


title: K-Ci

text: Cedric Renard Hailey (born September 2, 1969), known professionally as K-Ci (formerly Little Cedric as a member of Little Cedric and the Hailey Singers), is an American singer, songwriter and member of K-Ci & JoJo and Jodeci.


title: K-Ci

text: Although Hailey is best known as the lead singer of Jodeci and second-lead singer of K-Ci & JoJo, he participated on different solo projects as K-Ci, most notably his cover of Bobby Womack's "If You Think You're Lonely Now" in 1994.


title: K-Ci

text: Hailey was born in Charlotte, North Carolina, to Anita and Cliff Hailey both of whom were gospel singers. For a time, the Hailey family lived in Baltimore, MD where they performed gospel music. The family would later return to Charlotte when Cedric was a teen. He would eventually go on to attend Garinger High School.


title: K-Ci

text: Along with younger brother, Joel (known professionally as "JoJo") and his father, Hailey recorded three gospel albums as "Little Cedric and the Hailey Singers" beginning with the 1983 release "I'm Alright Now" by Atlanta International Records, Gospel. Though the album failed to place on any "Billboard" magazine charts, the next two releases, 1984's "Jesus Saves" and "God's Blessing" in 1985, both placed upon the "Billboard" Gospel Albums chart; the former at No. 4 and the latter at No. 22.


title: K-Ci

text: Cedric and Joel's gospel singing eventually connected them with the DeGrate brothers, Donald "DeVante Swing" DeGrate and Dalvin DeGrate, with whom they formed the R&B group Jodeci. As lead vocalist for the group, Hailey and Jodeci would release three multi-platinum albums between 1991 and 1995. In 1996, the group announced a hiatus from recording and releasing music. Hailey continued to record with his brother as the duo K-Ci & JoJo, releasing five albums between 1997 and 2013.


title: K-Ci

text: As K-Ci, his cover of Bobby Womack's "If You Think You're Lonely Now" was featured on the soundtrack to the 1994 film, "Jason's Lyric". It was released as a single and peaked at number 17 on the Billboard Hot 100.


title: K-Ci

text: Hailey dated fellow R&B singer and then label-mate Mary J. Blige from 1992 to 1997. Blige stated that they were engaged, but Hailey denied that they were going to get married.


title: K-Ci

text: The two Hailey brothers are cousins of R&B singers Fantasia Barrino, Dave Hollister, Calvin Richardson, and Stephanie Mills.


title: 2005 German federal election

text: Federal elections were held in Germany on 18 September 2005 to elect the members of the 16th Bundestag. The snap election was called after the government's defeat in a state election, which caused them to intentionally lose a motion of confidence to trigger an early federal election. The outgoing government was a coalition of the centre-left Social Democratic Party of Germany (SPD) and Alliance 90/The Greens, led by federal Chancellor Gerhard Schröder. The election was originally intended for the autumn of 2006.


title: 2005 German federal election

text: The opposition Christian Democratic Union of Germany (CDU), with its sister party the Christian Social Union in Bavaria (CSU), started the campaign with a strong lead over the SPD in opinion polls. The government was generally expected to suffer a major defeat and be replaced by a coalition of the CDU/CSU and the liberal Free Democratic Party (FDP), with CDU leader Angela Merkel becoming chancellor. However, the CDU/CSU ultimately lost vote share compared to its 2002 result, falling to 35%. The SPD suffered losses but finished just one percentage point behind the CDU/CSU, winning 34%. Exit polls showed clearly that neither the SPD–Green nor CDU/CSU–FDP coalitions had won a majority of seats in the Bundestag. The FDP placed third on just under 10% of votes, its best result since 1990, while the Greens suffered small losses. The major stumbling block to a parliamentary majority was the new Left Party, led by Gregor Gysi and former SPD chairman Oskar Lafontaine, which won 8.7% of votes and 54 seats. The CDU/CSU and SPD both rejected cooperation with the Left Party.


title: 2005 German federal election

text: Both Schröder and Merkel claimed victory, but the formation of a new government required careful negotiations, as no conventional arrangement could achieve a majority. The CDU/CSU sought talks with the Greens, but were unable to find common ground. Discussions ultimately began for a grand coalition between the CDU/CSU and SPD. On 10 October, officials from both parties indicated that negotiations had concluded successfully and that they would form a coalition government with Angela Merkel as chancellor. The Bundestag met on 22 November and Merkel was elected chancellor, with 397 votes in favour.


title: 2005 German federal election

text: On 22 May 2005, state elections were held in North Rhine-Westphalia, the most populous state of Germany, where the SPD had led the state government continuously since 1966. The election saw the government of Minister-President Peer Steinbrück defeated. It also resulted in the opposition CDU and FDP claiming a majority in the Bundesrat, the upper house of the federal legislature. The same day, federal Chancellor Schröder and SPD Bundestag group leader Franz Müntefering announced they would seek early federal elections. They claimed the North Rhine-Westphalia result was indicative of a lack of public confidence in the federal government.


title: 2005 German federal election

text: Early federal elections may only be held under two circumstances: if the Bundestag rejects a candidate for chancellor three times, or if a motion of confidence in the government fails to achieve an absolute majority in the Bundestag. In either case, the president may, at request of the chancellor, dissolve the Bundestag and order new elections. The latter method had been utilised on two occasions previously, in 1972 and 1983, by incumbent governments intentionally failing motions of confidence. Schröder became the third chancellor to do this, with a motion of confidence on 1 July failing with 151 votes in favour, 296 against, and 148 abstentions. Schröder called on SPD members to abstain from the vote, which would allow him to fall short of the required threshold. President Horst Köhler then dissolved the Bundestag and scheduled new elections.


title: 2005 German federal election

text: The CDU/CSU nominated Angela Merkel for chancellor, the first time in German history that one of the two larger parties had nominated a woman for this position. The CDU presented a platform involving increasing the pace and scope of economic deregulation in Germany and pursuing cuts in income tax and public spending (many commentators have compared Merkel with Margaret Thatcher). The CDU began the campaign with a 21% lead over the SPD and confidence in Merkel's victory led the Prime Minister of the United Kingdom, Tony Blair, to meet with her ahead of Chancellor Schröder during a visit to Berlin in June.


title: 2005 German federal election

text: The SPD had the goal of maintaining the current deregulation agenda. They added to their election program some minor corrections such as broadening the financing base of the healthcare system and the proposal of a 3% additional tax for people with annual incomes above 250,000 euro (after the governing coalition earlier in 2005 cut the highest income tax rate from 48.5% to 42%).


title: 2005 German federal election

text: The Greens decided on their program in July 2005. Compared to their previous federal election program, they increased the emphasis on economics and labour-market politics. For the first time this topic came before the classical green topic of environmental politics in the program. In general, the program moved slightly to the left; including stating the necessity for changes to some existing red-green governmental policies.


title: 2005 German federal election

text: The FDP announced its election program before any other party, publishing it on 24 July. It called for strong saving measures in public spending and more room for local negotiation between employees and employers, as opposed to central control by trade-union officials.


title: 2005 German federal election

text: The leaders of the left wing Party of Democratic Socialism (the "PDS") agreed to let candidates of the centre left Electoral Alternative for Labor and Social Justice (the "WASG") run on their party list, leaving open the possible future option of a merger between the two parties. In agreeing to this the WASG stipulated that the PDS rename itself as the Left Party. The WASG, with its front-runner Oskar Lafontaine (a former SPD leader), formed from breakaway elements within the SPD, angered at that party taking a "neoliberal" direction in economic reforms. The general membership has already approved this measure and awaits to hear from the PDS party convention to agree as well. If successful this could lead to a further erosion of the SPD's strength, as the PDS has never made inroads in the former West Germany (it lineally succeeded the former governing communist party (Socialist Unity Party of Germany) of the former German Democratic Republic), while the WASG has its base in western Germany and could garner substantial votes there.


title: 2005 German federal election

text: Two of Germany's small far-right parties, the National Democratic Party (NPD) and the German People's Union (DVU), announced that they would run on a common platform in this election, raising fears in the mainstream German political establishment that together they might succeed in gaining more than 5% of the national vote and thus in entering the Bundestag. Since German electoral law does not permit common lists of two or more parties, in practice the DVU did not enter the election, and members of that party appeared on the NPD list.


title: 2005 German federal election

text: Early election polls during summer 2005 from 6 organizations showed a solid lead for the CDU/CSU with a share of the vote ranging between 41% and 43%, and the SPD trailing at between 32% and 34%. The polls further showed the FDP, a possible coalition partner for the conservatives, at between 6.5% and 8%, and the Greens, the current coalition partner for the SPD, between 6% and 8%. Most polls indicated a likely majority for a CDU/CSU-FDP coalition. As for other parties, those polls which explicitly included the PDS-WASG electoral alliance showed it above the 5% hurdle at between 7% and 8.5%. No poll showed any other parties, including far-right parties, near 5%, although far-right parties have in the past sometimes polled below their actual support due to unwillingness by voters to admit their support.


title: 2005 German federal election

text: In early August support for Angela Merkel declined considerably. Reasons for this included conflicts about the election program in and between the conservative parties (the CDU and the CSU), and arguments with their preferred coalition partner, the FDP, as well as embarrassing gaffes. At one point the media criticized Merkel for confusing net and gross income figures during a campaign speech. Following this, polls suggested that the CDU/CSU and FDP would only win 48% of votes between them, and thus would not be able to form a government. Further damage occurred when two prominent CDU/CSU candidates, Jörg Schönbohm and the CSU leader Edmund Stoiber, made insulting remarks about East Germans. These remarks not only alienated voters in Eastern Germany but also made some question the CDU/CSU's confidence in Merkel, as she herself grew up in the East.


title: 2005 German federal election

text: However, polls carried out by the "Süddeutsche Zeitung" in late August showed the CDU/CSU/FDP bloc back up at 51% of the vote. Predictions suggested that the opposing bloc of incumbent Chancellor Gerhard Schröder's ruling Social Democrats, the Greens and the country's recently formed left-wing Left Party (PDS/WASG alliance) would win a combined total of only 46%. The leaders of the SPD and the Greens, Schröder and Fischer, as well as the Left Party's front-runner Gregor Gysi said they opposed the idea of a "red-red-green" coalition. With polls remaining so close, speculation increased that (as in the elections of 1994, 1998 and 2002) a small number of overhang seats might significantly impact the election results.


title: 2005 German federal election

text: On Sunday 4 September, Schröder and Merkel met in a head-to-head debate which was broadcast by four of Germany's major private and public television networks. Although most commentators gave the initial edge to Merkel, polls soon showed that the general public disagreed and ranked Schröder the clear winner. Later analysis suggested that Merkel's support for a flat-tax proposal by Paul Kirchhof, the shadow Finance Minister, further undermined her credibility on economic affairs and gave the impression that the CDU's economic reforms would only benefit the very rich.