title: DNA

text: DNA contains the genetic information that allows all forms of life to function, grow and reproduce. However, it is unclear how long in the 4-billion-year history of life DNA has performed this function, as it has been proposed that the earliest forms of life may have used RNA as their genetic material. RNA may have acted as the central part of early cell metabolism as it can both transmit genetic information and carry out catalysis as part of ribozymes. This ancient RNA world where nucleic acid would have been used for both catalysis and genetics may have influenced the evolution of the current genetic code based on four nucleotide bases. This would occur, since the number of different bases in such an organism is a trade-off between a small number of bases increasing replication accuracy and a large number of bases increasing the catalytic efficiency of ribozymes. However, there is no direct evidence of ancient genetic systems, as recovery of DNA from most fossils is impossible because DNA survives in the environment for less than one million years, and slowly degrades into short fragments in solution. Claims for older DNA have been made, most notably a report of the isolation of a viable bacterium from a salt crystal 250 million years old, but these claims are controversial.


title: DNA

text: Building blocks of DNA (adenine, guanine, and related organic molecules) may have been formed extraterrestrially in outer space. Complex DNA and RNA organic compounds of life, including uracil, cytosine, and thymine, have also been formed in the laboratory under conditions mimicking those found in outer space, using starting chemicals, such as pyrimidine, found in meteorites. Pyrimidine, like polycyclic aromatic hydrocarbons (PAHs), the most carbon-rich chemical found in the universe, may have been formed in red giants or in interstellar cosmic dust and gas clouds.


title: DNA

text: In February 2021, scientists reported, for the first time, the sequencing of DNA from animal remains, a mammoth in this instance over a million years old, the oldest DNA sequenced to date.


title: DNA

text: Methods have been developed to purify DNA from organisms, such as phenol-chloroform extraction, and to manipulate it in the laboratory, such as restriction digests and the polymerase chain reaction. Modern biology and biochemistry make intensive use of these techniques in recombinant DNA technology. Recombinant DNA is a man-made DNA sequence that has been assembled from other DNA sequences. They can be transformed into organisms in the form of plasmids or in the appropriate format, by using a viral vector. The genetically modified organisms produced can be used to produce products such as recombinant proteins, used in medical research, or be grown in agriculture.


title: DNA

text: Forensic scientists can use DNA in blood, semen, skin, saliva or hair found at a crime scene to identify a matching DNA of an individual, such as a perpetrator. This process is formally termed DNA profiling, also called "DNA fingerprinting". In DNA profiling, the lengths of variable sections of repetitive DNA, such as short tandem repeats and minisatellites, are compared between people. This method is usually an extremely reliable technique for identifying a matching DNA. However, identification can be complicated if the scene is contaminated with DNA from several people. DNA profiling was developed in 1984 by British geneticist Sir Alec Jeffreys, and first used in forensic science to convict Colin Pitchfork in the 1988 Enderby murders case.


title: DNA

text: The development of forensic science and the ability to now obtain genetic matching on minute samples of blood, skin, saliva, or hair has led to re-examining many cases. Evidence can now be uncovered that was scientifically impossible at the time of the original examination. Combined with the removal of the double jeopardy law in some places, this can allow cases to be reopened where prior trials have failed to produce sufficient evidence to convince a jury. People charged with serious crimes may be required to provide a sample of DNA for matching purposes. The most obvious defense to DNA matches obtained forensically is to claim that cross-contamination of evidence has occurred. This has resulted in meticulous strict handling procedures with new cases of serious crime.


title: DNA

text: DNA profiling is also used successfully to positively identify victims of mass casualty incidents, bodies or body parts in serious accidents, and individual victims in mass war graves, via matching to family members.


title: DNA

text: DNA profiling is also used in DNA paternity testing to determine if someone is the biological parent or grandparent of a child with the probability of parentage is typically 99.99% when the alleged parent is biologically related to the child. Normal DNA sequencing methods happen after birth, but there are new methods to test paternity while a mother is still pregnant.


title: DNA

text: Deoxyribozymes, also called DNAzymes or catalytic DNA, were first discovered in 1994. They are mostly single stranded DNA sequences isolated from a large pool of random DNA sequences through a combinatorial approach called in vitro selection or systematic evolution of ligands by exponential enrichment (SELEX). DNAzymes catalyze variety of chemical reactions including RNA-DNA cleavage, RNA-DNA ligation, amino acids phosphorylation-dephosphorylation, carbon-carbon bond formation, etc. DNAzymes can enhance catalytic rate of chemical reactions up to 100,000,000,000-fold over the uncatalyzed reaction. The most extensively studied class of DNAzymes is RNA-cleaving types which have been used to detect different metal ions and designing therapeutic agents. Several metal-specific DNAzymes have been reported including the GR-5 DNAzyme (lead-specific), the CA1-3 DNAzymes (copper-specific), the 39E DNAzyme (uranyl-specific) and the NaA43 DNAzyme (sodium-specific). The NaA43 DNAzyme, which is reported to be more than 10,000-fold selective for sodium over other metal ions, was used to make a real-time sodium sensor in cells.


title: DNA

text: Bioinformatics involves the development of techniques to store, data mine, search and manipulate biological data, including DNA nucleic acid sequence data. These have led to widely applied advances in computer science, especially string searching algorithms, machine learning, and database theory. String searching or matching algorithms, which find an occurrence of a sequence of letters inside a larger sequence of letters, were developed to search for specific sequences of nucleotides. The DNA sequence may be aligned with other DNA sequences to identify homologous sequences and locate the specific mutations that make them distinct. These techniques, especially multiple sequence alignment, are used in studying phylogenetic relationships and protein function. Data sets representing entire genomes' worth of DNA sequences, such as those produced by the Human Genome Project, are difficult to use without the annotations that identify the locations of genes and regulatory elements on each chromosome. Regions of DNA sequence that have the characteristic patterns associated with protein- or RNA-coding genes can be identified by gene finding algorithms, which allow researchers to predict the presence of particular gene products and their possible functions in an organism even before they have been isolated experimentally. Entire genomes may also be compared, which can shed light on the evolutionary history of particular organism and permit the examination of complex evolutionary events.


title: DNA

text: DNA nanotechnology uses the unique molecular recognition properties of DNA and other nucleic acids to create self-assembling branched DNA complexes with useful properties. DNA is thus used as a structural material rather than as a carrier of biological information. This has led to the creation of two-dimensional periodic lattices (both tile-based and using the "DNA origami" method) and three-dimensional structures in the shapes of polyhedra. Nanomechanical devices and algorithmic self-assembly have also been demonstrated, and these DNA structures have been used to template the arrangement of other molecules such as gold nanoparticles and streptavidin proteins. DNA and other nucleic acids are the basis of aptamers, synthetic oligonucleotide ligands for specific target molecules used in a range of biotechnology and biomedical applications.


title: DNA

text: Because DNA collects mutations over time, which are then inherited, it contains historical information, and, by comparing DNA sequences, geneticists can infer the evolutionary history of organisms, their phylogeny. This field of phylogenetics is a powerful tool in evolutionary biology. If DNA sequences within a species are compared, population geneticists can learn the history of particular populations. This can be used in studies ranging from ecological genetics to anthropology.


title: DNA

text: DNA as a storage device for information has enormous potential since it has much higher storage density compared to electronic devices. However, high costs, slow read and write times (memory latency), and insufficient reliability has prevented its practical use.


title: DNA

text: DNA was first isolated by the Swiss physician Friedrich Miescher who, in 1869, discovered a microscopic substance in the pus of discarded surgical bandages. As it resided in the nuclei of cells, he called it "nuclein". In 1878, Albrecht Kossel isolated the non-protein component of "nuclein", nucleic acid, and later isolated its five primary nucleobases.


title: DNA

text: In 1909, Phoebus Levene identified the base, sugar, and phosphate nucleotide unit of the RNA (then named "yeast nucleic acid"). In 1929, Levene identified deoxyribose sugar in "thymus nucleic acid" (DNA). Levene suggested that DNA consisted of a string of four nucleotide units linked together through the phosphate groups ("tetranucleotide hypothesis"). Levene thought the chain was short and the bases repeated in a fixed order. In 1927, Nikolai Koltsov proposed that inherited traits would be inherited via a "giant hereditary molecule" made up of "two mirror strands that would replicate in a semi-conservative fashion using each strand as a template". In 1928, Frederick Griffith in his experiment discovered that traits of the "smooth" form of "Pneumococcus" could be transferred to the "rough" form of the same bacteria by mixing killed "smooth" bacteria with the live "rough" form. This system provided the first clear suggestion that DNA carries genetic information.


title: DNA

text: In 1933, while studying virgin sea urchin eggs, Jean Brachet suggested that DNA is found in the cell nucleus and that RNA is present exclusively in the cytoplasm. At the time, "yeast nucleic acid" (RNA) was thought to occur only in plants, while "thymus nucleic acid" (DNA) only in animals. The latter was thought to be a tetramer, with the function of buffering cellular pH.


title: DNA

text: In 1937, William Astbury produced the first X-ray diffraction patterns that showed that DNA had a regular structure.


title: DNA

text: In 1943, Oswald Avery, along with co-workers Colin MacLeod and Maclyn McCarty, identified DNA as the transforming principle, supporting Griffith's suggestion (Avery–MacLeod–McCarty experiment). Erwin Chargaff developed and published observations now known as Chargaff's rules, stating that in DNA from any species of any organism, the amount of guanine should be equal to cytosine and the amount of adenine should be equal to thymine. Late in 1951, Francis Crick started working with James Watson at the Cavendish Laboratory within the University of Cambridge. DNA's role in heredity was confirmed in 1952 when Alfred Hershey and Martha Chase in the Hershey–Chase experiment showed that DNA is the genetic material of the enterobacteria phage T2.


title: DNA

text: In May 1952, Raymond Gosling, a graduate student working under the supervision of Rosalind Franklin, took an X-ray diffraction image, labeled as "Photo 51", at high hydration levels of DNA. This photo was given to Watson and Crick by Maurice Wilkins and was critical to their obtaining the correct structure of DNA. Franklin told Crick and Watson that the backbones had to be on the outside. Before then, Linus Pauling, and Watson and Crick, had erroneous models with the chains inside and the bases pointing outwards. Franklin's identification of the space group for DNA crystals revealed to Crick that the two DNA strands were antiparallel. In February 1953, Linus Pauling and Robert Corey proposed a model for nucleic acids containing three intertwined chains, with the phosphates near the axis, and the bases on the outside. Watson and Crick completed their model, which is now accepted as the first correct model of the double helix of DNA. On 28 February 1953 Crick interrupted patrons' lunchtime at The Eagle pub in Cambridge to announce that he and Watson had "discovered the secret of life".


title: DNA

text: The 25 April 1953 issue of the journal "Nature" published a series of five articles giving the Watson and Crick double-helix structure DNA and evidence supporting it. The structure was reported in a letter titled ""MOLECULAR STRUCTURE OF NUCLEIC ACIDS A Structure for Deoxyribose Nucleic Acid", in which they said, "It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material." This letter was followed by a letter from Franklin and Gosling, which was the first publication of their own X-ray diffraction data and of their original analysis method. Then followed a letter by Wilkins and two of his colleagues, which contained an analysis of "in vivo" B-DNA X-ray patterns, and which supported the presence "in vivo" of the Watson and Crick structure.


title: DNA

text: In 1962, after Franklin's death, Watson, Crick, and Wilkins jointly received the Nobel Prize in Physiology or Medicine. Nobel Prizes are awarded only to living recipients. A debate continues about who should receive credit for the discovery.


title: DNA

text: In an influential presentation in 1957, Crick laid out the central dogma of molecular biology, which foretold the relationship between DNA, RNA, and proteins, and articulated the "adaptor hypothesis". Final confirmation of the replication mechanism that was implied by the double-helical structure followed in 1958 through the Meselson–Stahl experiment. Further work by Crick and co-workers showed that the genetic code was based on non-overlapping triplets of bases, called codons, allowing Har Gobind Khorana, Robert W. Holley, and Marshall Warren Nirenberg to decipher the genetic code. These findings represent the birth of molecular biology.


title: Quantum mechanics

text: Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science.


title: Quantum mechanics

text: Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale.


title: Quantum mechanics

text: Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values (quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to how accurately the value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle).


title: Quantum mechanics

text: Quantum mechanics arose gradually from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, and the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. These early attempts to understand microscopic phenomena, now known as the "old quantum theory", led to the full development of quantum mechanics in the mid-1920s by Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Max Born, Paul Dirac and others. The modern theory is formulated in various specially developed mathematical formalisms. In one of them, a mathematical entity called the wave function provides information, in the form of probability amplitudes, about what measurements of a particle's energy, momentum, and other physical properties may yield.


title: Quantum mechanics

text: Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles. It has been demonstrated to hold for complex molecules with thousands of atoms, but its application to human beings raises philosophical problems, such as Wigner's friend, and its application to the universe as a whole remains speculative. Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy.


title: Quantum mechanics

text: A fundamental feature of the theory is that it usually cannot predict with certainty what will happen, but only give probabilities. Mathematically, a probability is found by taking the square of the absolute value of a complex number, known as a probability amplitude. This is known as the Born rule, named after physicist Max Born. For example, a quantum particle like an electron can be described by a wave function, which associates to each point in space a probability amplitude. Applying the Born rule to these amplitudes gives a probability density function for the position that the electron will be found to have when an experiment is performed to measure it. This is the best the theory can do; it cannot say for certain where the electron will be found. The Schrödinger equation relates the collection of probability amplitudes that pertain to one moment of time to the collection of probability amplitudes that pertain to another.


title: Quantum mechanics

text: One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between different measurable quantities. The most famous form of this uncertainty principle says that no matter how a quantum particle is prepared or how carefully experiments upon it are arranged, it is impossible to have a precise prediction for a measurement of its position and also at the same time for a measurement of its momentum.


title: Quantum mechanics

text: Another consequence of the mathematical rules of quantum mechanics is the phenomenon of quantum interference, which is often illustrated with the double-slit experiment. In the basic version of this experiment, a coherent light source, such as a laser beam, illuminates a plate pierced by two parallel slits, and the light passing through the slits is observed on a screen behind the plate. The wave nature of light causes the light waves passing through the two slits to interfere, producing bright and dark bands on the screen – a result that would not be expected if light consisted of classical particles. However, the light is always found to be absorbed at the screen at discrete points, as individual particles rather than waves; the interference pattern appears via the varying density of these particle hits on the screen. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit (as would a classical particle), and not through both slits (as would a wave). However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. Other atomic-scale entities, such as electrons, are found to exhibit the same behavior when fired towards a double slit. This behavior is known as wave–particle duality.


title: Quantum mechanics

text: Another counter-intuitive phenomenon predicted by quantum mechanics is quantum tunnelling: a particle that goes up against a potential barrier can cross it, even if its kinetic energy is smaller than the maximum of the potential. In classical mechanics this particle would be trapped. Quantum tunnelling has several important consequences, enabling radioactive decay, nuclear fusion in stars, and applications such as scanning tunnelling microscopy and the tunnel diode.


title: Quantum mechanics

text: When quantum systems interact, the result can be the creation of quantum entanglement: their properties become so intertwined that a description of the whole solely in terms of the individual parts is no longer possible. Erwin Schrödinger called entanglement "..."the" characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought". Quantum entanglement enables the counter-intuitive properties of quantum pseudo-telepathy, and can be a valuable resource in communication protocols, such as quantum key distribution and superdense coding. Contrary to popular misconception, entanglement does not allow sending signals faster than light, as demonstrated by the no-communication theorem.


title: Quantum mechanics

text: Another possibility opened by entanglement is testing for "hidden variables", hypothetical properties more fundamental than the quantities addressed in quantum theory itself, knowledge of which would allow more exact predictions than quantum theory can provide. A collection of results, most significantly Bell's theorem, have demonstrated that broad classes of such hidden-variable theories are in fact incompatible with quantum physics. According to Bell's theorem, if nature actually operates in accord with any theory of "local" hidden variables, then the results of a Bell test will be constrained in a particular, quantifiable way. Many Bell tests have been performed, using entangled particles, and they have shown results incompatible with the constraints imposed by local hidden variables.


title: Quantum mechanics

text: It is not possible to present these concepts in more than a superficial way without introducing the actual mathematics involved; understanding quantum mechanics requires not only manipulating complex numbers, but also linear algebra, differential equations, group theory, and other more advanced subjects. Accordingly, this article will present a mathematical formulation of quantum mechanics and survey its application to some useful and oft-studied examples.


title: Quantum mechanics

text: In the mathematically rigorous formulation of quantum mechanics, the state of a quantum mechanical system is a vector formula_1 belonging to a (separable) complex Hilbert space formula_2. This vector is postulated to be normalized under the Hilbert space inner product, that is, it obeys formula_3, and it is well-defined up to a complex number of modulus 1 (the global phase), that is, formula_1 and formula_5 represent the same physical system. In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space. The exact nature of this Hilbert space is dependent on the system – for example, for describing position and momentum the Hilbert space is the space of complex square-integrable functions formula_6, while the Hilbert space for the spin of a single proton is simply the space of two-dimensional complex vectors formula_7 with the usual inner product.


title: Quantum mechanics

text: Physical quantities of interestposition, momentum, energy, spinare represented by observables, which are Hermitian (more precisely, self-adjoint) linear operators acting on the Hilbert space. A quantum state can be an eigenvector of an observable, in which case it is called an eigenstate, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. More generally, a quantum state will be a linear combination of the eigenstates, known as a quantum superposition. When an observable is measured, the result will be one of its eigenvalues with probability given by the Born rule: in the simplest case the eigenvalue formula_8 is non-degenerate and the probability is given by formula_9, where formula_10 is its associated eigenvector. More generally, the eigenvalue is degenerate and the probability is given by formula_11, where formula_12 is the projector onto its associated eigenspace. In the continuous case, these formulas give instead the probability density.


title: Quantum mechanics

text: After the measurement, if result formula_8 was obtained, the quantum state is postulated to collapse to formula_10, in the non-degenerate case, or to formula_15, in the general case. The probabilistic nature of quantum mechanics thus stems from the act of measurement. This is one of the most difficult aspects of quantum systems to understand. It was the central topic in the famous Bohr–Einstein debates, in which the two scientists attempted to clarify these fundamental principles by way of thought experiments. In the decades after the formulation of quantum mechanics, the question of what constitutes a "measurement" has been extensively studied. Newer interpretations of quantum mechanics have been formulated that do away with the concept of "wave function collapse" (see, for example, the many-worlds interpretation). The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wave functions become entangled so that the original quantum system ceases to exist as an independent entity. For details, see the article on measurement in quantum mechanics.


title: Quantum mechanics

text: Here formula_17 denotes the Hamiltonian, the observable corresponding to the total energy of the system, and formula_18 is the reduced Planck constant. The constant formula_19 is introduced so that the Hamiltonian is reduced to the classical Hamiltonian in cases where the quantum system can be approximated by a classical system; the ability to make such an approximation in certain limits is called the correspondence principle.


title: Quantum mechanics

text: The operator formula_21 is known as the time-evolution operator, and has the crucial property that it is unitary. This time evolution is deterministic in the sense that – given an initial quantum state formula_22  – it makes a definite prediction of what the quantum state formula_23 will be at any later time.


title: Quantum mechanics

text: Some wave functions produce probability distributions that are independent of time, such as eigenstates of the Hamiltonian. Many systems that are treated dynamically in classical mechanics are described by such "static" wave functions. For example, a single electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics, it is described by a static wave function surrounding the nucleus. For example, the electron wave function for an unexcited hydrogen atom is a spherically symmetric function known as an "s" orbital ().


title: Quantum mechanics

text: Analytic solutions of the Schrödinger equation are known for very few relatively simple model Hamiltonians including the quantum harmonic oscillator, the particle in a box, the dihydrogen cation, and the hydrogen atom. Even the helium atom – which contains just two electrons – has defied all attempts at a fully analytic treatment.


title: Quantum mechanics

text: However, there are techniques for finding approximate solutions. One method, called perturbation theory, uses the analytic result for a simple quantum mechanical model to create a result for a related but more complicated model by (for example) the addition of a weak potential energy. Another method is called "semi-classical equation of motion", which applies to systems for which quantum mechanics produces only small deviations from classical behavior. These deviations can then be computed based on the classical motion. This approach is particularly important in the field of quantum chaos.


title: Quantum mechanics

text: One consequence of the basic quantum formalism is the uncertainty principle. In its most familiar form, this states that no preparation of a quantum particle can imply simultaneously precise predictions both for a measurement of its position and for a measurement of its momentum. Both position and momentum are observables, meaning that they are represented by Hermitian operators. The position operator formula_24 and momentum operator formula_25 do not commute, but rather satisfy the canonical commutation relation:


title: Quantum mechanics

text: Given a quantum state, the Born rule lets us compute expectation values for both formula_27 and formula_28, and moreover for powers of them. Defining


title: Quantum mechanics

text: Either standard deviation can in principle be made arbitrarily small, but not both simultaneously. This inequality generalizes to arbitrary pairs of self-adjoint operators formula_32 and formula_33. The commutator of these two operators is


title: Quantum mechanics

text: Another consequence of the canonical commutation relation is that the position and momentum operators are Fourier transforms of each other, so that a description of an object according to its momentum is the Fourier transform of its description according to its position. The fact that dependence in momentum is the Fourier transform of the dependence in position means that the momentum operator is equivalent (up to an formula_36 factor) to taking the derivative according to the position, since in Fourier analysis differentiation corresponds to multiplication in the dual space. This is why in quantum equations in position space, the momentum formula_37 is replaced by formula_38, and in particular in the non-relativistic Schrödinger equation in position space the momentum-squared term is replaced with a Laplacian times formula_39.


title: Quantum mechanics

text: When two different quantum systems are considered together, the Hilbert space of the combined system is the tensor product of the Hilbert spaces of the two components. For example, let and be two quantum systems, with Hilbert spaces formula_40 and formula_41, respectively. The Hilbert space of the composite system is then


title: Quantum mechanics

text: If the state for the first system is the vector formula_43 and the state for the second system is formula_44, then the state of the composite system is


title: Quantum mechanics

text: Not all states in the joint Hilbert space formula_46 can be written in this form, however, because the superposition principle implies that linear combinations of these "separable" or "product states" are also valid. For example, if formula_43 and formula_48 are both possible states for system formula_32, and likewise formula_44 and formula_51 are both possible states for system formula_33, then


title: Quantum mechanics

text: If the state for a composite system is entangled, it is impossible to describe either component system or system by a state vector. One can instead define reduced density matrices that describe the statistics that can be obtained by making measurements on either component system alone. This necessarily causes a loss of information, though: knowing the reduced density matrices of the individual systems is not enough to reconstruct the state of the composite system. Just as density matrices specify the state of a subsystem of a larger system, analogously, positive operator-valued measures (POVMs) describe the effect on a subsystem of a measurement performed on a larger system. POVMs are extensively used in quantum information theory.


title: Quantum mechanics

text: As described above, entanglement is a key feature of models of measurement processes in which an apparatus becomes entangled with the system being measured. Systems interacting with the environment in which they reside generally become entangled with that environment, a phenomenon known as quantum decoherence. This can explain why, in practice, quantum effects are difficult to observe in systems larger than microscopic.


title: Quantum mechanics

text: There are many mathematically equivalent formulations of quantum mechanics. One of the oldest and most common is the "transformation theory" proposed by Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics – matrix mechanics (invented by Werner Heisenberg) and wave mechanics (invented by Erwin Schrödinger). An alternative formulation of quantum mechanics is Feynman's path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over all possible classical and non-classical paths between the initial and final states. This is the quantum-mechanical counterpart of the action principle in classical mechanics.


title: Quantum mechanics

text: The Hamiltonian formula_17 is known as the "generator" of time evolution, since it defines a unitary time-evolution operator formula_55 for each value of formula_56. From this relation between formula_57 and formula_17, it follows that any observable formula_32 that commutes with formula_17 will be "conserved": its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator formula_32 can generate a family of unitary operators parameterized by a variable formula_56. Under the evolution generated by formula_32, any observable formula_33 that commutes with formula_32 will be conserved. Moreover, if formula_33 is conserved by evolution under formula_32, then formula_32 is conserved under the evolution generated by formula_33. This implies a quantum version of the result proven by Emmy Noether in classical (Lagrangian) mechanics: for every differentiable symmetry of a Hamiltonian, there exists a corresponding conservation law.


title: Quantum mechanics

text: The simplest example of a quantum system with a position degree of freedom is a free particle in a single spatial dimension. A free particle is one which is not subject to external influences, so that its Hamiltonian consists only of its kinetic energy:


title: Quantum mechanics

text: which is a superposition of all possible plane waves formula_72, which are eigenstates of the momentum operator with momentum formula_73. The coefficients of the superposition are formula_74, which is the Fourier transform of the initial quantum state formula_75.


title: Quantum mechanics

text: It is not possible for the solution to be a single momentum eigenstate, or a single position eigenstate, as these are not normalizable quantum states. Instead, we can consider a Gaussian wave packet:


title: Quantum mechanics

text: We see that as we make formula_78 smaller the spread in position gets smaller, but the spread in momentum gets larger. Conversely, by making formula_78 larger we make the spread in momentum smaller, but the spread in position gets larger. This illustrates the uncertainty principle.


title: Quantum mechanics

text: As we let the Gaussian wave packet evolve in time, we see that its center moves through space at a constant velocity (like a classical particle with no forces acting on it). However, the wave packet will also spread out as time progresses, which means that the position becomes more and more uncertain. The uncertainty in momentum, however, stays constant.


title: Quantum mechanics

text: The particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere "inside" a certain region, and therefore infinite potential energy everywhere "outside" that region. For the one-dimensional case in the formula_80 direction, the time-independent Schrödinger equation may be written


title: Quantum mechanics

text: with state formula_1 in this case having energy formula_85 coincident with the kinetic energy of the particle.


title: Quantum mechanics

text: The infinite potential walls of the box determine the values of formula_88 and formula_89 at formula_90 and formula_91 where formula_1 must be zero. Thus, at formula_90,


title: Quantum mechanics

text: in which formula_98 cannot be zero as this would conflict with the postulate that formula_1 has norm 1. Therefore, since formula_100, formula_101 must be an integer multiple of formula_102,


title: Quantum mechanics

text: A finite potential well is the generalization of the infinite potential well problem to potential wells having finite depth. The finite potential well problem is mathematically more complicated than the infinite particle-in-a-box problem as the wave function is not pinned to zero at the walls of the well. Instead, the wave function must satisfy more complicated mathematical boundary conditions as it is nonzero in regions outside the well. Another related problem is that of the rectangular potential barrier, which furnishes a model for the quantum tunneling effect that plays an important role in the performance of modern technologies such as flash memory and scanning tunneling microscopy.


title: Quantum mechanics

text: This problem can either be treated by directly solving the Schrödinger equation, which is not trivial, or by using the more elegant "ladder method" first proposed by Paul Dirac. The eigenstates are given by


title: Quantum mechanics

text: The Mach–Zehnder interferometer (MZI) illustrates the concepts of superposition and interference with linear algebra in dimension 2, rather than differential equations. It can be seen as a simplified version of the double-slit experiment, but it is of interest in its own right, for example in the delayed choice quantum eraser, the Elitzur–Vaidman bomb tester, and in studies of quantum entanglement.


title: Quantum mechanics

text: We can model a photon going through the interferometer by considering that at each point it can be in a superposition of only two paths: the "lower" path which starts from the left, goes straight through both beam splitters, and ends at the top, and the "upper" path which starts from the bottom, goes straight through both beam splitters, and ends at the right. The quantum state of the photon is therefore a vector formula_111 that is a superposition of the "lower" path formula_112 and the "upper" path formula_113, that is, formula_114 for complex formula_115. In order to respect the postulate that formula_116 we require that formula_117.


title: Quantum mechanics

text: Both beam splitters are modelled as the unitary matrix formula_118, which means that when a photon meets the beam splitter it will either stay on the same path with a probability amplitude of formula_119, or be reflected to the other path with a probability amplitude of formula_120. The phase shifter on the upper arm is modelled as the unitary matrix formula_121, which means that if the photon is on the "upper" path it will gain a relative phase of formula_122, and it will stay unchanged if it is in the lower path.


title: Quantum mechanics

text: A photon that enters the interferometer from the left will then be acted upon with a beam splitter formula_33, a phase shifter formula_28, and another beam splitter formula_33, and so end up in the state


title: Quantum mechanics

text: One can therefore use the Mach–Zehnder interferometer to estimate the phase shift by estimating these probabilities.


title: Quantum mechanics

text: It is interesting to consider what would happen if the photon were definitely in either the "lower" or "upper" paths between the beam splitters. This can be accomplished by blocking one of the paths, or equivalently by removing the first beam splitter (and feeding the photon from the left or the bottom, as desired). In both cases there will be no interference between the paths anymore, and the probabilities are given by formula_129, independently of the phase formula_122. From this we can conclude that the photon does not take one path or another after the first beam splitter, but rather that it is in a genuine quantum superposition of the two paths.


title: Quantum mechanics

text: Quantum mechanics has had enormous success in explaining many of the features of our universe, with regards to small-scale and discrete quantities and interactions which cannot be explained by classical methods. Quantum mechanics is often the only theory that can reveal the individual behaviors of the subatomic particles that make up all forms of matter (electrons, protons, neutrons, photons, and others). Solid-state physics and materials science are dependent upon quantum mechanics.


title: Quantum mechanics

text: In many aspects modern technology operates at a scale where quantum effects are significant. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the optical amplifier and the laser, the transistor and semiconductors such as the microprocessor, medical and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA.


title: Quantum mechanics

text: The rules of quantum mechanics assert that the state space of a system is a Hilbert space and that observables of the system are Hermitian operators acting on vectors in that space – although they do not tell us which Hilbert space or which operators. These can be chosen appropriately in order to obtain a quantitative description of a quantum system, a necessary step in making physical predictions. An important guide for making these choices is the correspondence principle, a heuristic which states that the predictions of quantum mechanics reduce to those of classical mechanics in the regime of large quantum numbers. One can also start from an established classical model of a particular system, and then try to guess the underlying quantum model that would give rise to the classical model in the correspondence limit. This approach is known as quantization.


title: Quantum mechanics

text: When quantum mechanics was originally formulated, it was applied to models whose correspondence limit was non-relativistic classical mechanics. For instance, the well-known model of the quantum harmonic oscillator uses an explicitly non-relativistic expression for the kinetic energy of the oscillator, and is thus a quantum version of the classical harmonic oscillator.


title: Quantum mechanics

text: Complications arise with chaotic systems, which do not have good quantum numbers, and quantum chaos studies the relationship between classical and quantum descriptions in these systems.


title: Quantum mechanics

text: Quantum decoherence is a mechanism through which quantum systems lose coherence, and thus become incapable of displaying many typically quantum effects: quantum superpositions become simply probabilistic mixtures, and quantum entanglement becomes simply classical correlations. Quantum coherence is not typically evident at macroscopic scales, except maybe at temperatures approaching absolute zero at which quantum behavior may manifest macroscopically.


title: Quantum mechanics

text: Many macroscopic properties of a classical system are a direct consequence of the quantum behavior of its parts. For example, the stability of bulk matter (consisting of atoms and molecules which would quickly collapse under electric forces alone), the rigidity of solids, and the mechanical, thermal, chemical, optical and magnetic properties of matter are all results of the interaction of electric charges under the rules of quantum mechanics.


title: Quantum mechanics

text: Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein–Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. Quantum electrodynamics is, along with general relativity, one of the most accurate physical theories ever devised.


title: Quantum mechanics

text: The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been used since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical formula_131 Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles.


title: Quantum mechanics

text: Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg.


title: Quantum mechanics

text: Even though the predictions of both quantum theory and general relativity have been supported by rigorous and repeated empirical evidence, their abstract formalisms contradict each other and they have proven extremely difficult to incorporate into one consistent, cohesive model. Gravity is negligible in many areas of particle physics, so that unification between general relativity and quantum mechanics is not an urgent issue in those particular applications. However, the lack of a correct theory of quantum gravity is an important issue in physical cosmology and the search by physicists for an elegant "Theory of Everything" (TOE). Consequently, resolving the inconsistencies between both theories has been a major goal of 20th- and 21st-century physics. This TOE would combine not only the models of subatomic physics but also derive the four fundamental forces of nature from a single force or phenomenon.


title: Quantum mechanics

text: One proposal for doing so is string theory, which posits that the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force.


title: Quantum mechanics

text: Another popular theory is loop quantum gravity (LQG), which describes quantum properties of gravity and is thus a theory of quantum spacetime. LQG is an attempt to merge and adapt standard quantum mechanics and standard general relativity. This theory describes space as an extremely fine fabric "woven" of finite loops called spin networks. The evolution of a spin network over time is called a spin foam. The characteristic length scale of a spin foam is the Planck length, approximately 1.616×10 m, and so lengths shorter than the Planck length are not physically meaningful in LQG.


title: Quantum mechanics

text: Since its inception, the many counter-intuitive aspects and results of quantum mechanics have provoked strong philosophical debates and many interpretations. The arguments centre on the probabilistic nature of quantum mechanics, the difficulties with wavefunction collapse and the related measurement problem, and quantum nonlocality. Perhaps the only consensus that exists about these issues is that there is no consensus. Richard Feynman once said, "I think I can safely say that nobody understands quantum mechanics." According to Steven Weinberg, "There is now in my opinion no entirely satisfactory interpretation of quantum mechanics."


title: Quantum mechanics

text: The views of Niels Bohr, Werner Heisenberg and other physicists are often grouped together as the "Copenhagen interpretation". According to these views, the probabilistic nature of quantum mechanics is not a "temporary" feature which will eventually be replaced by a deterministic theory, but is instead a "final" renunciation of the classical idea of "causality". Bohr in particular emphasized that any well-defined application of the quantum mechanical formalism must always make reference to the experimental arrangement, due to the complementary nature of evidence obtained under different experimental situations. Copenhagen-type interpretations remain popular in the 21st century.


title: Quantum mechanics

text: Albert Einstein, himself one of the founders of quantum theory, was troubled by its apparent failure to respect some cherished metaphysical principles, such as determinism and locality. Einstein's long-running exchanges with Bohr about the meaning and status of quantum mechanics are now known as the Bohr–Einstein debates. Einstein believed that underlying quantum mechanics must be a theory that explicitly forbids action at a distance. He argued that quantum mechanics was incomplete, a theory that was valid but not fundamental, analogous to how thermodynamics is valid, but the fundamental theory behind it is statistical mechanics. In 1935, Einstein and his collaborators Boris Podolsky and Nathan Rosen published an argument that the principle of locality implies the incompleteness of quantum mechanics, a thought experiment later termed the Einstein–Podolsky–Rosen paradox. In 1964, John Bell showed that EPR's principle of locality, together with determinism, was actually incompatible with quantum mechanics: they implied constraints on the correlations produced by distance systems, now known as Bell inequalities, that can be violated by entangled particles. Since then several experiments have been performed to obtain these correlations, with the result that they do in fact violate Bell inequalities, and thus falsify the conjunction of locality with determinism.


title: Quantum mechanics

text: Bohmian mechanics shows that it is possible to reformulate quantum mechanics to make it deterministic, at the price of making it explicitly nonlocal. It attributes not only a wave function to a physical system, but in addition a real position, that evolves deterministically under a nonlocal guiding equation. The evolution of a physical system is given at all times by the Schrödinger equation together with the guiding equation; there is never a collapse of the wave function. This solves the measurement problem.


title: Quantum mechanics

text: Everett's many-worlds interpretation, formulated in 1956, holds that "all" the possibilities described by quantum theory "simultaneously" occur in a multiverse composed of mostly independent parallel universes. This is a consequence of removing the axiom of the collapse of the wave packet. All possible states of the measured system and the measuring apparatus, together with the observer, are present in a real physical quantum superposition. While the multiverse is deterministic, we perceive non-deterministic behavior governed by probabilities, because we don't observe the multiverse as a whole, but only one parallel universe at a time. Exactly how this is supposed to work has been the subject of much debate. Several attempts have been made to make sense of this and derive the Born rule, with no consensus on whether they have been successful.


title: Quantum mechanics

text: Relational quantum mechanics appeared in the late 1990s as a modern derivative of Copenhagen-type ideas, and QBism was developed some years later.


title: Quantum mechanics

text: Quantum mechanics was developed in the early decades of the 20th century, driven by the need to explain phenomena that, in some cases, had been observed in earlier times. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803 English polymath Thomas Young described the famous double-slit experiment. This experiment played a major role in the general acceptance of the wave theory of light.


title: Quantum mechanics

text: During the early 19th century, chemical research by John Dalton and Amedeo Avogadro lent weight to the atomic theory of matter, an idea that James Clerk Maxwell, Ludwig Boltzmann and others built upon to establish the kinetic theory of gases. The successes of kinetic theory gave further credence to the idea that matter is composed of atoms, yet the theory also had shortcomings that would only be resolved by the development of quantum mechanics. While the early conception of atoms from Greek philosophy had been that they were indivisible units the word "atom" deriving from the Greek for "uncuttable" the 19th century saw the formulation of hypotheses about subatomic structure. One important discovery in that regard was Michael Faraday's 1838 observation of a glow caused by an electrical discharge inside a glass tube containing gas at low pressure. Julius Plücker, Johann Wilhelm Hittorf and Eugen Goldstein carried on and improved upon Faraday's work, leading to the identification of cathode rays, which J. J. Thomson found to consist of subatomic particles that would be called electrons.


title: Quantum mechanics

text: The black-body radiation problem was discovered by Gustav Kirchhoff in 1859. In 1900, Max Planck proposed the hypothesis that energy is radiated and absorbed in discrete "quanta" (or energy packets), yielding a calculation that precisely matched the observed patterns of black-body radiation. The word "quantum" derives from the Latin, meaning "how great" or "how much". According to Planck, quantities of energy could be thought of as divided into "elements" whose size ("E") would be proportional to their frequency ("ν"):


title: Quantum mechanics

text: where "h" is Planck's constant. Planck cautiously insisted that this was only an aspect of the processes of absorption and emission of radiation and was not the "physical reality" of the radiation. In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material. Niels Bohr then developed Planck's ideas about radiation into a model of the hydrogen atom that successfully predicted the spectral lines of hydrogen. Einstein further developed this idea to show that an electromagnetic wave such as light could also be described as a particle (later called the photon), with a discrete amount of energy that depends on its frequency. In his paper "On the Quantum Theory of Radiation," Einstein expanded on the interaction between energy and matter to explain the absorption and emission of energy by atoms. Although overshadowed at the time by his general theory of relativity, this paper articulated the mechanism underlying the stimulated emission of radiation, which became the basis of the laser.


title: Quantum mechanics

text: This phase is known as the old quantum theory. Never complete or self-consistent, the old quantum theory was rather a set of heuristic corrections to classical mechanics. The theory is now understood as a semi-classical approximation to modern quantum mechanics. Notable results from this period include, in addition to the work of Planck, Einstein and Bohr mentioned above, Einstein and Peter Debye's work on the specific heat of solids, Bohr and Hendrika Johanna van Leeuwen's proof that classical physics cannot account for diamagnetism, and Arnold Sommerfeld's extension of the Bohr model to include special-relativistic effects.


title: Quantum mechanics

text: In the mid-1920s quantum mechanics was developed to become the standard formulation for atomic physics. In 1923, the French physicist Louis de Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. Building on de Broglie's approach, modern quantum mechanics was born in 1925, when the German physicists Werner Heisenberg, Max Born, and Pascual Jordan developed matrix mechanics and the Austrian physicist Erwin Schrödinger invented wave mechanics. Born introduced the probabilistic interpretation of Schrödinger's wave function in July 1926. Thus, the entire field of quantum physics emerged, leading to its wider acceptance at the Fifth Solvay Conference in 1927.


title: Quantum mechanics

text: By 1930 quantum mechanics had been further unified and formalized by David Hilbert, Paul Dirac and John von Neumann with greater emphasis on measurement, the statistical nature of our knowledge of reality, and philosophical speculation about the 'observer'. It has since permeated many disciplines, including quantum chemistry, quantum electronics, quantum optics, and quantum information science. It also provides a useful framework for many features of the modern periodic table of elements, and describes the behaviors of atoms during chemical bonding and the flow of electrons in computer semiconductors, and therefore plays a crucial role in many modern technologies. While quantum mechanics was constructed to describe the world of the very small, it is also needed to explain some macroscopic phenomena such as superconductors and superfluids.


title: Quantum mechanics

text: The following titles, all by working physicists, attempt to communicate quantum theory to lay people, using a minimum of technical apparatus.


title: Heaven's Gate (religious group)

text: Heaven's Gate was an American new religious movement (often described as a cult), founded in 1974 and led by Bonnie Nettles (1927–1985) and Marshall Applewhite (1931–1997), known within the movement as Ti and Do, respectively. Ti and Do first met in 1972 and went on a journey of spiritual discovery, identifying themselves as the two witnesses of Revelation, attracting a following of several hundred people in the mid-1970s. In 1976, the group stopped recruiting and instituted a monastic lifestyle.


title: Heaven's Gate (religious group)

text: Scholars have described the theology of Heaven's Gate as a mixture of Christian millenarianism, New Age, and ufology, and as such it has been characterized as a UFO religion. The central belief of the group was that followers could transform themselves into immortal extraterrestrial beings by rejecting their human nature, and they would ascend to heaven, referred to as the "Next Level" or "The Evolutionary Level Above Human". The death of Nettles from cancer in 1985 challenged the group's views on ascension, where they originally believed that they would ascend to heaven while alive aboard a UFO, they later came to believe that the body was merely a "container" or "vehicle" for the soul, and that their consciousness would be transferred to new "Next Level bodies" upon death.


title: Heaven's Gate (religious group)

text: On March 26, 1997, deputies of the San Diego County Sheriff's Department discovered the bodies of the 39 active members of the group, including that of Applewhite, in a house in the San Diego suburb of Rancho Santa Fe. They had participated in a mass suicide, a coordinated series of ritual suicides, coinciding with the closest approach of Comet Hale–Bopp. Just before the mass suicide, the group's website was updated with the message: "Hale–Bopp brings closure to Heaven's Gate...our 22 years of classroom here on planet Earth is finally coming to conclusion—'graduation' from the Human Evolutionary Level. We are happily prepared to leave 'this world' and go with Ti's crew."


title: Heaven's Gate (religious group)

text: The name "Heaven's Gate" was only used for the final few years of the group's existence, and they had previously been known under the names Human Individual Metamorphosis and Total Overcomers Anonymous.


title: Heaven's Gate (religious group)

text: The son of a Presbyterian minister and a former soldier, Marshall Applewhite began his foray into Biblical prophecy in the early 1970s. After being fired from the University of St. Thomas in Houston, Texas over an alleged relationship with one of his male students, he met Bonnie Nettles, a 44-year-old married nurse with an interest in theosophy and Biblical prophecy, in March 1972. The circumstances of their meeting are unclear. According to Applewhite's writings, the two met in a hospital where she worked while he was visiting a sick friend there. It has been rumored that it was a psychiatric hospital, but another account had Nettles substituting for a nurse working with premature babies in the nursery. Applewhite later recalled that he felt that he had known Nettles for a long time and concluded that they had met in a past life. She told him their meeting had been foretold to her by extraterrestrials, persuading him that he had a divine assignment.


title: Heaven's Gate (religious group)

text: Applewhite and Nettles pondered the life of St. Francis of Assisi and read works by Helena Blavatsky, R. D. Laing, and Richard Bach. They kept a King James Bible and studied passages from the New Testament focusing on Christology, asceticism, and eschatology. Applewhite also read science fiction, including works by Robert A. Heinlein and Arthur C. Clarke. By June 19, Applewhite and Nettles's beliefs had solidified. They concluded that they had been chosen to fulfill biblical prophecies, and that they had been given higher-level minds than other people. They wrote a pamphlet that described Jesus' reincarnation as a Texan, a veiled reference to Applewhite. Furthermore, they concluded that they were the two witnesses described in the Book of Revelation and occasionally visited churches or other spiritual groups to speak of their identities, often referring to themselves as "The Two", or "The UFO Two". They believed they would be killed and then resurrected and, in view of others, transported onto a spaceship. This event, which they referred to as "the Demonstration", was to prove their claims. To their dismay, these ideas were poorly received by other religious groups.


title: Heaven's Gate (religious group)

text: The Two would gain their first follower, Sharon Morgan, in May 1974, abandoning her children to join them. A month later Sharon left The Two and returned to her family. Nettles and Applewhite were arrested and charged with credit card fraud for using Morgan's cards, despite the fact that she had consented to their use. The charges were later dropped. However a routine check brought up that Applewhite had stolen a rental car from St. Louis nine months earlier, which he still possessed. Applewhite then spent six months in jail primarily in Missouri, and was released in early 1975, subsequently rejoining Nettles.


title: Heaven's Gate (religious group)

text: Eventually, Applewhite and Nettles resolved to contact extraterrestrials, and they sought like-minded followers. They published advertisements for meetings, where they recruited disciples, whom they called "the crew". At the events, they purported to represent beings from another planet, the Next Level, who sought participants for an experiment. They stated that those who agreed to take part in the experiment would be brought to a higher evolutionary level. In April 1975, during a meeting with a metaphysical group of eighty people led by Clarence Klug in Joan Culpepper's Studio City, Los Angeles home, they shared their "simultaneous" revelation that they had been told they were the two witnesses in the Bible's story of the end time. According to Benjamin Zeller, while accounts of the meeting differ, all describe it as momentous and agree that Applewhite and Nettles presented themselves as charismatic leaders with an important spiritual message. Around 25 individuals were induced to join the group.


title: Heaven's Gate (religious group)

text: Later, in September 1975, Applewhite and Nettles preached at a motel hall in Waldport, Oregon. After selling all "worldly" possessions and saying farewell to loved ones, around 20 people vanished from the public eye and joined the group. Later that year, on "CBS Evening News", Walter Cronkite reported on the disappearances in one of the first national reports on the developing religious group: "A score of persons... have disappeared. It's a mystery whether they've been taken on a so-called trip to eternity — or simply been taken." In reality, Applewhite and Nettles had arranged for the group to go underground. From that point, "Do and Ti" (pronounced "doe and tee"), as the two now called themselves, led nearly one hundred members across the country, sleeping in tents and sleeping bags and begging in the streets. Evading detection by the authorities and media enabled the group to focus on Do and Ti's doctrine of helping members of the crew achieve a "higher evolutionary level" above human, which they claimed to have already reached.


title: Heaven's Gate (religious group)

text: Applewhite and Nettles used a variety of aliases over the years, notably "Bo and Peep" and "Do and Ti". The group also had several names prior to the adoption of the name Heaven's Gate. At the time Vallée studied the group it was known as Human Individual Metamorphosis (HIM). The group re-invented and renamed itself several times and had a variety of recruitment methods.


title: Heaven's Gate (religious group)

text: Applewhite believed he was directly related to Jesus, meaning he was an "Evolutionary Kingdom Level Above Human". His writings, which combined aspects of Millennialism, Gnosticism, and science fiction, suggest he believed himself to be Jesus' successor and the "Present Representative" of Christ on Earth. Do and Ti taught early on that Do's bodily "vehicle" was inhabited by the same alien spirit which belonged to Jesus; likewise, Ti (Nettles) was presented as God the Father.


title: Heaven's Gate (religious group)

text: The crew used numerous methods of recruitment as they toured the United States in destitution, proclaiming the gospel of higher level metamorphosis, the deceit of humans by false-god spirits, envelopment with sunlight for meditative healing, and the divinity of the "UFO Two".


title: Heaven's Gate (religious group)

text: In April 1976, the group stopped recruiting and became reclusive, and instituted a rigid set of behavioral guidelines, including banning sexual activity and the use of drugs. Applewhite and Nettles also solidified their temporal and religious authority over the group. Benjamin Zeller described the movement as having transformed "from a loosely organised social group to a centralized religious movement comparable to a roving monastery".


title: Heaven's Gate (religious group)

text: Some sociologists agree that the popular movement of alternative religious experience and individualism found in collective spiritual experiences during that period helped contribute to the growth of the new religious movement. "Sheilaism", as it became known, was a way for people to merge their diverse religious backgrounds and coalesce around a shared, generalized faith, which followers of new religious sects like Applewhite's crew found to be an appetizing alternative to traditional dogmas in Judaism, Catholicism and evangelical Christianity. Many of Applewhite and Nettles' crew hailed from these diverse backgrounds; most of them are described by researchers as having been "longtime truth-seekers", or spiritual hippies who had long since believed in attempting to "find themselves" through spiritual means, combining faiths in a sort of cultural milieu well into the mid-1980s. However, not all of Applewhite's crew were hippies recruited from alternative religious backgrounds— one such recruit early on was John Craig, a respected Republican and ranch owner who came close to winning a 1970 Colorado House of Representatives race, who joined the group in 1975. As numbers grew in its pre-Internet days, the clan of "UFO followers" seemed to have in common a need for communal belonging to an alternative path to higher existence outside the constraints of institutionalized faith.


title: Heaven's Gate (religious group)

text: Identifying themselves by the business name "Higher Source", they used their website to proselytize and recruit followers beginning in the early 1990s. Rumors began spreading among the group in the following years that the upcoming Comet Hale–Bopp housed the secret to their ultimate salvation and ascent into the kingdom of heaven.


title: Heaven's Gate (religious group)

text: Heaven's Gate received coverage in Jacques Vallée's book "Messengers of Deception" (1979), in which Vallée described an unusual public meeting organized by the group. Vallée expressed concerns about contactee groups' authoritarian political and religious outlooks, and Heaven's Gate did not escape criticism. Known to the media (though largely ignored), Heaven's Gate was better known in UFO circles, and through a series of academic studies by sociologist Robert Balch.


title: Heaven's Gate (religious group)

text: In January 1994, the "LA Weekly" ran an article on the group, then known as "The Total Overcomers". Richard Ford, who would later play a key role in the 1997 group suicide, discovered Heaven's Gate through this article and eventually joined them, renaming himself Rio DiAngelo.


title: Heaven's Gate (religious group)

text: "Coast to Coast AM" host Art Bell discussed the theory of the "companion object" in the shadow of Hale–Bopp on several programs as early as November 1996. Speculation has been raised as to whether Bell's programs contributed to Heaven's Gate's group suicide, which "Knowledge Fight" host Dan Friesen blames more on Courtney Brown rather than Bell.


title: Heaven's Gate (religious group)

text: Louis Theroux contacted Heaven's Gate for his BBC2 documentary series, "Louis Theroux's Weird Weekends", in early March 1997. In response to his e-mail, Theroux was told that Heaven's Gate could not take part in the documentary because "at the present time a project like this would be an interference with what we must focus on."


title: Heaven's Gate (religious group)

text: In October 1996, the group rented a large home which they called "The Monastery", a mansion located near 18341 Colina Norte (later changed to Paseo Victoria) in Rancho Santa Fe, California. They paid $7,000 per month, in cash. The same month, the group purchased alien abduction insurance that would cover up to fifty members and would pay out $1 million per person (the policy covered abduction, impregnation, or death by aliens). Prior to this, in June 1995 they had purchased land near Manzano, New Mexico and began creating a compound out of rubber tires and concrete, but had left abruptly in April 1996.


title: Heaven's Gate (religious group)

text: On March 1920, 1997, Marshall Applewhite taped himself in "Do's Final Exit", speaking of mass suicide and "the only way to evacuate this Earth". After asserting that a spacecraft was trailing Comet Hale–Bopp and that this event would represent the "closure to Heaven's Gate", Applewhite persuaded 38 followers to prepare for ritual suicide so their souls could board the supposed craft. Applewhite believed that after their deaths an unidentified flying object (UFO) would take their souls to another "level of existence above human", which he described as being both physical and spiritual. Their preparations included each member videotaping a farewell message.


title: Heaven's Gate (religious group)

text: To kill themselves, members took phenobarbital mixed with apple sauce or pudding and washed it down with vodka. They secured plastic bags around their heads after ingesting the mix to induce asphyxiation. All 39 were dressed in identical black shirts and sweat pants, brand new black-and-white Nike Decades athletic shoes, and armband patches reading "Heaven's Gate Away Team" (one of many instances of the group's use of the nomenclature of the fictional universe of "Star Trek"). Each member carried a five-dollar bill and three quarters in their pockets. According to former members, this was standard for members leaving the home for jobs and "a humorous way to tell us they all had left the planet permanently"; the five-dollar bill was for covering the cost of vagrancy laws and the quarters were for calling home from pay phones, although another former member known as "Sawyer" stated that it was a reference to a Mark Twain story which said $5.75 was "the cost to ride the tail of a comet to heaven." After each one died, a living member would arrange the body by removing the plastic bag from the person's head, followed by posing the body so that it lay neatly in its own bed, with faces and torsos covered by a square purple cloth for privacy. In an interview with Harry Robinson, the two surviving members said that the identical clothing was a uniform representing unity for the mass suicide, while the Nike Decades were chosen because the group "got a good deal on the shoes". Applewhite was also a fan of Nikes "and therefore everyone was expected to wear and like Nikes" within the group. Heaven's Gate also had a saying 'Just Do it,' echoing Nike's slogan. They pronounced Do as Doe, to reflect Applewhite's nickname.


title: Heaven's Gate (religious group)

text: The 39 adherents, 21 women and 18 men between the ages of 26 and 72, are believed to have died in three groups over three successive days, with remaining participants cleaning up after each prior group's deaths.


title: Heaven's Gate (religious group)

text: The suicides occurred in groups of fifteen, fifteen, and nine, between approximately March 22 and March 26. Among the dead was Thomas Nichols, brother of the actress Nichelle Nichols, who was best known for her role as Uhura in the original television series of "". Leader Applewhite was the third to last member to die; two people remained after him and were the only ones found with bags over their heads and not having purple cloths covering their top halves. Before the last of the suicides, similar sets of packages were sent to numerous Heaven's Gate affiliated (or formerly affiliated) individuals, and at least one media outlet, the BBC department responsible for "Louis Theroux's Weird Weekends", for which Heaven's Gate had earlier declined participation.


title: Heaven's Gate (religious group)

text: Among those in the list of recipients was Rio DiAngelo. The package DiAngelo received on the evening of March 25, as other packages sent had, contained two VHS videotapes, one with "Do's Final Exit", and the other with the "farewell messages" of group followers. It also contained a letter, stating that among other things, "we have exited our vehicles, just as we entered them." DiAngelo informed his boss of the contents of the packages and then received a ride from him from Los Angeles to the Heaven's Gate home in Rancho Santa Fe so he could verify the letter. DiAngelo found a back door intentionally left unlocked to allow access, and used a video camera to record what he found. After leaving the house, DiAngelo's boss, who had waited outside, encouraged him to make calls alerting the authorities.


title: Heaven's Gate (religious group)

text: The San Diego County Sheriff's Department received an anonymous tip through the 911 system at 3:15 p.m. on March 26, suggesting they "check on the welfare of the residents". Days after the suicides, the caller was revealed to be DiAngelo.


title: Heaven's Gate (religious group)

text: The lone deputy who first responded to the call entered the home through a side door, saw ten bodies, and was nearly overcome by a "pungent odor". (The bodies were already decomposing in the hot California spring.) After a cursory search by two more deputies found no one alive, they retreated until a search warrant could be procured. All 39 bodies were ultimately cremated.


title: Heaven's Gate (religious group)

text: The Heaven's Gate deaths were widely publicized in the media as an example of mass suicide. When the news broke of its relation to Comet Hale–Bopp, the co-discoverer of the comet, Alan Hale, was drawn into the story. Hale's phone "never stopped ringing the entire day". He chose not to respond until he spoke the next day at a press conference, after researching the details of the incident. Speaking at the Second World Skeptics Congress in Heidelberg, Germany on July 24, 1998:


title: Heaven's Gate (religious group)

text: News of the 39 deaths in Rancho Santa Fe motivated the copycat suicide of a 58-year-old man living near Marysville, California. The man left a note dated March 27, which said, "I'm going on the spaceship with Hale-Bopp to be with those who have gone before me," and imitated some of the details of the Heaven's Gate suicides as they had then been reported. The man was found dead by a friend on March 31, and had no known connection with Heaven's Gate.


title: Heaven's Gate (religious group)

text: At least three former members of Heaven's Gate died by suicide in the months following the mass suicide. On May 6, 1997, Wayne Cooke and Chuck Humphrey attempted suicide in a hotel in a manner similar to that used by the group. Cooke died but Humphrey survived. Another former member, James Pirkey Jr., died by suicide by a self-inflicted gunshot wound on May 11. Humphrey, who had survived his first attempt, ultimately killed himself in Arizona in February 1998.


title: Heaven's Gate (religious group)

text: Although most people considered the event a mass suicide, sociologist and former member of a cult, Janja Lalich, has referred to the event as "murder".


title: Heaven's Gate (religious group)

text: Two former members, Marc and Sarah King of Phoenix, Arizona, operating as the TELAH Foundation, are believed to maintain the group's website. there has been no evident growth, as after the mass suicide the group fell into obscurity, relying mainly on their website for recruitment.


title: Heaven's Gate (religious group)

text: Scholars disagree over whether the theology of Heaven's Gate is fundamentally either New Age or Christian in nature. Benjamin Zeller has argued that the theology of Heaven's Gate was primarily rooted in Evangelicalism, but with New Age elements, and a hermeneutic interpretation of the Bible read through the lens of extraterrestrial contact.


title: Heaven's Gate (religious group)

text: Initially the group had been told that they would be biologically and chemically transformed into extraterrestrial beings and would be transported with their bodies aboard a spacecraft that would come to Earth and take the crew to heaven, referred to as the "Next Level". When Bonnie Lou Nettles (Ti) died of cancer in 1985, it confounded the group's doctrine because Nettles was allegedly chosen by the next level to be a messenger on Earth, yet her body died instead of leaving physically to outer space. The belief system was then revised to include the leaving of consciousness from the body, as equivalent to leaving the Earth in a spacecraft.


title: Heaven's Gate (religious group)

text: The group declared that they were against suicide, as they defined "suicide" in their own context to mean "to turn against the Next Level when it is being offered" and believed their "human" bodies were only "vehicles" meant to help them on their journey. Suicide, therefore, would be "not" allowing their consciousness to leave their human bodies to join the next level; remaining alive instead of participating in the group suicide was considered suicide of their consciousness. In conversation, when referring to a person or a person's body, they routinely used the word "vehicle".


title: Heaven's Gate (religious group)

text: The members of the group gave themselves three letter names with the suffix -ody that they adopted in lieu of their original given names, which defines "children of the Next Level". This is mentioned in Applewhite's final video, "Do's Final Exit", filmed March 19–20, 1997, just days prior to the suicides.


title: Heaven's Gate (religious group)

text: They believed that, "to be eligible for membership in the Next Level, humans would have to shed every attachment to the planet". This meant all members had to give up all human-like characteristics, such as their family, friends, gender, sexuality, individuality, jobs, money, and possessions.


title: Heaven's Gate (religious group)

text: "The Evolutionary Level Above Human" (TELAH) was as a "physical, corporeal place", another world in our universe, where residents live in pure bliss and nourish themselves by absorbing pure sunlight. At the next level, beings do not engage in sexual intercourse, eating or dying, the things that make us "mammalian" here. Heaven's Gate believed that what the Bible calls God is actually a highly developed Extraterrestrial.


title: Heaven's Gate (religious group)

text: Members of Heaven's Gate believed that evil space aliens—called Luciferians—falsely represented themselves to Earthlings as "God" and conspired to keep humans from developing. Technically advanced humanoids, these aliens have spacecraft, space-time travel, telepathy, and increased longevity. They use holograms to fake miracles. Carnal beings with gender, they stopped training to achieve the Kingdom of God thousands of years ago. Heaven's Gate believed that all existing religions on Earth had been corrupted by these malevolent aliens.


title: Heaven's Gate (religious group)

text: Although these basic beliefs of the group stayed generally consistent over the years, "the details of their ideology were flexible enough to undergo modification over time." There are examples of the group's adding to or slightly changing their beliefs, such as: modifying the way one can enter the Next Level, changing the way they described themselves, placing more importance on the idea of Satan, and adding several other New Age concepts. One of these concepts was the belief of extraterrestrial walk-ins; when the group began, "Applewhite and Nettles taught their followers that they were extraterrestrial beings. However, after the notion of walk-ins became popular within the New Age subculture, the Two changed their tune and began describing themselves as extraterrestrial walk-ins." The idea of walk-ins is very similar to the concept of being possessed by spirits. A walk-in can be defined as "an entity who occupies a body that has been vacated by its original soul". Heaven's Gate came to believe an extraterrestrial walk-in is "a walk-in that is supposedly from another planet".


title: Heaven's Gate (religious group)

text: The concept of walk-ins aided Applewhite and Nettles in personally starting from what they considered to be clean slates. In this so-called clean slate, they were no longer considered by members of this Heaven's Gate group to be the people they had been prior to the start of the group, but had taken on a new life; this concept gave them a way to "erase their human personal histories as the histories of souls who formerly occupied the bodies of Applewhite and Nettles". Over time Applewhite also revised his identity in the group to encourage the belief that the "walk in" that was inhabiting his body was the same that had done so to Jesus 2,000 years ago. Similar to Nestorianism this belief stated that the personage of Jesus and the spirit of Jesus were separable. This meant that Jesus was simply the name of the body of an ordinary man that held no sacred properties that was taken over by an incorporeal sacred entity to deliver "next level" information.


title: Heaven's Gate (religious group)

text: Another New Age belief Applewhite and Nettles adopted was the ancient astronaut hypothesis. The term "ancient astronauts" is used to refer to various forms of the concept that extraterrestrials visited Earth in the distant past. Applewhite and Nettles took part of this concept and taught it as the belief that "aliens planted the seeds of current humanity millions of years ago, and have to come to reap the harvest of their work in the form of spiritually evolved individuals who will join the ranks of flying saucer crews. Only a select few members of humanity will be chosen to advance to this transhuman state. The rest will be left to wallow in the spiritually poisoned atmosphere of a corrupt world." Only the individuals who chose to join Heaven's Gate, follow Applewhite and Nettle's belief system, and make the sacrifices required by membership would be allowed to escape human suffering.


title: Heaven's Gate (religious group)

text: According to Heaven's Gate, once the individual has perfected himself through the "process", there were four methods to enter or "graduate" to the next level:


title: Heaven's Gate (religious group)

text: In a group open only to adults over the age of 18, members gave up their possessions and lived an ascetic life devoid of indulgences. The group was tightly knit and everything was communally shared. In public, each member of the group always carried a five-dollar bill and a roll of quarters. Eight of the male members of the group, including Applewhite, voluntarily underwent castration as an extreme means of maintaining the ascetic lifestyle. The group initially attempted castration by having one of its members, a former nurse, perform the castration, but this attempt was unsuccessful, almost resulted in the patient's death, and caused at least one member to leave Heaven's Gate. Every castration that followed the first one was done in a hospital.


title: Heaven's Gate (religious group)

text: The group earned revenue by offering professional website development under the business name "Higher Source".


title: Heaven's Gate (religious group)

text: The cultural theorist Paul Virilio described the group as a cybersect, due to its heavy reliance on computer mediated communication prior to its collective suicide.


title: Heaven's Gate (religious group)

text: In 1979, Gary Sherman produced the made-for-TV movie "Mysterious Two" for NBC, based on the exploits of Applewhite and Nettles, then relatively unknown, which aired in 1982. In its first live episode following the mass suicide, "Saturday Night Live" aired a sketch where the cult members made it to space. It was followed by a commercial parody for Keds, featuring the tagline, "Worn by level-headed Christians," as well as footage of the Nike-clad corpses of the Heaven's Gate members. "", a documentary miniseries about the cult, was released on HBO Max in 2020. In 2021, Heaven's Gate was one of the subjects in the first season of Vice Media's documentary television series "Dark Side of the 90's" entitled "A Tale of Two Cults". The cult is also parodied on Seth MacFarlane's adult animated series "Family Guy" in an episode titled "Chitty Chitty Death Bang" aired in April 1999.


title: Heaven's Gate (religious group)

text: Heaven's Gate was the subject of the 10-part podcast of the same name produced by Glynn Washington to commemorate the 20th anniversary of the mass suicide. They have also been the subject of numerous other podcasts.


title: Heaven's Gate (religious group)

text: The infamy caused by the mass suicides, limited availability, and their sudden and unceremonious discontinuation have been cited as reasons for the high resale value of Nike Decades.


title: Us (2019 film)

text: Us is a 2019 American psychological horror film written and directed by Jordan Peele, starring Lupita Nyong'o, Winston Duke, Elisabeth Moss, and Tim Heidecker. The film follows Adelaide Wilson (Nyong'o) and her family, who are attacked by a group of menacing doppelgängers.


title: Us (2019 film)

text: The project was announced in February 2018, and much of the cast joined in the following months. Peele produced the film alongside Jason Blum and Sean McKittrick (the trio previously having collaborated on "Get Out" and "BlacKkKlansman"), as well as Ian Cooper. Filming took place in California, mostly in Los Angeles, Pasadena and Santa Cruz, from July to October 2018.


title: Us (2019 film)

text: "Us" premiered at South by Southwest on March 8, 2019, and was theatrically released in the United States on March 22, 2019, by Universal Pictures. It was a critical and commercial success, grossing $256 million worldwide against a budget of $20 million, and received praise for Peele's screenplay and direction, Nyong'o's performance, and Michael Abels' musical score.


title: Us (2019 film)

text: In 1986, a young girl named Adelaide “Addy” Thomas watches a commercial for Hands Across America. At night, at the Santa Cruz Beach Boardwalk, she wanders away from her parents and enters a funhouse, where she encounters a doppelgänger of herself in the house of mirrors. Following the encounter she stops speaking and withdraws from her family.


title: Us (2019 film)

text: Years later, an adult Adelaide goes on vacation with her husband, Gabriel "Gabe" Wilson, and their children Zora and Jason. She is apprehensive about the trip, but despite her misgivings, the family meet with their friends Josh and Kitty Tyler and their twin daughters at the beach. On the way there, they witness paramedics taking away the bloody body of an old man. Jason later sees someone strangely similar to the old man, standing still with his arms outstretched and hands bloody.


title: Us (2019 film)

text: That night, Adelaide tells Gabe about her childhood experience, but she is interrupted when the lights go out. Jason notices a 'family' of four in the driveway, who soon gain entry into the house. Cornering the Wilsons in their own living room, Jason recognizes the intruders as the Wilsons' doppelgängers. They include Pluto (Jason's pyromaniac, facially scarred double), Umbrae (Zora's sadistic double), and Abraham (Gabe's animalistic double). They are led by Red (Adelaide's double), the only one who can speak, albeit in a guttural, raspy voice. Red explains that they are called "the Tethered” as they share a soul with their lookalike counterparts, and they have come to "untether" themselves. The Wilsons are separated and terrorized by their doppelgängers. Jason discovers that Pluto mirrors his actions. After Gabriel kills Abraham, the family escapes.


title: Us (2019 film)

text: Meanwhile, the Tyler family is assaulted and murdered by their own doppelgängers at home. The Wilsons arrive and are assaulted as well, but they manage to overpower and kill the Tylers' doubles. They turn on the news and learn that the Tethered have been murdering their equivalents across the U.S., and after doing so, joining hands to form a massive human chain. The Wilsons decide to drive along the coast and escape to Mexico. While they are leaving, Umbrae attacks the car, and Zora kills her.


title: Us (2019 film)

text: Arriving at the boardwalk, the Wilsons find the townspeople already slaughtered. The road is blocked by a burning car. Jason, realizing it is a trap set by Pluto, orders everyone out of the car. Before Pluto can ignite the family's car, Jason moves so that when Pluto mirrors him he walks into the burning car. While the Wilsons are distracted by Pluto burning to death, Red appears and snatches Jason away. Adelaide chases after Red to the funhouse where they first met. She finds a secret entrance that leads to an underground facility overrun by white rabbits, and she finds Red in a classroom.


title: Us (2019 film)

text: Red tells Adelaide that "the Tethered" are actually genetic clones created by the government to control the originals on the surface. When the experiment failed, the Tethered were abandoned underground for generations, mindlessly mimicking the actions of their counterparts and surviving on rabbit meat. After they realized that Red was "different from the others,” she spent years organizing them to escape and take vengeance by murdering their counterparts. Red and Adelaide begin to fight, with Red evading and countering all of Adelaide's attacks. When Adelaide allows Red to attack, she impales Red with a fireplace poker, then strangles her to death and breaks her neck. She rescues Jason from a locker, and Jason also rescues one of the rabbits.


title: Us (2019 film)

text: While Adelaide drives the family away in the ambulance, she thinks back to the night she first met Red in the hall of mirrors. She remembers that the clone had choked Adelaide unconscious (damaging her larynx, making her voice raspy and guttural-sounding), dragged her underground, handcuffed her there, and returned above ground to usurp Adelaide's place in her life, eventually learning to speak and adjusting to living as a human being - she is the Tethered clone, and Red was the original Adelaide. Jason looks at his mother, who smiles at him.


title: Us (2019 film)

text: The Tethered have formed a human chain, replicating the Hands Across America demonstration, stretching across the United States as helicopters hover overhead.


title: Us (2019 film)

text: After being dismayed with the "genre confusion" over his previous film, "Get Out", Peele opted to make his next film a "full-on" horror film. Peele has said that an inspiration for "Us" was "The Twilight Zone" episode "Mirror Image", which was centered on a young woman and her evil doppelgänger.


title: Us (2019 film)

text: Peele has also said that the idea of the "tethered" living underground came to him as a teenager when he would take the train home from work.


title: Us (2019 film)

text: "You get out of the train and you have to go down through an underpass and come out the other side. There's no one else there, just this dark, American town. I'd come up and I'd look over to the other side, and I'd picture seeing the tail end of myself going down that same tunnel, to presumably emerge right near me 30 seconds later. And I can't be seen by that other version of me...It was a very scary day as I saw my double but I instantly knew it wasn't real and the idea popped into my head."


title: Us (2019 film)

text: On May 8, 2018, it was announced that Lupita Nyong'o, Winston Duke and Elisabeth Moss were all in negotiations to star in the film, with Nyong'o and Duke portraying a black couple, and Moss portraying one half of a white couple. Nyong'o later confirmed her casting by posting the film's promotional poster on her Instagram. The rest of the cast, including Tim Heidecker, Yahya Abdul-Mateen II, Shahadi Wright Joseph and Evan Alex were all confirmed in July of that year.


title: Us (2019 film)

text: Peele saw the characters of the film as an "archetypal foursome," with Adelaide being the leader, Zora being the warrior, Gabe being jester/fool and Jason being the wiz/magician. For her role, Nyong'o had to use a different voice for the character of Red. She said her performance was inspired by the condition spasmodic dysphonia, a condition that causes a person's voice to go into periods of spasm. In order to perfect her voice, she, "...worked with an ear, nose, and throat doctor, a vocal therapist, and my dialect coach to try and make sure I could do it and do it safely. 'Cause I had two roles to play, I couldn't afford to damage my voice."


title: Us (2019 film)

text: Principal photography began on July 30, 2018, in Santa Cruz, California, including their famous Boardwalk. Most of the film was shot in Los Angeles, and the main house featured is located in Pasadena. The house had modifications and the team spent 6 weeks there. Filming wrapped on October 8, 2018.


title: Us (2019 film)

text: The 1995 Luniz song "I Got 5 on It" is featured in this film, first at the beginning, when the family is driving to the beach and then later on in the film when the "tethered" family breaks into the vacation home. The once-fun song transmogrifies into an eerie "Tethered Mix", slowing everything down, and fully indulging the ominous quality of the film. Due to the track's popularity upon the trailer's release, it was edited into the final cut of the film, appearing during the climax. Waxwork Records announced in August 2019 that they would release the soundtrack to the film on vinyl, which contained Abels' popular score. The N.W.A song "Fuck tha Police" is also heard when Kitty Tyler tells the voice assistant Ophelia to "call the police", moments before she is killed by her Tethered counterpart, Dahlia, and the song plays throughout when the Wilsons enter the Tyler family's home. The ending features the Minnie Riperton song "Les Fleurs".


title: Us (2019 film)

text: The official trailer was released on December 25, 2018. The trailer, which was set to a darker version of the song "I Got 5 on It", featured a similar tone, editing, and shots as Peele's "Get Out", prompting speculation that the two films were set in the same universe.


title: Us (2019 film)

text: A second trailer was released on February 3, 2019, for Super Bowl LIII. That trailer featured a narration by Lupita Nyong'o's character, Adelaide, speaking with her husband Gabriel about the strange coincidences happening since they arrived at their beach house, and describing it as a "black cloud" hanging over them. The new theatrical release date, March 22, was announced at the end of the trailer. "Deadline Hollywood" estimated the studio spent around $77 million on promotion and advertisements for the film.


title: Us (2019 film)

text: "Us" had its world premiere at the South by Southwest film festival (SXSW) on March 8, 2019. It was also screened on March 6, 2019, before its official release, at Howard University. The film was originally scheduled for theatrical release in the United States on March 15, 2019, but was pushed back a week to March 22, following the announcement of its SXSW premiere.


title: Us (2019 film)

text: "Us" was released on 4K UHD Blu-ray, Blu-ray and DVD on June 18, 2019. The 4K release is an upscale from the 2K master.