120-492: The UK National Quantum Technologies Programme ( UKNQTP ) is a programme set up by the UK government to translate academic work on quantum mechanics , and the effects of quantum superposition and quantum entanglement into new products and services. It brings UK physicists and engineers together with companies and entrepreneurs who have an interest in commercialising the technology. The "second quantum revolution", or "quantum 2.0"
240-480: A {\displaystyle a} larger we make the spread in momentum smaller, but the spread in position gets larger. This illustrates the uncertainty principle. 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
360-436: A vitalist vision of nature, closer to the pre-Socratic one, got reborn at the same time, especially after Charles Darwin . Within the various uses of the word today, "nature" often refers to geology and wildlife . Nature can refer to the general realm of living beings , and in some cases to the processes associated with inanimate objects—the way that particular types of things exist and change of their own accord, such as
480-498: A body of liquid on the surface of a world that is localized to the bottom of basin (another type of landform or terrain feature; that is, it is not global) and moves slowly if it moves at all. On Earth, a body of water is considered a lake when it is inland, not part of the ocean, is larger and deeper than a pond, and is fed by a river. The only world other than Earth known to harbor lakes is Titan , Saturn's largest moon, which has lakes of ethane , most likely mixed with methane . It
600-449: A continual basis. The total number of species is in rapid decline. The origin of life on Earth is not well understood, but it is known to have occurred at least 3.5 billion years ago, during the hadean or archean eons on a primordial Earth that had a substantially different environment than is found at present. These life forms possessed the basic traits of self-replication and inheritable traits. Once life had appeared,
720-466: A definite prediction of what the quantum state ψ ( t ) {\displaystyle \psi (t)} will be at any later time. 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,
840-517: A degree or two of average global temperature have historically had major effects on the ecological balance, and on the actual geography of the Earth. Geology is the science and study of the solid and liquid matter that constitutes the Earth. The field of geology encompasses the study of the composition, structure , physical properties , dynamics, and history of Earth materials , and the processes by which they are formed, moved, and changed. The field
960-406: A dependence on the seasonal variation of the weather, and sudden changes lasting only a few years can have a dramatic effect, both on the vegetation and on the animals which depend on its growth for their food. Climate is a measure of the long-term trends in the weather. Various factors are known to influence the climate , including ocean currents, surface albedo , greenhouse gases , variations in
1080-653: A distinction between the natural and the artificial, with the artificial being understood as that which has been brought into being by a human consciousness or a human mind . Depending on the particular context, the term "natural" might also be distinguished from the unnatural or the supernatural . The word nature is borrowed from the Old French nature and is derived from the Latin word natura , or "essential qualities, innate disposition", and in ancient times, literally meant " birth ". In ancient philosophy, natura
1200-587: A dynamic dimension then, especially for Heraclitus ), and has steadily gained currency ever since. Earth is the only planet known to support life , and its natural features are the subject of many fields of scientific research. Within the Solar System , it is third closest to the Sun; it is the largest terrestrial planet and the fifth largest overall. Its most prominent climatic features are its two large polar regions, two relatively narrow temperate zones, and
1320-510: A family of unitary operators parameterized by a variable t {\displaystyle t} . Under the evolution generated by A {\displaystyle A} , any observable B {\displaystyle B} that commutes with A {\displaystyle A} will be conserved. Moreover, if B {\displaystyle B} is conserved by evolution under A {\displaystyle A} , then A {\displaystyle A}
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#17327839652291440-471: 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. As described above, entanglement
1560-426: A mathematical formulation of quantum mechanics and survey its application to some useful and oft-studied examples. In the mathematically rigorous formulation of quantum mechanics, the state of a quantum mechanical system is a vector ψ {\displaystyle \psi } belonging to a ( separable ) complex Hilbert space H {\displaystyle {\mathcal {H}}} . This vector
1680-417: A measurement of its position and also at the same time for a measurement of its momentum . 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
1800-485: A metabolism, a capacity to grow, respond to stimuli, and reproduce. An entity with these properties is generally considered life. However, not every definition of life considers all of these properties to be essential. Human-made analogs of life may also be considered to be life. The biosphere is the part of Earth's outer shell—including land, surface rocks, water, air and the atmosphere—within which life occurs, and which biotic processes in turn alter or transform. From
1920-446: A meteorite collision probably triggered the extinction of the non-avian dinosaurs and other large reptiles, but spared small animals such as mammals . Over the past 66 million years, mammalian life diversified. Several million years ago, a species of small African ape gained the ability to stand upright. The subsequent advent of human life, and the development of agriculture and further civilization allowed humans to affect
2040-435: A minority of Fungi . These life forms are found in almost every location on the Earth where there is liquid water, including in the Earth's interior. Their reproduction is both rapid and profuse. The combination of a high mutation rate and a horizontal gene transfer ability makes them highly adaptable, and able to survive in new and sometimes very harsh environments, including outer space . They form an essential part of
2160-427: A number of different purposes. These include: quantum information processing, such as quantum computing , quantum simulation , quantum secure communications , quantum sensing and metrology and quantum imaging , and are widely believed to offer capabilities that will out-perform existing and future classical technologies. The programme has contributed to the vast number of quantum technologies start-ups within
2280-436: A pond from many other aquatic terrain features, such as stream pools and tide pools . A river is a natural watercourse , usually freshwater , flowing towards an ocean, a lake, a sea or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including stream, creek, brook, rivulet, and rill; there
2400-471: 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
2520-405: 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 ( Fig. 1 ). Analytic solutions of
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#17327839652292640-551: 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: The general solution of the Schrödinger equation is given by which is a superposition of all possible plane waves e i ( k x − ℏ k 2 2 m t ) {\displaystyle e^{i(kx-{\frac {\hbar k^{2}}{2m}}t)}} , which are eigenstates of
2760-399: A variety of biotic and abiotic components that function in an interrelated way. The structure and composition is determined by various environmental factors that are interrelated. Variations of these factors will initiate dynamic modifications to the ecosystem. Some of the more important components are soil , atmosphere , radiation from the sun , water, and living organisms. Central to
2880-502: A wide equatorial tropical to subtropical region. Precipitation varies widely with location, from several metres of water per year to less than a millimetre. 71 percent of the Earth's surface is covered by salt-water oceans. The remainder consists of continents and islands, with most of the inhabited land in the Northern Hemisphere . Earth has evolved through geological and biological processes that have left traces of
3000-473: Is and this provides the lower bound on the product of standard deviations: 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
3120-493: Is a chemical substance that is composed of hydrogen and oxygen (H2O) and is vital for all known forms of life. In typical usage, "water" refers only to its liquid form , but it also has a solid state, ice , and a gaseous state, water vapor , or steam . Water covers 71% of the Earth 's surface. On Earth, it is found mostly in oceans and other large bodies of water, with 1.6% of water below ground in aquifers and 0.001% in
3240-469: Is a fundamental theory that describes the behavior of nature at and below the scale of atoms . It is the foundation of all quantum physics , which includes quantum chemistry , quantum field theory , quantum technology , and quantum information science . Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary ( macroscopic and (optical) microscopic ) scale, but
3360-478: 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. There are many mathematically equivalent formulations of quantum mechanics. One of
3480-454: Is a major academic discipline , and is also important for mineral and hydrocarbon extraction, knowledge about and mitigation of natural hazards , some Geotechnical engineering fields, and understanding past climates and environments. The geology of an area evolves through time as rock units are deposited and inserted and deformational processes change their shapes and locations. Rock units are first emplaced either by deposition onto
3600-531: Is a term that is often used to describe quantum technologies based on superposition and entanglement. Originally described in a 1997 book by Gerard J. Milburn , which was then followed by a 2003 article by Jonathan P. Dowling and Gerard J. Milburn , as well as a 2003 article by David Deutsch . These technologies use equipment such as highly stabilised laser systems, magneto-optical traps , cryogenic cooled solid state devices, ion traps and vacuum systems to create, manipulate and then use quantum effects for
3720-424: Is a valid joint state that is not separable. States that are not separable are called entangled . If the state for a composite system is entangled, it is impossible to describe either component system A or system B 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
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3840-564: Is called a microecosystem . For example, a microsystem can be a stone and all the life under it. A macroecosystem might involve a whole ecoregion , with its drainage basin . Wilderness is generally defined as areas that have not been significantly modified by human activity. Wilderness areas can be found in preserves, estates, farms, conservation preserves, ranches, national forests , national parks , and even in urban areas along rivers, gulches, or otherwise undeveloped areas. Wilderness areas and protected parks are considered important for
3960-405: Is conserved under the evolution generated by B {\displaystyle B} . 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 . The simplest example of a quantum system with a position degree of freedom is a free particle in
4080-1066: 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. The Hamiltonian H {\displaystyle H} is known as the generator of time evolution, since it defines a unitary time-evolution operator U ( t ) = e − i H t / ℏ {\displaystyle U(t)=e^{-iHt/\hbar }} for each value of t {\displaystyle t} . From this relation between U ( t ) {\displaystyle U(t)} and H {\displaystyle H} , it follows that any observable A {\displaystyle A} that commutes with H {\displaystyle H} will be conserved : its expectation value will not change over time. This statement generalizes, as mathematically, any Hermitian operator A {\displaystyle A} can generate
4200-586: Is delivered by several UK public bodies: UK government Department for Science, Innovation and Technology , EPSRC , STFC , Innovate UK , Dstl , NPL , GCHQ and Innovate UK Business Connect. The UKQTP has received some attention from the UK media, with an interview with Professor Miles Padgett on the BBC Radio 4 Today programme on 11 November 2015 and articles in New Scientist , and Nature materials Quantum mechanics Quantum mechanics
4320-476: Is estimated to have formed 4.54 billion years ago from the solar nebula , along with the Sun and other planets . The Moon formed roughly 20 million years later. Initially molten, the outer layer of the Earth cooled, resulting in the solid crust. Outgassing and volcanic activity produced the primordial atmosphere. Condensing water vapor , most or all of which came from ice delivered by comets , produced
4440-448: Is given by The operator U ( t ) = e − i H t / ℏ {\displaystyle U(t)=e^{-iHt/\hbar }} 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 ψ ( 0 ) {\displaystyle \psi (0)} – it makes
4560-406: Is its associated eigenvector. More generally, the eigenvalue is degenerate and the probability is given by ⟨ ψ , P λ ψ ⟩ {\displaystyle \langle \psi ,P_{\lambda }\psi \rangle } , where P λ {\displaystyle P_{\lambda }} is the projector onto its associated eigenspace. In
4680-726: Is known as wave–particle duality . In addition to light, electrons , atoms , and molecules are all found to exhibit the same dual behavior when fired towards a double slit. Another non-classical 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 , tunnel diode and tunnel field-effect transistor . When quantum systems interact,
4800-549: Is mostly used as the Latin translation of the Greek word physis (φύσις), which originally related to the intrinsic characteristics of plants, animals, and other features of the world to develop of their own accord. The concept of nature as a whole, the physical universe , is one of several expansions of the original notion; it began with certain core applications of the word φύσις by pre-Socratic philosophers (though this word had
4920-534: Is no general rule that defines what can be called a river. Many names for small rivers are specific to geographic location; one example is Burn in Scotland and North-east England. Sometimes a river is said to be larger than a creek, but this is not always the case, due to vagueness in the language. A river is part of the hydrological cycle . Water within a river is generally collected from precipitation through surface runoff , groundwater recharge, springs , and
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5040-504: Is no universal agreement on the definition of life, scientists generally accept that the biological manifestation of life is characterized by organization , metabolism , growth , adaptation , response to stimuli , and reproduction . Life may also be said to be simply the characteristic state of organisms . Present day organisms from viruses to humans possess a self-replicating informational molecule (genome), either DNA or RNA (as in some viruses), and such an informational molecule
5160-415: Is not known if Titan's lakes are fed by rivers, though Titan's surface is carved by numerous river beds. Natural lakes on Earth are generally found in mountainous areas, rift zones , and areas with ongoing or recent glaciation . Other lakes are found in endorheic basins or along the courses of mature rivers. In some parts of the world, there are many lakes because of chaotic drainage patterns left over from
5280-444: 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 : which has Fourier transform, and therefore momentum distribution We see that as we make a {\displaystyle a} smaller the spread in position gets smaller, but the spread in momentum gets larger. Conversely, by making
5400-628: Is not sufficient for describing them at very small submicroscopic (atomic and subatomic ) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation, valid at large (macroscopic/microscopic) scale. Quantum systems have bound states that are quantized to discrete values of energy , momentum , angular momentum , and other quantities, in contrast to classical systems where these quantities can be measured continuously. Measurements of quantum systems show characteristics of both particles and waves ( wave–particle duality ), and there are limits to how accurately
5520-815: Is part of quantum 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 . 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 provides. 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
5640-540: Is postulated to be normalized under the Hilbert space inner product, that is, it obeys ⟨ ψ , ψ ⟩ = 1 {\displaystyle \langle \psi ,\psi \rangle =1} , and it is well-defined up to a complex number of modulus 1 (the global phase), that is, ψ {\displaystyle \psi } and e i α ψ {\displaystyle e^{i\alpha }\psi } represent
5760-503: Is probably intrinsic to life. It is likely that the earliest forms of life were based on a self-replicating informational molecule ( genome ), perhaps RNA or a molecule more primitive than RNA or DNA. The specific deoxyribonucleotide / ribonucleotide sequence in each currently extant individual organism contains sequence information that functions to promotes survival, reproduction , and the capacity to acquire resources necessary for reproduction, and such sequences probably emerged early in
5880-466: Is replaced by − i ℏ ∂ ∂ x {\displaystyle -i\hbar {\frac {\partial }{\partial x}}} , and in particular in the non-relativistic Schrödinger equation in position space the momentum-squared term is replaced with a Laplacian times − ℏ 2 {\displaystyle -\hbar ^{2}} . When two different quantum systems are considered together,
6000-415: Is the reduced Planck constant . The constant i ℏ {\displaystyle i\hbar } 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 . The solution of this differential equation
6120-469: Is then If the state for the first system is the vector ψ A {\displaystyle \psi _{A}} and the state for the second system is ψ B {\displaystyle \psi _{B}} , then the state of the composite system is Not all states in the joint Hilbert space H A B {\displaystyle {\mathcal {H}}_{AB}} can be written in this form, however, because
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#17327839652296240-505: The Born rule : in the simplest case the eigenvalue λ {\displaystyle \lambda } is non-degenerate and the probability is given by | ⟨ λ → , ψ ⟩ | 2 {\displaystyle |\langle {\vec {\lambda }},\psi \rangle |^{2}} , where λ → {\displaystyle {\vec {\lambda }}}
6360-797: The Indian Ocean , the Southern Ocean , and the Arctic Ocean . Smaller regions of the oceans are called seas, gulfs, bays and other names. There are also salt lakes , which are smaller bodies of landlocked saltwater that are not interconnected with the World Ocean. Two notable examples of salt lakes are the Aral Sea and the Great Salt Lake . A lake (from Latin word lacus ) is a terrain feature (or physical feature ),
6480-663: The Neoproterozoic era, freezing temperatures covered much of the Earth in glaciers and ice sheets. This hypothesis has been termed the " Snowball Earth ", and it is of particular interest as it precedes the Cambrian explosion in which multicellular life forms began to proliferate about 530–540 million years ago. Since the Cambrian explosion there have been five distinctly identifiable mass extinctions . The last mass extinction occurred some 66 million years ago, when
6600-454: The Northern and Southern Hemispheres experience opposite seasons. Weather is a chaotic system that is readily modified by small changes to the environment , so accurate weather forecasting is limited to only a few days. Overall, two things are happening worldwide: (1) temperature is increasing on the average; and (2) regional climates have been undergoing noticeable changes. Water
6720-587: The World Ocean or global ocean. This concept of a global ocean as a continuous body of water with relatively free interchange among its parts is of fundamental importance to oceanography . The major oceanic divisions are defined in part by the continents , various archipelagos , and other criteria: these divisions are (in descending order of size) the Pacific Ocean , the Atlantic Ocean ,
6840-422: The air as vapor , clouds, and precipitation . Oceans hold 97% of surface water, glaciers , and polar ice caps 2.4%, and other land surface water such as rivers, lakes, and ponds 0.6%. Additionally, a minute amount of the Earth's water is contained within biological bodies and manufactured products. An ocean is a major body of saline water , and a principal component of the hydrosphere. Approximately 71% of
6960-713: The canonical commutation relation : Given a quantum state, the Born rule lets us compute expectation values for both X {\displaystyle X} and P {\displaystyle P} , and moreover for powers of them. Defining the uncertainty for an observable by a standard deviation , we have and likewise for the momentum: The uncertainty principle states that Either standard deviation can in principle be made arbitrarily small, but not both simultaneously. This inequality generalizes to arbitrary pairs of self-adjoint operators A {\displaystyle A} and B {\displaystyle B} . The commutator of these two operators
7080-510: The kingdoms Vegetabilia (later Plantae ) and Animalia . Since then, it has become clear that the Plantae as originally defined included several unrelated groups, and the fungi and several groups of algae were removed to new kingdoms. However, these are still often considered plants in many contexts. Bacterial life is sometimes included in flora, and some classifications use the term bacterial flora separately from plant flora . Among
7200-738: The last ice age . All lakes are temporary over geologic time scales, as they will slowly fill in with sediments or spill out of the basin containing them. A pond is a body of standing water , either natural or human-made, that is usually smaller than a lake. A wide variety of human-made bodies of water are classified as ponds, including water gardens designed for aesthetic ornamentation, fish ponds designed for commercial fish breeding, and solar ponds designed to store thermal energy. Ponds and lakes are distinguished from streams via current speed. While currents in streams are easily observed, ponds and lakes possess thermally driven micro-currents and moderate wind driven currents. These features distinguish
7320-423: 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
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#17327839652297440-457: The tropical climate at the equator to the polar climate in the northern and southern extremes. Weather is also influenced by the seasons, which result from the Earth 's axis being tilted relative to its orbital plane . Thus, at any given time during the summer or winter, one part of the Earth is more directly exposed to the rays of the sun . This exposure alternates as the Earth revolves in its orbit. At any given time, regardless of season,
7560-562: 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. 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
7680-400: The Earth is held in place by gravity. Air is mostly nitrogen , oxygen , water vapor , with much smaller amounts of carbon dioxide, argon, etc. The atmospheric pressure declines steadily with altitude. The ozone layer plays an important role in depleting the amount of ultraviolet (UV) radiation that reaches the surface. As DNA is readily damaged by UV light, this serves to protect life at
7800-593: The Earth more rapidly than any previous life form, affecting both the nature and quantity of other organisms as well as global climate. By comparison, the Great Oxygenation Event , produced by the proliferation of algae during the Siderian period, required about 300 million years to culminate. The present era is classified as part of a mass extinction event , the Holocene extinction event,
7920-552: The Earth's surface (an area of some 361 million square kilometers) is covered by ocean, a continuous body of water that is customarily divided into several principal oceans and smaller seas. More than half of this area is over 3,000 meters (9,800 feet) deep. Average oceanic salinity is around 35 parts per thousand (ppt) (3.5%), and nearly all seawater has a salinity in the range of 30 to 38 ppt. Though generally recognized as several 'separate' oceans, these waters comprise one global, interconnected body of salt water often referred to as
8040-431: The Hilbert space for the spin of a single proton is simply the space of two-dimensional complex vectors C 2 {\displaystyle \mathbb {C} ^{2}} with the usual inner product. Physical quantities of interest – position, momentum, energy, spin – are represented by observables, which are Hermitian (more precisely, self-adjoint ) linear operators acting on
8160-411: The Hilbert space of the combined system is the tensor product of the Hilbert spaces of the two components. For example, let A and B be two quantum systems, with Hilbert spaces H A {\displaystyle {\mathcal {H}}_{A}} and H B {\displaystyle {\mathcal {H}}_{B}} , respectively. The Hilbert space of the composite system
8280-432: 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
8400-657: The Quantum hub for Networked Quantum Information Technologies , led by the University of Oxford . The UKQTP is advised by the Quantum Technologies Strategic Advisory Board, which is chaired by Professor David Delpy , it also consists of Professor Sir Peter Knight , Baroness Neville-Jones , Professor Gerald Milburn, Professor Ian Walmsley and other leading individuals from industry, academia and public sector. The programme
8520-489: 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, admitting no solution in closed form . However, there are techniques for finding approximate solutions. One method, called perturbation theory , uses
8640-508: The Schrödinger equation for the particle in a box are or, from Euler's formula , Nature Nature is an inherent character or constitution, particularly of the ecosphere or the universe as a whole. In this general sense nature refers to the laws , elements and phenomena of the physical world, including life . Although humans are part of nature, human activity or humans as a whole are often described as at times at odds, or outright separate and even superior to nature. During
8760-503: The UK. Examples include Orca Computing, Universal Quantum, Oxford Ionics, Delta g and Cerca Magnetics. The vision of the UK National Quantum Technologies programme is to "create a coherent government, industry and academic quantum technology community that gives the UK a world-leading position in the emerging multi-billion-pound new quantum technology markets, and to substantially enhance the value of some of
8880-530: The advent of modern scientific method in the last several centuries, nature became the passive reality , organized and moved by divine laws. With the Industrial Revolution , nature increasingly became seen as the part of reality deprived from intentional intervention: it was hence considered as sacred by some traditions ( Rousseau , American transcendentalism ) or a mere decorum for divine providence or human history ( Hegel , Marx ). However,
9000-403: 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 approximation method 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. One consequence of
9120-606: 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 X ^ {\displaystyle {\hat {X}}} and momentum operator P ^ {\displaystyle {\hat {P}}} do not commute, but rather satisfy
9240-708: The biggest UK-based industries." The UKNQTP was initiated by a £270 million investment by the UK Chancellor of the exchequer, George Osborne in the Autumn Statement 2013. In addition to this, the UK Defence Science and Technology Laboratory (Dstl) separately announced a £30 million investment into a programme to produce demonstrator devices. The primary focus of the UKNQTP are four 'hubs' for quantum technologies: Past hubs include
9360-477: The biosphere. Over nine-tenths of the total biomass on Earth is plant life, on which animal life depends very heavily for its existence. More than 2 million species of plant and animal life have been identified to date, and estimates of the actual number of existing species range from several million to well over 50 million. The number of individual species of life is constantly in some degree of flux, with new species appearing and others ceasing to exist on
9480-446: The broadest geophysiological point of view, the biosphere is the global ecological system integrating all living beings and their relationships, including their interaction with the elements of the lithosphere (rocks), hydrosphere (water), and atmosphere (air). The entire Earth contains over 75 billion tons (150 trillion pounds or about 6.8×10 kilograms) of biomass (life), which lives within various environments within
9600-404: The collection of probability amplitudes that pertain to another. One consequence of the mathematical rules of quantum mechanics is a tradeoff in predictability between 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
9720-626: The continuous case, these formulas give instead the probability density . After the measurement, if result λ {\displaystyle \lambda } was obtained, the quantum state is postulated to collapse to λ → {\displaystyle {\vec {\lambda }}} , in the non-degenerate case, or to P λ ψ / ⟨ ψ , P λ ψ ⟩ {\textstyle P_{\lambda }\psi {\big /}\!{\sqrt {\langle \psi ,P_{\lambda }\psi \rangle }}} , in
9840-431: The dependence in position means that the momentum operator is equivalent (up to an i / ℏ {\displaystyle i/\hbar } 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 p i {\displaystyle p_{i}}
9960-468: The ecosystem concept is the idea that living organisms interact with every other element in their local environment . Eugene Odum, a founder of ecology, stated: "Any unit that includes all of the organisms (ie: the "community") in a given area interacting with the physical environment so that a flow of energy leads to clearly defined trophic structure, biotic diversity, and material cycles (i.e.: exchange of materials between living and nonliving parts) within
10080-553: The equatorial oceans to the polar regions. These currents help to moderate the differences in temperature between winter and summer in the temperate zones. Also, without the redistributions of heat energy by the ocean currents and atmosphere, the tropics would be much hotter, and the polar regions much colder. Weather can have both beneficial and harmful effects. Extremes in weather, such as tornadoes or hurricanes and cyclones , can expend large amounts of energy along their paths, and produce devastation. Surface vegetation has evolved
10200-622: The evolution of life. Survival functions present early in the evolution of life likely also included genomic sequences that promote the avoidance of damage to the self-replicating molecule and also the capability to repair such damages that do occur. Repair of some genome damages may have involved using information from another similar molecule by a process of recombination (a primitive form of sexual interaction ). Properties common to terrestrial organisms (plants, animals, fungi , protists , archaea , and bacteria) are that they are cellular, carbon-and-water-based with complex organization, having
10320-444: The fastest ever to have occurred. Some, such as E. O. Wilson of Harvard University , predict that human destruction of the biosphere could cause the extinction of one-half of all species in the next 100 years. The extent of the current extinction event is still being researched, debated and calculated by biologists. The Earth's atmosphere is a key factor in sustaining the ecosystem . The thin layer of gases that envelops
10440-532: The first primitive life forms. When basic forms of plant life developed the process of photosynthesis the sun's energy could be harvested to create conditions which allowed for more complex life forms. The resultant oxygen accumulated in the atmosphere and gave rise to the ozone layer . The incorporation of smaller cells within larger ones resulted in the development of yet more complex cells called eukaryotes . Cells within colonies became increasingly specialized, resulting in true multicellular organisms. With
10560-415: 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,
10680-414: The geomagnetic field. The atmospheric conditions have been significantly altered from the original conditions by the presence of life-forms, which create an ecological balance that stabilizes the surface conditions. Despite the wide regional variations in climate by latitude and other geographic factors, the long-term average global climate is quite stable during interglacial periods, and variations of
10800-503: The immediate vicinity of a stream is called a riparian zone . Given the status of the ongoing Holocene extinction , streams play an important corridor role in connecting fragmented habitats and thus in conserving biodiversity . The study of streams and waterways in general involves many branches of inter-disciplinary natural science and engineering, including hydrology , fluvial geomorphology , aquatic ecology , fish biology , riparian ecology , and others. Ecosystems are composed of
10920-406: The initial sequence of rocks has been deposited, the rock units can be deformed and/or metamorphosed . Deformation typically occurs as a result of horizontal shortening, horizontal extension , or side-to-side ( strike-slip ) motion. These structural regimes broadly relate to convergent boundaries , divergent boundaries , and transform boundaries , respectively, between tectonic plates . Earth
11040-462: 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. This behavior
11160-430: 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;
11280-649: The many ways of classifying plants are by regional floras , which, depending on the purpose of study, can also include fossil flora , remnants of plant life from a previous era. People in many regions and countries take great pride in their individual arrays of characteristic flora, which can vary widely across the globe due to differences in climate and terrain . Regional floras commonly are divided into categories such as native flora or agricultural and garden flora . Some types of "native flora" actually have been introduced centuries ago by people migrating from one region or continent to another, and become an integral part of
11400-432: The momentum operator with momentum p = ℏ k {\displaystyle p=\hbar k} . The coefficients of the superposition are ψ ^ ( k , 0 ) {\displaystyle {\hat {\psi }}(k,0)} , which is the Fourier transform of the initial quantum state ψ ( x , 0 ) {\displaystyle \psi (x,0)} . It
11520-461: The native, or natural flora of the place to which they were introduced. This is an example of how human interaction with nature can blur the boundary of what is considered nature. Another category of plant has historically been carved out for weeds . Though the term has fallen into disfavor among botanists as a formal way to categorize "useless" plants, the informal use of the word "weeds" to describe those plants that are deemed worthy of elimination
11640-619: The oceans and other water sources. The highly energetic chemistry is believed to have produced a self-replicating molecule around 4 billion years ago. Continents formed, then broke up and reformed as the surface of Earth reshaped over hundreds of millions of years, occasionally combining to make a supercontinent . Roughly 750 million years ago, the earliest known supercontinent Rodinia , began to break apart. The continents later recombined to form Pannotia which broke apart about 540 million years ago, then finally Pangaea , which broke apart about 180 million years ago. During
11760-413: 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
11880-412: The one-dimensional case in the x {\displaystyle x} direction, the time-independent Schrödinger equation may be written With the differential operator defined by with state ψ {\displaystyle \psi } in this case having energy E {\displaystyle E} coincident with the kinetic energy of the particle. The general solutions of
12000-420: The original conditions. The outer surface is divided into several gradually migrating tectonic plates . The interior remains active, with a thick layer of plastic mantle and an iron-filled core that generates a magnetic field . This iron core is composed of a solid inner phase, and a fluid outer phase. Convective motion in the core generates electric currents through dynamo action, and these, in turn, generate
12120-455: The original quantum system ceases to exist as an independent entity (see Measurement in quantum mechanics ). The time evolution of a quantum state is described by the Schrödinger equation: Here H {\displaystyle H} denotes the Hamiltonian , the observable corresponding to the total energy of the system, and ℏ {\displaystyle \hbar }
12240-464: The ozone layer absorbing harmful ultraviolet radiation , life colonized the surface of Earth. The first form of life to develop on the Earth were unicellular , and they remained the only form of life until about a billion years ago when multi-cellular organisms began to appear. Microorganisms or microbes are microscopic , and smaller than the human eye can see. Microorganisms can be single-celled , such as Bacteria , Archaea , many Protista , and
12360-441: The planetary ecosystem. However, some microorganisms are pathogenic and can post health risk to other organisms. Viruses are infectious agents , but they are not autonomous life forms , as it is the case for viroids , satellites , DPIs and prions . Originally Aristotle divided all living things between plants, which generally do not move fast enough for humans to notice, and animals. In Linnaeus ' system, these became
12480-428: The position becomes more and more uncertain. The uncertainty in momentum, however, stays constant. 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
12600-411: The process of evolution by natural selection resulted in the development of ever-more diverse life forms. Species that were unable to adapt to the changing environment and competition from other life forms became extinct. However, the fossil record retains evidence of many of these older species. Current fossil and DNA evidence shows that all existing species can trace a continual ancestry back to
12720-400: 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
12840-528: The release of stored water in natural ice and snowpacks (i.e., from glaciers ). A stream is a flowing body of water with a current , confined within a bed and stream banks . In the United States, a stream is classified as a watercourse less than 60 feet (18 metres) wide. Streams are important as conduits in the water cycle , instruments in groundwater recharge , and they serve as corridors for fish and wildlife migration. The biological habitat in
12960-413: 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 quantum computing and
13080-566: The results of a Bell test will be constrained in a particular, quantifiable way. Many Bell tests have been performed and they have shown results incompatible with the constraints imposed by local hidden variables. It is not possible to present these concepts in more than a superficial way without introducing the 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
13200-463: 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 L 2 ( C ) {\displaystyle L^{2}(\mathbb {C} )} , while
13320-418: The solar luminosity, and changes to the Earth's orbit. Based on historical and geological records, the Earth is known to have undergone drastic climate changes in the past, including ice ages . The climate of a region depends on a number of factors, especially latitude . A latitudinal band of the surface with similar climatic attributes forms a climate region. There are a number of such regions, ranging from
13440-625: The superposition principle implies that linear combinations of these "separable" or "product states" are also valid. For example, if ψ A {\displaystyle \psi _{A}} and ϕ A {\displaystyle \phi _{A}} are both possible states for system A {\displaystyle A} , and likewise ψ B {\displaystyle \psi _{B}} and ϕ B {\displaystyle \phi _{B}} are both possible states for system B {\displaystyle B} , then
13560-419: The surface or intrude into the overlying rock . Deposition can occur when sediments settle onto the surface of the Earth and later lithify into sedimentary rock , or when as volcanic material such as volcanic ash or lava flows, blanket the surface. Igneous intrusions such as batholiths , laccoliths , dikes , and sills , push upwards into the overlying rock, and crystallize as they intrude. After
13680-425: The surface. The atmosphere also retains heat during the night, thereby reducing the daily temperature extremes. Terrestrial weather occurs almost exclusively in the lower part of the atmosphere , and serves as a convective system for redistributing heat. Ocean currents are another important factor in determining climate, particularly the major underwater thermohaline circulation which distributes heat energy from
13800-535: The survival of certain species , ecological studies, conservation , and solitude. Some nature writers believe wilderness areas are vital for the human spirit and creativity, and some ecologists consider wilderness areas to be an integral part of the Earth's self-sustaining natural ecosystem (the biosphere ). They may also preserve historic genetic traits and that they provide habitat for wild flora and fauna that may be difficult or impossible to recreate in zoos , arboretums , or laboratories . Although there
13920-441: The system is an ecosystem." Within the ecosystem, species are connected and dependent upon one another in the food chain , and exchange energy and matter between themselves as well as with their environment. The human ecosystem concept is based on the human/nature dichotomy and the idea that all species are ecologically dependent on each other, as well as with the abiotic constituents of their biotope . A smaller unit of size
14040-441: 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
14160-437: The universe as a whole remains speculative. Predictions of quantum mechanics have been verified experimentally to an extremely high degree of accuracy . For example, the refinement of quantum mechanics for the interaction of light and matter, known as quantum electrodynamics (QED), has been shown to agree with experiment to within 1 part in 10 when predicting the magnetic properties of an electron. A fundamental feature of
14280-526: The value of a physical quantity can be predicted prior to its measurement, given a complete set of initial conditions (the uncertainty principle ). Quantum mechanics arose gradually from theories to explain observations that 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
14400-537: The weather and geology of the Earth . It is often taken to mean the " natural environment " or wilderness —wild animals, rocks, forest, and in general those things that have not been substantially altered by human intervention, or which persist despite human intervention. For example, manufactured objects and human interaction generally are not considered part of nature, unless qualified as, for example, "human nature" or "the whole of nature". This more traditional concept of natural things that can still be found today implies
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