being saved from something, such as suffering or the punishment of sin - also called deliverance;
being saved for something, such as an afterlife or participating in the Reign of God - also called redemption
Salvation can also be understood in terms of social liberation, as in liberation theology.

The theological study of salvation is called Soteriology and also covers the means by which salvation is effected or achieved, and its results or effects.

Christians believe salvation is a gift by unmerited grace of God, who sent Jesus as the savior. Christians believe that through faith in Jesus one can be saved from sin and spiritual death. The crucifixion of Jesus is explained as an atoning sacrifice, which, in the words of the Gospel of John, “takes away the sins of the world”. Reception of salvation is related to justification.[24]

The operation and effects of grace are understood differently by different traditions. Catholicism and Eastern Orthodoxy teach the necessity of the free will to cooperate with grace.[25] Reformed theology places distinctive emphasis on grace by teaching that mankind is completely incapable of self-redemption, but the grace of God overcomes even the unwilling heart.[26]

http://en.wikipedia.org/wiki/Salvation

According to the Gospels, Jesus and his followers went to Jerusalem the week of the Passover where they were eagerly greeted by a crowd. In Jerusalem, Jesus cleansed the Temple,[19] and predicted its destruction[20] - heightening conflict with the Jewish authorities who were plotting his death.[21]

After sharing his last meal with his disciples, Jesus went to pray in the Garden of Gethsemane where he was betrayed by his disciple Judas Iscariot and arrested by the temple guard on orders from the Sanhedrin and the high priest Caiaphas. Jesus was convicted by the Sanhedrin of blasphemy and transferred to the Roman governor Pilate, who had him crucified for inciting rebellion. Jesus died by late afternoon and was entombed.

Christians believe that God raised Jesus from the dead on the third day, that Jesus appeared to his apostles and other disciples, commissioned his disciples to “make disciples of all nations, baptizing them in the name of the Father and of the Son (Jesus) and of the Holy Spirit.”[22] and ascended to heaven. Christians also believe that God sent the disciples the Holy Spirit (or Paraclete).[23]

The purpose of this death and resurrection is described in various doctrines of atonement. Some see Jesus as a Sacrifice or substitutionary atonement made to purify humanity like many other sacrifices described in the Old Testament. Others see Jesus’ dying and suffering on the cross as a sign and demonstration from God that he was willing to endure the sin and punishment because of his agape (parental, self-sacrificing) love for humanity. In another interpretation of Jesus’ death and resurrection, The Book of John compares the crucifixion of Jesus to the lifting up of the Nehushtan (brass serpent) saying that “Just as Moses lifted up the snake in the desert, so the Son of Man must be lifted up, that everyone who believes in him may have eternal life. For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life.” (John 3:14 - John 3:16)

All patriarchal religions present a common quality, the “hallmark of patriarchal religious thought”: the division of the world in two comprehensive domains, one sacred, the other profane. [1] Religion is often described as a communal system for the coherence of belief focusing on a system of thought, unseen being, person, or object, that is considered to be supernatural, sacred, divine, or of the highest truth. Moral codes, practices, values, institutions, tradition, rituals, and scriptures are often traditionally associated with the core belief, and these may have some overlap with concepts in secular philosophy. Religion is also often described as a “way of life”.

The development of religion has taken many forms in various cultures. “Organized religion” generally refers to an organization of people supporting the exercise of some religion with a prescribed set of beliefs, often taking the form of a legal entity (see religion-supporting organization). Other religions believe in personal revelation and responsibility. “Religion” is sometimes used interchangeably with “faith” or “belief system,”[2] but is more socially defined than that of personal convictions.

The etymology of the word “religion” has been debated for centuries. The English word clearly derives from the Latin religio, “reverence (for the gods)” or “conscientiousness”. The origins of religio, however, are obscure. Proposed etymological interpretations include:

From Relego
Re-reading–from Latin re (again) + lego (in the sense of “read”), referring to the repetition of scripture.
Treating carefully–from Latin re (again) + lego (in the sense of “choose”–this was the interpretation of Cicero) “go over again” or “consider carefully”.
From Religare
Re-connection to the divine–from Latin re (again) + ligare (to connect, as in English ligament). This interpretation is favoured by modern scholars such as Tom Harpur, but was made prominent by St. Augustine, following the interpretation of Lactantius.
To bind or return to bondage–an alternate interpretation of the “reconnection” etymology emphasizing a sense of servitude to God, this may have originated with Augustine. However, the interpretation, while popular with critics of religion, is often considered imprecise and possibly offensive to followers.
From Res + legere
Concerning a gathering — from Latin res (ablative re, with regard to) + legere (to gather), since organized religion revolves around a gathering of people.

Religion has been defined in a wide variety of ways. Most definitions attempt to find a balance somewhere between overly sharp definition and meaningless generalities. Some sources have tried to use formalistic, doctrinal definitions while others have emphasized experiential, emotive, intuitive, valuational and ethical factors.

Sociologists and anthropologists tend to see religion as an abstract set of ideas, values, or experiences developed as part of a cultural matrix. For example, in Lindbeck’s Nature of Doctrine, religion does not refer to belief in “God” or a transcendent Absolute. Instead, Lindbeck defines religion as, “a kind of cultural and/or linguistic framework or medium that shapes the entirety of life and thought… it is similar to an idiom that makes possible the description of realities, the formulation of beliefs, and the experiencing of inner attitudes, feelings, and sentiments.”[3] According to this definition, religion refers to one’s primary worldview and how this dictates one’s thoughts and actions.

Other religious scholars have put forward a definition of religion that avoids the reductionism of the various sociological and psychological disciplines that reduce religion to its component factors. Religion may be defined as the presence of a belief in the sacred or the holy. For example Rudolf Otto’s “The Idea of the Holy,” formulated in 1917, defines the essence of religious awareness as awe, a unique blend of fear and fascination before the divine. Friedrich Schleiermacher in the late 18th century defined religion as a “feeling of absolute dependence.”

The Encyclopedia of Religion defines religion this way:[4]

In summary, it may be said that almost every known culture involves the religious in the above sense of a depth dimension in cultural experiences at all levels — a push, whether ill-defined or conscious, toward some sort of ultimacy and transcendence that will provide norms and power for the rest of life. When more or less distinct patterns of behaviour are built around this depth dimension in a culture, this structure constitutes religion in its historically recognizable form. Religion is the organization of life around the depth dimensions of experience — varied in form, completeness, and clarity in accordance with the environing culture.”

Other encyclopedic definitions include: “A general term used… to designate all concepts concerning the belief in god(s) and goddess(es) as well as other spiritual beings or transcendental ultimate concerns”[5] and “human beings’ relation to that which they regard as holy, sacred, spiritual, or divine.”[6]

http://en.wikipedia.org/wiki/Religion

A diverse array of living organisms can be found in the biosphere on Earth. Properties common to these organisms – plants, animals, fungi, protists, archaea and bacteria – are a carbon and water-based cellular form with complex organization and genetic information. They undergo metabolism, possess a capacity to grow, respond to stimuli, reproduce and, through natural selection, adapt to their environment in successive generations.

An entity with the above properties is considered to be a living organism, that is an organism that is alive hence can be called a life form. However, not every definition of life considers all of these properties to be essential. For example, the capacity for descent with modification is often taken as the only essential property of life. This definition notably includes viruses, which do not qualify under narrower definitions as they are acellular and do not metabolise. Broader definitions of life may also include theoretical non-carbon-based life and other alternative biology. Some forms of artificial life, however, especially wet alife, might alternatively be classified as real life.

There is no universal definition of life; there are a variety of definitions proposed by different scientists.To define life in unequivocal terms is still a challenge for scientists[5][6].

Conventional definition: Often scientists say that life is a characteristic of organisms that exhibit the following phenomena:

Homeostasis: Regulation of the internal environment to maintain a constant state; for example, sweating to reduce temperature.
Organization: Being composed of one or more cells, which are the basic units of life.
Metabolism: Consumption of energy by converting nonliving material into cellular components (anabolism) and decomposing organic matter (catabolism). Living things require energy to maintain internal organization (homeostasis) and to produce the other phenomena associated with life.
Growth: Maintenance of a higher rate of synthesis than catalysis. A growing organism increases in size in all of its parts, rather than simply accumulating matter. The particular species begins to multiply and expand as the evolution continues to flourish.
Adaptation: The ability to change over a period of time in response to the environment. This ability is fundamental to the process of evolution and is determined by the organism’s heredity as well as the composition of metabolized substances, and external factors present.
Response to stimuli: A response can take many forms, from the contraction of a unicellular organism when touched to complex reactions involving all the senses of higher animals. A response is often expressed by motion, for example, the leaves of a plant turning toward the sun or an animal chasing its prey.
Reproduction: The ability to produce new organisms. Reproduction can be the division of one cell to form two new cells. Usually the term is applied to the production of a new individual (either asexually, from a single parent organism, or sexually, from at least two differing parent organisms), although strictly speaking it also describes the production of new cells in the process of growth.

Plant lifeHowever, others cite several limitations of this definition[7]. Thus, many members of several species do not reproduce, possibly because they belong to specialized sterile castes (such as ant workers), these are still considered forms of life. One could say that the property of life is inherited; hence, sterile or hybrid organisms such as the mule, liger or eunuchs are alive although they are not capable of self reproduction. However, non-reproducing organisms may still propagate through mechanisms such as kin selection.

Viruses and aberrant prion proteins are often considered replicators rather than forms of life, a distinction warranted because they cannot reproduce without very specialized substrates such as host cells or proteins, respectively. Also, the Rickettsia and Chlamydia are examples of bacteria that cannot independently fulfill many vital biochemical processes, and depend on entry, growth, and replication within the cytoplasm of eukaryotic host cells. However, most forms of life rely on foods produced by other species, or at least the specific chemistry of Earth’s environment.

Rhesus Macaques resting in the sunStill others contest such definitions of life on philosophical grounds. They offer the following as examples of life: viruses which reproduce; storms or flames which “burn”; certain computer software programs which are programmed to mutate and evolve; future software programs which may evince (even high-order) behavior; machines which can move; and some forms of proto-life consisting of metabolizing cells without the ability to reproduce.[citation needed] Still, most scientists would not call such phenomena expressive of life. Generally all seven characteristics are required for a population to be considered a life form.

The systemic definition of life is that living things are self-organizing and autopoietic (self-producing). These objects are not to be confused with dissipative structures (e.g. fire).

Variations of this definition include Stuart Kauffman’s definition of life as an autonomous agent or a multi-agent system capable of reproducing itself or themselves, and of completing at least one thermodynamic work cycle.

Marine life around a coral reefYet other definitions of life are:

Living things are systems that tend to respond to changes in their environment, and inside themselves, in such a way as to promote their own continuation.[citation needed]
Life is a characteristic of self-organizing, self-recycling systems consisting of populations of replicators that are capable of mutation, around most of which homeostatic, metabolizing organisms evolve. This definition includes worker caste ants, viruses and mules, and precludes flames. It also explains why bees can be alive and yet commit suicide in defending their hive. In this case the colony, not the individual, is the living system.
Type of organization of matter producing various interacting forms of variable complexity, whose main property is to replicate almost perfectly by using matter and energy available in their environment to which they may adapt. In this definition “almost perfectly” relates to mutations happening during replication of organisms that may have adaptive benefits.
Life is a potentially self-perpetuating open system of linked organic reactions, catalyzed simultaneously and almost isothermally by complex chemicals (enzymes) that are themselves produced by the open system.

Thomas Jay Oord has defined love in various scholarly publications as acting intentionally, in sympathetic response to others (including God), to promote overall well-being. Oord means for his definition to be sufficient for research in ethics, religion, and science.

The different aspects of love can be roughly illustrated by comparing their corollaries and opposites. As a general expression of positive sentiment (a stronger form of like), love is commonly contrasted with hate (or neutral apathy); as a less sexual and more mutual and “pure” form of romantic attachment, love is commonly contrasted with lust; and as an interpersonal relationship with romantic overtones, love is commonly contrasted with friendship, although other connotations of love may be applied to close friendships as well.

The very existence of love is sometimes subject to debate. Some categorically reject the notion as false or meaningless.[citation needed] Others call it a recently-invented abstraction, sometimes dating the “invention” to courtly Europe during or after the Middle Ages.[citation needed] Others maintain that love really exists, and is not an abstraction, but is undefinable, being essentially spiritual or metaphysical in nature.[citation needed] Some psychologists maintain that love is the action of lending one’s “boundary” or “self-esteem” to another.[citation needed] Others attempt to define love by applying the definition to everyday life.[citation needed]

Cultural differences make any universal definition of love difficult to establish. Expressions of love may include the love for a soul or mind, the love of laws and organizations, love for a body, love for nature, love of food, love of money, love for learning, love of power, love of fame, love for the respect of others, etc. Different people place varying degrees of importance on the kinds of love they receive. Love is essentially an abstract concept,[citation needed] easier to experience than to explain. Because of the complex and abstract nature of love, discourse on love is commonly reduced to a thought-terminating cliché, and there are a number of common proverbs regarding love, from Virgil’s “Love conquers all” to The Beatles’ “All you need is love”.

http://en.wikipedia.org/wiki/Love

According to Sloman,[2] emotions are cognitive processes. Some authors emphasize the difference between human emotions and the affective behavior of animals.

In Paul D. MacLean’s classic Triune brain model, emotions are defined as the responses of the Mammalian cortex. Emotion competes with even more instinctive responses from the Reptilian cortex and the more logical, reasoning neocortex. However, current research on the neural circuitry of emotion suggests that emotion is an essential part of human decision-making and planning, and that the famous distinction made by Descartes between reason and emotion is not as clear as it seems.[3]

Emotion is generally regarded by Western civilization as the antithesis of reason. This distinction stems from Western philosophy specifically stoic and Cartesian dualism approaches, and is reflected in common phrases like appeal to emotion or your emotions have taken over.

Emotions can be undesired either to the individual experiencing them, but also can be undesired to the other persons, groups of persons, organizations, sub-cultures, and civilisations such as Western civilization, which can be viewed as the emotion being subjected to the individual’s or someone else’s discouraging meta-emotion about the undesired emotion or can be even repressed by the meta-emotions. Thus one of the most distinctive, and perhaps challenging, facts about human beings is this potential for entanglement, or even opposition, between emotion, meta-emotion, will, and reason.

Some state that there is no empirical support for any generalization suggesting the antithesis between reason and emotion: indeed, anger or fear can often be thought of as a systematic response to observed facts. In any case, it is clear that the relation between logic and argument and emotion is one which merits careful study.

Emotion as the subject of scientific research has multiple dimensions: behavioral, physiological, subjective, and cognitive. Sloman argues that many emotions are side-effects of the operations of complex mechanisms (e.g. ‘alarm’ mechanisms) required in animals or machines with multiple motives and limited capacities and resources for coping with a changing and unpredictable world, just as ‘thrashing’ can sometimes occur as a side-effect of scheduling and memory management mechanisms required in a computer operating system for purposes other than producing thrashing. Such side effects are sometimes useful, but sometimes they are dysfunctional. Other theorists, often influenced by writings of Antonio Damasio argue that emotions themselves are necessary for any intelligent system (natural or artificial).

Psychiatrist William Glasser’s theory of the human control system states that behavior is composed of four simultaneous components: deeds, ideas, emotions, and physiological states. He asserts that we choose the idea and deed and that the associated emotions and physiological states also occur but cannot be chosen independently. He calls his construct a total behavior to distinguish it from the common concept of behavior. He uses the verbs to describe what is commonly seen as emotion. For example, he uses ‘to depress’ to describe the total behavior commonly known as depression which, to him, includes depressing ideas, actions, emotions, and physiological states. Dr. Glasser also further asserts that internal choices (conscious or unconscious) cause emotions instead of external stimuli.

According to Damasio, feeling can be viewed as the subjective experience of an emotion that arises physiologically in the brain. [4]

Many psychologists adopt the ABC model, which defines emotions in terms of three fundamental attributes: A. physiological arousal, B. behavioral expression (e.g. facial expressions), and C. conscious experience, the subjective feeling of an emotion. All three attributes are necessary for a full fledged emotional event, though the intensity of each may vary greatly.

Robert Masters makes the following distinctions between affect, feeling and emotion: “As I define them, affect is an innately structured, non-cognitive evaluative sensation that may or may not register in consciousness; feeling is affect made conscious, possessing an evaluative capacity that is not only physiologically based, but that is often also psychologically (and sometimes relationally) oriented; and emotion is psychosocially constructed, dramatized feeling.”[5]

In pop culture there are sub-cultures which cultivate the expressions of anger and rebelliousness even when they are not really angry, its members encouraging each other to express the anger by internalizing meta-gladness about it. Encouragement (i.e. meta-gladness) and discouragement (i.e. psychological repression) of selected emotions - instead of mere awareness and equal interest in all emotions - can be considered as additional source of organizational climate, family dynamics, psychodynamics, personality traits, and of mental disorders, including depression among others.

Often the verb “to hate” is used casually as an exaggeration to describe things one merely dislikes, such as a particular style of architecture, a certain climate, one’s job, or some particular kind of food.

“Hatred” is also used to describe feelings of prejudice, bigotry or condemnation (see shunning) against a class of people and members of that class. Racism is the most well-known example of this. The term hate crime is used to designate crimes committed out of hatred in this sense.

According to evolutionary psychologists, hate is a rational reaction to people whose interests consistently conflict with one’s own. Hate is an emotion, hence it serves the protective mode of a person. People whose behavior threatens one’s own survival interests are to be hated, while people whose behavior enhances one’s survival prospects are to be liked or even loved (as in the case of offspring and other genetic kin).

The passions of hate arise from several features of our thinking process. These include a desire to strengthen our community and to alleviate our fear. The ability to quickly separate friend from foe is essential to self-defense and safety and provides the origins of hate.[1]

Also, the feelings of hate can arise unexpectedly. If one has experienced maltreatment in the past, it is proven that one is more likely to maltreat and learn to dislike or “hate” people before they get to know the person. This is shown clearly in the pattern of people who are abused, ignored, neglected, or maltreated by their parents, and those children’s tendency to become abusive or angry.

Very few avenues for experimental verification of the theory have been claimed.[1] With the construction of the Large Hadron Collider in CERN some scientists hope to produce relevant data. However, it is generally expected that any theory of quantum gravity would require much higher energies to probe.

There are different versions of string theory, depending on factors such as whether or not supersymmetry is incorporated into the formulation. These versions are thought to be related to each other as different limits of one theory, coined M-theory. However, there is a huge number of possible solutions to string theory as it is currently understood.[2] Thus it has been claimed by some scientists that string theory may not be falsifiable and may have no predictive power.[3][4][5][6]

Studies of string theory have revealed that it predicts higher-dimensional objects called branes. String theory strongly suggests the existence of ten or eleven (in M-theory[7]) spacetime dimensions, as opposed to the usual four (three spatial and one temporal) used in relativity theory; however the theory can describe universes with four effective (observable) spacetime dimensions by a variety of methods.

An important branch of the field is dealing with a conjectured duality between string theory as a theory of gravity and gauge theory. It is hoped that research in this direction will lead to new insights on quantum chromodynamics, the fundamental theory of strong nuclear force. This direction of research has better hopes to make contact with experiment, compared to string theory as a quantum theory of gravity,[8][9][10][11] though currently the alternative, Lattice QCD, is doing a much better job and has already made contact with experiments at various fields with good results [12], though the computations are numerical rather than analytic.

The basic idea behind all string theories is that the constituents of reality are strings of extremely small size (possibly of the order of the Planck length, about 10−35 m) which vibrate at specific resonant frequencies.[13] Thus, any particle should be thought of as a tiny vibrating object, rather than as a point. This object can vibrate in different modes (just as a guitar string can produce different notes), with every mode appearing as a different particle (electron, photon, etc.). Strings can split and combine, which would appear as particles emitting and absorbing other particles, presumably giving rise to the known interactions between particles.

In addition to strings, this theory also includes objects of higher dimensions, such as D-branes and NS-branes. Furthermore, all string theories predict the existence of degrees of freedom which are usually described as extra dimensions. String theory is thought to include some 10, 11, or 26 dimensions, depending on the specific theory and on the point of view.

Interest in string theory is driven largely by the hope that it will prove to be a consistent theory of quantum gravity or even a theory of everything. It can also naturally describe interactions similar to electromagnetism and the other forces of nature. Superstring theories include fermions, the building blocks of matter, and incorporate supersymmetry, a conjectured (but unobserved) symmetry of nature. It is not yet known whether string theory will be able to describe a universe with the precise collection of forces and particles that is observed, nor how much freedom the theory allows to choose those details.

String theory as a whole has not yet made falsifiable predictions that would allow it to be experimentally tested, though various planned observations and experiments could confirm some essential aspects of the theory, such as supersymmetry and extra dimensions. In addition, the full theory is not yet understood. For example, the theory does not yet have a satisfactory definition outside of perturbation theory; the quantum mechanics of branes (higher dimensional objects than strings) is not understood; the behavior of string theory in cosmological settings (time-dependent backgrounds) is still being worked out; finally, the principle by which string theory selects its vacuum state is a hotly contested topic (see string theory landscape).

String theory is thought to be a certain limit of another, more fundamental theory - M-theory - which is only partly defined and is not well understood.[14]

It is necessary to use quantum mechanics to understand the behavior of systems at atomic length scales and smaller. For example, if Newtonian mechanics governed the workings of an atom, electrons would rapidly travel towards and collide with the nucleus. However, in the natural world the electrons normally remain in an unknown orbital path around the nucleus, defying classical electromagnetism.

Quantum mechanics was initially developed to explain the atom, especially the spectra of light emitted by different atomic species. The quantum theory of the atom developed as an explanation for the electron’s staying in its orbital, which could not be explained by Newton’s laws of motion and by Maxwell’s laws of classical electromagnetism.

In the formalism of quantum mechanics, the state of a system at a given time is described by a complex wave function (sometimes referred to as orbitals in the case of atomic electrons), and more generally, elements of a complex vector space. This abstract mathematical object allows for the calculation of probabilities of outcomes of concrete experiments. For example, it allows one to compute the probability of finding an electron in a particular region around the nucleus at a particular time. Contrary to classical mechanics, one cannot ever make simultaneous predictions of conjugate variables, such as position and momentum, with arbitrary accuracy. For instance, electrons may be considered to be located somewhere within a region of space, but with their exact positions being unknown. Contours of constant probability, often referred to as “clouds” may be drawn around the nucleus of an atom to conceptualize where the electron might be located with the most probability. It should be stressed that the electron itself is not spread out over such cloud regions. It is either in a particular region of space, or it is not. Heisenberg’s uncertainty principle quantifies the inability to precisely locate the particle.

The other exemplar that led to quantum mechanics was the study of electromagnetic waves such as light. When it was found in 1900 by Max Planck that the energy of waves could be described as consisting of small packets or quanta, Albert Einstein exploited this idea to show that an electromagnetic wave such as light could be described by a particle called the photon with a discrete energy dependent on its frequency. This led to a theory of unity between subatomic particles and electromagnetic waves called wave-particle duality in which particles and waves were neither one nor the other, but had certain properties of both. While quantum mechanics describes the world of the very small, it also is needed to explain certain “macroscopic quantum systems” such as superconductors and superfluids.

Broadly speaking, quantum mechanics incorporates four classes of phenomena that classical physics cannot account for: (i) the quantization (discretization) of certain physical quantities, (ii) wave-particle duality, (iii) the uncertainty principle, and (iv) quantum entanglement. Each of these phenomena will be described in greater detail in subsequent sections.

Theory

There are numerous mathematically equivalent formulations of quantum mechanics. One of the oldest and most commonly used formulations is the transformation theory invented by Cambridge theoretical physicist Paul Dirac, which unifies and generalizes the two earliest formulations of quantum mechanics, matrix mechanics (invented by Werner Heisenberg)[2] and wave mechanics (invented by Erwin Schrödinger).

In this formulation, the instantaneous state of a quantum system encodes the probabilities of its measurable properties, or “observables”. Examples of observables include energy, position, momentum, and angular momentum. Observables can be either continuous (e.g., the position of a particle) or discrete (e.g., the energy of an electron bound to a hydrogen atom).

Generally, quantum mechanics does not assign definite values to observables. Instead, it makes predictions about probability distributions; that is, the probability of obtaining each of the possible outcomes from measuring an observable. Naturally, these probabilities will depend on the quantum state at the instant of the measurement. There are, however, certain states that are associated with a definite value of a particular observable. These are known as “eigenstates” of the observable (”eigen” meaning “own” in German). In the everyday world, it is natural and intuitive to think of everything being in an eigenstate of every observable. Everything appears to have a definite position, a definite momentum, and a definite time of occurrence. However, quantum mechanics does not pinpoint the exact values for the position or momentum of a certain particle in a given space in a finite time, but, rather, it only provides a range of probabilities of where that particle might be. Therefore, it became necessary to use different words for (a) the state of something having an uncertainty relation and (b) a state that has a definite value. The latter is called the “eigenstate” of the property being measured.

For example, consider a free particle. In quantum mechanics, there is wave-particle duality so the properties of the particle can be described as a wave. Therefore, its quantum state can be represented as a wave, of arbitrary shape and extending over all of space, called a wavefunction. The position and momentum of the particle are observables. The Uncertainty Principle of quantum mechanics states that both the position and the momentum cannot simultaneously be known with infinite precision at the same time. However, one can measure just the position alone of a moving free particle creating an eigenstate of position with a wavefunction that is very large at a particular position x, and zero everywhere else. If one performs a position measurement on such a wavefunction, the result x will be obtained with 100% probability. In other words, the position of the free particle will be known. This is called an eigenstate of position. If the particle is in an eigenstate of position then its momentum is completely unknown. An eigenstate of momentum, on the other hand, has the form of a plane wave. It can be shown that the wavelength is equal to h/p, where h is Planck’s constant and p is the momentum of the eigenstate. If the particle is in an eigenstate of momentum then its position is completely blurred out.

Usually, a system will not be in an eigenstate of whatever observable we are interested in. However, if one measures the observable, the wavefunction will instantaneously be an eigenstate of that observable. This process is known as wavefunction collapse. It involves expanding the system under study to include the measurement device, so that a detailed quantum calculation would no longer be feasible and a classical description must be used. If one knows the wavefunction at the instant before the measurement, one will be able to compute the probability of collapsing into each of the possible eigenstates. For example, the free particle in the previous example will usually have a wavefunction that is a wave packet centered around some mean position x0, neither an eigenstate of position nor of momentum. When one measures the position of the particle, it is impossible to predict with certainty the result that we will obtain. It is probable, but not certain, that it will be near x0, where the amplitude of the wavefunction is large. After the measurement is performed, having obtained some result x, the wavefunction collapses into a position eigenstate centered at x.

Wave functions can change as time progresses. An equation known as the Schrödinger equation describes how wave functions change in time, a role similar to Newton’s second law in classical mechanics. The Schrödinger equation, applied to the aforementioned example of the free particle, predicts that the center of a wave packet will move 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 uncertain. This also has the effect of turning position eigenstates (which can be thought of as infinitely sharp wave packets) into broadened wave packets that are no longer position eigenstates.

Some wave functions produce probability distributions that are constant in time. 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, spherically symmetric wavefunction surrounding the nucleus (Fig. 1). (Note that only the lowest angular momentum states, labeled s, are spherically symmetric).

The time evolution of wave functions is deterministic in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random. It should be noted, however, that in quantum mechanics, “random” has come to mean “random for all practical purposes,” and not “absolutely random.” Those new to quantum mechanics often confuse quantum mechanical theory’s inability to predict exactly how nature will behave with the conclusion that nature is actually random.

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. Interpretations of quantum mechanics have been formulated to do away with the concept of “wavefunction collapse”; see, for example, the relative state interpretation. The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions 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.

Relativity and quantum mechanics
The modern world of physics is notably founded on two tested and demonstrably sound theories of general relativity and quantum mechanics —theories which appear to contradict one another. The defining postulates of both Einstein’s theory of relativity and quantum theory are indisputably supported by rigorous and repeated empirical evidence. However, while they do not directly contradict each other theoretically (at least with regard to primary claims), they are resistant to being incorporated within one cohesive model.

Einstein himself is well known for rejecting some of the claims of quantum mechanics. While clearly inventive in his field, he did not accept the more exotic corollaries of quantum mechanics, such as the lack of deterministic causality, and the assertion that a single subatomic particle can occupy numerous areas of space at one time. He also noticed some of the more exotic consequences of entanglement and used them to formulate the Einstein-Podolsky-Rosen paradox, in the hope of showing that quantum mechanics has unacceptable implications. The Einstein-Podolsky-Rosen paradox shows that measuring the state of one particle can instantaneously change the state of its entangled partner, although the two particles can be an arbitrary distance apart. However, this effect does not violate causality, since no transfer of information is possible.

Moreover, there do exist quantum theories which incorporate special relativity—for example, quantum electrodynamics (QED), which is currently the most accurately-tested physical theory [1] —and these lie at the very heart of modern particle physics. 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 applications. However, the lack of a correct theory of quantum gravity is an important issue in cosmology.

Quantum mechanics and classical physics
Predictions of quantum mechanics have been verified experimentally to a very high degree of accuracy. Thus, current logic of correspondence principle between classical and quantum mechanics is that all objects obey laws of quantum mechanics, and classical mechanics is just a quantum mechanics of a large system (or a statistical quantum mechanics of a large collection of particles). Laws of classical mechanics thus follow from laws of quantum mechanics at the limit of large system or large quantum numbers.

Many “macroscopical” properties of “classic” systems are direct consequences of quantum behavior of its parts. For example, stability of bulk matter (which consists of atoms and molecules which would quickly collapse under electric forces alone), rigidity of this matter, mechanical, thermal, chemical, optical and magnetic properties of this matter - they are all results of interaction of electric charges under rules of quantum mechanics.

Because seemingly exotic behavior of matter posited by quantum mechanics and relativity theory become more apparent when dealing with extremely fast-moving or extremely tiny particles, the laws of classical “Newtonian” physics still remain accurate in predicting the behavior of surrounding us (”large”) objects - of the order of the size of large molecules and bigger.

Despite the proposal of many novel ideas, the unification of quantum mechanics—which reigns in the domain of the very small—and general relativity—a superb description of the very large—remains a tantalizing future possibility. (See quantum gravity, string theory.)

In the mathematically rigorous formulation of quantum mechanics, developed by Paul Dirac and John von Neumann, the possible states of a quantum mechanical system are represented by unit vectors (called “state vectors”) residing in a complex separable Hilbert space (variously called the “state space” or the “associated Hilbert space” of the system) well defined up to a complex number of norm 1 (the phase factor). In other words, the possible states are points in the projectivization of a Hilbert space. The exact nature of this Hilbert space is dependent on the system; for example, the state space for position and momentum states is the space of square-integrable functions, while the state space for the spin of a single proton is just the product of two complex planes. Each observable is represented by a densely defined Hermitian (or self-adjoint) linear operator acting on the state space. Each eigenstate of an observable corresponds to an eigenvector of the operator, and the associated eigenvalue corresponds to the value of the observable in that eigenstate. If the operator’s spectrum is discrete, the observable can only attain those discrete eigenvalues.

The time evolution of a quantum state is described by the Schrödinger equation, in which the Hamiltonian, the operator corresponding to the total energy of the system, generates time evolution.

The inner product between two state vectors is a complex number known as a probability amplitude. During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states. The possible results of a measurement are the eigenvalues of the operator - which explains the choice of Hermitian operators, for which all the eigenvalues are real. We can find the probability distribution of an observable in a given state by computing the spectral decomposition of the corresponding operator. Heisenberg’s uncertainty principle is represented by the statement that the operators corresponding to certain observables do not commute.

The Schrödinger equation acts on the entire probability amplitude, not merely its absolute value. Whereas the absolute value of the probability amplitude encodes information about probabilities, its phase encodes information about the interference between quantum states. This gives rise to the wave-like behavior of quantum states.

It turns out that analytic solutions of Schrödinger’s equation are only available for a small number of model Hamiltonians, of which the quantum harmonic oscillator, the particle in a box, the hydrogen-molecular ion and the hydrogen atom are the most important representatives. Even the helium atom, which contains just one more electron than hydrogen, defies all attempts at a fully analytic treatment. There exist several techniques for generating approximate solutions. For instance, in the method known as perturbation theory one uses the analytic results for a simple quantum mechanical model to generate results for a more complicated model related to the simple model by, for example, the addition of a weak potential energy. Another method is the “semi-classical equation of motion” approach, which applies to systems for which quantum mechanics produces weak deviations from classical behavior. The deviations can be calculated based on the classical motion. This approach is important for the field of quantum chaos.

An alternative formulation of quantum mechanics is Feynman’s path integral formulation, in which a quantum-mechanical amplitude is considered as a sum over histories between initial and final states; this is the quantum-mechanical counterpart of action principles in classical mechanics.

[edit] Interactions with other scientific theories
The fundamental rules of quantum mechanics are very broad. They state that the state space of a system is a Hilbert space and the observables are Hermitian operators acting on that space, but do not tell us which Hilbert space or which operators. These must be chosen appropriately in order to obtain a quantitative description of a quantum system. An important guide for making these choices is the correspondence principle, which states that the predictions of quantum mechanics reduce to those of classical physics when a system moves to higher energies or equivalently, larger quantum numbers. In other words, classic mechanics is simply a quantum mechanics of large systems. This “high energy” limit is known as the classical or correspondence limit. One can therefore start from an established classical model of a particular system, and attempt to guess the underlying quantum model that gives rise to the classical model in the correspondence limit.

Unsolved problems in physics: In the correspondence limit of quantum mechanics: Is there a preferred interpretation of quantum mechanics? How does the quantum description of reality, which includes elements such as the superposition of states and wavefunction collapse, give rise to the reality we perceive?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.

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.

The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one employed 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 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.

Quantum field theories for the strong nuclear force and the weak nuclear force have been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of the subnuclear particles: 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.

It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity, the most accurate theory of gravity currently known, and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity.

Typical thermodynamic system - heat moves from hot (boiler) to cold (condenser), (both not shown) and work is extracted, in this case by a series of pistons.The starting point for most thermodynamic considerations are the laws of thermodynamics, which postulate that energy can be exchanged between physical systems as heat or work.[4] They also postulate the existence of a quantity named entropy, which can be defined for any system.[5] In thermodynamics, interactions between large ensembles of objects are studied and categorized. Central to this are the concepts of system and surroundings. A system is composed of particles, whose average motions define its properties, which in turn are related to one another through equations of state. Properties can be combined to express internal energy and thermodynamic potentials, which are useful for determining conditions for equilibrium and spontaneous processes.

With these tools, thermodynamics describes how systems respond to changes in their surroundings. This can be applied to a wide variety of topics in science and engineering, such as engines, phase transitions, chemical reactions, transport phenomena, and even black holes. The results of thermodynamics are essential for other fields of physics and for chemistry, chemical engineering, aerospace engineering, mechanical engineering, cell biology, biomedical engineering, and materials science to name a few.[6][7]

The laws of thermodynamics

In thermodynamics, there are four laws of very general validity, and as such they do not depend on the details of the interactions or the systems being studied. Hence, they can be applied to systems about which one knows nothing other than the balance of energy and matter transfer. Examples of this include Einstein’s prediction of spontaneous emission around the turn of the 20th century and current research into the thermodynamics of black holes.

The four laws are:

Zeroth law of thermodynamics, stating that thermodynamic equilibrium is an equivalence relation.
If two thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other.
First law of thermodynamics, about the conservation of energy
The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to the system and the work done on the system.
Second law of thermodynamics, about entropy
The total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value.
Third law of thermodynamics, about absolute zero temperature
As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value; also stated as: “the entropy of all systems and of all states of a system is zero at absolute zero” or equivalently “it is impossible to reach the absolute zero of temperature by any finite number of processes”.
See also: Bose–Einstein condensate and negative temperature.

The laws of thermodynamics, in principle, describe the specifics for the transport of heat and work in thermodynamic processes. Since their conception, however, these laws have become some of the most important in all of physics and other branches of science connected to thermodynamics. They are often associated with concepts far beyond what is directly stated in the wording.

http://en.wikipedia.org/wiki/Laws_of_thermodynamics