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Many-worlds interpretation

The many-worlds interpretation (MWI) is a philosophical position about how the mathematics used in quantum mechanics relates to physical reality. It asserts that the universal wavefunction is objectively real, and that there is no wave function collapse. This implies that all possible outcomes of quantum measurements are physically realized in some "world" or universe. In contrast to some other interpretations of quantum mechanics, the evolution of reality as a whole in MWI is rigidly deterministic and local. Many-worlds is also called the relative state formulation or the Everett interpretation, after physicist Hugh Everett, who first proposed it in 1957. Bryce DeWitt popularized the formulation and named it many-worlds in the 1970s.

In modern versions of many-worlds, the subjective appearance of wave function collapse is explained by the mechanism of quantum decoherence. Decoherence approaches to interpreting quantum theory have been widely explored and developed since the 1970s. MWI is considered a mainstream interpretation of quantum mechanics, along with the other decoherence interpretations, the Copenhagen interpretation, and hidden variable theories such as Bohmian mechanics.

The many-worlds interpretation implies that there are most likely an uncountable number of universes. It is one of a number of multiverse hypotheses in physics and philosophy. MWI views time as a many-branched tree, wherein every possible quantum outcome is realized. This is intended to resolve the measurement problem and thus some paradoxes of quantum theory, such as Wigner's friend, the EPR paradox   and Schrödinger's cat, since every possible outcome of a quantum event exists in its own universe.

Overview of the interpretation
The many-worlds interpretation's key idea is that the linear and unitary dynamics of quantum mechanics applies everywhere and at all times and so describes the whole universe. In particular, it models a measurement as a unitary transformation, a correlation-inducing interaction, between observer and object, without using a collapse postulate, and models observers as ordinary quantum-mechanical systems. This stands in contrast to the Copenhagen interpretation, in which a measurement is a "primitive" concept, not describable by unitary quantum mechanics; using the Copenhagen interpretation the universe is divided into a quantum and a classical domain, and the collapse postulate is central. In MWI there is no division between classical and quantum: everything is quantum and there is no collapse. MWI's main conclusion is that the universe (or multiverse in this context) is composed of a quantum superposition of an uncountable or undefinable amount or number of increasingly divergent, non-communicating parallel universes or quantum worlds. Sometimes dubbed Everett worlds, each is an internally consistent and actualized alternative history or timeline.

The many-worlds interpretation uses decoherence to explain the measurement process and the emergence of a quasi-classical world. Wojciech H. Zurek, one of decoherence theory's pioneers, said: "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected." Zurek emphasizes that his work does not depend on a particular interpretation.

The many-worlds interpretation shares many similarities with the decoherent histories interpretation, which also uses decoherence to explain the process of measurement or wave function collapse. MWI treats the other histories or worlds as real, since it regards the universal wave function as the "basic physical entity" or "the fundamental entity, obeying at all times a deterministic wave equation". The decoherent histories interpretation, on the other hand, needs only one of the histories (or worlds) to be real.

Several authors, including Everett, John Archibald Wheeler and David Deutsch, call many-worlds a theory or metatheory, rather than just an interpretation. Everett argued that it was the "only completely coherent approach to explaining both the contents of quantum mechanics and the appearance of the world." Deutsch dismissed the idea that many-worlds is an "interpretation", saying that to call it an interpretation "is like talking about dinosaurs as an 'interpretation' of fossil records."

Formulation
In his 1957 doctoral dissertation, Everett proposed that, rather than relying on external observation for analysis of isolated quantum systems, one could mathematically model an object, as well as its observers, as purely physical systems within the mathematical framework developed by Paul Dirac, John von Neumann, and others, discarding altogether the ad hoc mechanism of wave function collapse.

Relative state
Everett's original work introduced the concept of a relative state. Two (or more) subsystems, after a general interaction, become correlated, or as is now said, entangled. Everett noted that such entangled systems can be expressed as the sum of products of states, where the two or more subsystems are each in a state relative to each other. After a measurement or observation one of the pair (or triple...) is the measured, object or observed system, and one other member is the measuring apparatus (which may include an observer) having recorded the state of the measured system. Each product of subsystem states in the overall superposition evolves over time independently of other products. Once the subsystems interact, their states have become correlated or entangled and can no longer be considered independent. In Everett's terminology, each subsystem state was now correlated with its relative state, since each subsystem must now be considered relative to the other subsystems with which it has interacted.

In the example of Schrödinger's cat, after the box is opened, the entangled system is the cat, the poison vial and the observer. One relative triple of states would be the alive cat, the unbroken vial and the observer seeing an alive cat. Another relative triple of states would be the dead cat, the broken vial and the observer seeing a dead cat.

In the example of a measurement of a continuous variable (e.g. position q) the object-observer system decomposes into a continuum of pairs of relative states: the object system's relative state becomes a Dirac delta function each centered on a particular value of q and the corresponding observer relative state representing an observer having recorded the value of q. The states of the pairs of relative states are, post measurement, correlated with each other.

In Everett's scheme, there is no collapse; instead, the Schrödinger equation, or its quantum field theory, relativistic analog, holds all the time, everywhere. An observation or measurement is modeled by applying the wave equation to the entire system, comprising the object being observed and the observer. One consequence is that every observation causes the combined observer–object's wavefunction to change into a quantum superposition of two or more non-interacting branches.

Thus the process of measurement or observation, or any correlation-inducing interaction, splits the system into sets of relative states, where each set of relative states, forming a branch of the universal wave function, is consistent within itself, and all future measurements (including by multiple observers) will confirm this consistency.

Renamed many-worlds
Everett had referred to the combined observer–object system as split by an observation, each split corresponding to the different or multiple possible outcomes of an observation. These splits generate a branching tree, where each branch is a set of all the states relative to each other. Bryce DeWitt popularized Everett's work with a series of publications calling it the Many Worlds Interpretation. Focusing on the splitting process, DeWitt introduced the term "world" to describe a single branch of that tree, which is a consistent history. All observations or measurements within any branch are consistent with each other.

Since many observation-like events have happened and are constantly happening, Everett's model implies that there are an enormous and growing number of simultaneously existing states or "worlds".

Properties
MWI removes the observer-dependent role in the quantum measurement process by replacing wave function collapse with the established mechanism of quantum decoherence. As the observer's role lies at the heart of all "quantum paradoxes" such as the EPR paradox and von Neumann's "boundary problem", this provides a clearer and easier approach to their resolution.

Since the Copenhagen interpretation requires the existence of a classical domain beyond the one described by quantum mechanics, it has been criticized as inadequate for the study of cosmology. While there is no evidence that Everett was inspired by issues of cosmology, he developed his theory with the explicit goal of allowing quantum mechanics to be applied to the universe as a whole, hoping to stimulate the discovery of new phenomena. This hope has been realized in the later development of quantum cosmology.

MWI is a realist, deterministic and local theory. It achieves this by removing wave function collapse, which is indeterministic and nonlocal, from the deterministic and local equations of quantum theory.

MWI (like other, broader multiverse theories) provides a context for the anthropic principle, which may provide an explanation for the fine-tuned universe.

MWI depends crucially on the linearity of quantum mechanics, which underpins the superposition principle. If the final theory of everything is non-linear with respect to wavefunctions, then many-worlds is invalid. All quantum field theories are linear and compatible with the MWI, a point Everett emphasized as a motivation for the MWI. While quantum gravity or string theory may be non-linear in this respect, there is as yet no evidence of this.

Alternative to wavefunction collapse
As with the other interpretations of quantum mechanics, the many-worlds interpretation is motivated by behavior that can be illustrated by the double-slit experiment. When particles of light (or anything else) pass through the double slit, a calculation assuming wavelike behavior of light can be used to identify where the particles are likely to be observed. Yet when the particles are observed in this experiment, they appear as particles (i.e., at definite places) and not as non-localized waves.

Some versions of the Copenhagen interpretation of quantum mechanics proposed a process of "collapse" in which an indeterminate quantum system would probabilistically collapse onto, or select, just one determinate outcome to "explain" this phenomenon of observation. Wave function collapse was widely regarded as artificial and ad hoc, so an alternative interpretation in which the behavior of measurement could be understood from more fundamental physical principles was considered desirable.

Everett's PhD work provided such an interpretation. He argued that for a composite system—such as a subject (the "observer" or measuring apparatus) observing an object (the "observed" system, such as a particle)—the claim that either the observer or the observed has a well-defined state is meaningless; in modern parlance, the observer and the observed have become entangled: we can only specify the state of one relative to the other, i.e., the state of the observer and the observed are correlated after the observation is made. This led Everett to derive from the unitary, deterministic dynamics alone (i.e., without assuming wave function collapse) the notion of a relativity of states.

Everett noticed that the unitary, deterministic dynamics alone entailed that after an observation is made each element of the quantum superposition of the combined subject–object wave function contains two "relative states": a "collapsed" object state and an associated observer who has observed the same collapsed outcome; what the observer sees and the state of the object have become correlated by the act of measurement or observation. The subsequent evolution of each pair of relative subject–object states proceeds with complete indifference as to the presence or absence of the other elements, as if wave function collapse has occurred, which has the consequence that later observations are always consistent with the earlier observations. Thus the appearance of the object's wave function's collapse has emerged from the unitary, deterministic theory itself. (This answered Einstein's early criticism of quantum theory: that the theory should define what is observed, not for the observables to define the theory.) Since the wave function appears to have collapsed then, Everett reasoned, there was no need to actually assume that it had collapsed. And so, invoking Occam's razor, he removed the postulate of wave function collapse from the theory.

Testability
In 1985, David Deutsch proposed a variant of the Wigner's friend thought experiment as a test of many-worlds versus the Copenhagen interpretation. It consists of an experimenter (Wigner's friend) making a measurement on a quantum system in an isolated laboratory, and another experimenter (Wigner) who would make a measurement on the first one. According to the many-worlds theory, the first experimenter would end up in a macroscopic superposition of seeing one result of the measurement in one branch, and another result in another branch. The second experimenter could then interfere these two branches in order to test whether it is in fact in a macroscopic superposition or has collapsed into a single branch, as predicted by the Copenhagen interpretation. Since then Lockwood, Vaidman, and others have made similar proposals, which require placing macroscopic objects in a coherent superposition and interfering them, a task currently beyond experimental capability.

Probability and the Born rule
Since the many-worlds interpretation's inception, physicists have been puzzled about the role of probability in it. As put by Wallace, there are two facets to the question: the incoherence problem, which asks why we should assign probabilities at all to outcomes that are certain to occur in some worlds, and the quantitative problem, which asks why the probabilities should be given by the Born rule.

Everett tried to answer these questions in the paper that introduced many-worlds. To address the incoherence problem, he argued that an observer who makes a sequence of measurements on a quantum system will in general have an apparently random sequence of results in their memory, which justifies the use of probabilities to describe the measurement process. To address the quantitative problem, Everett proposed a derivation of the Born rule based on the properties that a measure on the branches of the wave function should have. His derivation has been criticized as relying on unmotivated assumptions. Since then several other derivations of the Born rule in the many-worlds framework have been proposed. There is no consensus on whether this has been successful.

Frequentism
DeWitt and Graham and Farhi et al., among others, have proposed derivations of the Born rule based on a frequentist interpretation of probability. They try to show that in the limit of uncountably many measurements, no worlds would have relative frequencies that didn't match the probabilities given by the Born rule, but these derivations have been shown to be mathematically incorrect.

Decision theory
A decision-theoretic derivation of the Born rule was produced by David Deutsch (1999) and refined by Wallace  and Saunders. They consider an agent who takes part in a quantum gamble: the agent makes a measurement on a quantum system, branches as a consequence, and each of the agent's future selves receives a reward that depends on the measurement result. The agent uses decision theory to evaluate the price they would pay to take part in such a gamble, and concludes that the price is given by the utility of the rewards weighted according to the Born rule. Some reviews have been positive, although these arguments remain highly controversial; some theoretical physicists have taken them as supporting the case for parallel universes. For example, a New Scientist story on a 2007 conference about Everettian interpretations quoted physicist Andy Albrecht as saying, "This work will go down as one of the most important developments in the history of science." In contrast, the philosopher Huw Price, also attending the conference, found the Deutsch–Wallace–Saunders approach fundamentally flawed.

Symmetries and invariance
In 2005, Zurek produced a derivation of the Born rule based on the symmetries of entangled states; Schlosshauer and Fine argue that Zurek's derivation is not rigorous, as it does not define what probability is and has several unstated assumptions about how it should behave.

In 2016, Charles Sebens and Sean M. Carroll, building on work by Lev Vaidman, proposed a similar approach based on self-locating uncertainty. In this approach, decoherence creates multiple identical copies of observers, who can assign credences to being on different branches using the Born rule. The Sebens–Carroll approach has been criticized by Adrian Kent, and Vaidman does not find it satisfactory.

Branch counting
In 2021, Simon Saunders produced a branch counting derivation of the Born rule. The crucial feature of this approach is to define the branches so that they all have the same magnitude or 2-norm. The ratios of the numbers of branches thus defined give the probabilities of the various outcomes of a measurement, in accordance with the Born rule.

The preferred basis problem
As originally formulated by Everett and DeWitt, the many-worlds interpretation had a privileged role for measurements: they determined which basis of a quantum system would give rise to the eponymous worlds. Without this the theory was ambiguous, as a quantum state can equally well be described (e.g.) as having a well-defined position or as being a superposition of two delocalized states. The assumption is that the preferred basis to use is the one which assigns a unique measurement outcome to each world. This special role for measurements is problematic for the theory, as it contradicts Everett and DeWitt's goal of having a reductionist theory and undermines their criticism of the ill-defined measurement postulate of the Copenhagen interpretation. This is known today as the preferred basis problem.

The preferred basis problem has been solved, according to Saunders and Wallace, among others, by incorporating decoherence into the many-worlds theory. In this approach, the preferred basis does not have to be postulated, but rather is identified as the basis stable under environmental decoherence. In this way measurements no longer play a special role; rather, any interaction that causes decoherence causes the world to split. Since decoherence is never complete, there will always remain some infinitesimal overlap between two worlds, making it arbitrary whether a pair of worlds has split or not. Wallace argues that this is not problematic: it only shows that worlds are not a part of the fundamental ontology, but rather of the emergent ontology, where these approximate, effective descriptions are routine in the physical sciences. Since in this approach the worlds are derived, it follows that they must be present in any other interpretation of quantum mechanics that does not have a collapse mechanism, such as Bohmian mechanics.

This approach to deriving the preferred basis has been criticized as creating circularity with derivations of probability in the many-worlds interpretation, as decoherence theory depends on probability and probability depends on the ontology derived from decoherence. Wallace contends that decoherence theory depends not on probability but only on the notion that one is allowed to do approximations in physics.

History
MWI originated in Everett's Princeton University PhD thesis "The Theory of the Universal Wave Function", developed under his thesis advisor John Archibald Wheeler, a shorter summary of which was published in 1957 under the title "Relative State Formulation of Quantum Mechanics" (Wheeler contributed the title "relative state"; Everett originally called his approach the "Correlation Interpretation", where "correlation" refers to quantum entanglement). The phrase "many-worlds" is due to Bryce DeWitt, who was responsible for the wider popularization of Everett's theory, which had been largely ignored for a decade after publication in 1957.

Everett's proposal was not without precedent. In 1952, Erwin Schrödinger gave a lecture in Dublin in which at one point he jocularly warned his audience that what he was about to say might "seem lunatic". He went on to assert that while the Schrödinger equation seemed to be describing several different histories, they were "not alternatives but all really happen simultaneously". According to David Deutsch, this is the earliest known reference to many-worlds; Jeffrey A. Barrett describes it as indicating the similarity of "general views" between Everett and Schrödinger. Schrödinger's writings from the period also contain elements resembling the modal interpretation originated by Bas van Fraassen. Because Schrödinger subscribed to a kind of post-Machian neutral monism, in which "matter" and "mind" are only different aspects or arrangements of the same common elements, treating the wave function as physical and treating it as information became interchangeable.

Leon Cooper and Deborah Van Vechten developed a very similar approach before reading Everett's work. Zeh also came to the same conclusions as Everett before reading his work, then built a new theory of quantum decoherence based on these ideas.

According to people who knew him, Everett believed in the literal reality of the other quantum worlds. His son and wife reported that he "never wavered in his belief over his many-worlds theory". In their detailed review of Everett's work, Osnaghi, Freitas, and Freire Jr. note that Everett consistently used quotes around "real" to indicate a meaning within scientific practice.

Reception
MWI's initial reception was overwhelmingly negative, in the sense that it was ignored, with the notable exception of DeWitt. Wheeler made considerable efforts to formulate the theory in a way that would be palatable to Bohr, visited Copenhagen in 1956 to discuss it with him, and convinced Everett to visit as well, which happened in 1959. Nevertheless, Bohr and his collaborators completely rejected the theory. Everett had already left academia in 1957, never to return, and in 1980, Wheeler disavowed the theory.

Support
One of MWI's strongest longtime advocates is David Deutsch. According to him, the single photon interference pattern observed in the double slit experiment can be explained by interference of photons in multiple universes. Viewed this way, the single photon interference experiment is indistinguishable from the multiple photon interference experiment. In a more practical vein, in one of the earliest papers on quantum computing, Deutsch suggested that parallelism that results from MWI could lead to "a method by which certain probabilistic tasks can be performed faster by a universal quantum computer than by any classical restriction of it". He also proposed that MWI will be testable (at least against "naive" Copenhagenism) when reversible computers become conscious via the reversible observation of spin.

Equivocal
Philosophers of science James Ladyman and Don Ross say that MWI could be true, but do not embrace it. They note that no quantum theory is yet empirically adequate for describing all of reality, given its lack of unification with general relativity, and so do not see a reason to regard any interpretation of quantum mechanics as the final word in metaphysics. They also suggest that the multiple branches may be an artifact of incomplete descriptions and of using quantum mechanics to represent the states of macroscopic objects. They argue that macroscopic objects are significantly different from microscopic objects in not being isolated from the environment, and that using quantum formalism to describe them lacks explanatory and descriptive power and accuracy.

Rejection
Some scientists consider some aspects of MWI to be unfalsifiable and hence unscientific because the multiple parallel universes are non-communicating, in the sense that no information can be passed between them.

Victor J. Stenger remarked that Murray Gell-Mann's published work explicitly rejects the existence of simultaneous parallel universes. Collaborating with James Hartle, Gell-Mann worked toward the development of a more "palatable" post-Everett quantum mechanics. Stenger thought it fair to say that most physicists find MWI too extreme, though it "has merit in finding a place for the observer inside the system being analyzed and doing away with the troublesome notion of wave function collapse".

Roger Penrose argues that the idea is flawed because it is based on an oversimplified version of quantum mechanics that does not account for gravity. In his view, applying conventional quantum mechanics to the universe implies the MWI, but the lack of a successful theory of quantum gravity negates the claimed universality of conventional quantum mechanics. According to Penrose, "the rules must change when gravity is involved". He further asserts that gravity helps anchor reality and "blurry" events have only one allowable outcome: "electrons, atoms, molecules, etc., are so minute that they require almost no amount of energy to maintain their gravity, and therefore their overlapping states. They can stay in that state forever, as described in standard quantum theory". On the other hand, "in the case of large objects, the duplicate states disappear in an instant due to the fact that these objects create a large gravitational field".

Philosopher of science Robert P. Crease says that MWI is "one of the most implausible and unrealistic ideas in the history of science" because it means that everything conceivable happens. Science writer Philip Ball calls MWI's implications fantasies, since "beneath their apparel of scientific equations or symbolic logic, they are acts of imagination, of 'just supposing.

Theoretical physicist Gerard 't Hooft also dismisses the idea: "I do not believe that we have to live with the many-worlds interpretation. Indeed, it would be a stupendous number of parallel worlds, which are only there because physicists couldn't decide which of them is real."

Asher Peres was an outspoken critic of MWI. A section of his 1993 textbook had the title Everett's interpretation and other bizarre theories. Peres argued that the various many-worlds interpretations merely shift the arbitrariness or vagueness of the collapse postulate to the question of when "worlds" can be regarded as separate, and that no objective criterion for that separation can actually be formulated.

Polls
A poll of 72 "leading quantum cosmologists and other quantum field theorists" conducted before 1991 by L. David Raub showed 58% agreement with "Yes, I think MWI is true".

Max Tegmark reports the result of a "highly unscientific" poll taken at a 1997 quantum mechanics workshop. According to Tegmark, "The many worlds interpretation (MWI) scored second, comfortably ahead of the consistent histories and Bohm interpretations."

In response to Sean M. Carroll's statement "As crazy as it sounds, most working physicists buy into the many-worlds theory", Michael Nielsen counters: "at a quantum computing conference at Cambridge in 1998, a many-worlder surveyed the audience of approximately 200 people... Many-worlds did just fine, garnering support on a level comparable to, but somewhat below, Copenhagen and decoherence." But Nielsen notes that it seemed most attendees found it to be a waste of time: Peres "got a huge and sustained round of applause…when he got up at the end of the polling and asked 'And who here believes the laws of physics are decided by a democratic vote?

A 2005 poll of fewer than 40 students and researchers taken after a course on the Interpretation of Quantum Mechanics at the Institute for Quantum Computing University of Waterloo found "Many Worlds (and decoherence)" to be the least favored.

A 2011 poll of 33 participants at an Austrian conference on quantum foundations found 6 endorsed MWI, 8 "Information-based/information-theoretical", and 14 Copenhagen; the authors remark that MWI received a similar percentage of votes as in Tegmark's 1997 poll.

Speculative implications
DeWitt has said that Everett, Wheeler, and Graham "do not in the end exclude any element of the superposition. All the worlds are there, even those in which everything goes wrong and all the statistical laws break down." Tegmark affirmed that absurd or highly unlikely events are rare but inevitable under MWI: "Things inconsistent with the laws of physics will never happen—everything else will... it's important to keep track of the statistics, since even if everything conceivable happens somewhere, really freak events happen only exponentially rarely." David Deutsch speculates in his book The Beginning of Infinity that some fiction, such as alternate history, could occur somewhere in the multiverse, as long as it is consistent with the laws of physics.

According to Ladyman and Ross, many seemingly physically plausible but unrealized possibilities, such as those discussed in other scientific fields, generally have no counterparts in other branches, because they are in fact incompatible with the universal wave function. According to Carroll, human decision-making, contrary to common misconceptions, is best thought of as a classical process, not a quantum one, because it works on the level of neurochemistry rather than fundamental particles. Human decisions do not cause the world to branch into equally realized outcomes; even for subjectively difficult decisions, the "weight" of realized outcomes is almost entirely concentrated in a single branch.

Quantum suicide is a thought experiment in quantum mechanics and the philosophy of physics that can purportedly distinguish between the Copenhagen interpretation of quantum mechanics and the many-worlds interpretation by a variation of the Schrödinger's cat thought experiment, from the cat's point of view. Quantum immortality refers to the subjective experience of surviving quantum suicide. Most experts believe the experiment would not work in the real world, because the world with the surviving experimenter has a lower "measure" than the world before the experiment, making it less likely that the experimenter will experience their survival.

title: Many-worlds interpretation


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Talk:Extraterrestrial life

Recent bad source
I'm sort of dismayed that we actually have to discuss this, but if so, then here it is. The recent source that was added (this article from The Guardian) should not be in the lead. Per WP:LEADCITE, "Because the lead will usually repeat information that is in the body, editors should balance the desire to avoid redundant citations in the lead with the desire to aid readers in locating sources for challengeable material. Leads are usually less specific than the body, and information in the lead section of non-controversial subjects is less likely to be challenged and less likely to require a source [...]".

This was a case of a source in search of text, rather than the other way around, and this is not how sources should be added. The text in the lead was a very very broad, general statement which is gone into in much more detail in the body of the article with dozens of appropriate citations for more specific aspects. The Guardian article, on the other hand, was much more specific, talking mostly about missions to some of the Jovian moons. 35.139.154.158 (talk) 16:07, 9 March 2023 (UTC)

 * I cannot agree with your rather aggressive attitude and your constant hiding behind a IP number, rather than creating an account - so that we may something about you; your interests and motivations. Having said that would you be happy if the Guardian story was referenced in the Jupiter and moons section further in the page text?  I am trying to resolve what I, and others, consider the Guardian article to be relevant to the page.  Regards, David J Johnson (talk) 17:06, 9 March 2023 (UTC)

Embargo?
I was checking the sources and the first one at the Exoplanets section, this one, says "EMBARGO NOTICE: All information provided on this page and its links is embargoed until Wed 25-Jan, 18:00 GMT". What is that even supposed to mean? Cambalachero (talk) 19:12, 10 July 2023 (UTC)

David Grusch UFO whistleblower claims
There should be an article around the leadup to David Grusch's Whistleblower claims on this page and his claims Nabotor (talk) 18:55, 27 July 2023 (UTC)
 * Mmm? That article already exists: David Grusch UFO whistleblower claims. 35.139.154.158 (talk) 19:57, 27 July 2023 (UTC)

Enceladus - more possible life chemicals found?
NOTE: May not be worth addng to the main extraterrestrial life article (after all, no such life has yet been found), but perhaps worth being aware of the latest related news about extraterrestrial life chemicals found in the solar system?

On 14 December 2023, astronomers reported the first time discovery, in the plumes of Enceladus, moon of the planet Saturn, of hydrogen cyanide, a possible chemical essential for life as we know it, as well as other organic molecules, some of which are yet to be better identified and understood. According to the researchers, "these [newly discovered] compounds could potentially support extant microbial communities or drive complex organic synthesis leading to the origin of life." Drbogdan (talk) 17:48, 15 December 2023 (UTC)

Wiki Education assignment: EEB 4611-Biogeochemical Processes-Spring 2024
— Assignment last updated by LynSchwendy (talk) 07:07, 16 May 2024 (UTC)

UFOs
UFOs are mentioned in a paragraph at the "Recent history" section. Is that enough, or should the UFO phenomenon have a section of its own? Cambalachero (talk) 17:46, 30 January 2024 (UTC)
 * WP:ONEWAY. This: serious article. UFOs: connection to aliens is wacko. --Hob Gadling (talk) 06:27, 31 January 2024 (UTC)

Other universes and Fermi
I don't see how the paper arguing (I think) that life might be possible in a variety of random universes gives "a potential explanation to the Fermi paradox" Justin the Just (talk) 19:34, 14 May 2024 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Extraterrestrial life


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E-commerce

E-commerce (electronic commerce) is the activity of electronically buying or selling products on online services or over the Internet. E-commerce draws on technologies such as mobile commerce, electronic funds transfer, supply chain management, Internet marketing, online transaction processing, electronic data interchange (EDI), inventory management systems, and automated data collection systems. E-commerce is the largest sector of the electronics industry and is in turn driven by the technological advances of the semiconductor industry.

Defining e-commerce
The term was coined and first employed by Robert Jacobson, Principal Consultant to the California State Assembly's Utilities & Commerce Committee, in the title and text of California's Electronic Commerce Act, carried by the late Committee Chairwoman Gwen Moore (D-L.A.) and enacted in 1984.

E-commerce typically uses the web for at least a part of a transaction's life cycle although it may also use other technologies such as e-mail. Typical e-commerce transactions include the purchase of products (such as books from Amazon) or services (such as music downloads in the form of digital distribution such as the iTunes Store). There are three areas of e-commerce: online retailing, electronic markets, and online auctions. E-commerce is supported by electronic business. The existence value of e-commerce is to allow consumers to shop online and pay online through the Internet, saving the time and space of customers and enterprises, greatly improving transaction efficiency, especially for busy office workers, and also saving a lot of valuable time.

E-commerce businesses may also employ some or all of the following:
 * Online shopping for retail sales direct to consumers via web sites and mobile apps, conversational commerce via live chat, chatbots, and voice assistants.
 * Providing or participating in online marketplaces, which process third-party business-to-consumer (B2C) or consumer-to-consumer (C2C) sales;
 * Business-to-business (B2B) buying and selling.
 * Gathering and using demographic data through web contacts and social media.
 * B2B electronic data interchange.
 * Marketing to prospective and established customers by e-mail or fax (for example, with newsletters).
 * Engaging in pretail for launching new products and services.
 * Online financial exchanges for currency exchanges or trading purposes.

There are five essential categories of E-commerce:

 * Business to Business
 * Business to Consumer
 * Business to Government
 * Consumer to Business
 * Consumer to Consumer

Forms
Contemporary electronic commerce can be classified into two categories. The first category is business based on types of goods sold (involves everything from ordering "digital" content for immediate online consumption, to ordering conventional goods and services, to "meta" services to facilitate other types of electronic commerce). The second category is based on the nature of the participant (B2B, B2C, C2B and C2C).

On the institutional level, big corporations and financial institutions use the internet to exchange financial data to facilitate domestic and international business. Data integrity and security are pressing issues for electronic commerce.

Aside from traditional e-commerce, the terms m-Commerce (mobile commerce) as well (around 2013) t-Commerce have also been used.

Governmental regulation
In the United States, California's Electronic Commerce Act (1984), enacted by the Legislature, the more recent California Privacy Rights Act (2020), enacted through a popular election proposition and to control specifically how electronic commerce may be conducted in California. In the US in its entirety, electronic commerce activities are regulated more broadly by the Federal Trade Commission (FTC). These activities include the use of commercial e-mails, online advertising and consumer privacy. The CAN-SPAM Act of 2003 establishes national standards for direct marketing over e-mail. The Federal Trade Commission Act regulates all forms of advertising, including online advertising, and states that advertising must be truthful and non-deceptive. Using its authority under Section 5 of the FTC Act, which prohibits unfair or deceptive practices, the FTC has brought a number of cases to enforce the promises in corporate privacy statements, including promises about the security of consumers' personal information. As a result, any corporate privacy policy related to e-commerce activity may be subject to enforcement by the FTC.

The Ryan Haight Online Pharmacy Consumer Protection Act of 2008, which came into law in 2008, amends the Controlled Substances Act to address online pharmacies.

Conflict of laws in cyberspace is a major hurdle for harmonization of legal framework for e-commerce around the world. In order to give a uniformity to e-commerce law around the world, many countries adopted the UNCITRAL Model Law on Electronic Commerce (1996).

Internationally there is the International Consumer Protection and Enforcement Network (ICPEN), which was formed in 1991 from an informal network of government customer fair trade organisations. The purpose was stated as being to find ways of co-operating on tackling consumer problems connected with cross-border transactions in both goods and services, and to help ensure exchanges of information among the participants for mutual benefit and understanding. From this came Econsumer.gov, an ICPEN initiative since April 2001. It is a portal to report complaints about online and related transactions with foreign companies.

There is also Asia Pacific Economic Cooperation. APEC was established in 1989 with the vision of achieving stability, security and prosperity for the region through free and open trade and investment. APEC has an Electronic Commerce Steering Group as well as working on common privacy regulations throughout the APEC region.

In Australia, trade is covered under Australian Treasury Guidelines for electronic commerce and the Australian Competition & Consumer Commission regulates and offers advice on how to deal with businesses online, and offers specific advice on what happens if things go wrong.

The European Union undertook an extensive enquiry into e-commerce in 2015-16 which observed significant growth in the development of e-commerce, along with some developments which raised concerns, such as increased use of selective distribution systems, which allow manufacturers to control routes to market, and "increased use of contractual restrictions to better control product distribution". The European Commission felt that some emerging practices might be justified if they could improve the quality of product distribution, but "others may unduly prevent consumers from benefiting from greater product choice and lower prices in e-commerce and therefore warrant Commission action" in order to promote compliance with EU competition rules.

In the United Kingdom, the Financial Services Authority (FSA) was formerly the regulating authority for most aspects of the EU's Payment Services Directive (PSD), until its replacement in 2013 by the Prudential Regulation Authority and the Financial Conduct Authority. The UK implemented the PSD through the Payment Services Regulations 2009 (PSRs), which came into effect on 1 November 2009. The PSR affects firms providing payment services and their customers. These firms include banks, non-bank credit card issuers and non-bank merchant acquirers, e-money issuers, etc. The PSRs created a new class of regulated firms known as payment institutions (PIs), who are subject to prudential requirements. Article 87 of the PSD requires the European Commission to report on the implementation and impact of the PSD by 1 November 2012.

In India, the Information Technology Act 2000 governs the basic applicability of e-commerce.

In China, the Telecommunications Regulations of the People's Republic of China (promulgated on 25 September 2000), stipulated the Ministry of Industry and Information Technology (MIIT) as the government department regulating all telecommunications related activities, including electronic commerce. On the same day, the Administrative Measures on Internet Information Services were released, the first administrative regulations to address profit-generating activities conducted through the Internet, and lay the foundation for future regulations governing e-commerce in China. On 28 August 2004, the eleventh session of the tenth NPC Standing Committee adopted an Electronic Signature Law, which regulates data message, electronic signature authentication and legal liability issues. It is considered the first law in China's e-commerce legislation. It was a milestone in the course of improving China's electronic commerce legislation, and also marks the entering of China's rapid development stage for electronic commerce legislation.

Global trends
E-commerce has become an important tool for small and large businesses worldwide, not only to sell to customers, but also to engage them.

Cross-border e-Commerce is also an essential field for e-Commerce businesses. It has responded to the trend of globalization. It shows that numerous firms have opened up new businesses, expanded new markets, and overcome trade barriers; more and more enterprises have started exploring the cross-border cooperation field. In addition, compared with traditional cross-border trade, the information on cross-border e-commerce is more concealed. In the era of globalization, cross-border e-commerce for inter-firm companies means the activities, interactions, or social relations of two or more e-commerce enterprises. However, the success of cross-border e-commerce promotes the development of small and medium-sized firms, and it has finally become a new transaction mode. It has helped the companies solve financial problems and realize the reasonable allocation of resources field. SMEs ( small and medium enterprises) can also precisely match the demand and supply in the market, having the industrial chain majorization and creating more revenues for companies.

In 2012, e-commerce sales topped $1 trillion for the first time in history.

Mobile devices are playing an increasing role in the mix of e-commerce, this is also commonly called mobile commerce, or m-commerce. In 2014, one estimate saw purchases made on mobile devices making up 25% of the market by 2017.

For traditional businesses, one research stated that information technology and cross-border e-commerce is a good opportunity for the rapid development and growth of enterprises. Many companies have invested an enormous volume of investment in mobile applications. The DeLone and McLean Model stated that three perspectives contribute to a successful e-business: information system quality, service quality and users' satisfaction. There is no limit of time and space, there are more opportunities to reach out to customers around the world, and to cut down unnecessary intermediate links, thereby reducing the cost price, and can benefit from one on one large customer data analysis, to achieve a high degree of personal customization strategic plan, in order to fully enhance the core competitiveness of the products in the company.

Modern 3D graphics technologies, such as Facebook 3D Posts, are considered by some social media marketers and advertisers as a preferable way to promote consumer goods than static photos, and some brands like Sony are already paving the way for augmented reality commerce. Wayfair now lets you inspect a 3D version of its furniture in a home setting before buying.

China
Among emerging economies, China's e-commerce presence continues to expand every year. With 668 million Internet users, China's online shopping sales reached $253 billion in the first half of 2015, accounting for 10% of total Chinese consumer retail sales in that period. The Chinese retailers have been able to help consumers feel more comfortable shopping online. e-commerce transactions between China and other countries increased 32% to 2.3 trillion yuan ($375.8 billion) in 2012 and accounted for 9.6% of China's total international trade. In 2013, Alibaba had an e-commerce market share of 80% in China. In 2014, Alibaba still dominated the B2B marketplace in China with a market share of 44.82%, followed by several other companies including Made-in-China.com at 3.21%, and GlobalSources.com at 2.98%, with the total transaction value of China's B2B market exceeding 4.5 billion yuan. In 2014, there were 600 million Internet users in China (twice as many as in the US), making it the world's biggest online market.

China is also the largest e-commerce market in the world by value of sales, with an estimated US$899 billion in 2016. It accounted for 42.4% of worldwide retail e-commerce in that year, the most of any country. Research shows that Chinese consumer motivations are different enough from Western audiences to require unique e-commerce app designs instead of simply porting Western apps into the Chinese market.

The expansion of e-commerce in China has resulted in the development of Taobao villages, clusters of e-commerce businesses operating in rural areas. Because Taobao villages have increased the incomes or rural people and entrepreneurship in rural China, Taobao villages have become a component of rural revitalization strategies.

In 2015, the State Council promoted the Internet Plus initiative, a five-year plan to integrate traditional manufacturing and service industries with big data, cloud computing, and Internet of things technology. The State Council provided support for Internet Plus through policy support in area including cross-border e-commerce and rural e-commerce.

In 2019, the city of Hangzhou established a pilot program artificial intelligence-based Internet Court to adjudicate disputes related to e-commerce and internet-related intellectual property claims.

Europe
In 2010, the United Kingdom had the highest per capita e-commerce spending in the world. As of 2013, the Czech Republic was the European country where e-commerce delivers the biggest contribution to the enterprises' total revenue. Almost a quarter (24%) of the country's total turnover is generated via the online channel.

Arab states
The rate of growth of the number of internet users in the Arab countries has been rapid – 13.1% in 2015. A significant portion of the e-commerce market in the Middle East comprises people in the 30–34 year age group. Egypt has the largest number of internet users in the region, followed by Saudi Arabia and Morocco; these constitute 3/4th of the region's share. Yet, internet penetration is low: 35% in Egypt and 65% in Saudi Arabia.

The Gulf Cooperation Council countries have a rapidly growing market and are characterized by a population that becomes wealthier (Yuldashev). As such, retailers have launched Arabic-language websites as a means to target this population. Secondly, there are predictions of increased mobile purchases and an expanding internet audience (Yuldashev). The growth and development of the two aspects make the GCC countries become larger players in the electronic commerce market with time progress. Specifically, research shows that the e-commerce market is expected to grow to over $20 billion by 2020 among these GCC countries (Yuldashev). The e-commerce market has also gained much popularity among western countries, and in particular Europe and the U.S. These countries have been highly characterized by consumer-packaged goods (CPG) (Geisler, 34). However, trends show that there are future signs of a reverse. Similar to the GCC countries, there has been increased purchase of goods and services in online channels rather than offline channels. Activist investors are trying hard to consolidate and slash their overall cost and the governments in western countries continue to impose more regulation on CPG manufacturers (Geisler, 36). In these senses, CPG investors are being forced to adapt to e-commerce as it is effective as well as a means for them to thrive.

The future trends in the GCC countries will be similar to that of the western countries. Despite the forces that push business to adapt e-commerce as a means to sell goods and products, the manner in which customers make purchases is similar in countries from these two regions. For instance, there has been an increased usage of smartphones which comes in conjunction with an increase in the overall internet audience from the regions. Yuldashev writes that consumers are scaling up to more modern technology that allows for mobile marketing. However, the percentage of smartphone and internet users who make online purchases is expected to vary in the first few years. It will be independent on the willingness of the people to adopt this new trend (The Statistics Portal). For example, UAE has the greatest smartphone penetration of 73.8 per cent and has 91.9 per cent of its population has access to the internet. On the other hand, smartphone penetration in Europe has been reported to be at 64.7 per cent (The Statistics Portal). Regardless, the disparity in percentage between these regions is expected to level out in future because e-commerce technology is expected to grow to allow for more users.

The e-commerce business within these two regions will result in competition. Government bodies at the country level will enhance their measures and strategies to ensure sustainability and consumer protection (Krings, et al.). These increased measures will raise the environmental and social standards in the countries, factors that will determine the success of the e-commerce market in these countries. For example, an adoption of tough sanctions will make it difficult for companies to enter the e-commerce market while lenient sanctions will allow ease of companies. As such, the future trends between GCC countries and the Western countries will be independent of these sanctions (Krings, et al.). These countries need to make rational conclusions in coming up with effective sanctions.

India
India has an Internet user base of about 460 million as of December 2017. Despite being the third largest user base in the world, the penetration of the Internet is low compared to markets like the United States, United Kingdom or France but is growing at a much faster rate, adding around six million new entrants every month. In India, cash on delivery is the most preferred payment method, accumulating 75% of the e-retail activities. The India retail market is expected to rise from 2.5% in 2016 to 5% in 2020.

Brazil
In 2013, Brazil's e-commerce was growing quickly with retail e-commerce sales expected to grow at a double-digit pace through 2014. By 2016, eMarketer expected retail e-commerce sales in Brazil to reach $17.3 billion.

Logistics
Logistics in e-commerce mainly concerns fulfillment. Online markets and retailers have to find the best possible way to fill orders and deliver products. Small companies usually control their own logistic operation because they do not have the ability to hire an outside company. Most large companies hire a fulfillment service that takes care of a company's logistic needs. The optimization of logistics processes that contains long-term investment in an efficient storage infrastructure system and adoption of inventory management strategies is crucial to prioritize customer satisfaction throughout the entire process, from order placement to final delivery.

Impact on markets and retailers
E-commerce markets are growing at noticeable rates. The online market is expected to grow by 56% in 2015–2020. In 2017, retail e-commerce sales worldwide amounted to 2.3 trillion US dollars and e-retail revenues are projected to grow to 4.891 trillion US dollars in 2021. Traditional markets are only expected 2% growth during the same time. Brick and mortar retailers are struggling because of online retailer's ability to offer lower prices and higher efficiency. Many larger retailers are able to maintain a presence offline and online by linking physical and online offerings.

E-commerce allows customers to overcome geographical barriers and allows them to purchase products anytime and from anywhere. Online and traditional markets have different strategies for conducting business. Traditional retailers offer fewer assortment of products because of shelf space where, online retailers often hold no inventory but send customer orders directly to the manufacturer. The pricing strategies are also different for traditional and online retailers. Traditional retailers base their prices on store traffic and the cost to keep inventory. Online retailers base prices on the speed of delivery.

There are two ways for marketers to conduct business through e-commerce: fully online or online along with a brick and mortar store. Online marketers can offer lower prices, greater product selection, and high efficiency rates. Many customers prefer online markets if the products can be delivered quickly at relatively low price. However, online retailers cannot offer the physical experience that traditional retailers can. It can be difficult to judge the quality of a product without the physical experience, which may cause customers to experience product or seller uncertainty. Another issue regarding the online market is concerns about the security of online transactions. Many customers remain loyal to well-known retailers because of this issue.

Security is a primary problem for e-commerce in developed and developing countries. E-commerce security is protecting businesses' websites and customers from unauthorized access, use, alteration, or destruction. The type of threats include: malicious codes, unwanted programs (ad ware, spyware), phishing, hacking, and cyber vandalism. E-commerce websites use different tools to avert security threats. These tools include firewalls, encryption software, digital certificates, and passwords.

Impact on supply chain management
For a long time, companies had been troubled by the gap between the benefits which supply chain technology has and the solutions to deliver those benefits. However, the emergence of e-commerce has provided a more practical and effective way of delivering the benefits of the new supply chain technologies.

E-commerce has the capability to integrate all inter-company and intra-company functions, meaning that the three flows (physical flow, financial flow and information flow) of the supply chain could be also affected by e-commerce. The affections on physical flows improved the way of product and inventory movement level for companies. For the information flows, e-commerce optimized the capacity of information processing than companies used to have, and for the financial flows, e-commerce allows companies to have more efficient payment and settlement solutions.

In addition, e-commerce has a more sophisticated level of impact on supply chains: Firstly, the performance gap will be eliminated since companies can identify gaps between different levels of supply chains by electronic means of solutions; Secondly, as a result of e-commerce emergence, new capabilities such implementing ERP systems, like SAP ERP, Xero, or Megaventory, have helped companies to manage operations with customers and suppliers. Yet these new capabilities are still not fully exploited. Thirdly, technology companies would keep investing on new e-commerce software solutions as they are expecting investment return. Fourthly, e-commerce would help to solve many aspects of issues that companies may feel difficult to cope with, such as political barriers or cross-country changes. Finally, e-commerce provides companies a more efficient and effective way to collaborate with each other within the supply chain.

Impact on employment
E-commerce helps create new job opportunities due to information related services, software app and digital products. It also causes job losses. The areas with the greatest predicted job-loss are retail, postal, and travel agencies. The development of e-commerce will create jobs that require highly skilled workers to manage large amounts of information, customer demands, and production processes. In contrast, people with poor technical skills cannot enjoy the wages welfare. On the other hand, because e-commerce requires sufficient stocks that could be delivered to customers in time, the warehouse becomes an important element. Warehouse needs more staff to manage, supervise and organize, thus the condition of warehouse environment will be concerned by employees.

Impact on customers
E-commerce brings convenience for customers as they do not have to leave home and only need to browse websites online, especially for buying products which are not sold in nearby shops. It could help customers buy a wider range of products and save customers' time. Consumers also gain power through online shopping. They are able to research products and compare prices among retailers. Thanks to the practice of user-generated ratings and reviews from companies like Bazaarvoice, Trustpilot, and Yelp, customers can also see what other people think of a product, and decide before buying if they want to spend money on it. Also, online shopping often provides sales promotion or discounts code, thus it is more price effective for customers. Moreover, e-commerce provides products' detailed information; even the in-store staff cannot offer such detailed explanation. Customers can also review and track the order history online.

E-commerce technologies cut transaction costs by allowing both manufactures and consumers to skip through the intermediaries. This is achieved through by extending the search area best price deals and by group purchase. The success of e-commerce in urban and regional levels depend on how the local firms and consumers have adopted to e-commerce.

However, e-commerce lacks human interaction for customers, especially who prefer face-to-face connection. Customers are also concerned with the security of online transactions and tend to remain loyal to well-known retailers. In recent years, clothing retailers such as Tommy Hilfiger have started adding Virtual Fit platforms to their e-commerce sites to reduce the risk of customers buying the wrong sized clothes, although these vary greatly in their fit for purpose. When the customer regret the purchase of a product, it involves returning goods and refunding process. This process is inconvenient as customers need to pack and post the goods. If the products are expensive, large or fragile, it refers to safety issues.

Impact on the environment
In 2018, E-commerce generated 1.3 e6ST of container cardboard in North America, an increase from 1.1 e6ST) in 2017. Only 35 percent of North American cardboard manufacturing capacity is from recycled content. The recycling rate in Europe is 80 percent and Asia is 93 percent. Amazon, the largest user of boxes, has a strategy to cut back on packing material and has reduced packaging material used by 19 percent by weight since 2016. Amazon is requiring retailers to manufacture their product packaging in a way that does not require additional shipping packaging. Amazon also has an 85-person team researching ways to reduce and improve their packaging and shipping materials.

Accelerated movement of packages around the world includes accelerated movement of living things, with all its attendant risks. Weeds, pests, and diseases all sometimes travel in packages of seeds. Some of these packages are part of brushing manipulation of e-commerce reviews.

Impact on traditional retail
E-commerce has been cited as a major force for the failure of major U.S. retailers in a trend frequently referred to as a "retail apocalypse." The rise of e-commerce outlets like Amazon has made it harder for traditional retailers to attract customers to their stores and forced companies to change their sales strategies. Many companies have turned to sales promotions and increased digital efforts to lure shoppers while shutting down brick-and-mortar locations. The trend has forced some traditional retailers to shutter its brick and mortar operations.

E-commerce during COVID-19
In March 2020, global retail website traffic hit 14.3 billion visits signifying an unprecedented growth of e-commerce during the lockdown of 2020. Later studies show that online sales increased by 25% and online grocery shopping increased by over 100% during the crisis in the United States. Meanwhile, as many as 29% of surveyed shoppers state that they will never go back to shopping in person again; in the UK, 43% of consumers state that they expect to keep on shopping the same way even after the lockdown is over.

Retail sales of e-commerce shows that COVID-19 has a significant impact on e-commerce and its sales are expected to reach $6.5 trillion by 2023.

Business application
Some common applications related to electronic commerce are:

• B2B e-commerce (business-to-business)

• B2C e-commerce (business-to-consumer)

• Conversational commerce: e-commerce via chat

• Digital Wallet

• Document automation in supply chain and logistics

• Electronic tickets

• Enterprise content management

• Group buying

• Instant messaging

• Internet security

• Online auction

• Online banking

• Online office suites

• Online shopping and order tracking

• Online transaction processing

• Pretail

• Print on demand

• Shopping cart software

• Social networking

• Teleconference

• Usenet newsgroup

• Virtual assistant

• Domestic and international payment systems

Timeline
A timeline for the development of e-commerce:
 * 1971 or 1972: The ARPANET is used to arrange a cannabis sale between students at the Stanford Artificial Intelligence Laboratory and the Massachusetts Institute of Technology, later described as "the seminal act of e-commerce" in John Markoff's book What the Dormouse Said.
 * 1979: Michael Aldrich demonstrates the first online shopping system.
 * 1981: Thomson Holidays UK is the first business-to-business (B2B) online shopping system to be installed.
 * 1982: Minitel was introduced nationwide in France by France Télécom and used for online ordering.
 * 1983: California State Assembly holds first hearing on "electronic commerce" in Volcano, California. Testifying are CPUC, MCI Mail, Prodigy, CompuServe, Volcano Telephone, and Pacific Telesis. (Not permitted to testify is Quantum Technology, later to become AOL.) California's Electronic Commerce Act was passed in 1984.
 * 1983: Karen Earle Lile (AKA Karen Bean) and Kendall Ross Bean create e-commerce service in San Francisco Bay Area. Buyers and sellers of pianos connect through a database created by Piano Finders on a Kaypro personal computer using DOS interface. Pianos for sale are listed on a Bulletin board system. Buyers print list of pianos for sale by a dot matrix printer. Customer service happened through a Piano Advice Hotline listed in the San Francisco Chronicle classified ads and money transferred by a bank wire transfer when a sale was completed.
 * 1984: Gateshead SIS/Tesco is first B2C online shopping system and Mrs Snowball, 72, is the first online home shopper
 * 1984: In April 1984, CompuServe launches the Electronic Mall in the US and Canada. It is the first comprehensive electronic commerce service.
 * 1989: In May 1989, Sequoia Data Corp. introduced Compumarket, the first internet based system for e-commerce. Sellers and buyers could post items for sale and buyers could search the database and make purchases with a credit card.
 * 1990: Tim Berners-Lee writes the first web browser, WorldWideWeb, using a NeXT computer.
 * 1992: Book Stacks Unlimited in Cleveland opens a commercial sales website (www.books.com) selling books online with credit card processing.
 * 1993: Paget Press releases edition No. 3 of the first app store, The Electronic AppWrapper
 * 1994: Netscape releases the Navigator browser in October under the code name Mozilla. Netscape 1.0 is introduced in late 1994 with SSL encryption that made transactions secure.
 * 1994: Ipswitch IMail Server becomes the first software available online for sale and immediate download via a partnership between Ipswitch, Inc. and OpenMarket.
 * 1994: "Ten Summoner's Tales" by Sting becomes the first secure online purchase through NetMarket.
 * 1995: The US National Science Foundation lifts its former strict prohibition of commercial enterprise on the Internet.
 * 1995: Thursday 27 April 1995, the purchase of a book by Paul Stanfield, product manager for CompuServe UK, from W H Smith's shop within CompuServe's UK Shopping Centre is the UK's first national online shopping service secure transaction. The shopping service at launch featured W H Smith, Tesco, Virgin Megastores/Our Price, Great Universal Stores (GUS), Interflora, Dixons Retail, Past Times, PC World (retailer) and Innovations.
 * 1995: Amazon is launched by Jeff Bezos.
 * 1995: eBay is founded by computer programmer Pierre Omidyar as AuctionWeb. It is the first online auction site supporting person-to-person transactions.
 * 1995: The first commercial-free 24-hour, internet-only radio stations, Radio HK and NetRadio start broadcasting.
 * 1996: The use of Excalibur BBS with replicated "storefronts" was an early implementation of electronic commerce started by a group of SysOps in Australia and replicated to global partner sites.
 * 1998: Electronic postal stamps can be purchased and downloaded for printing from the Web.
 * 1999: Alibaba Group is established in China. Business.com sold for US$7.5 million to eCompanies, which was purchased in 1997 for US$149,000. The peer-to-peer filesharing software Napster launches. ATG Stores launches to sell decorative items for the home online.
 * 1999: Global e-commerce reaches $150 billion
 * 2000: The dot-com bust.
 * 2001: eBay has the largest userbase of any e-commerce site.
 * 2001: Alibaba.com achieved profitability in December 2001.
 * 2002: eBay acquires PayPal for $1.5 billion. Niche retail companies Wayfair and NetShops are founded with the concept of selling products through several targeted domains, rather than a central portal.
 * 2003: Amazon posts first yearly profit.
 * 2004: DHgate.com, China's first online B2B transaction platform, is established, forcing other B2B sites to move away from the "yellow pages" model.
 * 2007: Business.com acquired by R.H. Donnelley for $345 million.
 * 2014: US e-commerce and online retail sales projected to reach $294 billion, an increase of 12 percent over 2013 and 9% of all retail sales. Alibaba Group has the largest Initial public offering ever, worth $25 billion.
 * 2015: Amazon accounts for more than half of all e-commerce growth, selling almost 500 Million SKU's in the US.
 * 2016: The Government of India launches the BHIM UPI digital payment interface. In the year 2020 it has 2 billion digital payment transactions.
 * 2017: Retail e-commerce sales across the world reaches $2.304 trillion, which was a 24.8 percent increase than previous year.
 * 2017: Global e-commerce transactions generate US$29.267 trillion, including US$25.516 trillion for business-to-business (B2B) transactions and US$3.851 trillion for business-to-consumer (B2C) sales.

title: E-commerce


text:
Euler's formula

Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that, for any real number $x$, one has $$e^{i x} = \cos x + i \sin x, $$ where $e$ is the base of the natural logarithm, $i$ is the imaginary unit, and $cos$ and $sin$ are the trigonometric functions cosine and sine respectively. This complex exponential function is sometimes denoted $cis x$ ("cosine plus i sine"). The formula is still valid if $x$ is a complex number, and is also called Euler's formula in this more general case.

Euler's formula is ubiquitous in mathematics, physics, chemistry, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".

When $x = π$, Euler's formula may be rewritten as $e^{iπ} + 1 = 0$ or $e^{iπ} = -1$, which is known as Euler's identity.

History
In 1714, the English mathematician Roger Cotes presented a geometrical argument that can be interpreted (after correcting a misplaced factor of $$\sqrt{-1}$$) as: Cotes wrote: "Nam si quadrantis circuli quilibet arcus, radio CE descriptus, sinun habeat CX sinumque complementi ad quadrantem XE ; sumendo radium CE pro Modulo, arcus erit rationis inter $$EX + XC \sqrt{-1}$$& CE mensura ducta in $$\sqrt{-1}$$." (Thus if any arc of a quadrant of a circle, described by the radius CE, has sinus CX and sinus of the complement to the quadrant XE ; taking the radius CE as modulus, the arc will be the measure of the ratio between $$EX + XC \sqrt{-1}$$ & CE multiplied by $$\sqrt{-1}$$.) That is, consider a circle having center E (at the origin of the (x,y) plane) and radius CE. Consider an angle θ with its vertex at E having the positive x-axis as one side and a radius CE as the other side. The perpendicular from the point C on the circle to the x-axis is the "sinus" CX ; the line between the circle's center E and the point X at the foot of the perpendicular is XE, which is the "sinus of the complement to the quadrant" or "cosinus". The ratio between $$EX + XC \sqrt{-1}$$ and CE is thus $$\cos \theta + \sqrt{-1} \sin \theta \ $$. In Cotes' terminology, the "measure" of a quantity is its natural logarithm, and the "modulus" is a conversion factor that transforms a measure of angle into circular arc length (here, the modulus is the radius (CE) of the circle). According to Cotes, the product of the modulus and the measure (logarithm) of the ratio, when multiplied by $$\sqrt{-1}$$, equals the length of the circular arc subtended by θ, which for any angle measured in radians is CE • θ. Thus, $$\sqrt{-1} CE \ln{\left ( \cos \theta + \sqrt{-1} \sin \theta \right ) \ } = (CE) \theta $$. This equation has a misplaced factor: the factor of $$\sqrt{-1}$$ should be on the right side of the equation, not the left side. If the change of scaling by $$\sqrt{-1}$$ is made, then, after dividing both sides by CE and exponentiating both sides, the result is: $$\cos \theta + \sqrt{-1} \sin \theta = e^{\sqrt{-1} \theta}$$, which is Euler's formula.

See:

$$ix = \ln(\cos x + i\sin x).$$ Exponentiating this equation yields Euler's formula. Note that the logarithmic statement is not universally correct for complex numbers, since a complex logarithm can have infinitely many values, differing by multiples of $2πi$. Around 1740 Leonhard Euler turned his attention to the exponential function and derived the equation named after him by comparing the series expansions of the exponential and trigonometric expressions. The formula was first published in 1748 in his foundational work Introductio in analysin infinitorum.
 * Roger Cotes (1714) "Logometria," Philosophical Transactions of the Royal Society of London, 29 (338) : 5-45; see especially page 32. Available on-line at:  Hathi Trust
 * Roger Cotes with Robert Smith, ed., Harmonia mensurarum … (Cambridge, England: 1722), chapter:  "Logometria",  p. 28.
 * https://nrich.maths.org/1384

Johann Bernoulli had found that $$\frac{1}{1 + x^2} = \frac 1 2 \left( \frac{1}{1 - ix} + \frac{1}{1 + ix}\right).$$

And since $$\int \frac{dx}{1 + ax} = \frac{1}{a} \ln(1 + ax) + C,$$ the above equation tells us something about complex logarithms by relating natural logarithms to imaginary (complex) numbers. Bernoulli, however, did not evaluate the integral.

Bernoulli's correspondence with Euler (who also knew the above equation) shows that Bernoulli did not fully understand complex logarithms. Euler also suggested that complex logarithms can have infinitely many values.

The view of complex numbers as points in the complex plane was described about 50 years later by Caspar Wessel.

Definitions of complex exponentiation
The exponential function $e^{x}$ for real values of $x$ may be defined in a few different equivalent ways (see Characterizations of the exponential function). Several of these methods may be directly extended to give definitions of $e^{z}$ for complex values of $z$ simply by substituting $z$ in place of $x$ and using the complex algebraic operations. In particular, we may use any of the three following definitions, which are equivalent. From a more advanced perspective, each of these definitions may be interpreted as giving the unique analytic continuation of $e^{x}$ to the complex plane.

Differential equation definition
The exponential function $$f(z) = e^z$$ is the unique differentiable function of a complex variable for which the derivative equals the function $$\frac{df}{dz} = f$$ and $$f(0) = 1.$$

Power series definition
For complex $z$ $$e^z = 1 + \frac{z}{1!} + \frac{z^2}{2!} + \frac{z^3}{3!} + \cdots = \sum_{n=0}^{\infty} \frac{z^n}{n!}.$$

Using the ratio test, it is possible to show that this power series has an infinite radius of convergence and so defines $e^{z}$ for all complex $z$.

Limit definition
For complex $z$ $$e^z = \lim_{n \to \infty} \left(1+\frac{z}{n}\right)^n.$$

Here, $n$ is restricted to positive integers, so there is no question about what the power with exponent $n$ means.

Proofs
Various proofs of the formula are possible.

Using differentiation
This proof shows that the quotient of the trigonometric and exponential expressions is the constant function one, so they must be equal (the exponential function is never zero, so this is permitted).

Consider the function $f(θ)$ $$ f(\theta) = \frac{\cos\theta + i\sin\theta}{e^{i\theta}} = e^{-i\theta} \left(\cos\theta + i \sin\theta\right) $$ for real $θ$. Differentiating gives by the product rule $$ f'(\theta) = e^{-i\theta} \left(i\cos\theta - \sin\theta\right) - ie^{-i\theta} \left(\cos\theta + i\sin\theta\right) = 0$$ Thus, $f(θ)$ is a constant. Since $f(0) = 1$, then $f(θ) = 1$ for all real $θ$, and thus $$e^{i\theta} = \cos\theta + i\sin\theta.$$

Using power series

Here is a proof of Euler's formula using power-series expansions, as well as basic facts about the powers of $i$: $$\begin{align} i^0 &= 1, & i^1 &= i, & i^2 &= -1, & i^3 &= -i, \\ i^4 &= 1, & i^5 &= i, & i^6 &= -1, & i^7 &= -i \\ &\vdots  & &\vdots   & &\vdots    & &\vdots \end{align}$$

Using now the power-series definition from above, we see that for real values of $x$ $$\begin{align} e^{ix} &= 1 + ix + \frac{(ix)^2}{2!} + \frac{(ix)^3}{3!} + \frac{(ix)^4}{4!} + \frac{(ix)^5}{5!} + \frac{(ix)^6}{6!} + \frac{(ix)^7}{7!} + \frac{(ix)^8}{8!} + \cdots \\[8pt] &= 1 + ix - \frac{x^2}{2!} - \frac{ix^3}{3!} + \frac{x^4}{4!} + \frac{ix^5}{5!} - \frac{x^6}{6!} - \frac{ix^7}{7!} + \frac{x^8}{8!} + \cdots \\[8pt] &= \left( 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \cdots \right) + i\left( x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \right) \\[8pt] &= \cos x + i\sin x , \end{align}$$ where in the last step we recognize the two terms are the Maclaurin series for $e^{it}$ and $t = 2$. The rearrangement of terms is justified because each series is absolutely convergent.

Using polar coordinates
Another proof is based on the fact that all complex numbers can be expressed in polar coordinates. Therefore, for some $r$ and $θ$ depending on $x$, $$e^{i x} = r \left(\cos \theta + i \sin \theta\right).$$ No assumptions are being made about $r$ and $θ$; they will be determined in the course of the proof. From any of the definitions of the exponential function it can be shown that the derivative of $cos x$ is $sin x$. Therefore, differentiating both sides gives $$i e ^{ix} = \left(\cos \theta + i \sin \theta\right) \frac{dr}{dx} + r \left(-\sin \theta + i \cos \theta\right) \frac{d\theta}{dx}.$$ Substituting $e^{ix}$ for $ie^{ix}$ and equating real and imaginary parts in this formula gives $r(cos θ + i sin θ)$ and $e^{ix}$. Thus, $r$ is a constant, and $θ$ is $dr⁄dx = 0$ for some constant $C$. The initial values $dθ⁄dx = 1$ and $x + C$ come from $r(0) = 1$, giving $θ(0) = 0$ and $e^{0i} = 1$. This proves the formula $$e^{i \theta} = 1(\cos \theta +i \sin \theta) = \cos \theta + i  \sin \theta.$$

Interpretation of the formula
This formula can be interpreted as saying that the function $r = 1$ is a unit complex number, i.e., it traces out the unit circle in the complex plane as $φ$ ranges through the real numbers. Here $φ$ is the angle that a line connecting the origin with a point on the unit circle makes with the positive real axis, measured counterclockwise and in radians.

The original proof is based on the Taylor series expansions of the exponential function $θ = x$ (where $z$ is a complex number) and of $e^{iφ} = cos φ + i sin φ$ and $e^{iφ}$ for real numbers $x$ (see above). In fact, the same proof shows that Euler's formula is even valid for all complex numbers $x$.

A point in the complex plane can be represented by a complex number written in cartesian coordinates. Euler's formula provides a means of conversion between cartesian coordinates and polar coordinates. The polar form simplifies the mathematics when used in multiplication or powers of complex numbers. Any complex number $e^{z}$, and its complex conjugate, $sin x$, can be written as $$\begin{align} z &= x + iy = |z| (\cos \varphi + i\sin \varphi) = r e^{i \varphi}, \\ \bar{z} &= x - iy = |z| (\cos \varphi - i\sin \varphi) = r e^{-i \varphi}, \end{align}$$ where
 * $cos x$ is the real part,
 * $z = x + iy$ is the imaginary part,
 * $\overline{z} = x − iy$ is the magnitude of $z$ and

$φ$ is the argument of $z$, i.e., the angle between the x axis and the vector z measured counterclockwise in radians, which is defined up to addition of $x = Re z$. Many texts write $y = Im z$ instead of $r = |z| = √x^{2} + y^{2}$, but the first equation needs adjustment when $φ = arg z = atan2(y, x)$. This is because for any real $x$ and $y$, not both zero, the angles of the vectors $2π$ and $φ = tan^{−1} y⁄x$ differ by $\pi$ radians, but have the identical value of $φ = atan2(y, x)$.

Use of the formula to define the logarithm of complex numbers
Now, taking this derived formula, we can use Euler's formula to define the logarithm of a complex number. To do this, we also use the definition of the logarithm (as the inverse operator of exponentiation): $$a = e^{\ln a}, $$ and that $$e^a e^b = e^{a + b}, $$ both valid for any complex numbers $a$ and $b$. Therefore, one can write: $$z = \left|z\right| e^{i \varphi} = e^{\ln\left|z\right|} e^{i \varphi} = e^{\ln\left|z\right| + i \varphi}$$ for any $x ≤ 0$. Taking the logarithm of both sides shows that $$\ln z = \ln \left|z\right| + i \varphi,$$ and in fact, this can be used as the definition for the complex logarithm. The logarithm of a complex number is thus a multi-valued function, because $φ$ is multi-valued.

Finally, the other exponential law $$\left(e^a\right)^k = e^{a k},$$ which can be seen to hold for all integers $k$, together with Euler's formula, implies several trigonometric identities, as well as de Moivre's formula.

Relationship to trigonometry
Euler's formula, the definitions of the trigonometric functions and the standard identities for exponentials are sufficient to easily derive most trigonometric identities. It provides a powerful connection between analysis and trigonometry, and provides an interpretation of the sine and cosine functions as weighted sums of the exponential function: $$\begin{align} \cos x &= \operatorname{Re} \left(e^{ix}\right) =\frac{e^{ix} + e^{-ix}}{2}, \\ \sin x &= \operatorname{Im} \left(e^{ix}\right) =\frac{e^{ix} - e^{-ix}}{2i}. \end{align}$$

The two equations above can be derived by adding or subtracting Euler's formulas: $$\begin{align} e^{ix} &= \cos x + i \sin x, \\ e^{-ix} &= \cos(- x) + i \sin(- x) = \cos x - i \sin x \end{align}$$ and solving for either cosine or sine.

These formulas can even serve as the definition of the trigonometric functions for complex arguments $x$. For example, letting $(x, y)$, we have: $$\begin{align} \cos iy &= \frac{e^{-y} + e^y}{2} = \cosh y, \\ \sin iy &= \frac{e^{-y} - e^y}{2i} = \frac{e^y - e^{-y}}{2}i = i\sinh y. \end{align}$$

In addition $$\begin{align} \cosh ix &= \frac{e^{ix} + e^{-ix}}{2} = \cos x, \\ \sinh ix &= \frac{e^{ix} - e^{-ix}}{2} = i\sin x. \end{align}$$

Complex exponentials can simplify trigonometry, because they are easier to manipulate than their sinusoidal components. One technique is simply to convert sinusoids into equivalent expressions in terms of exponentials. After the manipulations, the simplified result is still real-valued. For example:

$$\begin{align} \cos x \cos y &= \frac{e^{ix}+e^{-ix}}{2} \cdot \frac{e^{iy}+e^{-iy}}{2} \\ &= \frac 1 2 \cdot \frac{e^{i(x+y)}+e^{i(x-y)}+e^{i(-x+y)}+e^{i(-x-y)}}{2} \\ &= \frac 1 2 \bigg( \frac{e^{i(x+y)} + e^{-i(x+y)}}{2} + \frac{e^{i(x-y)} + e^{-i(x-y)}}{2} \bigg)\\ &= \frac 1 2 \left( \cos(x+y) + \cos(x-y) \right). \end{align} $$

Another technique is to represent the sinusoids in terms of the real part of a complex expression and perform the manipulations on the complex expression. For example: $$\begin{align} \cos nx &= \operatorname{Re} \left(e^{inx}\right) \\ &= \operatorname{Re} \left( e^{i(n-1)x}\cdot e^{ix} \right) \\ &= \operatorname{Re} \Big( e^{i(n-1)x}\cdot \big(\underbrace{e^{ix} + e^{-ix}}_{2\cos x } - e^{-ix}\big) \Big) \\ &= \operatorname{Re} \left( e^{i(n-1)x}\cdot 2\cos x - e^{i(n-2)x} \right) \\ &= \cos[(n-1)x] \cdot [2 \cos x] - \cos[(n-2)x]. \end{align}$$

This formula is used for recursive generation of $(−x, −y)$ for integer values of $n$ and arbitrary $x$ (in radians).

Considering $tan φ = y⁄x$ a parameter in equation above yields recursive formula for Chebyshev polynomials of the first kind.

Topological interpretation
In the language of topology, Euler's formula states that the imaginary exponential function $$t \mapsto e^{it}$$ is a (surjective) morphism of topological groups from the real line $$\mathbb R$$ to the unit circle $$\mathbb S^1$$. In fact, this exhibits $$\mathbb R$$ as a covering space of $$\mathbb S^1$$. Similarly, Euler's identity says that the kernel of this map is $$\tau \mathbb Z$$, where $$\tau = 2\pi$$. These observations may be combined and summarized in the commutative diagram below:

Other applications
In differential equations, the function $z ≠ 0$ is often used to simplify solutions, even if the final answer is a real function involving sine and cosine. The reason for this is that the exponential function is the eigenfunction of the operation of differentiation.

In electrical engineering, signal processing, and similar fields, signals that vary periodically over time are often described as a combination of sinusoidal functions (see Fourier analysis), and these are more conveniently expressed as the sum of exponential functions with imaginary exponents, using Euler's formula. Also, phasor analysis of circuits can include Euler's formula to represent the impedance of a capacitor or an inductor.

In the four-dimensional space of quaternions, there is a sphere of imaginary units. For any point $r$ on this sphere, and $x$ a real number, Euler's formula applies: $$\exp xr = \cos x + r \sin x,$$ and the element is called a versor in quaternions. The set of all versors forms a 3-sphere in the 4-space.

Other special cases
The special cases that evaluate to units illustrate rotation around the complex unit circle:

The special case at $x = iy$ (where $cos nx$, one turn) yields $cos x$. This is also argued to link five fundamental constants with three basic arithmetic operations, but, unlike Euler's identity, without rearranging the addends from the general case: $$\begin{align} e^{i\tau} &= \cos \tau + i \sin \tau \\ &= 1 + 0 \end{align}$$ An interpretation of the simplified form $e^{ix}$ is that rotating by a full turn is an identity function.

title: Euler's formula