Facts About Diamonds

Diamond is the allotrope of carbon in which the carbon atoms are arranged in the specific type of cubic lattice called diamond cubic. Diamond is an optically isotropic crystal that is transparent to opaque. Diamond is the hardest naturally occurring material known. Yet, due to important structural weaknesses, diamond's toughness is only fair to good. The precise tensile strength of bulk diamond is unknown; however, compressive strength up to 60 GPa has been observed, and it could be as high as 90–100 GPa in the form of nanometer-sized wires or needles (~100-300 nanometers in diameter),with a corresponding local maximum tensile elastic strain in excess of 9%. The anisotropy of diamond hardness is carefully considered during diamond cutting.

Diamond has a high refractive index (2.417) and moderate dispersion (0.044) properties that give cut diamonds their brilliance. Scientists classify diamonds into four main types according to the nature of crystallographic defects present. Trace impurities substitutionally replacing carbon atoms in a diamond's crystal structure, and in some cases structural defects, are responsible for the wide range of colors seen in diamond. Most diamonds are electrical insulators and extremely efficient thermal conductors. Unlike many other minerals, the specific gravity of diamond crystals (3.52) has rather small variation from diamond to diamond.

Hardness and Crystal Structure

Known to the ancient Greeks as ἀδάμας – adámas ("proper", "unalterable", "unbreakable") and sometimes called adamant, diamond is the hardest known naturally occurring material, scoring 10 on the Mohs scale of mineral hardness. Diamond is extremely strong owing to the structure of its carbon atoms, where each carbon atom has four neighbors joined to it with covalent bonds. The material boron nitride, when in a form structurally identical to diamond (zincblende structure), is nearly as hard as diamond; a currently hypothetical material, beta carbon nitride, may also be as hard or harder in one form. It has been shown that some diamond aggregates having nanometer grain size are harder and tougher than conventional large diamond crystals, thus they perform better as abrasive material. 

Owing to the use of those new ultra-hard materials for diamond testing, more accurate values are now known for diamond hardness. A surface perpendicular to the [111] crystallographic direction (that is the longest diagonal of a cube) of a pure (i.e., type IIa) diamond has a hardness value of 167 GPa when scratched with a nanodiamond tip, while the nanodiamond sample itself has a value of 310 GPa when tested with another nanodiamond tip. Because the test only works properly with a tip made of harder material than the sample being tested, the true value for nanodiamond is likely somewhat lower than 310 GPa.

The precise tensile strength of diamond is unknown, however strength up to 60 GPa has been observed, and theoretically it could be as high as 90–225 GPa depending on the sample volume/size, the perfection of diamond lattice and on its orientation: Tensile strength is the highest for the [100] crystal direction (normal to the cubic face), smaller for the [110] and the smallest for the [111] axis (along the longest cube diagonal). Diamond also has one of the smallest compressibilities of any material.

Cubic diamonds have a perfect and easy octahedral cleavage, which means that they only have four planes—weak directions following the faces of the octahedron where there are fewer bonds—along which diamond can easily split upon blunt impact to leave a smooth surface. Similarly, diamond's hardness is markedly directional: the hardest direction is the diagonal on the cube face, 100 times harder than the softest direction, which is the dodecahedral plane. The octahedral plane is intermediate between the two extremes. The diamond cutting process relies heavily on this directional hardness, as without it a diamond would be nearly impossible to fashion. Cleavage also plays a helpful role, especially in large stones where the cutter wishes to remove flawed material or to produce more than one stone from the same piece of rough (e.g. Cullinan Diamond).

Diamonds crystallize in the diamond cubic crystal system (space group Fd3m) and consist of tetrahedrally, covalently bonded carbon atoms. A second form called lonsdaleite, with hexagonal symmetry, has also been found, but it is extremely rare and forms only in meteorites or in laboratory synthesis. The local environment of each atom is identical in the two structures. From theoretical considerations, lonsdaleite is expected to be harder than diamond, but the size and quality of the available stones are insufficient to test this hypothesis. In terms of crystal habit, diamonds occur most often as euhedral (well-formed) or rounded octahedra and twinned, flattened octahedra with a triangular outline. Other forms include dodecahedra and (rarely) cubes. There is evidence that nitrogen impurities play an important role in the formation of well-shaped euhedral crystals. The largest diamonds found, such as the Cullinan Diamond, were shapeless. These diamonds are pure (i.e. type II) and therefore contain little if any nitrogen.

The faces of diamond octahedrons are highly lustrous owing to their hardness; triangular shaped growth defects (trigons) or etch pits are often present on the faces. A diamond's fracture may be step-like, conchoidal (shell-like, similar to glass) or irregular. Diamonds which are nearly round, due to the formation of multiple steps on octahedral faces, are commonly coated in a gum-like skin (nyf). The combination of stepped faces, growth defects, and nyf produces a "scaly" or corrugated appearance. Many diamonds are so distorted that few crystal faces are discernible. Some diamonds found in Brazil and the Democratic Republic of the Congo are polycrystalline and occur as opaque, darkly colored, spherical, radial masses of tiny crystals; these are known as ballas and are important to industry as they lack the cleavage planes of single-crystal diamond. Carbonado is a similar opaque microcrystalline form which occurs in shapeless masses. Like ballas diamond, carbonado lacks cleavage planes and its specific gravity varies widely from 2.9 to 3.5. Bort diamonds, found in Brazil, Venezuela, and Guyana, are the most common type of industrial-grade diamond. They are also polycrystalline and often poorly crystallized; they are translucent and cleave easily.

Because of its great hardness and strong molecular bonding, a cut diamond's facets and facet edges appear the flattest and sharpest. A curious side effect of diamond's surface perfection is hydrophobia combined with lipophilia. The former property means a drop of water placed on a diamond will form a coherent droplet, whereas in most other minerals the water would spread out to cover the surface. 

Similarly, diamond is unusually lipophilic, meaning grease and oil readily collect on a diamond's surface. Whereas on other minerals oil would form coherent drops, on a diamond the oil would spread. This property is exploited in the use of so-called "grease pens," which apply a line of grease to the surface of a suspect diamond simulant. Diamond surfaces are hydrophobic when the surface carbon atoms terminate with a hydrogen atom and hydrophilic when the surface atoms terminate with an oxygen atom or hydroxyl radical. Treatment with gases or plasmas containing the appropriate gas, at temperatures of 450 °C or higher, can change the surface property completely. Naturally occurring diamonds have a surface with less than a half monolayer coverage of oxygen, the balance being hydrogen and the behavior is moderately hydrophobic. This allows for separation from other minerals at the mine using the so-called "grease-bell.”

Toughness

Unlike hardness, which denotes only resistance to scratching, diamond's toughness or tenacity is only fair to good. Toughness relates to the ability to resist breakage from falls or impacts. Because of diamond's perfect and easy cleavage, it is vulnerable to breakage. A diamond will shatter if hit with an ordinary hammer. The toughness of natural diamond has been measured as 2.0 MPa m^1/2, which is good compared to other gemstones, but poor compared to most engineering materials. As with any material, the macroscopic geometry of a diamond contributes to its resistance to breakage. Diamond has a cleavage plane and is therefore more fragile in some orientations than others. Diamond cutters use this attribute to cleave some stones, prior to faceting.

Ballas and carbonado diamond are exceptional, as they are polycrystalline and therefore much tougher than single-crystal diamond; they are used for deep-drilling bits and other demanding industrial applications. Particular faceting shapes of diamonds are more prone to breakage and thus may be uninsurable by reputable insurance companies. The brilliant cut of gemstones is designed specifically to reduce the likelihood of breakage or splintering.

Solid foreign crystals are commonly present in diamond. They are mostly minerals, such as olivine, garnets, ruby, and many others. These and other inclusions, such as internal fractures or "feathers", can compromise the structural integrity of a diamond. Cut diamonds that have been enhanced to improve their clarity via glass infilling of fractures or cavities are especially fragile, as the glass will not stand up to ultrasonic cleaning or the rigors of the jeweler's torch. Fracture-filled diamonds may shatter if treated improperly.

                            https://en.wikipedia.org/wiki/Material_properties_of_diamond

"Collusion" Explained

Collusion is a secret cooperation or deceitful agreement in order to deceive others, although not necessarily illegal, as a conspiracy. A secret agreement between two or more parties to limit open competition by deceiving, misleading, or defrauding others of their legal rights, or to obtain an objective forbidden by law typically by defrauding or gaining an unfair market advantage is an example of collusion. It is an agreement among firms or individuals to divide a market, set prices, limit production or limit opportunities. It can involve "unions, wage fixing, kickbacks, or misrepresenting the independence of the relationship between the colluding parties".  In legal terms, all acts effected by collusion are considered void.

Definition

In the study of economics and market competition, collusion takes place within an industry when rival companies cooperate for their mutual benefit. Collusion most often takes place within the market structure of oligopoly, where the decision of a few firms to collude can significantly impact the market as a whole. Collusion which is covert, on the other hand, is known as tacit collusion, and is legal. Adam Smith in the Wealth of Nations explains that since the masters (business owners) are fewer in numbers, it becomes much easier for them to collude in order to serve common interests among them, such as keeping the wages of workers low, while it is much more difficult for the labor to coordinate in order to protect their own interests due to their vast numbers. Therefore, business owners have a bigger advantage over the working class. Nevertheless, according to Adam Smith, people rarely hear about the coordination and collaboration that happens between business owners as it happens in an informal way.

Variations

According to neoclassical price-determination theory and game theory, the independence of suppliers forces prices to their minimum, increasing efficiency and decreasing the price determining ability of each individual firm. However, if firms collude to all increase prices, loss of sales is minimized, as consumers lack alternative choices at lower prices. This benefits the colluding firms at the cost of efficiency to society.

One variation of this traditional theory is the theory of kinked demand. Firms face a kinked demand curve if, when one firm decreases its price, other firms are expected to follow suit in order to maintain sales; when one firm increases its price, however, its rivals are unlikely to follow, as they would lose the sales' gains that they would otherwise get by holding prices at the previous level. Kinked demand potentially fosters supra-competitive prices because any one firm would receive a reduced benefit from cutting price, as opposed to the benefits accruing under neoclassical theory and certain game theoretic models such as Bertrand competition.

Indicators of Collusion

Practices that suggest possible collusion include:

• Uniform prices
• A penalty for price discounts
• Advance notice of price changes
• Information exchange

Examples of Collusion

Collusion is illegal in the United States, Canada and most of the EU due to antitrust laws, but implicit collusion in the form of price leadership and tacit understandings still takes place. Several examples of collusion in the United States include:

• Market division and price-fixing among manufacturers of heavy electrical equipment in the 1960s, including General Electric.
• An attempt by Major League Baseball owners to restrict players' salaries in the mid-1980s.
• The sharing of potential contract terms by NBA free agents in an effort to help a targeted franchise circumvent the salary cap.
• Price fixing within food manufacturers providing cafeteria food to schools and the military in 1993.
• Market division and output determination of livestock feed additive, called lysine, by companies in the US, Japan and South Korea in 1996, Archer Daniels Midland being the most notable of these.
• Chip dumping in poker or any other card game played for money.
• Ben and Jerry's and Häagen-Dazs collusion of products in 2013: Ben and Jerry's makes chunkier flavors with more treats in them, while Häagen-Dazs sticks to smoother flavors.
• The Google and Apple against employee poaching collusion case in 2015, in which it was revealed that both companies agreed not to hire employees from one another in order to halt the rise of wages.

In the EU:

• The illegal collusion between the giant German automakers BMW, Daimler and Volkswagen, discovered by the European Commission in 2019, to hinder technological progress in improving the quality of vehicle emissions in order to reduce the cost of production and maximize profits.

There are many ways that implicit collusion tends to develop:

• The practice of stock analyst conference calls and meetings of industry participants almost necessarily results in tremendous amounts of strategic and price transparency. This allows each firm to see how and why every other firm is pricing their products.
• If the practice of the industry causes more complicated pricing, which is hard for the consumer to understand (such as risk-based pricing, hidden taxes and fees in the wireless industry, negotiable pricing), this can cause competition based on price to be meaningless (because it would be too complicated to explain to the customer in a short advertisement). This causes industries to have essentially the same prices and compete on advertising and image, something theoretically as damaging to consumers as normal price fixing.

Barriers to Collusion

There can be significant barriers to collusion. In any given industry, these may include:

• The number of firms: As the number of firms in an industry increases, it is more difficult to successfully organize, collude and communicate.
• Cost and demand differences between firms: If costs vary significantly between firms, it may be impossible to establish a price at which to fix output.
• Cheating: There is considerable incentive to cheat on collusion agreements; although lowering prices might trigger price wars, in the short term the defecting firm may gain considerably. This phenomenon is frequently referred to as "chiseling".
• Potential entry: New firms may enter the industry, establishing a new baseline price and eliminating collusion (though anti-dumping laws and tariffs can prevent foreign companies entering the market).
• Economic recession: An increase in average total cost or a decrease in revenue provides incentive to compete with rival firms in order to secure a larger market share and increased demand.
• Anticollusion legal framework and collusive lawsuit.

                                                 https://en.wikipedia.org/wiki/Collusion

What Is a Mathematical Conjecture?

In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof or disproof has yet been found. Conjectures such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (which was a conjecture until proven in 1995 by Andrew Wiles) have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.

Important Examples

Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than two.

This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems"

Four color theorem

In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color. Two regions are called adjacent if they share a common boundary that is not a corner, where corners are the points shared by three or more regions. For example, in the map of the United States of America, Utah and Arizona are adjacent, but Utah and New Mexico, which only share a point that also belongs to Arizona and Colorado, are not.

Möbius  mentioned the problem in his lectures as early as 1840. The conjecture was first proposed on October 23, 1852 when Francis Guthrie, while trying to color the map of countries of England, noticed that only four different colors were needed. The five color theorem, which has a short elementary proof, states that five colors suffice to color a map and was proven in the late 19th century (Heawood 1890); however, proving that four colors suffice turned out to be significantly harder. A number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852.

The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken0. It was the first major theorem to be proved using a computer. Appel and Haken's approach started by showing that there is a particular set of 1,936 maps, each of which cannot be part of a smallest-sized counterexample to the four color theorem. (If they did appear, you could make a smaller counter-example.) Appel and Haken used a special-purpose computer program to confirm that each of these maps had this property. Additionally, any map that could potentially be a counterexample must have a portion that looks like one of these 1,936 maps. Showing this required hundreds of pages of hand analysis, Appel and Haken concluded that no smallest counterexamples exists because any must contain, yet do not contain, one of these 1,936 maps. This contradiction means there are no counterexamples at all and that the theorem is therefore true. Initially, their proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand (Swart 1980). Since then the proof has gained wider acceptance, although doubts remain (Wilson 2002, 216–222).

Hauptvermutung

The Hauptvermutung (German for main conjecture) of geometric topology is the conjecture that any two triangulations of a triangulable space have a common refinement, a single triangulation that is a subdivision of both of them. It was originally formulated in 1908, by Steinitz and Tietze.

This conjecture is now known to be false. The non-manifold version was disproved by John Milnor in 1961 using Reidemeister torsion.

The manifold version is true in dimensions m ≤ 3. The cases m = 2 and 3 were proved by Tibor Radó and Edwin E. Moise in the 1920s and 1950s, respectively.

Weil conjectures

In mathematics, the Weil conjectures were some highly influential proposals by André Weil (1949) on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.

A variety V over a finite field with q elements has a finite number of rational points, as well as points over every finite field with q^k elements containing that field. The generating function has coefficients derived from the numbers N_k of points over the (essentially unique) field with q^k elements.

Weil conjectured that such zeta-functions should be rational functions, should satisfy a form of functional equation, and should have their zeroes in restricted places. The last two parts were quite consciously modeled on the Riemann zeta function and Riemann hypothesis. The rationality was proved by Dwork (1960), the functional equation by Grothendieck (1965), and the analogue of the Riemann hypothesis was proved by Deligne (1974).

Poincaré conjecture

In mathematics, the Poincaré conjecture is a theorem about the characterization of the 3-sphere, which is the hypersphere that bounds the unit ball in four-dimensional space. The conjecture states:

Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.

An equivalent form of the conjecture involves a coarser form of equivalence than homeomorphism called homotopy equivalence: if a 3-manifold is homotopy equivalent to the 3-sphere, then it is necessarily homeomorphic to it.

Originally conjectured by Henri Poincaré, the theorem concerns a space that locally looks like ordinary three-dimensional space but is connected, finite in size, and lacks any boundary (a closed 3-manifold). The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere. An analogous result has been known in higher dimensions for some time.

After nearly a century of effort by mathematicians, Grigori Perelman presented a proof of the conjecture in three papers made available in 2002 and 2003 on arXiv. The proof followed on from the program of Richard S. Hamilton to use the Ricci flow to attempt to solve the problem. Hamilton later introduced a modification of the standard Ricci flow, called Ricci flow with surgery to systematically excise singular regions as they develop, in a controlled way, but was unable to prove this method "converged" in three dimensions. Perelman completed this portion of the proof. Several teams of mathematicians have verified that Perelman's proof is correct.

The Poincaré conjecture, before being proven, was one of the most important open questions in topology.

Riemann hypothesis

In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture that the non-trivial zeros of the Riemann zeta function all have real part 1/2. The name is also used for some closely related analogues, such as the Riemann hypothesis for curves over finite fields.

The Riemann hypothesis implies results about the distribution of prime numbers. Along with suitable generalizations, some mathematicians consider it the most important unresolved problem in pure mathematics (Bombieri 2000). The Riemann hypothesis, along with the Goldbach conjecture, is part of Hilbert's eighth problem in David Hilbert's list of 23 unsolved problems; it is also one of the Clay Mathematics Institute Millennium Prize Problems.

P versus NP problem

The P versus NP problem is a major unsolved problem in computer science. Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer; it is widely conjectured that the answer is no. It was essentially first mentioned in a 1956 letter written by Kurt Gödel to John von Neumann. Gödel asked whether a certain NP-complete problem could be solved in quadratic or linear time. The precise statement of the P=NP problem was introduced in 1971 by Stephen Cook in his seminal paper "The complexity of theorem proving procedures" and is considered by many to be the most important open problem in the field. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US$1,000,000 prize for the first correct solution.

Other conjectures

• Goldbach's conjecture
• The twin prime conjecture
• The Collatz conjecture
• The Manin conjecture
• The Maldacena conjecture
• The Euler conjecture, proposed by Euler in the 18th century but for which counterexamples for a number of exponents starting with n=4 were found beginning in the mid 20th century
• The Hardy-Littlewood conjectures are a pair of conjectures concerning the distribution of prime numbers, the first of which expands upon the twin prime conjecture mentioned above. Neither one has either been proven or disproven, but it has been proven that both cannot simultaneously be true. At least one must be false. It has not been proven which one is false, but it is widely believed that the first conjecture is true and the second one is false.
• The Langlands program is a far-reaching web of these ideas of 'unifying conjectures' that link different subfields of mathematics, e.g. number theory and representation theory of Lie groups; some of these conjectures have since been proved.

Resolution of Conjectures

Proof

Formal mathematics is based on provable truth. In mathematics, any number of cases supporting a conjecture, no matter how large, is insufficient for establishing the conjecture's veracity, since a single counterexample would immediately bring down the conjecture. Mathematical journals sometimes publish the minor results of research teams having extended the search for a counterexample farther than previously done. For instance, the Collatz conjecture, which concerns whether or not certain sequences of integers terminate, has been tested for all integers up to 1.2 × 10¹² (over a trillion). However, the failure to find a counterexample after extensive search does not constitute a proof that no counterexample exists nor that the conjecture is true, because the conjecture might be false but with a very large minimal counterexample.

Instead, a conjecture is considered proven only when it has been shown that it is logically impossible for it to be false. There are various methods of doing so; see Mathematical proof#Methods for details. 

One method of proof, usable when there are only a finite number of cases that could lead to counterexamples, is known as "brute force": in this approach, all possible cases are considered and shown not to give counterexamples. Sometimes the number of cases is quite large, in which situation a brute-force proof may require as a practical matter the use of a computer algorithm to check all the cases: the validity of the 1976 and 1997 brute-force proofs of the four color theorem by computer was initially doubted, but was eventually confirmed in 2005 by theorem-proving software.

When a conjecture has been proven, it is no longer a conjecture but a theorem. Many important theorems were once conjectures, such as the Geometrization theorem (which resolved the Poincaré conjecture), Fermat's Last Theorem, and others.

Disproof

Conjectures disproven through counterexample are sometimes referred to as false conjectures (cf. the Pólya conjecture and Euler's sum of powers conjecture). In the case of the latter, the first counterexample found for the n=4 case involved numbers in the millions, although subsequently it has been found that the minimal counterexample is smaller than that.

Undecidable conjectures

Not every conjecture ends up being proven true or false. The continuum hypothesis, which tries to ascertain the relative cardinality of certain infinite sets, was eventually shown to be undecidable (or independent) from the generally accepted set of axioms of set theory. It is therefore possible to adopt this statement, or its negation, as a new axiom in a consistent manner (much as we can take Euclid's parallel postulate as either true or false).

In this case, if a proof uses this statement, researchers will often look for a new proof that doesn't require the hypothesis (in the same way that it is desirable that statements in Euclidean geometry be proved using only the axioms of neutral geometry, i.e. no parallel postulate.) The one major exception to this in practice is the axiom of choice—unless studying this axiom in particular, the majority of researchers do not usually worry whether a result requires the axiom of choice.

Conditional Proofs

Sometimes a conjecture is called a hypothesis when it is used frequently and repeatedly as an assumption in proofs of other results. For example, the Riemann hypothesis is a conjecture from number theory that (amongst other things) makes predictions about the distribution of prime numbers. Few number theorists doubt that the Riemann hypothesis is true. In anticipation of its eventual proof, some have proceeded to develop further proofs which are contingent on the truth of this conjecture. These are called conditional proofs: the conjectures assumed appear in the hypotheses of the theorem, for the time being.

These "proofs", however, would fall apart if it turned out that the hypothesis was false, so there is considerable interest in verifying the truth or falsity of conjectures of this type.

In Other Sciences

Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is related to hypothesis, which in science refers to a testable conjecture.

                                                 https://en.wikipedia.org/wiki/Conjecture

Black Holes "Ring" with Gravity Waves

Results support Einstein's theory and the idea that black holes have no 'hair'

MIT – September 11, 2019 -- If Albert Einstein's theory of general relativity holds true, then a black hole, born from the cosmically quaking collisions of two massive black holes, should itself "ring" in the aftermath, producing gravitational waves much like a struck bell reverbates sound waves. Einstein predicted that the particular pitch and decay of these gravitational waves should be a direct signature of the newly formed black hole's mass and spin.

Now, physicists from MIT and elsewhere have "heard" the ringing of an infant black hole for the first time, and found that the pattern of this ringing does, in fact, predict the black hole's mass and spin -- more evidence that Einstein was right all along.

The findings, published today in Physical Review Letters, also favor the idea that black holes lack any sort of "hair" -- a metaphor referring to the idea that black holes, according to Einstein's theory, should exhibit just three observable properties: mass, spin, and electric charge. All other characteristics, which the physicist John Wheeler termed "hair," should be swallowed up by the black hole itself, and would therefore be unobservable.

The team's findings today support the idea that black holes are, in fact, hairless. The researchers were able to identify the pattern of a black hole's ringing, and, using Einstein's equations, calculated the mass and spin that the black hole should have, given its ringing pattern. These calculations matched measurements of the black hole's mass and spin made previously by others.

If the team's calculations deviated significantly from the measurements, it would have suggested that the black hole's ringing encodes properties other than mass, spin, and electric charge -- tantalizing evidence of physics beyond what Einstein's theory can explain. But as it turns out, the black hole's ringing pattern is a direct signature of its mass and spin, giving support to the notion that black holes are bald-faced giants, lacking any extraneous, hair-like properties.

"We all expect general relativity to be correct, but this is the first time we have confirmed it in this way," says the study's lead author, Maximiliano Isi, a NASA Einstein Fellow in MIT's Kavli Institute for Astrophysics and Space Research. "This is the first experimental measurement that succeeds in directly testing the no-hair theorem. It doesn't mean black holes couldn't have hair. It means the picture of black holes with no hair lives for one more day."

A chirp, decoded

On Sept. 9, 2015, scientists made the first-ever detection of gravitational waves -- infinitesimal ripples in space-time, emanating from distant, violent cosmic phenomena. The detection, named GW150914, was made by LIGO, the Laser Interferometer Gravitational-wave Observatory. Once scientists cleared away the noise and zoomed in on the signal, they observed a waveform that quickly crescendoed before fading away. When they translated the signal into sound, they heard something resembling a "chirp."

Scientists determined that the gravitational waves were set off by the rapid inspiraling of two massive black holes. The peak of the signal -- the loudest part of the chirp -- linked to the very moment when the black holes collided, merging into a single, new black hole. While this infant black hole likely gave off gravitational waves of its own, its signature ringing, physicists assumed, would be too faint to decipher amid the clamor of the initial collision.

Isi and his colleagues, however, found a way to extract the black hole's reverberation from the moments immediately after the signal's peak. In previous work led by Isi's co-author, Matthew Giesler, the team showed through simulations that such a signal, and particularly the portion right after the peak, contains "overtones" -- a family of loud, short-lived tones. When they reanalyzed the signal, taking overtones into account, the researchers discovered that they could successfully isolate a ringing pattern that was specific to a newly formed black hole.

In the team's new paper, the researchers applied this technique to actual data from the GW150914 detection, concentrating on the last few milliseconds of the signal, immediately following the chirp's peak. Taking into account the signal's overtones, they were able to discern a ringing coming from the new, infant black hole. Specifically, they identified two distinct tones, each with a pitch and decay rate that they were able to measure.

"We detect an overall gravitational wave signal that's made up of multiple frequencies, which fade away at different rates, like the different pitches that make up a sound," Isi says. "Each frequency or tone corresponds to a vibrational frequency of the new black hole."

Listening beyond Einstein

Einstein's theory of general relativity predicts that the pitch and decay of a black hole's gravitational waves should be a direct product of its mass and spin. That is, a black hole of a given mass and spin can only produce tones of a certain pitch and decay. As a test of Einstein's theory, the team used the equations of general relativity to calculate the newly formed black hole's mass and spin, given the pitch and decay of the two tones they detected.

They found their calculations matched with measurements of the black hole's mass and spin previously made by others. Isi says the results demonstrate that researchers can, in fact, use the very loudest, most detectable parts of a gravitational wave signal to discern a new black hole's ringing, where before, scientists assumed that this ringing could only be detected within the much fainter end of the gravitational wave signal, and only with much more sensitive instruments than what currently exist.

"This is exciting for the community because it shows these kinds of studies are possible now, not in 20 years," Isi says.

As LIGO improves its resolution, and more sensitive instruments come online in the future, researchers will be able to use the group's methods to "hear" the ringing of other newly born black holes. And if they happen to pick up tones that don't quite match up with Einstein's predictions, that could be an even more exciting prospect.

"In the future, we'll have better detectors on Earth and in space, and will be able to see not just two, but tens of modes, and pin down their properties precisely," Isi says. "If these are not black holes as Einstein predicts, if they are more exotic objects like wormholes or boson stars, they may not ring in the same way, and we'll have a chance of seeing them."

This research was supported, in part, by NASA, the Sherman Fairchild Foundation, the Simons Foundation, and the National Science Foundation.

                       https://www.sciencedaily.com/releases/2019/09/190911121948.htm

Old Manuscript Defies AI Computers

See:

https://singularityhub.com/2019/09/12/how-a-mysterious-manuscript-keeps-confounding-ai/

An Exoplanet with Water

Astronomers have detected water vapor on the exoplanet K2-18b -- a major discovery in the search of alien life.

Université de Montréal – September 11, 2019 -- Ever since the discovery of the first exoplanet in the 1990s, astronomers have made steady progress towards finding and probing planets located in the habitable zone of their stars, where conditions can lead to the formation of liquid water and the proliferation of life.

Results from the Kepler satellite mission, which discovered nearly 2/3 of all known exoplanets to date, indicate that 5 to 20% of Earths and super-Earths are located in the habitable zone of their stars. However, despite this abundance, probing the conditions and atmospheric properties on any of these habitable zone planets is extremely difficult and has remained elusive... until now.

A new study by Professor Björn Benneke of the Institute for Research on Exoplanets at the Université de Montréal, his doctoral student Caroline Piaulet and several of their collaborators reports the detection of water vapour and perhaps even liquid water clouds in the atmosphere of the planet K2-18b. This exoplanet is about nine times more massive than our Earth and is found in the habitable zone of the star it orbits. This M-type star is smaller and cooler than our Sun, but due to K2-18b's close proximity to its star, the planet receives almost the same total amount of energy from its star as our Earth receives from the Sun.

The similarities between the exoplanet K2-18b and the Earth suggest to astronomers that the exoplanet may potentially have a water cycle possibly allowing water to condense into clouds and liquid water rain to fall. This detection was made possible by combining eight transit observations -- the moment when an exoplanet passes in front of its star -- taken by the Hubble Space Telescope.

The Université de Montréal is no stranger to the K2-18 system located 111 light years away. The existence of K2-18b was first confirmed by Prof. Benneke and his team in a 2016 paper using data from the Spitzer Space Telescope. The mass and radius of the planet were then determined by former Université de Montréal and University of Toronto PhD student Ryan Cloutier. These promising initial results encouraged the iREx team to collect follow-up observations of the intriguing world."

Scientists currently believe that the thick gaseous envelope of K2-18b likely prevents life as we know it from existing on the planet's surface. However, the study shows that even these planets of relatively low mass which are therefore more difficult to study can be explored using astronomical instruments developed in recent years. By studying these planets which are in the habitable zone of their star and have the right conditions for liquid water, astronomers are one step closer to directly detecting signs of life beyond our Solar System.

"This represents the biggest step yet taken towards our ultimate goal of finding life on other planets, of proving that we are not alone. Thanks to our observations and our climate model of this planet, we have shown that its water vapour can condense into liquid water. This is a first," says Björn Benneke.

                    https://www.sciencedaily.com/releases/2019/09/190911121950.htm

Hong Kong Activist Joshua Wong

Joshua Wong Chi-fung (born 13 October 1996) is a Hong Kong student activist and politician who serves as secretary-general of pro-democracy party Demosistō. Wong was previously convenor and founder of the Hong Kong student activist group Scholarism. Wong first rose to international prominence during the 2014 Hong Kong protests, and his pivotal role in the Umbrella Movement resulted in his inclusion in TIME magazine's Most Influential Teens of 2014 and nomination for its 2014 Person of the Year; he was further called one of the "world's greatest leaders" by Fortune magazine in 2015, and nominated for the Nobel Peace Prize in 2017.

                                                             Joshua Wong in 2017           

                                

In August 2017, Wong and two other pro-democracy activists were convicted and jailed for their roles in the occupation of Civic Square at the incipient stage of the 2014 Occupy Central protests; in January 2018, Wong was convicted and jailed again for failing to comply with a court order for clearance of the Mong Kok protest site during the Mong Kong protests in 2014.

Early Life

Joshua Wong was born in Hong Kong on 13 October 1996, and was diagnosed with dyslexia in early childhood. The son of middle-class couple Grace and Roger Wong, Wong was raised as a Protestant Christian in the Lutheran tradition. His social awareness stems from his father, a retired IT professional, who often took him as a child to visit the underprivileged.

Wong studied at the United Christian College (Kowloon East), a private Christian middle school in Kowloon, and developed organisational and speaking skills through involvement in church groups.

Emergence as an Activist

The 2010 anti-high speed rail protests were the first political protests in which Wong took part.

On 29 May 2011, Wong and schoolmate Ivan Lam Long-yin established Scholarism, a student activist group. The group began with simple means of protest, such as the distribution of leaflets against the newly-announced moral and national education (MNE). In time, however, Wong's group grew in both size and influence, and in 2012 managed to organise a political rally attended by over 100,000 people. Wong received widespread attention as the group's convenor.

Role in 2014 Hong Kong Protests

In June 2014, Scholarism drafted a plan to reform Hong Kong's electoral system to push for universal suffrage, under one country, two systems. His group strongly advocated for the inclusion of civic nomination in the 2017 Hong Kong Chief Executive Election. Wong as a student leader started a class boycott among Hong Kong's students to send a pro-democracy message to Beijing.

On 27 September 2014, Wong was one of the 78 people arrested by the police during a massive pro-democracy protest, after hundreds of students occupied Civic Square in front of the Central Government Complex as a sign of protest against Beijing's decision on the 2014 Hong Kong electoral reform. Unlike fellow protesters, only in response to a court order obtained by writ of habeas corpus was Wong released by police, after 46 hours in custody.

During the protests, Wong stated: "Among all the people in Hong Kong, there is only one person who can decide whether the current movement will last and he is [Chief Executive of the region] Leung. If Leung can accept our demands ... (the) movement will naturally come to an end." On 25 September 2014 the state-owned Wen Wei Po published an article which claimed that "US forces" had worked to cultivate Wong as a "political superstar". Wong in turn denied every detail in the report through a statement that he subsequently posted online. Wong also said that he was mentioned by name in mainland China's Blue Paper on National Security, which identified internal threats to the stability of Communist Party rule; quoting a line in V for Vendetta, he in turn said that "People should not be afraid of their government, the government should be afraid of their people."

Wong was charged on 27 November 2014 with obstructing a bailiff clearing one of Hong Kong's three protest areas. His lawyer described the charge as politically motivated. He was banned from a large part of Mong Kok, one of the protester-occupied sites, as one of the bail conditions. Wong claimed that police beat him and tried to injure his groin as he was arrested, and taunted and swore at him while he was in custody.

After Wong's appearance at Kowloon City Magistrates' Court on 27 November 2014, he was pelted with eggs by two assailants. They were arrested and each fined $3,000 in August 2015, sentences which, on application for review by the prosection, were subsequently enhanced to two weeks' imprisonment.

On 2 December 2014, Wong and two other students began an indefinite hunger strike to demand renewed talks with the Hong Kong government. He decided to end the hunger strike after four days on medical advice.

Aftermath of the Occupy Protests

Wong was arrested and held for three hours on Friday, 16 January 2015, for his alleged involvement in offences of calling for, inciting and participating in an unauthorized assembly.

The same month, an article appeared in the Pro-Beijing newspaper Wen Wei Po alleging that Wong had met with the US consul-general in Hong Kong Stephen M. Young during the latter's visit in 2011. It suggested that Wong had links with the Central Intelligence Agency of the United States, which had supposedly offered him military training by the US Army. Wong responded that the claims were pure fiction and "more like jokes."

Wong was denied entry into Malaysia at Penang International Airport, on 26 May 2015, on the basis that he was considered "a threat to Malaysia's ties with China", largely due to his supposed "anti-China" stance in participating in the 2014 Hong Kong protests.

On 28 June 2015, two days before a protest in favor of democracy, Wong and his girlfriend were attacked by an unknown man after watching a film in Mong Kok. The assault sent the two to hospital. Wong sustained injuries to his nose and eyes. No one was arrested.

On 19 August 2015, Wong was formally charged by the Hong Kong Department of Justice with inciting other people to join an unlawful assembly and also joining an unlawful assembly, alongside Alex Chow, the former leader of the Hong Kong Federation of Students.

While traveling to Taiwan for a political seminar, "pro-China" protesters attempted to assault Wong at the arrival hall of Taoyuan's Taiwan Taoyuan International Airport, necessitating police protection. It was later found that local gangsters were involved.

Demosisto

In April 2016, Wong founded a new political party, Demosistō, with other Scholarism leaders including Agnes Chow, Oscar Lai and Umbrella activists, the original student activist group Scholarism having been disbanded. The party advocates for a referendum to be held to determine Hong Kong's sovereignty after 2047, when the One Country, Two Systems principle as enshrined in the Sino-British Joint Declaration and the Hong Kong Basic Law expires. As the founding secretary-general of the party, Wong also planned to contest the 2016 Legislative Council election. Wong was still only 19 and being below the statutory minimum age of 21 for candidacy, he filed an application (ultimately unsuccessful) for judicial review of the election law, in October 2015. After his decision to found his own political party, Wong became a focus of criticism, especially on social networks.

Detention in Thailand

Joshua Wong was detained on arrival in Thailand on 5 October 2016. He had been invited to speak about his Umbrella Movement experience at an event marking the 40th anniversary of the Thammasat University massacre, hosted by Chulalongkorn University.

A Thai student activist who invited Wong, Netiwit Chotiphatphaisal, said that Thai authorities had received a request from the Chinese government earlier regarding Wong's visit. His own request to see Wong was denied.

After nearly 12 hours' detention, Wong was deported to Hong Kong. Wong claimed that, upon detention, the authorities would say no more than that he had been blacklisted but, just prior to deportation, they had informed him that his deportation was pursuant to Sections 19, 22 and 54 of the Immigration Act B.E. 2522.

Hong Kong Legislator Claudia Mo called the incident "despicable" and stated: "If this becomes a precedent it means it could happen to you or me at any time if somehow Beijing thinks you are a dangerous, unwelcome person". Jason Y. Ng, a Hong Kong journalist and author, stated that Wong's detention showed "how ready Beijing is to flex its diplomatic muscles and [how it] expects neighbouring governments to play ball".

Wong eventually spoke with a Thai audience from Hong Kong via Skype.

CAN Singapore Incident

On 23 December 2016, Singapore Police Force investigated organisers of a Community Action Network Singapore event in which Joshua Wong had participated from Hong Kong via Skype, for Wong's failure to hold an employment visa and police permit to participate as a foreigner in a domestic talk, notwithstanding his not even being present.

Imprisonment

Wong, along with two other prominent Hong Kong pro-democracy student leaders Nathan Law and Alex Chow, were jailed for six to eight months on 17 August 2017 for unlawful assembly (Wong and Law) and incitement to assemble unlawfully (Chow) at Civic Square, at the Central Government Complex in the Tamar site, during a protest that triggered the 79-day Occupy sit-ins of 2014. The sentences halted their political careers, as they would be barred from running for public office for five years.

On the third anniversary of the 2014 protests, 28 September 2017, Wong started the first of a series of columns for the Guardian, written from the Pik Uk Correctional Institution, where he says that despite a dull and dry life there, he remains proud of his commitment to the movement.

On 13 October 2017, Wong was convicted with 19 others of contempt of court for obstructing execution of the court's order for clearance of part of the Occupy Central protest zone in Mong Kok in October 2014. The order had been obtained by a public minibus association.

On 14 November 2017, Wong, together with Ivan Lam, commenced an application for judicial review in the High Court challenging the constitutionality of the provision in the Legislative Council Ordinance preventing persons sentenced to terms of imprisonment exceeding three   months from standing for office for five years from the date of conviction.

On 18 January 2018, Wong was sentenced by Mr Justice Andrew H C Chan of the High Court to three months' imprisonment in respect of his October 2017 conviction for contempt of court.  Nineteen other protesters convicted in respect of the same incident all received prison terms, though the terms were suspended for all but Wong and fellow protester Raphael Wong. As part of his reasoning, Chan expressed the view that, by November 2014, the protests had become      pointless and their only effect was to impact the lives of "ordinary citizens" of the region.

Nobel Peace Prize Nomination

On 1 February 2018, a bipartisan group of US lawmakers, led by Congressional-Executive Commission on China (CECC) Chair US Senator Marco Rubio and co-chair US Representative Chris Smith announced they had nominated Wong, Nathan Law, Alex Chow and the entire Umbrella Movement for the 2018 Nobel Peace Prize, for "their peaceful efforts to bring political reform and protect the autonomy and freedoms guaranteed Hong Kong in the Sino-British Joint Declaration.”

Imprisonments in 2019

Joshua Wong was sentenced to two months of prison on May 16, 2019 for his involvement in events on 26 November 2014 in Mong Kok, an area in Hong Kong, where demonstrators opposed the police during the Umbrella revolution.

Joshua Wong was released on 17 June 2019 (he had completed the two months' term because he also spent some time in jail in 2018, regarding this case, before being freed on bail).

His release coincided with the ongoing protests against extradition bill. Upon his release, Wong criticized the oppression of protesters by the Hong Kong police, and the extradition draft law as pro-Beijing and called for the Chief Executive of Hong Kong Carrie Lam to resign.

Wong did not take part with the protestors who forcibly broke into the Hong Kong's parliamentary Legislative Council building on July 1, but he explained the need behind the move. According to him, the reason behind people entering the Legislative Council is that the council is “never democratically elected by people”.

 

Wong was then arrested again on 29th August 2019 the day before a planned demonstration, which was not given city approval.

In September Wong met with the German Foreign Minister. The Chinese Foreign Ministry called this move “disrespectful of China’s sovereignty and an interference in China’s internal affairs.”

                                          https://en.wikipedia.org/wiki/Joshua_Wong