uttered the famous phrase : " pay attention to him : he will make a noise in the world some day or other ", it is now impossible to say, but it is likely that the 16 - year - old beethoven made a considerable impression as franz joseph haydn refers to a " ludwig " in a letter to a friend in vienna in june 1787 asking him what all the fuss was about. but 1787 was memorable for ludwig in more chilling ways : in july his much - loved mother died of consumption, the illness accelerated by her escalating alcoholism. in november of the same year his young sister died. during the following two years ludwig broadened his circle of friends to include count waldstein, a music - loving nobleman eager to help the young composer financially and spiritually, and the countess of hatzfield, the recipient of ludwig ' s dedication in his variations on vincenzo righini ' s venni amore. in 1788 the elector max franz reorganized his musical establishment, appointing anton reicha as its director and moving neefe to the position of pianist and stage manager. beethoven played second violin as well as keeping up his duties as organist. the new company performed most of the best operas of the day, including mozart ' s. son now overtook father both within the family and the court : with johann now an alcoholic and his singing voice gone, the family was so poverty - stricken that the elector decided to pay the greater part of johann ' s salary to young ludwig, thus ensuring that the family would at least eat and be clothed. at the age of 17 ludwig had become the sole reliable source of income for the beethoven family. the only other event of note between then and beethoven ' s departure for vienna in 1792 was a visit by haydn on his return from london, during which ludwig presented his funeral cantata, which was duly praised by the great man. in 1792, for reasons which remain obscure, the elector decided to finance beethoven ' s removal to vienna, there to study at bonn ' s expense. by this time beethoven had a group of nobles convinced of his musical worth, ( including count waldstein ) who – perhaps encouraged by haydn ' s praise – had helped inform the elector ' s decision. in november beethoven departed for the austrian capital, speeded on his journey by the entry by waldstein in his leaving album : " dear beethoven, you are traveling to vienna in fulfillment of your long - standing wish … labor assiduously and receive mozart ' s spirit from the hands of haydn ". within weeks of his arrival, his father


quartets ( op. 18 ). later the same year his concerto for piano and orchestra no. 3 appeared. beethoven now turned from performance to concentrate on composition. he moved from prince lichnowsky ' s and took his first summer holiday in the country – a practice which was to become increasingly important to him in the future. the next five years contained the most extraordinary outpouring of masterpieces : his second symphony was published in 1804, but by then the eroica was well under way ( he had been mulling it over since 1798 ), while his ballet prometheus and the oratorio christ on the mount of olives had been premiered in 1801 and 1803 respectively. by this time beethoven had also experienced the vicissitudes of getting his music published in an accurate and acceptable form : his rages, brought on by the number of mistakes he found at proofing stage, became legendary, particularly when, in 1803, he found that one zurich publisher had not only amended idiosyncrasies in one of his piano sonatas, but had had the effrontery to add four bars to make one passage more palatable to a conservative ear. one later printed work that beethoven corrected received this tirade : " i have passed the whole morning today – and yesterday afternoon – in correcting these two pieces, and am quite hoarse with stamping and swearing ". in early 1804 the third symphony was being prepared for publication. it had always privately been known as the " napoleon bonaparte " symphony – beethoven saw the great corsican as a force for freedom and the emancipation of the common man – but in may news filtered through to vienna of bonaparte ' s coronation as emperor. disgusted beyond measure, beethoven tore the title - page from his fair copy and substituted instead sinfonia eroica per festeggiore il souvenire d ' un gran uomo. prince lobkowitz having received the dedication and exclusive rights to its use, symphony no. 3, op. 55 ( " eroica " ) was to remain unpublished until 1806. it was characteristic of beethoven to be engaged upon more than one composition at a time. his restless creative energy would continually spill from one idea to another, one form of expression to another, so it is no surprise to find him working next on the opera fidelio and its possible production ( 1806, but destined to be shelved for the best part of a decade ) as well as the beautiful fourth piano concerto, the violin concerto, the fourth symphony and the beginning


to find him working next on the opera fidelio and its possible production ( 1806, but destined to be shelved for the best part of a decade ) as well as the beautiful fourth piano concerto, the violin concerto, the fourth symphony and the beginning of the fifth symphony. yet all this was only the beginning of his ascendancy in the world of classical music, for there was much to come of equal merit. by this time beethoven was already aware of the distressing rate at which his hearing was deteriorating. in 1802 he wrote a statement – later dubbed the heiligenstadt testament – to his two brothers, karl and johann, in which he detailed his physical frailty and his attitude towards the death which he saw as alarmingly close, although in reality he still had 25 years to live. his hearing was long thought to be a casualty of hereditary syphilis, but more recent research has come down on the side of other non - venereal diseases of which beethoven himself had no knowledge and over which he had no control. by 1807, when in one concert he premiered symphonies 1, 2, 3 and 4, ( the program lasted over two and a half hours ), beethoven had difficulty in hearing the music. the following year ' s concert in vienna premiered the fifth and sixth symphonies, the choral fantasia, plus the last - minute addition of concerto for piano no. 4, and a couple of arias. beethoven himself was at the piano, but his deafness had reached the point where he could no longer properly follow the orchestra ' s tempo. the concert was given in december, the hall was bitterly cold and the performance so ragged as to be almost bizarre in places. yet his will prevailed : all the music was played, and he remained at the keyboard throughout. in 1809, with austrian exertions against napoleon at a fever - pitch, beethoven intimated that he would leave vienna for better - paid work elsewhere. the general consternation caused archduke rudolph, prince lobkowitz and prince kinsky to club together to pay beethoven a small but helpful annuity. though the composer made it clear that he would have preferred to have been made imperial kapellmeister, he remained in vienna. he not only stayed, but when the french bombarded the city in the autumn, he completed the composition of his fifth and last piano concerto, the emperor. he also wrote a piano sonata which he named les adieux when archduke rudolf ( a close friend as well as a patron ) left the besieged capital. the disastrous effect


autumn, he completed the composition of his fifth and last piano concerto, the emperor. he also wrote a piano sonata which he named les adieux when archduke rudolf ( a close friend as well as a patron ) left the besieged capital. the disastrous effect of the napoleonic wars on the austrian economy meant that by the end of 1810 the true value of beethoven ' s annuity had shrunk to a tenth of its value. a reorganization of the austrian currency only made the position worse, but archduke rudolf continued to support beethoven, as did lobkowitz. but with kinsky he was less fortunate : the prince had removed to prague, dying in 1812 before making arrangements for beethoven ' s revised payments. undeterred, beethoven sued kinsky ' s heirs, and after three years of dogged legal action, secured not only a proper restitution of his annuity, but also payment in arrears. this success followed a year of triumphs, for 1814 had been in many ways a public culmination of beethoven ' s career : fidelio finally saw the light of day, his seventh symphony was premiered, and he was commissioned to write new music and mount concerts for the congress of vienna. two concerts were held, and beethoven was presented by the archduke to all the visiting royalty and potentates, including the empress of russia. from this point on beethoven ' s problems multiplied. a confirmed bachelor and a difficult man – who frequently fell out with friends and patrons – he nevertheless retained strong family feelings. when his brother karl died in 1815, leaving his nine - year - old son ( also named karl ) in ludwig ' s care, the composer entered into a long and vexatious dispute with the boy ' s mother, whom he detested. unfortunately, the boy held his mother in too great esteem to ever permanently take sides with beethoven. uncle ludwig spent the best part of three years in suits and counter - suits and in making arrangements for the education of the child – who proved a very ordinary boy – and it is no surprise that the sum total of his compositions during this period of stress was the three piano sonatas, op. 106, op. 109 and op. 110, plus a number of songs and arrangements. his finances strained ( prince lobkowitz ' s share of his annuity had ceased with the prince ' s death in 1816 ), his nerves in tatters, beethoven was prematurely aged by the exigencies of these years. nonetheless, by 1819 he had completed a commission to supply a mass for the


of his annuity had ceased with the prince ' s death in 1816 ), his nerves in tatters, beethoven was prematurely aged by the exigencies of these years. nonetheless, by 1819 he had completed a commission to supply a mass for the installation of archduke rudolf as archbishop of olmutz : this was his great missa solemnis. in the next few years he took up the task of completing a symphony in d minor which he had actually started in 1812 : as late as 1822 he finally came up with the idea of including schiller ' s ode to joy in a choral final movement. his ninth symphony, choral was at last taking on its final shape, and was completed in the summer of 1823. beethoven had originally planned to premiere it in berlin, but disgusted by the lack of interest in his new music occasioned by the " rossini - fever " then sweeping austria, premiered it instead in vienna. it was sufficiently successful to produce a second concert, but neither made a great deal of money after the substantial costs had been defrayed. beethoven was now anxious to make more money on account of the needs of his nephew, and his anxiety to take his fair share, or perhaps more than his fair share, led to conflicts with his erstwhile friends. that this anxiety was well - founded was borne out by the series of disasters perpetrated by nephew karl : in late 1824 he joined vienna university, but soon dropped out and moved to a polytechnic with the intention of learning a trade. by the end of 1825 this idea had also foundered and, seemingly without a path to tread, the young man tried to shoot himself. he even failed to do this properly, and was arrested by the police as an attempted suicide. within a few days he had been ordered out of vienna, joining the army soon after. he spent the latter part of 1826 with his uncle ludwig at the house of uncle johann, but this broke up in a series of ugly scenes and in december ludwig and karl returned to vienna. the journey was made in haste in the freezing cold and precipitated beethoven ' s final illness. he languished for four months, scarcely aided by the attentions of one of the few doctors in vienna still prepared to visit the rude and grumpy old man. composing was now beyond him, and although in 1824 - 25 he had written the last three string quartets – the famous op. 127, op. 130, op. 132 and grosse fuge, op. 133 – and had sketch


its a very general and regular ways to use clause with column name to specifies the sort order used on columns returned in a select statement. order by columnname asc / desc i am also using the same method but do you know we can use column index ( integer representing the position of column name ) instead of specifying the name or column alias in a sql server order by expression. order by column _ index _ number asc / desc we can use both queries because both of these queries having the same results. let check both syntax and result too here i am going to query based on adventurework database example : - getting top 10 value from employee table based on employeeid in asc order select top 10 * from humanresources. employee order by employeeid asc output will be as given below : - when using column index instead of column name for same query note : - column index can be changed as 1, 2, 3, etc based on column name condition select top 10 * from humanresources. employee order by 1 asc then output will be same as given below : - reference link : - matt berseth articles [ ^ note : - order by clause is only clause where we can you use the ordinal position [ column numbers ], because it ' s based on the column ( s ) specified in the select clause. its generally recommended that to use column name instead of column number. but in some cases using column number can be useful like it can be used it in a dynamic sql where column names are unknown for getting practical way you can follow this


washington - march 24 - fifteen years after the exxon valdez ran aground on a reef in prince william sound, alaska, dumping 11 million gallons of crude oil, the bush administration has failed to learn important lessons about protecting fragile coastlines, landscapes and wildlife from oil development. the disaster dealt biological and economic shocks to the sound and its adjacent communities, none of which has fully recovered. " the lingering images of oil drenched beaches and suffering wildlife should serve as a stark reminder to the bush administration of the consequences of america ' s dependence on oil, " said carl pope, sierra club executive director. " instead, the administration has pursued reckless policies that put america ' s pristine places at risk and failed to cut america ' s oil dependence by making vehicles go further on a gallon of gas. " the biggest single step to cutting america ' s oil dependence and protecting our communities from the harmful effects of oil and pollution is by raising fuel economy standards to 40 miles per gallon within 10 years. taking this step would save enough oil to prevent more than 789 exxon valdez - size tanker trips every year. " the bush administration has a choice : either lead america with a safe and clean energy future or allow corporate polluters to dictate our energy policy with disastrous consequences, " said pope. in 1991, the ship ' s owner - now exxonmobil - reached a $ 900 million civil settlement with the federal government and alaska, but its obligations to the thousands of fishermen and others who suffered from the spill remain unresolved. bush administration policies continue to threaten alaskan communities and wildlands. these policies include : arctic national wildlife refuge : the bush administration continues to aggressively push for oil drilling in one of america ' s last great wilderness areas. just last week the administration ' s own energy information administration stated that oil drilling in the refuge would do next to nothing to actually meet america ' s energy needs. according to the report, " assuming that world oil markets continue to work as they do today, the organization of petroleum exporting countries could countermand any potential price impact of anwr coastal plain production by reducing its exports by an equal amount. " ( http : / / www. eia. doe. gov / oiaf / servicerpt / ogp / pdf / sroiaf ( 2004 ) 04. pdf ) bristol bay : in response to the exxon valdez spill president george h. walker bush put in place a moratorium on oil and gas development in bristol bay, ak. now, almost 15 years to the


##f ( 2004 ) 04. pdf ) bristol bay : in response to the exxon valdez spill president george h. walker bush put in place a moratorium on oil and gas development in bristol bay, ak. now, almost 15 years to the day president george w bush is lifting this moratorium to allow for full scale oil development in the bay ' s world - renown salmon habitat. chugach national forest : the 3, 500 miles of shoreline spanning prince william sound make up the biological heart of the chugach national forest. although the total harm done to fish and wildlife populations could not be precisely identified, the exxon valdez oil spill killed an estimated 250, 000 seabirds, 2, 800 sea otters, 300 harbor seals, 250 bald eagles, up to 22 killer whales, and billions of salmon and herring eggs. crude oil still exists in surprising quantities on some prince william sound beaches and only 7 of 26 species have fully recovered. despite the delicate nature of the sound, the bush administration has removed nearly one million acres in the nellie juan wilderness study area through the chugach land management plan and has recently said it has plans to remove the chugach from the roadless rule. the chugach is 98 percent roadless and does not have a single acre of designated wilderness, leaving it vulnerable. without roadless protection, prince william sound may never fully recover. western arctic : the bush administration is continuing to press for full scale development of the western arctic region in alaska. ignoring sound science and the american public, the bush administration is seeking to turn over control of this area to oil companies like exxonmobil. as development proceeds the administration should recommend that some areas receive permanent protection. energy bill : the bush administration ' s energy policy makes oil and gas drilling the dominant purpose of our public lands. it also exempts oil and gas activities from such landmark environmental safeguards as the safe drinking water act and clean water act. in addition, it puts coastlines at risk by weakening individual states ability to manage oil and gas exploration and facilities. corporate average fuel economy ( cafe ) : cafe is the most successful oil - savings law ever passed by congress. the bush administration fought attempts to raise federal fuel economy standards and has even proposed regulatory changes that would weaken existing law. loopholes in the existing law cause the average fuel economy of new vehicles sold last year to fall below 1989 levels.


omphalism is a school of thought ( titled after the philip henry gosse work omphalos ) which holds that the entire universe was created with the appearance of age, and thus no date of creation for the universe can be definitively proven. examples of omphalism : - the belief that our memories, experiences, and physical appearances were " implanted " into us at our creation, possibly at a time during what we imagine to be our own lifetimes. - that nature shows signs of growth, renewal and damage which were posited into being, rather than occurring " naturally ". these include trees ( growth rings, fire scares ), mountains ( upheaval, erosion ), and animals ( offspring or supposed " evolution " ). - that starlight was " already " moving towards earth when god created it, thus disallowing accurate gauging of the universe ' s age. reception among philosophers omphalism has been declaimed by many creationists, as it appears to accuse god of deceit. the movement has been mocked by both creationists and evolutionist atheists as " last thursdayism ", with the claim that the entire universe, with all the appearances of age and function, could very well have been created at some point in the past ( such as " last thursday " ). omphalism occupies a strange place in theology, as, while supporting the notion of god as an omnipotent being, who has provided us with all the signs of a growing, changing word to give our lives context and function ( in addition to instilling many humans with the love and faith of christ ), it does in fact appear to accuse god of deceit, since these emotions and sentiments can be said to be " programmed " into humans ex nihilo. it can thus be described as heretical.


the united states securities and exchange commission ( sec ) is a united states government agency having primary responsibility for enforcing the federal securities laws and regulating the securities industry / stock market. the sec was created by section 4 of the securities exchange act of 1934 ( now codified as 15 u. s. c. § 78d and commonly referred to as the 1934 act ). in addition to the 1934 act that created it, the sec enforces the securities act of 1933, the trust indenture act of 1939, the investment company act of 1940, the investment advisers act of 1940, the sarbanes - oxley act of 2002 and other statutes. christopher cox is the present chairman of the sec. to president george he was appointed by president george w. bush. president franklin delano roosevelt appointed joseph p. kennedy, sr., father of president john f. kennedy, to serve as the first chairman of the sec. for a full list of sec chairs and commissioners, see : securities and exchange commission appointees. he sees : assigned people of the commission of securities and interchange. the sec was established by the congress of the united states in 1934 like an independent one, an independent one, years of following quasi - judicial of the regulating agency near the excessive production caused depression of merchandise, the introduction of the consumer credit, and the great collapse of 1929. the main reason of the creation of the sec was to regulate stock - market and to prevent corporative abuses referring the offer and the sale with securities and the corporative spreading. the sec was given the energy to license and of regulating stock markets. at the moment, the sec is responsible to administer six important laws that they govern the industry of securities. they are : the act of the 1933 securities, the act of interchange of 1934 securities, the act of the contract of 1939 confidence, the act of company of 1940 investment, the act of the advisors of investment of 1940 and, more recently possible one, the sarbanes - oxley act of 2002. the enforcement authority given by congress allows the sec to bring civil enforcement actions against individuals or companies found to have committed accounting fraud, provided false information, or engaged in insider trading or other violations of the securities law. the sec also works with the agencies of the application of the penal right to also process individuals and to companies for the offenses that include a criminal violation. in order to reach their mandate, the sec makes fulfill the requirement statutory that the public companies put under quarterly and annual information, as well as other periodic reports. in addition


common lisp the language, 2nd edition several kinds of numbers are defined in common lisp. they are divided into integers ; ratios ; floating - point numbers, with names provided for up to four different floating - point representations ; and complex numbers. x3j13 voted in march 1989 ( real - number - type ) to add the type real. the number data type encompasses all kinds of numbers. for convenience, there are names for some subclasses of numbers as well. integers and ratios are of type rational. rational numbers and floating - point numbers are of type real. real numbers and complex numbers are of type number. although the names of these types were chosen with the terminology of mathematics in mind, the correspondences are not always exact. integers and ratios model the corresponding mathematical concepts directly. numbers of type float may be used to approximate real numbers, both rational and irrational. the real type includes all common lisp numbers that represent mathematical real numbers, though there are mathematical real numbers ( irrational numbers ) that do not have an exact common lisp representation. only real numbers may be ordered using the <, >, < =, and > = functions. a translation of an algorithm written in fortran or pascal that uses real data usually will use some appropriate precision of common lisp ' s float type. some algorithms may gain accuracy or flexibility by using common lisp ' s rational or real type instead.


anti de - sitter space bubbles, filaments, voids and sheets condensed matter system cosmic microwave background deep field survey degrees of freedom grand unification theory heisenberg uncertainty principle hubble ' s law and constant intercommuting and loop production laws of thermodynamics nematic liquid crystal quantum field theory speed of light strong and electroweak forces surface of last scattering the great attractor theory of everything when dealing with geometries that take place within the universe, we deal not with conventional three - dimensional euclidean geometry, we have to adapt it to represent a four - dimensional spacetime. this results in what is known as a lorentzian manifold. within this geometry, we deal with three types of space, de - sitter space, anti de - sitter space and minkowski space. they are analogues of spherical, hyperbolic and euclidean space with regards to four - dimensional spacetime. this is a type of hypothetical particle of zero electrical charge that has come out of the framework of quantum chromodynamics. it is hypothesised that these were created during the very early universe. they have little mass and do not easily interact with normal matter. no experimental evidence for them exists as of yet, but they are one of the possible contenders for dark matter. a baryon is a category of subatomic particle which is composed of three quarks. this is opposed to a meson, which is composed of one quark and one antiquark. baryons include protons and neutrons and make up the majority of the mass of visible matter in the universe ( i. e. the mass of the universe that is not dark matter or dark energy ). they participate in the strong nuclear force. about thirteen billion years ago, the universe began in a gigantic explosion. every particle started rushing apart from every other particle in an early super - dense phase. the fact that galaxies are receding from us in all directions is a consequence of this initial explosion. projecting galaxy trajectories backwards in time means that they converge to a high - density state. this is one of the possible ends to the universe as we know it. cosmic inflation is expands the universe and gravitation brings matter together. depending on the density of the universe, one of these forces may overcome the other, or alternatively the universe may be of critical density, which would result in a " flat " universe. if the universe has a density higher than this critical density, then gravitation will eventually overcome the forces working to


these forces may overcome the other, or alternatively the universe may be of critical density, which would result in a " flat " universe. if the universe has a density higher than this critical density, then gravitation will eventually overcome the forces working to expand the universe, and the matter in the universe would start to converge on other matter, until all the matter in the universe converges into a singularity. given that we now know that the expansion of the universe is accelerating, it now seems unlikely that this situation will arise. a black hole is a region of spacetime from which nothing can escape, even light. to see why this happens, imagine throwing a tennis ball into the air. the harder you throw the tennis ball, the faster it is travelling when it leaves your hand and the higher the ball will go before turning back. if you were able to throw it hard enough, it would never return ; the gravitational attraction will not be able to pull it back down. the velocity the ball must have to escape is known as the escape velocity. as a body is crushed into a smaller and smaller volume, the gravitational attraction it exerts increases, and the escape velocity required to overcome this gets bigger. things have to be thrown harder and harder to escape. eventually, a point is reached when even light, which travels at 186 thousand miles a second, is not travelling fast enough to escape. at this point, nothing can get out as nothing can travel faster than light. this is a black hole. black hole formation starts when a large star has burnt all its fuel, exploding into a supernova. what remains after the supernova collapses down into a neutron star, which is extremely dense. if the neutron star is too large, its gravity overwhelms its internal pressure and the star collapses to form a black hole. a blackbody is a theoretical construct that absorbs all radiation that strikes it. no known material absorbs all radiation - some is always reflected off of it. such a body would therefore appear completely black to all types of radiation spectrography. blackbody radiation is radiation emitted from the said theoretical construct, a perfect emission of radiation with 100 % efficiency. at a certain temperature, for example, the blackbody would radiate the maximum amount of energy for that temperature. it must emit this radiation across all possible wavelengths and frequencies and is must also absorb all possible wavelengths and frequencies, which means that it can emit radiation at infinite wavelength. named after indian physicist satyendra nath bose, these are particles


. it must emit this radiation across all possible wavelengths and frequencies and is must also absorb all possible wavelengths and frequencies, which means that it can emit radiation at infinite wavelength. named after indian physicist satyendra nath bose, these are particles with full integer spin, i. e. 1, 2, 3. ( as opposed to fermions, which possess half integer spin ). there are two categories of fundamental boson ( bosons not composed of a combination of other particles ) ; gauge bosons, which mediate the fundamental forces of nature ; and scalar bosons, which are constituents of a scalar field, and include the elusive higgs boson. bosons can also be created from other particles whose spin totals an integer, for example, any meson. brane inflation uses fundamental object of string theory, called branes. in this theory, the universe is a three dimensional slide ( a brane ) in a high dimensional space ( the bulk ), which may also contain other branes. these slices of spacetime have mass and can attract each other by gravity, so two almost parallel branes separated by some distance will start moving towards each other. in brane inflation, the closer the two branes get to each other, the more the branes expand, giving rise to inflation. the process ends with the violent collision of the branes, leading to the copious production of radiation and relativistic particles. hence, the new brane resulting from the collision is filled with a hot plasma, which is the starting point of the standard big bang model. there is another prediction in the model : the collision is also accompanied by the production of cosmic strings. these are all types of large - scale structure formed from galactic distribution in the universe. galaxies form clusters and superclusters which arrange into sheets and filaments through the universe. between these sheets of galaxies, there is very low galaxy density, which leads to voids. these fill approximately 90 % of space. bubble nucleation is a form of first - order phase transition. a phase transition occurs when temperatures and densities increase such that matter changes its form and properties, such as in the very early universe, during the big bang. a simple analogy is water, which melts from ice to liquid, and then boils to gas as temperatures increase. for physicists, it is important to note that as the temperature increases, the symmetry of the matter increases. thinking this through, we know that gas is more symmetry than


colour is a degree of freedom that allows quarks to exist together to form hadrons, such as protons or neutrons, in otherwise identical quantum states. this is necessary as otherwise they would be in violation of the pauli exclusion principle, which states that no two identical fermions may occupy identical quantum states simultaneously. comoving distance is the distance between two objects as it appears if the expansion of the universe is factored out. at any given time, it is equal to the proper distance, which is the actual distance between two objects, and will change over time due to the expansion of the universe. the comoving horizon is therefore the actual distance to the edge of what we can see at any given time. condensed matter systems deal with, as the name suggests, condensed matter. this includes matter in the liquid, solid, superconducting phases. condensed matter systems can be used to study the effects of phase transitions on matter. around 370, 000 years after the big bang, the temperature of the universe dropped sufficiently for electrons and protons to combine into hydrogen atoms : p + e = h. from this time onwards, radiation was effectively unable to interact with the background gas, so it has propagated freely ever since, while constantly losing energy as its wavelength is being stretched by the expansion of the universe. originally, the radiation temperature was about 3000 degrees kelvin ( i. e. approximately 3300 degrees celsius, 5000 degrees fahrenheit ), whereas today it has fallen to only 3k. observers detecting this radiation today are able to see the universe at a very early stage. photons in the cmb have been travelling towards us for over ten billion years, and have covered a distance of about a million, billion, billion miles. the cmb was discovered in 1964. these are one - dimensional ( that is, line - like ) objects which form when an axial or cylindrical symmetry is broken. strings can be associated with grand unified particle physics models, or they can form at the electroweak scale. they are very thin and may stretch across the visible universe. a typical gut ( grand unified theory ) string has a thickness that is less then a trillion times smaller that the radius of an hydrogen atom. still, a 10 km length of one such string will weigh as much as the earth itself! originally proposed by einstein as a modification to general relativity to result in a universe which would neither expand nor contract. he later famously called it his greatest mistake after hubble discovered that other galaxies were moving away


string will weigh as much as the earth itself! originally proposed by einstein as a modification to general relativity to result in a universe which would neither expand nor contract. he later famously called it his greatest mistake after hubble discovered that other galaxies were moving away from us using redshift. different values of the constant can be used to explain different scenarios in which the universe might contract or expand. given that we now know that the expansion of the universe is accelerating, physicists are now looking to the cosmological constant as a possible explanation. specifically, the cosmological constant may be related to the dark energy that pervades our universe, working against gravity to expand the universe. this states that the universe appears the same in every direction from every point in space. it asserts that our position in the universe - on the very largest scales - is in no sense preferred. there is considerable observational evidence for this assertion, including the measured distributions of galaxies and faint radio sources, though the best evidence comes from the near - perfect uniformity of the cosmic microwave background radiation. this means that any observer anywhere in the universe will enjoy much the same view as we do, including the observation that galaxies are moving away from them. it should be noted that this does not mean local structures will be different, i. e. local stars etc. will be different for different observers, but more that the physical laws which govern these observable phenomena will be the same and background effects across the universe will be equal. cosmology is the study of the large scale universe, its origins, evolution, laws and its eventual fate. whereas astronomy is concerned with objects within the universe, cosmologists are more concerned by the universe as a whole. the uk ' s national cosmology supercomputer. it is housed within the department of applied mathematics and theoretical physics, here in cambridge. having recently undergone its ninth iteration, it is the most powerful shared memory system in europe. it is available for use for both academic and non - academic users, and is part of the stfc ' s high - performance computing dirac facility. this reference to the density of our universe. matter density in the universe plays a critical role towards understanding what will happen to the universe in the future, specifically, whether it will continue expanding until perhaps the universe grows so cold that life is unsustainable, or that matter is literally ripped apart, or whether gravitation will eventually overcome expansionary forces and the universe will collapse in some big crunch. a universe with less


continue expanding until perhaps the universe grows so cold that life is unsustainable, or that matter is literally ripped apart, or whether gravitation will eventually overcome expansionary forces and the universe will collapse in some big crunch. a universe with less than critical density will continue expanding at a forever accelerating rate, whereas a supercritical universe will invariably collapse. in the late 1990s, it was discovered that the expansion of the universe is accelerating. it is expected that due to gravity ’ s influence, bringing matter together, would slow down the acceleration of the expansion of the universe. therefore either whatever is responsible for this acceleration is not normal matter, or gravity must get weaker on large scales. this unknown physical phenomenon responsible for this acceleration is known as dark energy. to completely explain the acceleration then there isn ’ t only a little dark energy in the universe, there ’ s a lot of it. in fact, it must make up 74 % of the mass of the universe. dark matter must make up 22 % of the universe, with only 4 % of the universe being the matter that is currently known to us. there is strong evidence that the universe consists primarily of dark ( non - luminous ) matter, also that this matter is of an exotic, non - baryonic form. baryons are made up of three quarks, a type of elementary particle. baryons include protons and neutrons. a deep field survey is a galaxy survey which looks deeper into the sky than the average galaxy survey. because electromagnetic waves have a speed limit ( the speed of light ), the further away from us that we look, the further back in time we are looking, as the waves that are currently reaching us will have been radiated billions of years ago. hubble ultra - deep field, the deepest image of the universe that we currently have, shows us a time period corresponding to roughly 400 - 800 million years after the big bang. a degree of freedom, in physics ( as opposed to mathematics, which can have different meanings ), is a parameter that can help define the state of an object to differentiate it from others. a simple example would be charge amongst particles. some particles are charged, some are not, and as a result they behave differently. at a quantum level this becomes important because certain particles with the same values for their varying degrees of freedom ( i. e. spin, charge etc. ) cannot exist in the same place at the same time. an object which generates a magnetic field emanates that field from two opposite poles


certain particles with the same values for their varying degrees of freedom ( i. e. spin, charge etc. ) cannot exist in the same place at the same time. an object which generates a magnetic field emanates that field from two opposite poles, an example of this would be a bar magnet, which has a north and south pole. each of these poles is a magnetic monopole. the magnet itself, having two of these poles, is a dipole. this is similar to an electric field, in which the field emanates from positive and negative charges. whereas in electricity, negative and positive charges can be easily isolated in the form of electrons and positrons, magnetic monopole particles have yet to be discovered. for example, when you break up a bar magnet, you do not isolate the two monopoles, you simply have two bar magnets half the size of the previous one. these are two - dimensional objects that form when a discrete symmetry is broken at a phase transition. a network of domain walls effectively partitions the universe into various ' cells '. domain walls have some rather peculiar properties. for example, the gravitational field of a domain wall is repulsive rather than attractive. when the source of a wave moves away from us, we observe a change of frequency of that wave. an example would be an ambulance or fire - truck - we hear a lower pitch in its siren once it has passed us by. this is the doppler - shift. it is not, however, limited to sound waves, but any kind of waves, including electromagnetic. ( b. 1879 d. 1955 ), was a german theoretical physicist who spent much of his career at the kaiser wilhelm institute for physics and princeton university. he is regarded as one of the greatest physicists of the 20th century, and indeed, one of the most academically brilliant minds of all time. awarded the nobel prize in physics in 1921, for his work on the photoelectric effect where he described photons as discrete packets, known as quanta. this was in direct conflict with previous, classical descriptions of physics which defined photons as wave. his theories are now the basis of modern physics. these theories, whilst too numerous to list here, include special relativity, which describes how relative motion can result in different laws of physics being experienced by different observers as well as the energy - mass equivalence relationship, e = mc2, and general relativity, which generalises special relativity with respect to gravity and incorporates this with newtonian laws of gravity to describe a


in different laws of physics being experienced by different observers as well as the energy - mass equivalence relationship, e = mc2, and general relativity, which generalises special relativity with respect to gravity and incorporates this with newtonian laws of gravity to describe a how gravity is a geometry property of spacetime. when hitler came to power in 1933, he was on a trip to america and did not return to german, instead opting to become an american citizen. his warning to president roosevelt about the german research into nuclear weapons led to the eventual development of the atomic bomb, a weapon he later denounced and crusaded against. such was einstein ' s genius that upon his death his brain was removed for future study. an elementary particle carrying a negative elementary electric charge ( that is, the most fundamental electric charge, particles do not carry charge smaller than this ). a fermion with spin 1 / 2. it is a lepton and therefore is a constituent of matter, but does not participate in the strong nuclear force. it does interact with electromagnetism, gravitation and the weak nuclear force. energy unit equal to approximately 1. 6 x 10 - 19 joules. it is the amount of energy gained by the charge of one electron as it moves across a one volt electric potential difference. a period in time. in cosmology it is used to refer to different time periods in the chronology of the universe. these include the planck epoch ; the grand unification epoch ; the electroweak epoch ; the quark epoch ; the hadron epoch ; the lepton epoch ; and the photon epoch ( all of the epochs prior to the photon epoch occurred within the first 10 seconds of time! ). time periods after this include nucleosynthesis, recombination and reionization. this is the speed required for any object to break free of another objects gravitational field. for the earth, this is approximately 7, 000 miles per second. mathematically, it is described as the velocity at which the escaping object ' s kinetic energy and gravitational potential energy summate to zero. as the gravitational force exerted by an object on another object increases as the distance between the two decreases, the further away the escaping object is, the lower the escape velocity. for black holes, at the distance known as the event horizon, the escape velocity is greater than the speed of light, and therefore nothing can escape. eternal inflation refers to a series of models by which at least one region of the universe is undergoing inflation at any one point in


the distance known as the event horizon, the escape velocity is greater than the speed of light, and therefore nothing can escape. eternal inflation refers to a series of models by which at least one region of the universe is undergoing inflation at any one point in time. due to the exponential increase in volume during these periods of inflation, it is theorised that at any given point the majority of the volume of the universe is still expanding. this creates a multiverse, whereby each expanding area of the universe appears, to be its own universe, and the beginning period of expansion equivalent to the big bang. in eternal inflation it is possible for these expanding areas of space to decay into a lower energy phase, resulting in inflation ceasing. named after euclid, a greek mathematician of the third century bc. it is a system of geometry based around the geometry of the three dimensions that we are all taught at school ; x, y and z. points within the system can be described by a set of cartesian coordinates. it is described by a system of postulates, or premises, for example, the parallel postulate, which states that " if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles ". in contrast to this is non - euclidean geometry, which deals with curved space. the event horizon is the boundary that marks the point where the escape velocity of a black hole exceeds the speed of light. once the event horizon has been crossed, nothing can escape from the black hole ’ s gravitational pull, not even light. exotic particles are those made up of theorised particles not currently part of the standard model. an example of this would be the heavier partners of the current set of particles that make up the standard model, that are described within the theory of supersymmetry. full title : the fermi national accelerator laboratory. located near chicago, il., it is a united states department of energy laboratory focussed on high - energy physics. until 2011, it house the tevatron particle accelerator, which until the opening of the large hadron collider at cern, the largest in the world. in 1995 work done at the tevatron led to the discovery of the top quark, one of the six different flavours of quark, and the most massive of them all. these are particles with half integer spin. this is


world. in 1995 work done at the tevatron led to the discovery of the top quark, one of the six different flavours of quark, and the most massive of them all. these are particles with half integer spin. this is opposed to bosons, which have full integer spin. only one fermion can occupy the same quantum state and space at any given time, this is known as the pauli exclusion principle, and does not apply to the other class of particles, bosons. elementary fermions ( those not composed of other particles ) are constituents of visible matter in the universe, and include electrons and quarks. particles composed of fundamental fermions, however, can have full integer spin and therefore can be classed as bosons. a ferromagnet is an object which exhibits the property of ferromagnetism. ferromagnetism is the strongest type of magnetism, and as such ferromagnets are the magnets that the average reader will be familiar with. they are the ones used in physics classes at school, they are the ones used to pick up scrap metal, they are the magnets on your fridge. ferromagnetism is the only type of magnetism that has the strength to produce a force that can be felt. a ferromagnet can be defined as a material that can exhibit a net magnetic moment in the absence of an external magnetic field. ( b. 1918 - d. 1988 ), was a physicist who spent most of his life working at the california institute of technology ( caltech ). also worked on the manhattan project at los alamos national laboratory, where he helped develop the atomic bomb. won the nobel prize in physics in 1965 for his work in quantum electrodynamics ( qed ). developed the path integral formulation that we use today, and developed an illustrative representation scheme for the behaviour of subatomic particles which has become known as feynman diagrams. caltech has a named chair of physics in his honour. outside of his life in physics, he also was a member of the panel that investigated the space shuttle challenge crash, and wrote two popular science books : " surely you ' re joking, mr. feynman! " and " what do you care what other people think? ". there are four fundamental forces in nature. they are electromagnetism, the weak nuclear force, the strong nuclear force and gravitation. the weak nuclear force is associated with radioactivity


what do you care what other people think? ". there are four fundamental forces in nature. they are electromagnetism, the weak nuclear force, the strong nuclear force and gravitation. the weak nuclear force is associated with radioactivity in unstable nuclei, specifically the decay of a neutron into a proton in the form of beta radiation. the gauge bosons that mediate the force are the w and z bosons. this interaction can cause quarks to change flavours. the strong nuclear force binds together quarks to form nucleons, in turn, it also acts to bind these nucleons together, forming atomic nuclei. the force is mediated by an exchange of gluons, which are a type of gauge boson. the charge associated with this force, analogous to the electric charge associated with electromagnetism, is the colour charge, of which there are three varieties ; red, green and blue. the mathematical theory describing the elementary particles interacting with this force, quarks and gluons, is known as quantum chromodynamics ( qcd ). at atomic levels, it is by far the strongest of all forces, but only interacts on a scale on the order of 10 - 15m, and therefore, whilst incredibly important for the formation of matter, does not play any observable role in day to day life. electromagnetism is a force associated with the electric charge associated with certain molecules. along with gravitation, is is one of the four forces that has a major noticeable effect on day to day human life. it manifests as two different fields electric fields and magnetic fields, although they are aspects of the same force and therefore interact with each other through electromagnetic induction. the gauge boson that mediates this force is the photon, which is also the quanta ( discrete packet ) of light and other forms of electromagnetic radiation, such as infra - red radiation ( most thermal radiation ), x - rays, ultraviolet radiation etc.. gravitation is a force of attraction between two massive bodies. objects on earth are attracted to the earth via gravitation, why is why, when an apple falls from a tree, it falls down towards the earth, instead of in any other direction. gravitation also gives weight to objects, weight being the mass of an object multiplied by the gravitational force acted upon it by another object. gravitation on a universal scale is described by einstein ' s theory of general relativity, where it is described as being


allows us to build up a three dimensional map of the sky, which allows us to gain insight into the large - scale structures within the universe. a gauge group is a set of gauge transformations which effect a system in similar manners. a gauge transformation is a transformation that acts on redundant degrees of freedom within a system, that is, it effects a property that does not really have any physical significance at the level at which the system operates. a gauge transformation which is globally symmetric effects all points of space in the same way. an example of this would be a transformation of voltage that states that voltage1 = voltage2 + c ( a constant ). if we substitute the left hand side of the equation with the right in classical equations dealing with electromagnetism, there is no difference in the outcome and therefore this will hold across any difference in voltage. if we impose a local symmetry on the gauge transformation, also known as gauge invariance, then these transformations become very significant. this is because the transformation holds true, but the transformation is now a function of the position in space and time. through introducing these conditions of gauge invariance into quantum equations, one can extrapolate that for particles that interact with fundamental forces, such as the electron, which carries electrical charge and is acted upon by electromagnetism, there is an underlying field which is also undergoing a gauge transformation. in the case of the electron, it is the electromagnetic field, which physicists were already aware of, however, gauge invariance has postulated the gluon field which is the basis for quantum chromodynamics, the theory which explains the strong nuclear force. this is the modern geometric description of gravity. it says that the gravitational force is related to the curvature of spacetime itself, i. e. to its geometry. to this end, it generalises einstein ' s theory of special relativity, and links it to newton ' s laws of gravity. unlike for non - gravitational physics, spacetime is not just an arena in which physical processes take place, but it is a dynamical field. the gravitational field at a fixed time can be described by the geometry of the three spatial dimensions at that time. these are gauge bosons which mediate the strong nuclear force, one of the fundamental forces. similar to the photons which mediate the electromagnetic force, gluons have no rest mass and so travel at the speed of light. although unlike photons, which whilst mediating the electromagnetic force, are themselves electrically neutral, gluons


. similar to the photons which mediate the electromagnetic force, gluons have no rest mass and so travel at the speed of light. although unlike photons, which whilst mediating the electromagnetic force, are themselves electrically neutral, gluons have charge associated with the strong nuclear force, or colour. there are 8 different colours of gluon. gluons are confined within hadrons, particles made up of quarks ( which have a colour charge ), and are limited in interaction to a distance of approximately 10 - 15 metres. see grand unified theory. in the aftermath of the big bang, the universe was extremely hot and extremely dense. at these energies, the laws of nature that we know were changed. the fundamental forces that we see in nature were unified - the universe was in a state of grand unification - it is only as the universe expanded and cooled that gravitation, electromagnetism and the strong and weak nuclear forces all ceased to be as one. electroweak theory describes the unification of the weak nuclear force and electromagnetism. a grand unified theory will marry up electroweak theory with the strong nuclear force, brining us closer to a unification of the four fundamental forces. gravitational waves are propagating disturbances in spacetime. the effect of a passing gravitational wave is to periodically stretch and compress space in the two directions perpendicular to the direction of propagation. the expected strain on the earth due to these disturbances, which can be caused by black holes merging, is very small, making detection extremely difficult. this is an as yet undiscovered particle that is believed to mediate the force of gravitation. much like the photon, which mediates the electromagnetic force and the gluon which mediates the strong nuclear force, it has no mass, and therefore travels at the speed of light. it has a spins quantum number of 2, and is the only massless particle with that spin number. it has zero electrical charge. experimentally, the graviton is incredibly difficult to observe, and is beyond the reach of current physics. the detection of gravitational waves may lead to some further information about gravitons, but these have not yet been detected. theories of quantum gravity are one of the largest standing issues in cosmology, and there are currently few mathematically consistent theories that can explain it. one of these theories is m - theory, which we believe to be the best explanation at this point in time. this is a type of blackbody radiation emitted by


should contain at most one degree of freedom per planck area. within m - theory, the holographic principle suggests we are the shadows on the wall. the ' room ' is some larger, five - dimensional spacetime and our four - dimensional world is just the boundary of this larger space. if we try to move away from the wall, we are moving into an extra dimension of space - a fifth dimension. ( b. 1889 - d. 1953 ) was one of the main figures of astronomy in the 20th century. using the hooker 100 inch telescope at mount wilson observatory in california, discovered the galaxies are receding away from us and from each other via the changes in frequency that they exhibit - the shifting of frequency of electromagnetic emissions to the red end of the spectrum. this realisation was crucial as evidence for an expanding universe, which, if reversed, supports the notion of a big bang at the beginning of the universe. famously not awarded the nobel prize on the basis that at the time, research in astronomy was not eligible for the nobel prize in physics. hubble ' s law states that all objects in deep space ( i. e. galaxies ) are receding away from us and each other ( as can be seen by the fact that they are doppler - shifted ), and that the velocity of this recession is proportional to their distance away from the earth and other astral bodies. it is summarised mathematically by the equation : v = h0d, where v is the recession velocity, h0 is the hubble constant and d is the distance away from us that the body is. h0 has an approximate value of 70 kms - 1mpc - 1 ( kilometers per second, per megaparsec ), but a there is disagreement over its precise value. according to the theory of inflation, the early universe expanded exponentially fast for a fraction of a second after the big bang. a simple model for the expansion of the universe is to consider the inflation of a balloon. a person at any point on the balloon might consider himself or herself to be at the centre of the expansion, as all neighbouring points are getting further away. during inflation the universe expanded by a factor of about e60 = 1026. this number is a one followed by 26 zeros. it transcends normal political / economic discussions of inflation. this is a hypothetical particle and scalar field associated with the inflation of the universe that occurred moments after the big bang. it is theorized that this occurred because of a phase transition


surfaces of spheres with the three geometry slicing the sphere in half. they can be used to calculate the quantum process of universe creation, which cannot be described using classical general relativity. they only usually exist for small three geometries, corresponding to the creation of a small universe. note that the concept of time does not arise in this process. universe creation is not something that takes place inside some bigger spacetime arena - the instanton describes the spontaneous appearance of a universe from literally nothing. once the universe exists, quantum cosmology can be approximated by general relativity so time appears. there are properties exhibited by cosmic strings. intercommuting refers to a process whereby strings exchange ends whenever they meet. a loop is produced whenever a string intercommutes with itself. although cosmic strings have not been detected, this process of intercommuting can be seen in certain liquid crystals. an interferometer is a machine that uses a process of wave interference to learn about the waves in question. that is, the waves are superimposed upon themselves to discover their properties. kaluza - klein theory is a theory that seeks to unify two of the four fundamental interactions ; gravitation and electromagnetism. a similar theory, electroweak theory, already unifies the weak nuclear force and electromagnetism. its proposals extend general relativity into five - dimensional spacetime. the si ( or base ) unit for temperature measurement. kelvin and celsius have the same magnitude scale, therefore you can transform one kelvin into celsius by adding 273. 16 to the number. whereas the celsius scale was created by dividing the difference in temperature between water freezing and boiling by one hundred and labelling the freezing point of water as 0, 0 kelvin is the point described by lord kelvin ( after whom the unit is named ) as " infinite cold ", or absolute zero. this is the mechanism by which cosmic topological defects form during a phase transition. causal effects in the early universe can only propagate at the speed of light. this means that at a time t, regions of the universe separated by more than a distance d = ct can know nothing about each other. in a symmetry breaking phase transition, different regions of the universe will choose to fall into different minima in the set of possible states. topological defects are precisely the ' boundaries ' between these regions with different choices of minima, and their formation is therefore an inevitable consequence of the fact that different regions cannot agree on their choices. these are laws which define the


the set of possible states. topological defects are precisely the ' boundaries ' between these regions with different choices of minima, and their formation is therefore an inevitable consequence of the fact that different regions cannot agree on their choices. these are laws which define the fundamental physical properties which characterize ) thermodynamic systems. these are temperature, energy and entropy ( a property that works systems towards equilibrium ). they are : the zeroth law : if two systems are in thermal equilibrium with a third, they must be in thermal equilibrium with each other also. the first law : heat and work are forms of energy transfer. this is the law of the conservation of energy. internal energy in a closed system may change if heat or work are transferred in or out of the system. the second law : the entropy of any isolated system not in thermal equilibrium almost always increases. that is, an isolated system will work towards thermal equilibrium. the third law : the entropy of a system approaches a constant value as the temperature approaches zero. this is not, despite the name, a measure of time, but rather a measure of length. it is the length that light will travel in a vacuum in a year, that is 365. 25 days. its exact value is 9, 460, 730, 472, 580, 800 metres, but is approximately given by 9. 4607x1015m. this is calculated by multiplying the number of days ( 365. 25 ) by the number of seconds in each day ( 86, 400 ) and then multiplying that by the speed of light in a vacuum, which is 299, 792, 458 metres per second. in a mathematical function, the highest and lowest values of that function, over the domain of said function, are defined as the maximum or minimum points respectively. a local minimum or maximum value is defined by taking the highest or lowest value in the function over only part of the domain. an example of a function with several local minimum and maximums would be a graph of sin ( x ), which has no overall maximum or minimum value, but several local maximums and minimums of equal respective values. an object ' s ( in our context, an astronomical object ) brightness as measured by the flux, or intensity of electromagnetic radiation, that the object gives out. during the radiation era, shortly after the big bang, the universe consisted of free moving protons, neutrons and electrons and other particles, including helium ions. all radiation was absorbed by these free electrons, making the universe opaque


the object gives out. during the radiation era, shortly after the big bang, the universe consisted of free moving protons, neutrons and electrons and other particles, including helium ions. all radiation was absorbed by these free electrons, making the universe opaque. when the universe was sufficiently expanded the radiation could no longer interact with the electrons, causing the universe became transparent. this process is called decoupling, and it marked the beginning of the matter era. electrons, now no longer absorbing radiation, instead joined with ions to form neutral atoms. through gravity, these atoms clumped together, eventually forming stars, galaxies and other stellar bodies. these are zero - dimensional ( point - like ) objects which form when a spherical symmetry is broken. monopoles are predicted to be supermassive and carry magnetic charge. the existence of monopoles is an inevitable prediction of grand unified theories ( guts ) ; this is one of the puzzles of the standard cosmology. we have five consistent string theories that can describe both the forces and the matter in our universe. we do not, however, have the tools to explore the theories overall possible values of the parameters in the theories. over the past few years, however, we have been able to explore these theories more thoroughly, and we now believe that these five string theories are all different aspects of the same underlying theory : m - theory. m - theory goes beyond string theory, in that it predicts not ten, but eleven dimensions of spacetime. the theory could have as a fundamental object as a membrane, as opposed to a string, which would look like strings when curled up in the eleventh dimension. it is for this reason that the m in m - theory originally referred to a membrane. nowadays, however, the m doesn ’ t specifically refer to anything, and can stand for mystery, or “ mother of all ”, because m - theory is still largely unknown. vast clouds of interstellar dusk, hydrogen, helium and ionized gas. as the mass of a nebula grows due to the slight gravitational attracts of dust towards each other, the mass compacts enough to form stars. other material within the nebula, such as dust, can clump together to form planets and other planetary objects. originally, any large astronomical object was referred to as a nebula - other galaxies, in particular. a liquid crystal is a phase of matter which exhibits properties somewhere between those exhibited by a liquid and solid crystal. when viewed in high resolution, they can appear to be textured, as the molecules may be free


nebula - other galaxies, in particular. a liquid crystal is a phase of matter which exhibits properties somewhere between those exhibited by a liquid and solid crystal. when viewed in high resolution, they can appear to be textured, as the molecules may be free to flow in a limited manner around, provided that they stay within a crystal like structure. liquid crystals are used extensively in televisions and computer screens. the nematic phase of a liquid crystal is temperature dependent. when in this phase, clamitic ( rod - like ) molecules align themselves individually roughly parallel to each other on their long - side axis, in a similar way to cigarettes in a package. the result of this is that the molecules are free - flowing within this directional order. in this phase, the crystals can show signs of intercommuting and loop production, which are properties expected to be exhibited by cosmic strings. a neutron star is formed from the collapse of a larger star which has undergone supernova. these stars, as the name suggests, are composed mostly of neutrons. neutron stars are extremely hot. they typically have masses between about 1 and 2 solar masses ( 1 solar mass is approximately 2x1030kg, which is about 333, 000 times the mass of the earth ), despite being somewhere on the order of 1015 smaller in radius than the sun, which makes them extremely dense. the more compact a neutron star is, the more likely it is to form a black hole. this occurs when the star ' s density become so great that the gravitational force it exerts on itself is greater than its internal pressure, causing a collapse into a black hole. this was developed in 1983 by stephen hawking and james hartle. describes a situation whereby the universe can spontaneously come into existence from literally nothing. once the universe exists, quantum cosmology can be approximated by general relativity so that time appears. a particle is a nucleon if it is a particle that forms an atomic nucleus. there are two nucleons : protons and neutrons. these are complicated manifolds which, like calabi - yau manifolds, may be the space in which six extra dimensions proposed by certain string theories are found within. the study of the universe up to around 10 - 11 seconds after the big bang. during this time, the electroweak and strong forces were unified in a grand unified phase, which quickly changed to separate out strong and the electroweak forces. further on in time the electroweak interaction separated to become electromagnetism


. during this time, the electroweak and strong forces were unified in a grand unified phase, which quickly changed to separate out strong and the electroweak forces. further on in time the electroweak interaction separated to become electromagnetism and the weak nuclear force. it is possible to reach temperature regimes within this cosmology, allowing us to experimentally test theories. speculation, however, is still required within this time period. a mathematical approach to non - gravitational quantum theory, introduced by richard feynman of caltech. in the path integral approach, the probability that a system in an initial state a will evolve to a final state b is given by adding up a contribution from every possible history of the system that starts in a and ends in b. for this reason a path integral is often referred to as a ' sum over histories '. for large systems, contributions from similar histories cancel each other in the sum and only one history is important. this history is the history that classical physics would predict. for example, a system in the starting position of a ball on a non - symmetrical hill. the probability that the system will end up in the final position of the ball at the bottom of the hill on the side that is steepest is given by the summation of the probabilities of all paths that that ball could take, including going down the other side of the hill. for mathematical reasons, path integrals are formulated in a background with four spatial dimensions rather than three spatial dimensions and one time dimension. there is a procedure known as ' analytic continuation ' which is used to convert results expressed in terms of four spatial dimensions into results expressed in terms of three spatial dimensions and one time dimension. this effectively converts one of the spatial dimensions into the time dimension. this spatial dimension is sometimes referred to as ' imaginary ' time because it involves the use of so - called imaginary numbers. the path integral formulation of quantum gravity has many mathematical problems. it is also not clear how it relates to more modern attempts at constructing a theory of quantum gravity such as string / m - theory. however it can be used to correctly calculate quantities that can be calculated independently in other ways e. g. black hole temperatures and entropies. a phase transition is the change in properties and form of matter due to temperature changes. for example, water changes from solid ice to liquid water to gaseous steam or vapour. as temperature drops and phase transitions occur, the symmetry of the resulting matter is reduced - again, vapour is more symmetric than water


due to temperature changes. for example, water changes from solid ice to liquid water to gaseous steam or vapour. as temperature drops and phase transitions occur, the symmetry of the resulting matter is reduced - again, vapour is more symmetric than water, which is more symmetric than ice. in terms of cosmology, when a phase transition in the early universe occurs, topological defects are formed. some of the symmetries that were broken in the early universe led to the four fundamental forces becoming discrete forces. at higher temperatures, they reunite in a unified state. the photon is an elementary particle. it is a gauge boson, in that it mediates one of the fundamental forces. in the case of the photon, it is the electromagnetic force. as mediators of the electromagnetic force, they allow us to see things through the visible light part of the electromagnetic spectrum, and are therefore often interchanged with " light ". as they have no rest mass, they are able to travel at the fastest possible speed, which is know as the " speed of light " ( 299, 792, 458 metres per second ) in a perfect vacuum. their spin is 1 and no electrical charge. this is simply the planck length squared. given that the planck length is a fundamental unit of length, so too is the planck area a fundamental unit of area. this is the size of energy quanta ( discrete packets of energy ) in quantum mechanics - it is therefore the smallest amount of energy that anything can hold. it is the proportionality constant between the energy of a photon and the frequency of the associated electromagnetic wave, as denoted in the planck - einstein equation which links the two : e = hv, where v is frequency, h is planck ' s constant and e is energy. it ' s value is 6. 6260695729×10−34 j. s this is the earliest period of time, from the beginning of time to 10 - 43 seconds after the beginning of time. during this period, the fundamental forces of nature were all unified due to the unimaginable temperature of the universe, and it is believed that gravity was as strong as the other forces ( it is now by far the weakest of the forces ). a very, very small unit of length. its precise value is 1. 61619997x10 - 35m. it is a base unit within the planck unit system and it is calculated using the speed of light, c, planck ' s constant, h and the gravitational


. its precise value is 1. 61619997x10 - 35m. it is a base unit within the planck unit system and it is calculated using the speed of light, c, planck ' s constant, h and the gravitational constant, g. specifically, it is given by the square root of ħg / c3 where ħ is the reduced planck ' s constant, or planck ' s constant divided by 2π. it is the shortest measureable length in existence. to discuss length on scale shorter than this would be meaningless because it is a physical impossibility to measure below this length. a theory that could describe physical laws at this level would be of great use in the search for a theory of everything. this is the energy that exists in a body due to its position within a system. forces act upon the body to restore it to a lower energy state or configuration, this difference in the energy states is the potential energy. when the force acts upon the body, the energy held within the body is converted into some other form of energy, this occurs because the conservation of energy law states that energy cannot be created or destroyed. an example of potential energy being converted into other energy would be in someone skydiving. the position of the person ( the body in the system ) in the system ( the earth ), i. e. being high up in the air in a plane, gives the person gravitational potential energy. once they leap from the plane, this gravitational potential is turned into kinetic energy as the person falls toward earth. once they have landed, their position, at the surface of the earth, means that they have lower amounts of gravitational potential energy, and they have been restored to a lower energy state. this is the theory that explains the strong nuclear force that is mediated by gluons between different quarks. the charge of this force is known as colour. the force, which occurs due to an exchange of these gluons, does not weaken over distance, as say gravity does, but rather remains constant, on the order of several thousand newtons. this means that at no point does any quark separate from another one, and so quarks can only be observed on a hadron level. this property is called confinement. another property within qcd is asymptotic freedom. this results in a very weak interaction between quarks and gluons during extremely high energy reactions. this is the study of cosmology at temperature regimes where all four fundamental forces were unified. this


qcd is asymptotic freedom. this results in a very weak interaction between quarks and gluons during extremely high energy reactions. this is the study of cosmology at temperature regimes where all four fundamental forces were unified. this unification, it is theorised, occurred from the big bang to some 10 - 43 seconds after the big bang. due to the temperatures involved all quantum cosmology is theoretical and highly speculative. quantum field theory is a framework that allows for the extension of quantum mechanics, which deals with individual particles, to field systems operating relativistically. quantum field theories have been used to describe how three of the four fundamental forces act, being mediated by and exchange of particles called bosons. the photon and the gluon, for example, are exchanged between electrons and quarks in the case of electromagnetism and the strong nuclear force respectively. with quantum field theory, these natural fields pervade an area of space. particles that mediate these fields, the gauge bosons associated with the field ( like the aforementioned photon with electromagnetism ), are quanta of these fields, that is, ripples in the field carrying small amounts of energy, other particles that act within the field, for example the electron within the electromagnetic field, are though of in a similar manner., albeit different ripples and excitations. these fields are of variable range. the colour field within the quantum chromodynamic field theory, for example, acts in a range between quarks within a nucleon. other fields, such as the electromagnetic field, are infinite in scope and range. the search for a theory of quantum gravity is the search for a theory that can explain the effects of the fundamental force of gravity as explained by general relativity at a quantum level, and marry these up with quantum mechanics, which is a series of models which explain the other fundamental forces ; the strong nuclear ; weak nuclear and electromagnetic forces. examples of quantum gravity include string theory, loop quantum gravity and m - theory. this phase transmission occurred approximately one millionth of a second after the big bang. this was when quark - gluon plasma underwent a phase transition, resulting in quarks forming into hadronic matter, i. e. nucleons. quintessence is a theory of dark energy, given to explain the acceleration of the universe ’ s expansion. it is a dynamic equation, resulting in an attractive or repulsive force depending on the amount of kinetic energy


e. nucleons. quintessence is a theory of dark energy, given to explain the acceleration of the universe ’ s expansion. it is a dynamic equation, resulting in an attractive or repulsive force depending on the amount of kinetic energy relative to potential energy in the universe. as a repulsive force, it overcomes gravity ’ s attraction over large scales, resulting in an accelerated expansion. quintessence is hypothesised to have become repulsive approximately 10 billion years ago. this refers to a period of time from just after big bang to approximately 300, 000 years after its beginning. during this time, the universe consisted of free moving protons, neutrons and electrons and other particles. all radiation was absorbed by these free electrons, making the universe opaque. protons and neutrons were combining to form deuterium, a heavy isotope of hydrogen, and then helium, however, the temperature of the universe was so high that these existed as free ions in the plasma that was the universe. it was only when the universe was sufficiently expanded that the electrons no longer absorbed the radiation and instead joined with the ions to form neutral atoms. this forms the beginning of the matter era, in which we still exist. recombination was a time period, approximately 300, 000 years after the big bang, when electrons and protons bound to form atoms of hydrogen. before 300, 000 years had passed, the universe was still too hot for atoms for hydrogen to form. only after the universe had expanded sufficiently did the universe cool down sufficiently, making the formation of hydrogen possible. when the source of a wave moves away from us, we observe a change of frequency of that wave. an example would be an ambulance or fire - truck - we hear a lower pitch in its siren once it has passed us by. this is the doppler effect. it is not, however, limited to sound waves, but any kind of waves, including electromagnetic. this means that as an electromagnetic wave source is moving away from us, the frequency of the wave will decrease. as frequency and wavelength are inversely related, one goes up and the other goes down, the wavelength will increase. this shifts the wavelength closer to the red end of the spectrum ( this, when talking about the visible part of the electromagnetic spectrum, of course the wavelength may not be in the visible part ). this is redshift, and it is something we detect from far away galaxies and other electromagnetic sources. this leads us to the conclusion that the universe is expanding. these


electromagnetic spectrum, of course the wavelength may not be in the visible part ). this is redshift, and it is something we detect from far away galaxies and other electromagnetic sources. this leads us to the conclusion that the universe is expanding. these associate a scalar ( either a number, or a physical quantity ) value to every point in a space within the field. examples of scalar fields include pressure distribution, temperature variation, and gravitational fields. this is a point in spacetime where the curvature of spacetime becomes infinite. it is an area of extremely high density into which matter or light is attracted. singularities can be found both at the centre of black holes and on their own. inside a singularity, the laws of physics are distorted to the point that they are no longer applicable. spacetime is the concept of space and time being part of the same continuum. we use the typical three dimensions that are everyday and commonplace - the x, y and z dimensions used in geometry - ascribing a fourth dimension of time. this allows us to map out any event that takes place in the universe by a set of coordinates ; three of space to give us the location, and one of time to give us when the event occurred. this merging of time and space is important and must be accounted for, because relativity tells us that the observed rate of time passing changes with the respect to an objects velocity relative to the observer. gravitational fields can also change the passage of time. on quantum scales, therefore, it is important to account for time within theoretical frameworks, whereas in classical physics this is unnecessary. the structure of spacetime is detailed in einstein ' s theory of special relativity. this theory lays out the structure of spacetime. it draws on the principle of relativity as laid out by galileo, which states that there is no absolute state of rest, and that all motion is relative to other motion. there are two principles that are laid out in the theory ; that the laws of physics are the same for observers whose motion is uniform relative to each other and that the speed of light in a vacuum is the same for all observers, regardless of any relative motion. this means that with different relative velocities, observers will experience different physical laws. effects of these principles can be seen in various manners. one of the most interesting is time dilation. a clock that is sitting stationary in front of you will tick faster than a clock which is moving away from you. this is has been shown to be true for astronauts, who come


in various manners. one of the most interesting is time dilation. a clock that is sitting stationary in front of you will tick faster than a clock which is moving away from you. this is has been shown to be true for astronauts, who come back from space younger than they would have been had they remained on earth. another well known consequence of the theory is the energy - mass equivalence relationship, as defined by the equation e = mc2, probably the most famous equation of all time. this states that energy and mass are interchangeable and are related by a function of the speed of light in a vacuum, c. the speed of light in a vacuum, c, is shown not to be just a speed that photons travel at, it is a key cosmological constant that is related to the nature of space and time. special relativity shows us that any object with rest mass cannot travel at the speed of light. the speed that photons, or indeed any particle with zero rest mass ( as energy and mass are equivalent as shown by the equation e = mc2, a particle that is travelling will have kinetic energy and therefore more mass than a particle at rest ), will travel at in a vacuum. its value is 299, 792, 458 metres per second ( ms - 1 ). as explained in the theory of special relativity, the speed of light is the fastest that any form of energy or information can travel in the universe. an intrinsic quantum property of particles that is defined by a spin number that can be either a whole integer ( 1, 2, 3 etc. ) or a half integer ( 1 / 2, 3 / 2, 5 / 2 etc. ), and can be positive or negative. it is a property that all particles exhibit, the sole known exception being the higgs boson, although other particles with zero spin, such as the inflaton, have been hypothesised. to an extent, it is easy to make an analogy of quantum spin with the classic rotational spin that we encounter in everyday life, for example with a spinning top. particles that are electrically charged, such as electrons or positrons, will generate a magnetic field through their spin, as movement of an electric charge will automatically generate magnetic fields. this analogy, however, only takes us so far. different spin quantum numbers can give us ideas as to the symmetry of these particles. a particle with zero spin looks exactly the same from all sides. a particle with spin will look different if rotated, but will regain its symmetry if it


us so far. different spin quantum numbers can give us ideas as to the symmetry of these particles. a particle with zero spin looks exactly the same from all sides. a particle with spin will look different if rotated, but will regain its symmetry if it is rotated a certain number of time. in this instance, an analogy of a deck of cards is useful. consider any face card, these are symmetrical every time you spin them half way around, or 180 degrees. consider now the ace of spaces. this card, if places with the point of the space facing up as you look at it, will require a full 360 degree rotation until it looks the same again. a particle with spin 1 will act like an ace of spaces, requiring a full rotation, whereas a spin 2 particle will be symmetrical through 180 degree rotations. a half spin particle will require two rotations to be symmetrical. this kind of rotational symmetry does not have an analogue in the macroscopic world. crucially, whether a particle has half or whole integer spin tells us about how it reacts. particles with half integer spin, or fermions, obey a set of statistics known as fermi - dirac statistics. particles with whole integer spin, or bosons, obey a set called bose - einstein statistics. one of the key differences between these two sets of statistics is that those particles which obey fermi - dirac statistics are subject to the pauli exclusion principle. this states that particles may not occupy the same quantum state as each other. crucially, this means that you cannot make fermions of the same quantum state occupy the same space. this is why fermions are the particles which make up the matter of the universe. they include quarks, which combine to make protons and neutrons, and leptons, a set of particles that include electrons. bosons, which do not obey fermi - dirac statistics and are consequently not subject to the pauli exclusion principle, fulfill other roles, some mediate the fundamental forces of nature, these are the gauge bosons, and the higgs boson gives rise to mass in other particles. also known as the λcdm or lambda - cdm model, this is the best and most widely used model to explain the expansion of the universe, origins of the cosmic microwave background, nucleosynthesis of light elements and the formation of galaxies and large - scale structure. this is a set of mathematical tools that allow us to study thermodynamical properties, such as work


, origins of the cosmic microwave background, nucleosynthesis of light elements and the formation of galaxies and large - scale structure. this is a set of mathematical tools that allow us to study thermodynamical properties, such as work, heat and entropy, of a large number of particles, allowing us to look at both atomic level and macroscopic level detail of the system. this allows us to explain thermodynamics in ways that apply to both classical and quantum physics, and allows us to extrapolate macroscopic predictions from microscopic properties. in the standard model of particle physics, particles are considered to be points moving through space, tracing out a line called the world line. to take into account the different interactions observed in nature, one has to provide particles with more degrees of freedom than only their position and velocity. these include mass, electric charge, colour ( which is the “ charge ” associated with the strong interaction ) and spin. this model was designed within a framework known as quantum field theory ( qft ), which allows us to build theories consistent with both quantum mechanics and the special theory of relativity. these theories describe with great success three of the four known interactions in nature : electromagnetism, the strong and weak nuclear forces. unfortunately, gravity, as described by einstein ’ s general relativity, does not fit into this scheme. string theory replaces these different particle types with a single fundamental building block : a “ string ”. these can be closed, like loops, or open, like a hair. as the string moves through time it traces out a tube or a sheet ( depending on whether it is closed or open ). this string is free to vibrate, and different vibrational modes of the string represent the different particle types, as difference modes are seen as different masses or spins. one mode of vibration, or ‘ note ’, makes the string appear as an electron, another as a photon. there is even a mode describing the graviton, the particle carrying the force of gravity. this means we can make sense of the interaction of gravitons in a way we could not in qft. it is this ability of string theory to create a valid model that includes all four fundamental interactions that has dubbed it to be a ‘ theory of everything ’. the problem is that there are five different versions of string theory. this is why we now look to m - theory, which has place for all five theories, as the greatest solution to our ‘ theory of everything ’. as a point of


’. the problem is that there are five different versions of string theory. this is why we now look to m - theory, which has place for all five theories, as the greatest solution to our ‘ theory of everything ’. as a point of note, string theory predicts that spacetime has ten dimensions. although we only have three dimensions of space and one of time, we can assume that six of these dimensions are curled up very tightly, so that we may never be aware of their existence. having these so - called compact dimensions is very beneficial, as we can suggest that the degrees of freedom, such as electric charge of an electron, can simply arise as motion in the extra compact dimensions. there are four fundamental forces in nature. they are electromagnetism, the weak nuclear force, the strong nuclear force and gravitation. the weak nuclear force is associated with radioactivity in unstable nuclei, specifically the decay of a neutron into a proton. when the temperature is hot enough, such as that of the universe shortly after the big bang, electromagnetism and the weak nuclear force will merge to form the electroweak force. the strong nuclear force binds together neutrons and protons inside nuclei. the mathematical theory describing the elementary particles in this theory, quarks and gluons, is known as quantum chromodynamics ( qcd ). theories that unify the strong nuclear force with electroweak theory are known as grand unified theories, of guts. a supercluster is a vast ( the are some of the largest structures in the universe ) grouping of smaller galaxy clusters and groups. they can span between several hundred million light years to over one billion light years. superclusters can contain galaxy bubbles, sheets, voids and filaments, which are smaller structures within the supercluster. nearly all galaxies are found within superclusters, and inbetween superclusters thee are usually large voids. our own supercluster, called the virgo supercluster, contains the local group, the virgo cluster and some 100 other galactic groups and clusters. its diameter is approximately 100 million light years. supergravity is a theory which follows on from supersymmetry. it is theorised that in the same way that photons mediate the electromagnetism, gluons the strong nuclear force and w and z bosons the weak nuclear force, so to does the as - yet undiscovered gravi


theorised that in the same way that photons mediate the electromagnetism, gluons the strong nuclear force and w and z bosons the weak nuclear force, so to does the as - yet undiscovered graviton the gravitational force. in supergravity, the graviton has a heavier superpartner whose spin differs by 1 / 2. so far, as with supersymmetry, there has been no observational evidence for supergravity. this is a very powerful stellar explosion that can quite often outshine galaxies. a star undergoes a supernova either when a very old massive star undergoes sudden gravitational collapse, releasing vast quantities of gravitational energy, or through the reignition of the nuclear fusion reaction in a degenerate star ' s ( such as a white dwarf or neutron star ) core. the explosion releases huge quantities of the star ' s matter, resulting in a supernova remnant. certain types of supernova have luminosities of known quantity, such that they can be used as ' standard candles ', which means that we can detect how far away the object is by comparing its known luminosity with our observed brightness. string theory states that all particles are representations of different vibrations on a fundamental building block ; a string. as a theory, it is able to describe the interactions of the particle that mediates gravitation : the graviton. in this way, and by being able to describe all other particles and interactions thereof, it is able to unite the four fundamental forces in nature, and is therefore a ‘ theory of everything ’. the original string theory only described particles with integer spins, called bosons. these are the particles that mediate the fundamental forces, and include the photon, electron, gluon and graviton. the other class of particle, which have half integer spin, called fermions, were not described. these are particles that constitute matter as we know it, such as quarks and electrons. by introducing supersymmetry to bosonic string theory, we obtain a new theory that describes both the forces and the matter that make up the universe. this is superstring theory. there are three different superstring theories that have no mathematical inconsistencies. in two of them, the fundamental object is a closed string, whilst in the third, the string is open. by mixing the best aspects of bosonic string theory and superstring theory, we can create two other consistent theories of strings, heterotic