JANUARY 2013 ISSUE
P
4-5 s e ag
TO REALITY SF’S ANSWER
CONST ELLAT ION PE
RSEUS
Pages 8-9
Relativity Special
EDITORIAL
Editor: Chloe Partridge Copy Editor: Martin Griffiths Contributors: Chloe Partridge, Ana Gavrila Columnists: Phill Wallace, Martin Griffiths
A Happy New Year to one and all! With the New Year come some new opportunities to make a contribution to this, your student magazine. Articles are welcome from anyone across all years of the Observational Astronomy course and it is important to get as many voices heard as possible. So if you want to send a piece of work, run it by Chloe or Martin and get your name up in lights! The university is promoting this magazine, so this is your chance to get yourself noticed. If your essay has been marked highly, if your magazine articles in your first year have done well, send them in!
In this month’s issue we have articles on the night sky, the constellation of Perseus and a focus on Relativity and FTL travel. Hopefully the New Year will bring a resolution in some new contributors too!
If you would like to contribute in any way, either by sending us your Faulkes images, or perhaps even writing an article , then get in touch, we would love to hear from you. Editorial Contacts : 10017607@glam.ac.uk mgriffi8@glam.ac.uk
IMAGE REFERENCES: PG 1. Front cover image courtesy of Maksim Zhuk, at www.behance.net/sychuan. PG 4-5. Wikimedia Commons PG 6-7. All images Martin Griffiths, Sky Map — Heavensabove.com PG 8-9. Wikimedia Commons PG 10-11. Wikimedia Commons PG 12. Wikimedia Commons
GLMAORGAN ASTRONOMY
JANUARY 2013 ISSUE
CO SMO LO G ICAL NEW S
4-5. SF’S ANSWER TO REALITY HYPERDRIVES AND JUMP ENGINES A BOUND AS I EXPLORE THE MANY WA YS SF W RITERS EVA DE EINS TEIN ’S A NNOYING LA WS. 4-5
6-7
6-7. THE NIGHT SKY IN JANUARY THE COLD W IN TER EVEN IN GS A RE A S UP ERB TIM E FOR OBSERVING TH E S K Y A S THE N IG HTS A R E LO N G A N D THE S TA R S TW IN K LE W I TH THA T EX TRA SPA RKLE IN THE FROS TY A IR. MA RTIN GRIFFITHS COVERS W HA T CA N BE SEEN IN THE JA NUA RY S KY.
8-9. CONSTELLATION OF PERSEUS ONE OF THE OLDES T CLASSICA L MYTHS IS THA T OF PERSEUS AND A NDROM EDA . THE CONS TELLA TION OCCUP IES THE M ILKY WA Y DIREC TLY OVERHEA D IN W IN TER A S SEEN FROM THE UK. A NA GA VRILA EXP LORES THE W ON DERS OF THIS WIN TER GROUP .
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10-13. SPECIAL RELATIVITY A LOOK A T HOW THIN GS CA N CON TRA C T IN LENG TH, A ND TIM E W HEN TRA VELING A T THE SP EED OF LIGH T. 10-13
COSMOLOGICAL NEWS
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USS Enterprise Space ship Relativity is a real pain for science fiction engines are possible, Star Trek warp engines block; “negative mass.” Negative mass, or (hereafter referred to as SF, not sci-fi like are not. The engines of the USS Enterprise work exotic matter, is physically possible (that is to those pesky Americans would say). Even going by forming a “bubble” of spacetime around the say, the laws of physics as we understand them as fast as possible travelling to the stars would ship that is “submerged” into subspace; a do not disallow it) and may have been take decades or centuries. With no possibility of strange netherworld existing “beneath” our own experimentally observed in the Cassimir Effect. reprieve or parole interstellar travel looks space-time. This bubble is then made to move at However, Alcubierre calculated you would need doomed. But wait…this is SF! We don’t need to let those
great speeds in a realm where there is no at least 1019 kg of exotic mater for the system to speed limit. Fanciful, crazy, impossible.
pesky laws of physics hamper our fun. So SF The “real” warp drive was worked out writers have come up with a bewildering array mathematically by Miguel Alcubierre and of solutions to the lightspeed barrier. Warp suggests that a large enough mass in front of
work. That’s about the mass of Mar’s moon Deimos. Yeah, not likely. Plus the difficulty of making this whole apparatus move without touching it.
engines, hyperdrives, slipstream portals, the ship and a corresponding negative mass Hyperdrive: An incredibly common method of wormholes and jump gates are scattered behind the ship, all moving, would allow the ship FTL is the wonderfully generic hyperdrive. Most across science fiction almost as liberally as the to “surf” the wave of space-time. So the ship commonly it carries the starship into another planet-killing weapons of my last article. So itself is at relative rest, it’s just riding a wave of those alternate space-times called let’s have a look at some of the more popular that happens to be moving at near-lightspeed. hyperspace, this time it is “above” our universe, FTL methods.
Warp Engines: A staple of Star Trek since its very beginning, warp engines are in fact
Relativity is avoided and causality is maintained so it (apparently) has a much higher energy and as long as the starship cannot communicate no speed limit and no relativity either. Hence, with the universe while moving.
starships can accelerate indefinitely without its
mass increasing as that annoying Einstein physically possible. Or rather, actual warp You may have noticed that little stumbling-
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predicted. Hyperspace turns up throughout sci- just hop across the gap and boom, from an some long-lost species. Wormholes are regions fi, from Star Wars to Stargate to Babylon 5 to observer’s point of view you have jumped of space-time that take shortcuts across or Homeworld and on. Even my own SF works across a huge distance. So, we take a short cut through higher dimensions; they are like feature starships powered by hyperdrives. As with exotic matter, the laws of physics do not denounce hyperspace, but the fact that we have no idea how to reach a higher dimension does not bode well for the idea of a hyperdrive.
across two-dimensional space by folding it and bridges across the space around the sheet of hopping across the third dimension. Now add paper described above. another dimension to the drawing at the 2D sheet becomes a 3D cube and the air you jumped across becomes….well no one has any idea, but it’s presumably that damn hyperspace
Space Folding “Jump” Drives: Found in again. newer works such as the re-imagined Battlestar Galactica, space folding jump drives (or jump drives for short) function very differently from warp engines or hyperdrives. They allow a starship to disappear from one location and appear near-instantaneously in another, much more distant location. This could get complicated, so I’ll explain the basics: Suppose space-time is a flat sheet of paper and your starship is a neat little drawing at one corner. You want to reach a destination at the far corner of the sheet. You could fly straight across, or you could be rather clever and fold the sheet of paper so that the two opposite corners are right next to each other. Then you
Travelling through a wormhole is just like travelling through space so relativity can still be present. Several stories allow wormholes to connect different points in time as well as points in space, allowing for some interesting
Jump drives are very distinct from other FTL “apparent” FTL. One instance involved massive engines. For one, they function in a series of sleeper ships flying out to wormholes over “hops” rather than a continuous flight. Second, many centuries, travelling through a wormhole many universes contend that jump drives can’t to the past then continuing the journey. The ship be used for FTL communication except via still takes hundreds or thousands of years to courier. This allows for lots of dramatic arrive, but from the observer’s viewpoint it only potential which writers just love.
takes a few weeks.
Wormholes and Stargates : Finally we Finally, we have perhaps the ultimate in come to wormholes as a means of travel. These wormhole travel; the eponymous Stargates. tend to crop up in “harder” SF universes; to Large superconducting rings that connect to allow FTL travel while keeping technology each other via artificial, stable wormholes, they plausible. Normally there is a pre-existing allow interstellar and intergalactic travel in a network of wormholes, either naturally matter of seconds. If enough power is available occurring (very conveniently) or left behind by it can take you billions of light years across the universe. Stargates represent an interesting type of FTL; it’s only useable on personal scales. It can carry people, small vehicles and cargo but it totally useless for starships. This is of course highly convenient for an SF series since it can focus on small groups of characters. This is naturally something the Stargate’s builders did intentionally. BY PHIL WALLACE
Artist’s impression of a stargate
COSMOLOGICAL NEWS
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The Night Sky in January The winter constellations are at their best in January with Orion dominating the southern horizon and Auriga and Perseus at the zenith and the winter Milky Way arcing from NW to SE, peppered with star clusters and nebulae.
Moon In January On the early evening of the 21st a gibbous Moon will accompany Jupiter in the west. They will be within 2 degrees of each other.
First quarter: 18th January Full: 27th January Last Quarter: 5th January New: 11th January
Planets in January Mercury: is in conjunction with the Sun this month and is not well placed for observation apart from a few days early in January in the dawn sky.
Jupiter: visible for most of the night as a brilliant magnitude -2.3 object in Taurus located just above the northern part of the Hyades. The Galilean satellites provide an ever changing prospect and the belts and zones are wonderfully displayed.
Uranus: Is an evening object in Pisces shining at a dim magnitude 5.8 and is low in the southwest heading for conjunction with the Sun in March.
Venus: Is low in the predawn sky in the constellation of Sagittarius and rises just before the Saturn: Is a morning object in the constellation Sun. Its magnitude is a bright -3.9 of Libra shining at magnitude 0.8. The rings are opening up and the planet makes a lovely sight Mars: Is low in the southwest setting just after in a small scope. the sun and is not well placed for good observation this month as it sets at 6:30pm and shines at a dim magnitude 1.6.
Neptune: is a faint object in Aquarius shining at magnitude 7.9 but is not well placed in the south western sky after sunset.
Constellation of the month: The constellation of Gemini, "The Twins" is one that abounds in legends of its origin. The names of the twins are Castor and Pollux, who are thought to be sons of Zeus by Leda, wife of the king of Sparta. The Romans also claim them to be guardsmen of the eternal city, and they have been identified in ancient manuscripts with Romulus and Remus, the founders of Rome. The constellation is also identified with sailors as the twins went with Jason on his famous quest in the Argo; the twins brought the sailors good luck by intervening with the elements whenever the weather was set against them thanks to their heavenly connections. They have since became know to seamen as the Laedean lights, now corrupted to “leading lights” – a reference to their knack of allowing safe passage if followed, as Horace in his work Odes testifies: “So Leda’s twins, bright-shining at their beck, Oft have delivered stricken barks from wreck”. The power to help sailors has since been immortalised, sailors remarking on the presence of the twins in an electrical phenomenon known as St Elmo’s fire.
The sky in January The sky as it would appear at 22:00 on the 1st
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The constellation of Gemini is seen by the Celts not as twins but as two men battling over the love of a woman. They are Gwyn and Gwyrthur, the sons of Greidawl who want the hand of the lady in red, Creudyladd. Ladies in red are perceived as of dubious repute, but to the ancients, red was the colour of a bride, an outward expression of her virginity. This story has become synonymous with Sir Gawain and the Green Knight in Arthurian legend and is referred to in the folk song, green grow the rushes oh. In Celtic traditions, Gwyn and Gwyrthur are known as the “Rivals of May” and are interpreted as being the light and dark halves of the year battling it out as they set at midnight on May 1st, the Celtic feast of Beltane, the start of the summer season and hence important agriculturally for the growth and harvest of crops.
flashes of light sparkle like diamonds against the backdrop of night as stars come into view. The cluster is situated at a distance of 2200 light years, and contains upwards of 150 stars or more, most of which are blue or white giants to be visible over such a vast distance with such brilliance. M35 is one of the showpieces of the Winter sky, a cluster that will delight you over many years of observing. If you look closely at the surrounding field of M35, you will notice a faint patch of stardust to the southwest. This is the galactic cluster NGC 2158. This luminous gauze of light lies at least twice the distance of M35, which is a great pity; if it were as close, then it would overshadow its famous neighbour. NGC 2158 seems to be an intermediate type of cluster, midway between a Globular and a Galactic cluster. It is extremely compressed and rich, containing over 500 suns in a very small area of space, shining with a comGemini is unmistakeable; the twin rows of stars bined magnitude of 9.2. It is not easy to resolve ending in opposite "turns" at the feet of the with a small telescope, but it should be easily constellation are obvious beacons on a Winter’s visible nevertheless. night. In addition, the two stars named Castor and Pollux are of similar brightness yet are of different colours. Castor is a brilliant white, Not far from this group of clusters, along the whilst Pollux has a golden hue. Despite the fact foot of the northern twin, is an object that will that Bayer assigned Castor the appellation not be visible to amateurs, but may well show Alpha Geminorum, it is in fact Pollux that is the up in a photographic exposure of the area. This brighter of the pair, although this is not readily is the nebulae I.C. 443, a crescent shaped gaseous mass of diffuse light. This object is the apparent without close scrutiny. remains of a star that exploded as a supernova over 50,000 years ago. Astronomers are bafCastor is a binary star, in fact is one of the fled and delighted by its shape, it's as if the greatest binaries known, as no less than five explosion was all one sided! Inequalities in the companions have been recorded both optically interstellar medium may be responsible for this and spectroscopically. Its most obvious com- appearance. In long exposure photographs, it panion is now quite close to its parent star, a shows up as a lovely orange - red wisp of light. very small separation of 1.9" makes it difficult to spot in a small telescope, but it has a magniOne of the most enigmatic objects in Gemini is tude of 2.8, making it surprisingly bright. the planetary nebulae NGC 2392 at RA 07h 29m Gemini lies along the Milky Way, and is there25s Dec 20°54m. This small planetary has been fore packed with objects of interest to the amanicknamed "The Eskimo Nebulae", as in large teur observer. Coloured stars, and doubles can telescopes the gaseous rings of matter surbe found in profusion throughout the group, and rounding the central star appear to look like a several star clusters are worth searching for. M57 The Ring Nebula fur lined hood, whilst condensations of gas in the centre of the nebulae outline a crude face. The most famous of these clusters is M35, The nebula is about 9th magnitude, but is easy close to the northern foot of the twins. Two to see lying about midway between kappa and beautiful red stars lead onto this cluster if you lambda Geminorum. In a small telescope with wish to look through binoculars, but the sight of low power it looks like an out of focus star, a this region of star drops is unsurpassed light blue in colour. Once located good seeing through a telescope. M35 is a very rich cluster, conditions and a high power may reveal some roughly the size of the full moon. Star chains of this startling detail. It is a very distant obradiate out of the compressed centre, and ject, apparently lying over 3000 light years
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away. Its high luminosity is doubtless due to the huge amount of ultra violet radiation causing the gas shell to fluoresce energetically. One object well worth watching as a long-term project is the star U Geminorum. This is a very faint (mag 14) red dwarf star, mostly beyond the reach of average amateur equipment. However, it belongs to a class of objects known as Cataclysmic Variables, and can brighten by up to 5 magnitudes in a short space of time. The field to explore and find this elusive object is slightly to the north of 85 Geminorum. This star will be difficult to spot, if you can see it at all, as it lies in a rich portion of the Milky Way. Yet, if you learn the star field well enough, despite not seeing U Geminorum, when it does put in an appearance you will see it straight away. Other objects of interest in Gemini include two small rich star clusters NGC 2266 and NGC 2420. Both clusters are faint and compressed, containing about 50 stars each. The magnitude ranges from 11 to 15th magnitude thus making them rather unremarkable objects for a small telescope. An extrasolar planet also resides in the constellation. The star HD 59686 has a planet sic times the mass of Jupiter in orbit at a distance of and orbit of 303 days. The coordinates are RA 07h 31m 48s, Dec17 05m 09s and the star shines at magnitude 6.5 making this an easy binocular object. The stellar spectrum is K2III so the star should show as slightly orange. For those observers who purely own binoculars, the Milky Way in this region is well worth scanning. The presence of millions of stars will show up as a faint blue white mottled background against which the bright gems of the Winter Milky Way will be displayed prominently. Lose yourself as you reflect upon the treasures of this ancient constellation. BY MARTIN GRIFFITHS
COSMOLOGICAL NEWS
At any one time, about 1000–1500 stars can be seen in the sky (above the horizon). Under ideal conditions, the number of stars visible to the naked eye can be as high as 3000 on a hemisphere, or 6000 altogether. Some stars seem to form figures vaguely resembling something; they have been ascribed to various mythological creatures and other animals. This grouping of stars into constellations is a product of human imagination without any physical basis. Different cultures have different constellations, depending on their mythology, history and environment. The constellation system that we are using today originates from the figures recognized by the Greeks and Romans. The oldest writing mentioning the antique Greek constellations comes from the poet Aratus from Soli (around 315-245 BC). His poem, Phaenomena, written sometime around 275 BC, based on the e p o n ym ous b oo k of t h e G r e e k astronomer Eudoxus , describes the story of the night sky and identifies 47 constellations. The oldest stellar catalogue dates back from
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the 2nd century BC and is a part of the Greek geographer Ptolemeus’s book called Almagest. He records the position and the brightness of 1 000 stars, arranged in 48 constellations, based on Hipparchus’s catalogue. In the 10th century BC, an Arab astronomer, al Sufi, rewrote the Almagest in a new book, The Book of the Fixed Stars, which comprises the Arab names of most of the stars, names that are still being used today. The oldest stellar map was put together in 1515 by the German artist Albrecht Durer, but the best stellar atlas was Johann Bayer’s Uranometria, in 1903. This atlas is up until today one of the most beautiful examples of artistic cartography of the heavens. Perseus is a major winter constellation of the northern sky, lying in the Milky Way between Auriga and Cassiopeia, representing the mythical Greek hero who saved princess Andromeda from the jaws of a sea-monster. Perseus, son of Zeus and Danae, was fated to live a life full of adventure. Sent to kill Medusa the Gorgon and Cetus the sea-monster, he was aided in his mission by the goddess Athene who
gave him a bronze shield, by Hefaistos, whose gift was a sword made out of diamond and by Hermes, from whom he got a pair of magical shoes. He was able to stay alive through his confrontation with Medusa and win the fight by looking at her reflection on his shield. All the characters in the legend joined Perseus in the eternity of the night sky as constellations: Andromeda, Cassiopeia, Cetus, Cepheus, Pegasus. It is a very rewarding constellation for the observer, lying along the Milky Way as it does. The Perseus arm is the next spiral arm of the Galaxy after the Orion arm, moving away from its centre. At its closest it is about 5000 light years from the Sun and it contains the Crab Nebula and the Rosette Nebula. It extends in the sky from Cassiopeia to Gemini. It may best be traced from its 21 cm radio emissions from hydrogen and by the presence of young blue stars. Now let us examine this constellation in detail.
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In Perseus, the brightest star, Mirphak, is surrounded by a scattered cluster of bright stars covering six Moon diameters of sky. β Persei is Algol, a famous eclipsing binary star. ε, ζ and η Persei are all doubles with much fainter companions. Rho Persei is a semiregular variable, ranging from 3.3 to 4.0 in magnitude, with a period of roughly seven weeks. There are various open clusters that can be seen in Perseus, notably the double cluster, also known as the Sword Handle, designated NGC 869 and 884. M34 is another open cluster easily visible with binoculars, but far less rich and condensed than the Double Cluster. M76 is a planetary nebula known as the Little Dumbbell, the faintest object in Messier’s catalogue and hence a challenge for small telescopes. Perseus contains the California Nebula (NGC 1499), a large emission nebula that shows up well only on photographs. The year’s best meteor shower, the Perseids, radiates from the northern part of the constellation, near γ Persei, in August every year. Mirphak (Algenib) is the Alpha Persei star. It is a star of spectral type F5 and has a 1.79 visual magnitude. Its name, which is also spelled Mirfak, comes from the Arabic mirfaq, meaning ‘elbow’. Its alternative name, Algenib, comes from the Arabic al-janib, meaning ‘the side’. Algol is a prototype of the algol stars , a subtype of the eclipsing binary stars. However, it is known that Algol is somewhat atypical of its subtype. The first recorded observation of Algol was made by Geminiano Montonari. Algol’s variability was periodic and, gradually, the concept of an eclipsing companion became accepted and was finally confirmed in 1889 by Hermann Vogel. By this time, Algol was known to be a triple system.
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more quickly. In Algol the more evolved star is the less massive; this apparent anomaly gives rise to what is known as the ‘Algol paradox’. The cause seems to be mass transfer from B to A. The angular separation of Algol C has never exceeded 0.1’’, which explains why the star has never been seen by visual observers. The real nature of the Algol system is still far from clear. Even after 200 years of continuous observation it still evokes considerable interest from astronomers. The California Nebula (NGC 1499) is an emission nebula in the eastern part of the Constellation Perseus (RA 04h 0.7m DEC. 36º37’). The nebula is illuminated by the hot, young O-class star ξ Persei. Although visually faint, the nebula shows up well in long-exposure photographs taken on red-sensitive films. It takes its name from its resemblance, in outline, to the American state. The California Nebula covers an area of 160’x 40’, elongated roughly north–south. The Little Dumbbell is a planetary nebula in northern Perseus (RA 01h 42m.4 DEC 51º34’) composed of M76, NGC 650 and NGC 651. At magnitude +10.1, it is reckoned to be the most difficult to observe of the Messier objects. Like the Dumbell, M76 shows two principal conspicuous lobes of nebulosity, each of which has been given its own NGC designation. M76 has an apparent diameter of 65’’, and lies at a distance of 3400 light years. It is sometimes described as the Butterfly Nebula.
Mirphak and Algol you will find a small cluster of approximately 30 stars, NGC 1245, that is also worth exploring with only a pair of binoculars. Another couple of highlights in the Perseus constellation are the reflection nebula of NGC 1333, a location of star formation, belonging to the Pererseus molecular cloud, NGC 1260, a spiral galaxy that was home, on the 18th of September 2006, to the second brightest object in the observable universe, supernova SN 2006gy. This was an extremely energetic supernova, first observed by Robert Quimby and P. Mondol. Perseus also contains a giant molecular cloud, the Perseus molecular cloud that is part of the Orion Spur and is well known for its low-mass star formation. Unlike the Orion molecular cloud, it is almost invisible, and emits mostly in the infrared and the submillimeter, because of the dust heated by the newly formed stars. Several star clusters, relatively close to one another, can also be found where the arm of Perseus curves around to hold his shield. Two interesting ones are NGC 1528, a 7.5 magnitude cluster of 30 stars, and NGC 1545, containing around 20 stars; this is definitely an area that is worth the time and effort to find and explore.
The Perseus constellation provides many rewards for the observer, when the only sound in the cold winter night is the sound of his heart beating to the sound of the universe he was The twin clusters in Perseus are marking the born from. These beautiful starry condensations “Sword Handle” of the legendary hero. To the are a treat for the astronomer haunting for naked eye the only indication of their presence ‘celestial delights’. is an ill-defined misty patch, but a telescope reveals two rich star-clusters, a field ‘dripping with star dust and chains and patterns of all descriptions’. The two clusters are NGC 869 and
NGC 884, very remote, 7 500 and respectively 1 000 light years away. Considering their In 1906, the Russian astronomer Aristarkh luminosity, the stars of both star clusters are Belopolski (1854- 1934) confirmed the existence supergiants of O and B type, NGC 884 being the of Algol C. There are two companions, of owner of a most distinctive red giant. spectral types B8 and G, rotating about each other. The B8 star is a dwarf and the visible Another cluster in Perseus that merits attention component of the system; the fainter star is a is M34, approximately the size of the full Moon, sub-giant. In the current theories of stellar containing 50 stars of the 6th to the 10th evolution, stars advance in spectral type as they magnitude. This rich filed is easily visible in evolve, and the rate at which they do so is a binoculars. function of their initial masses. Thus, if two stars form together from interstellar material, Somewhere along a straight line between the more massive of the two should evolve
ANA GAVRILA
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COSMOLOGICAL NEWS
The New Fragrance By Albert Einstein.
Special Relativity- The new fragrance by Albert with reference to the 'Ether'. However, in 1887 1. The laws of nature are the same in all inertial Einstein, well actually its quite an old fragrance the Michelson-Morley experiment discovered frames of reference which has been making space and time smell that there was no 'Ether'. This meant that light good since 1905; when it first hit the shelves of must be invariant. science. This complicated concoction
2. The speed of light in a vacuum is the same in all inertial frames of reference.
In 1889 George F. Fitzgerald tried to account for
In order to show how postulate 2 works we can however, can make the user contract in the null result of the Michelson-Morley perform a thought experiment. Let’s imagine a length, increase in mass (women experiment by saying that an object moving beware!) and experience strange time train traveling a velocity V where V is very close effects. So how is this possible I hear you ask? through the 'Ether' was physically contracted in to the speed of light C. Now imagine in one of the
Well quite simply if we use Einstein’s logic. First we need to go back in time to an era when the world of science conducted experiments under the Newtonian laws of physics and in particular under a principle known as Galilean relativity.
length. Fitzgerald described how objects would physically contract when moving through the ‘Ether’. This was an ad hoc suggestion though
coaches a passenger switches on a light. What happens to this light and what does the passenger see?
as there is no reason why objects would just contract. The only solution then was to include light as an A
invariant in Galilean transformation which is
B
Galilean Relativity states that Newton’s laws are what Hendrik Lorentz did in later years. He invariant under Galilean transformation. demonstrated that the speed of light was
To the passenger light travels at C and hits wall Under Galilean relativity the speed of light was invariant in a new transformation (which had A/B at exactly the same time. By the second considered a variant; it was believed to move been used by Fitzgerald) which took time into postulate the onlooker must also see light travel account. at C even if the light is from a moving Invariant: Means the same under all circumstance Galilean transformation: This is the link between one inertial frame and another inertial frame. frame Inertial frame of reference: An inertial frame of reference is any frame in which a free particle executes uniform motion (constant velocity, no acceleration)
bulb. However, what the onlooker will observe is (1.0) the light hitting wall A before it hits wall B. Where Lc is the contracted length and Lo is the original length. It was this idea that Einstein expanded in 1905. Einstein stated two postulates about his new theory:
A
B
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What the two observers describe is the light Therefore the equation which relates both delay effect. The value of C does not change but persons is:
How to calculate d using trigonometry.
somehow time t does. This is time dilation. This can be explained using a little bit of maths and a
(1.6)
slightly new scenario on the train. So now the passenger has a light bulb which he (1.7) or she flicks on then off really quickly, creating a flash of light. The event for light hitting a mirror on the ceiling and reflecting back down where tb > ta to the floor of the train can be expressed for passenger and the onlooker in the following way. As we dealing with speeds less than c the time taken for the light to hit the mirror and reflect back towards the floor will always be greater for an observer moving with respect to the train.
The time for passenger ta=
(1.1)
The time for onlooker tb =
(1.2)
The contraction of mass and velocity however are a little more complicated to explain, so you will just have to trust me when I say that if women could travel at C they would appear to look super super skinny, but they would also be very massive!� —something to explore for next A thought experiment can also be performed for time. the observed displacement of the train between two points for the passenger and the onlooker which is expressed as follows: If the onlooker and the passenger were to swap positions and carry out the experiment again both would obtain the same results for each of the frames they were in. This concept in called the principle of reciprocity.
(1.8)
Equations 1.1 and 1.2 is just s=d/t re-arranged. Where
and
Vtb is the displacement (x) of the train. (1.3)
The proper length measured will always be the length which is measured in its own rest frame. The proper length will always be the longer of the two measured distances as you cannot create length; it must already exist and appear shorter. There can only be a contraction in length along the direction relative to motion as (1.4) this is the only component which has any effect (1.5) upon the Lorentz transformation.
In order to get one equation which relates the time of the event to both the passenger and the onlooker, equations (1.1) and (1.2) must be expressed in terms of h and d and substituted into (1.3).
d
,
The passenger will measure the distance between two points to be shorter than the distance measured by the onlooker. CHLOE PARTRIDGE
An intelligent man is sometimes forced to be drunk to spend time with his fools. - Ernest Hemingway
BSc (Hons) Observational Astronomy