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## Relativity

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**Of light and time…**• Light takes a certain amount of time to travel from an object/ event to us…. The further away something is, the greater that amount of time is • Sooo… We look at stars…. We see the past • Light year (ly) - distance that light travels in a year • If a star is 1000 ly away, what we are seeing the star do actually happened a 1000 years ago • Light from the sun takes 8 minutesto reach us. • Sun could explode right now, and we would have no idea for 8 minutes Speed of light (c) - 3.0 x 108 m/s Or about 180,000 miles/sec But what if we could travel on a beam of light….. ???**Theory of Special Relativity**• Einstein in 1905– 26 years old • Came up with this notion when pondering what it would be like to travel on a beam of light • Describes the motion of particles moving at close to the speed of light. • Gives the correct laws of motion for any particle • In moving through space we also change our rate of moving through time • Newton’s Laws good approximation….. Einstein’s Laws Always right**Space- Time**• Einstein states that space & time are inter-related and form what’s called space-time • Space-time exists in the universe, not the other way around • There would be no time if no universe • So the universe, and what you are doing in the universe affects your time • Time and Space are two parts of one whole known as “Space-time**Special Relativity**• 1st Postulate. The laws of physics are the same in any inertial (non-accelerated) frame of reference. This means that there is no experiment that can tell you if you are moving or not…. As long as you are not accelerating • 2nd Postulate. The speed of light is the same for all observers, no matter what their relative speeds. • Car example • Effects include Time Dilation and Length Contraction**Time Dilation**• When traveling at speeds very close to the speed of light • Fast clocks move slow • The faster your moving the slower time is going by for you relative to a stationary observer • Twin Paradox • One twin stay on Earth, other goes on trip at a speed close to the speed of light…. Twin comes back and twin on Earth is now much older than him • Travelling twin is effectively travelling forward through time Note- The travelling twin thinks his time is running normally… does not feel like his clock is “slow”**Planet of the Apes**http://www.youtube.com/watch?v=JdG5t7p8ji8**Why does time dilation happen?**• The speed of light is a constancy of nature, it is not only a finite speed, light waves play a special role in connecting space and time in ‘spacetime’ • As well as connecting mass and energy in the equation E=mc2 • Light clock example • If speed of light constant for all observers and different observers see a beam of light take 2 different paths (one longer than the other) then the speed can’t be different to account for the greater distance so the time must account for this. • Or imagine flying away from a clock at a super high speed. Each tick from that clock takes longer to get to you. In other words longer amount of time goes by for you between ticks than does a stationary person. • Video • Travelling near the speed of light alters (stretches out) the spacetime around the object**Only noticeable at high speeds….**• http://www.etsu.edu/physics/plntrm/relat/special.htm • A smarter powerpoint • equation describes time dilation Δt - dilated time interval (Earth’s clock) Δt’ - proper time interval (Spaceship’s clock) *Notice that if v is close to c then Δt is large *If v is small compared to c then Δt’ is approximately equal to Δt**Time dilation is not noticeable at all until we get to very**high speeds… • http://www.shellac.org/slu/slutime.html • Relativity calculator Graph shows that time dilation is only significant at very high speeds… speeds approaching the speed of light! Y axis – number of seconds past for stationary observer for every 1 second past for moving observer X –axis -- Fraction of speed of light traveller is moving at**Special relativity video**• http://www.youtube.com/watch?v=V7vpw4AH8QQ • http://www.youtube.com/watch?v=02tchltLm3c&feature=related • http://www.youtube.com/watch?v=YzMrNFd4oOk&safe=active**Proof of time dilation**• Experiments with atomic clocks and jet plane • In 1972. Very accurate clocks flown around world on commercial flights • Very small Time Dilation Noticeable on clocks • Amount of Dilation nearly exactly what was predicted by Einstein’s Equations • Video clip http://www.relativitycalculator.com/stationary_moving_clocks.shtml**A closer look at airplanes experiment…**• More complicated than it sounds • One flew East…. And LOST TIME…. Another flew west and GAINED time • See data here… http://hyperphysics.phy-astr.gsu.edu/HBASE/Relativ/airtim.html • Many things to consider • Gravitational time dilation • Kinematic time dilation • Neither perspective is an “inertial reference frame” • Spin of the Earth**More proof**• Particle Accelerator is used to accelerate small particles called ‘Muons’ at rest compared to decay of Muons moving at .995c. • Muons decay slower at relativistic speeds – meaning time slows down for them Decay of muons moving at a speed of 0.995c with respect to the observer**More Proof… Lifespan of supernovae**• Supernovae seem to have longer “lives” when moving away from us at relativistic speeds.**Other things….**• Sergei Avdeyev spent 747 days in space traveling around 17,000 mph relative to people on earth allowing him to time travel 1/50th of a second into the future. (Guiness World Book of Records 2006, pg 109) • Light does not experience time….. It travels through space w/out travelling through time • Light takes 1000 years (from our perspective) to travel to something 1000 light years away, but from its perspective it makes that same trip instantaneously. • Can we make a trip to a star 1000 light years away in less than 1000 years? • From our (the traveller’s) perspective, YES. From the Earth’s perspective, NO. • GPS Satellites & receivers have to take into account relativistic effects when calculating position, otherwise they would be extremely inaccurate**Length Contraction**• When travelling at speed close to the speed of light… • An object will shrink in length, according to a stationary observer • If a meterstick is travelling at .87 c, then it would appear to be only 50 cm in length. • If a meterstick is travelling at .995 c, then it would appear to be only 10 cm in length • What one observer see as time dilation, another sees as length contraction • http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/lec11.html**Illustration of length contraction**• Figure n shows an artist’s rendering of the length contraction for the collision of two gold nuclei at relativistic speeds in the RHIC accelerator in Long Island, New York, which went on line in 2000. The gold nuclei would appear nearly spherical (or just slightly lengthened like an American football) in frames moving along with them, but in the laboratory’s frame, they both appear drastically foreshortened as they approach the point of collision. The later pictures show the nuclei merging to form a hot soup, in which experimenters hope to observe a new form of matter.**Also Simultaneity can be disagreed upon**• Different observers can disagree on the simultaneity of events • http://www.scivee.tv/node/3025 • Above video.. Train example You and Jackie disagree on the simultaneity of the red and green light flashes**What would happen if you were travelling close to the speed**of light? • As you get closer to ‘c’ mass increases… as defined by E=mc2 • Therefore the amount of energy required to accelerate you becomes huge, at ‘c’ it would become infinity • Traveller moving at a speeds close to ‘c’ would be red-shifted if travelling away from stationary observer • Would be blue-shifted if travelling towards stationary observer • View in front of traveller would be pulled into small porthole, blue towards the center…. red towards the edges • http://www.youtube.com/watch?v=Uy7rrrCQh2w&feature=related Carl Sagan • Family Guy spoof of Carl Sagan http://www.youtube.com/watch?v=DI9ImScQGAo • http://www.youtube.com/watch?v=JQnHTKZBTI4 weird optical effects**General Relativity**• http://www.youtube.com/watch?v=0rocNtnD-yI**General Relativity**• Special Relativity was an incomplete, • only dealt w/ the ‘special’ case of constant motion • Einstein sought to create a theory of the universe that explained all types of motion and (ie the accelerated motion caused by gravity) • 1916 Theory of General Relativity • General Relativity explained acceleration’s and gravity’s role in his earlier notions of space-time • This combined w/ Special Relativity threw out Classical Mechanics (Newton stuff) and ushered in the era of “Modern Physics”**General Relativity**• Many consider to be the greatest scientific discovery OF ALL TIME • **Gravity and acceleration appear to be same phenomenon • Einstein’s Elevator • No difference between inertial effects in hypothetical accelerating elevator and the feeling of gravity • *In short, Gravity is not a force at all and is instead the curvature of space-time around a large mass • Curvature demonstrated • “spacetime tells matter how to move; matter tells spacetime how to curve” • This curvature has many consequences • Time dilation near large masses • Slower clocks when experiencing more gravity • Faster clocks when experiencing less gravity • Black Holes • Explanation of Big Bang and acceleration of an expanding universe**Uncurved Space-Time**Curved Space-Time • http://www.youtube.com/watch?v=DbhuRcmSkMg&feature=related**Confirmation of General Relativity**• Newton vs. Einstein Throwdown with the Sundown … May 29, 1919 • The Story • In order to confirm GR, scientist needed to prove this somehow… but how • They figured… if true, light should bend when travelling by a huge object… like for instance the sun. • So needed to observe stars that are behind the sun to see if their position was shifted from normal • Only time that you can see stars with sun in the sky is during a Total Solar Eclipse • After several failed attempts and measuring this another occurred 5/29/19**Amount of shift in the stars around that sun is represented**in Red The path of the famous eclipse through South America After this confirmation (over 3 years after GR was theorized) Einstein became an instant celebrity and world renowned scientist**After the eclipse**• Einstein instantly became a worldwide celebrity both in the science world and in pop culture • His redefinition of the universe was now complete • Sits as what many consider to be singly the greatest scientific discovery of all time**Einstein Videos**• History Channel**Other Proof of General Relativity**• Orbit of Mercury • Einstein’s Theory was able to accurately predict the orbit of Mercury whereas no previous notion of gravity was able to**Black Holes**• Consequence of General Relativity • So weird that Einstein himself doubted their existence, even though his theory predicted them • What they are? • Remnants of a collapsed star • Shrunk to such a small size, that its gravity became infinitely strong…. So strong its escape velocity is faster than the speed of light • One of the most interesting objects in the Universe • Nothing can escape a black hole • Creates an infinitely deep hole in Space-Time,**How a black hole forms**• Large star runs on nuclear fuel (fusion) • Star was previously held together by balance of outward pushing fusion and inward pulling gravity • Outward force gone, so gravity takes over • Star will go into a supernova on outside but inside pulls together • If star is big enough it will keep shrinking until black hole forms • Becomes infinitely dense w/ incredible amounts of gravity, escape speed is larger than speed of light**Parts of a black hole**• Event Horizon • “opening” of a black hole • Point of no return • Beyond this point not even light can escape • Singularity • “bottom” of a black hole • No one knows what happens at the singularity • Where all the ‘stuff’ is**Different things stars can turn into upon collapse…**• White dwarf • Star with an original mass of about 0.4 to 3.4 times the mass of our Sun will collapse to a white dwarf • If the mass of the star is less than about 1.2 solar masses after collapse, then will turn into a white dwarf • A ball of dead slag gradually cooling down as it radiates away its thermal energy • radius is on the order of 5000 km, and the density is about 1 ton per cubic centimeter. • Eventually become a black dwarf… universe is not old enough to have any black dwarfs in existence • Inside is thought to be one massive diamond…. Solid carbon • Neutron Star • Stars with an original mass of about 4 -20 solar masses will collapse to this • If mass of star left over after supernova is between 1.4 and three to four times as massive as our sun, it will become a dense neutron star (a neutron star is about 11 kilometers in diameter • Almost a black hole • Super dense • Teaspoonful weighs a billion tons • Black Hole • Stars an original mass of about 20 solar masses or greater will form into black holes • If star remnants after supernova has more than about 2.5 solar masses, gravity wins and the neutron star collapses into a black hole**Multiwavelength X-ray, infrared, and optical compilation**image of Kepler's Supernova Remnant, SN 1604. ( Chandra X-ray Observatory) This is a mosaic image, one of the largest ever taken by NASA's Hubble Space Telescope of the Crab Nebula, a six-light-year-wide expanding remnant of a star's supernova explosion. Japanese and Chinese astronomers recorded this violent event nearly 1,000 years ago in 1054, as did, almost certainly, Native Americans. Located at a distance of about 6,500 light-years (2 kpc) from Earth, the nebula has a diameter of 11 ly (3.4 pc) and is expanding at a rate of about 1,500 kilometers per second. At the centre of the nebula lies the Crab Pulsar, a rotating neutron star**Light bending around a black hole… animation**• “gravitational lensing”**Classifications of Black Holes**• Stellar-Mass Black Holes • “Regular” size black holes • Formed from death of star and haven’t grown to be significantly larger • Supermassive Black Holes • Believed to be at the center of every galaxy**Proof of black holes**• Stars orbiting very fast around “nothing” • Binary systems • Star and black hole in a dance together • Accretion disk around a black hole • Bursts of x-rays Paths of stars orbiting around an empty point in space, once orbital data calculated the only object that could be causing objects to move like this is a black hole. “empty” space objects are orbiting**An artists concept of a microquasar, like V404 Cygni. The**black hole is stealing gas from a companion star (left). The gas forms a thin, hot disk (accretion disk) around the black hole. When enough gas builds up there is a bright flare-up of X-rays, and jets of charged particles squirt away at close to the speed of light. [ESA] X-rays that can be detected**Videos**• http://fora.tv/2008/02/19/Neil_DeGrasse_Tyson_Death_by_Black_Hole#fullprogram • http://www.youtube.com/watch?v=D3AfNXdg2Tk • Morgan Freeman – Through the Wormhole**Swartzchild Radius**• The radius to which an object will need to shrink to in order to turn into a black hole • Anything can ‘technically’ get turned into a BH if made small enough • In actuality, only appropriately large enough stars will when they die • Found with equation • R = 2GM/c2