Special RelativityHow Fast Are You Moving Right Now?A world without etherSpeed of light is constant: so what?Simultaneity is relative, not absoluteOne person’s space is another’s timeThe Lorentz TransformationThe gamma factorWhat does  do?Why don’t we see relativity every day?Velocity AdditionClassic ParadoxesIf I’m in a car, traveling at the speed of light…What would I experience at light speed?E = mc2 as a consequence of relativityE = mc2, continuedExperimental ConfirmationReferencesUCSDPhysics 10Special RelativitySpecial RelativityEinstein messes with space and timeEinstein messes with space and timeSpring 2008 2UCSDPhysics 10How Fast Are You Moving Right Now?How Fast Are You Moving Right Now?•0 m/s 0 m/s relative torelative to your chair your chair•400 m/s 400 m/s relative torelative to earth center (rotation) earth center (rotation)•30,000 m/s 30,000 m/s relative torelative to the sun (orbit) the sun (orbit)•220,000 m/s 220,000 m/s relative torelative to the galaxy center (orbit) the galaxy center (orbit)•370,000 m/s 370,000 m/s relative torelative to the CMB cosmic wallpaper the CMB cosmic wallpaperRelative to What??Relative to What??•This is part of the gist of special relativityThis is part of the gist of special relativity–it’s the exploration of the physics of relative motion–only relative velocities matter: no absolute frame–very relevant comparative velocity is c = 300,000,000 m/sSpring 2008 3UCSDPhysics 10A world without etherA world without ether•For most of the 19th century, physicists thought that space For most of the 19th century, physicists thought that space was permeated by “was permeated by “luminiferous etherluminiferous ether””–this was thought to be necessary for light to propagate•Michelson and Morley performed an experiment to Michelson and Morley performed an experiment to measure earth’s velocity through this substancemeasure earth’s velocity through this substance–first result in 1887–Michelson was first American to win Nobel Prize in physics•Found that light waves Found that light waves don’tdon’t bunch up in direction of earth bunch up in direction of earth motionmotion–shocked the physics world: no ether!!–speed of light is not measured relative to fixed medium–unlike sound waves, water waves, etc.Spring 2008 4UCSDPhysics 10Speed of light is constant: so what?Speed of light is constant: so what?•Einstein pondered: what would be the Einstein pondered: what would be the consequences of a consequences of a constant speed of lightconstant speed of light–independent of state of motion (if at const. velocity)–any observer traveling at constant velocity will see light behave “normally,” and always at the same speed•Mathematical consequences are very clearMathematical consequences are very clear–forced to give up Newtonian view of space and time as completely separate concepts–provides rules to compute observable comparisons between observers with relative velocity•thus “relativity”: means relative state of motionSpring 2008 5UCSDPhysics 10Simultaneity is relative, not absoluteSimultaneity is relative, not absoluteObserver riding in spaceship atconstant velocity sees a flash oflight situated in the center of theship’s chamber hit both ends atthe same timeBut to a stationary observer (or anyobserver in relative motion), thecondition that light travels each wayat the same speed in their own framemeans that the events will not be simultaneous. In the case pictured,the stationary observer sees the flashhit the back of the ship before thefrontSpring 2008 6UCSDPhysics 10One person’s space is another’s timeOne person’s space is another’s time•If simultaneity is broken, no one can agree on a If simultaneity is broken, no one can agree on a universal universal timetime that suits all that suits all–the relative state of motion is important•Because the speed of light is constant (and finite) for all Because the speed of light is constant (and finite) for all observers, space and time are observers, space and time are unavoidablyunavoidably mixed mixed–we’ve seen an aspect of this in that looking into the distance is the same as looking back in time•Imagine a spaceship flying by with a strobe flashing once Imagine a spaceship flying by with a strobe flashing once per second (as timed by the occupant)per second (as timed by the occupant)–the occupant sees the strobe as stationary–you see flashes in different positions, and disagree on the timing between flashes: space and time are mixed•see description of light clock in text•Space and time mixing promotes unified view of Space and time mixing promotes unified view of spacetimespacetime–“events” are described by three spatial coordinates plus a timeSpring 2008 7UCSDPhysics 10The Lorentz TransformationThe Lorentz Transformation•There is a prescription for transforming between There is a prescription for transforming between observers in relative motionobservers in relative motionct’ = (ct  vx/c); x’ = (x  vt); y’ = y; z’ = z–“primed” coordinates belong to observer moving at speed v along the x direction (relative to unprimed)–note mixing of x and t into x’ and t’•time and space being nixed up–multiplying t by c to put on same footing as x•now it’s a distance, with units of meters–the  (gamma) factor is a function of velocity:Spring 2008 8UCSDPhysics 10The gamma factorThe gamma factor•Gamma (Gamma () is a measure of how whacked-out relativistic ) is a measure of how whacked-out relativistic you areyou are•When When vv = 0, = 0,  = 1.0 = 1.0–and things are normal•At At vv = 0.6 = 0.6cc, ,  = 1.25 = 1.25–a little whacky•At At vv = 0.8 = 0.8cc, ,  = 1.67 = 1.67–getting to be funky•As As vvcc, , Spring 2008 9UCSDPhysics 10What does What does  do? do? •Time dilationTime dilation: clocks on a moving platform appear to tick : clocks on a moving platform appear to tick slower by the factor slower by the factor –at 0.6c,  = 1.25, so moving clock seems to tick off 48 seconds per minute–standing on platform, you see the clocks on a fast-moving train tick slowly: people age more slowly, though to them, all is normal•Length contractionLength contraction: moving objects appear to be : moving objects appear to be “compressed” along the direction of travel by the