Part VI 2 Mass Energy General Relativity Time

Part VI. 2 • Mass & Energy • General Relativity • Time Travel NSCI 122 Part VI 1

Mass Rest Mass (mo) Mass of object at rest. Relativistic Mass (m) Mass of object when it is moving. v m = g mo NSCI 122 Part VI 2

Energy Rest Energy (moc 2) Energy of object due to its rest mass. Total Energy (E) Energy of object due to its rest mass and its motion. E = g moc 2 = mc 2 v NSCI 122 Part VI 3

Mass and Energy Conversion Change speed of object. FORCE WORK Change mass of object. • The way the work splits depends on the current speed of the object. • As the object goes faster, more and more of the work goes into changing mass. NSCI 122 Part VI 4

Mass and Energy Conversion To increase an object’s speed from vi to vf requires work of DE = (gf - gi ) m 0 c 2 Example: How much work is required to get an electron to go from rest to 0. 90 c? How much additional work is required to get it to travel at 0. 99 c? v g 0 1 0. 90 c 2. 29 0. 99 c 7. 09 DE = 0. 66 Me. V DE = 2. 45 Me. V (moc 2 = 0. 511 Me. V for electron) How much additional work is required to get it to travel at c? v c g An infinite amount of energy is needed! Objects with rest masses cannot travel at c! NSCI 122 Part VI 5

Mass and Energy Conversion FORCE The change in speed (acceleration) of the object is given by The acceleration goes to zero! Objects with rest masses cannot travel at c! NSCI 122 Part VI 6

Photons Bundles of energy Only they can travel at c No rest mass No acceleration needed – they’re traveling at c upon creation NSCI 122 Part VI 7

General Relativity Equivalence Principle Gravity is equivalent to mass warping space & time. Example: • Sun curves space & time • Earth travels straight line but the path is curved because space is curved Gravity exerted by Earth NSCI 122 Part VI 8

General Relativity If gravity is really just mass warping space and time, then the path of light should be bent by this warping. NSCI 122 Part VI 9

General Relativity Guess what? It is! “Gravitational Lensing” NSCI 122 Part VI 10

General Relativity Hubble Telescope Image http: //homepage. mac. com/dtrapp/e. Physics. f/lab. II__11. html • Bright spots are galaxies in Abell 2218 cluster (~3 billion light-years away) • Faint stretched-out arcs are multiple images of more distant galaxies caused by the gravitational lensing of the cluster’s large mass NSCI 122 Part VI 11

General Relativity We have been saying that mass also warps time. We have performed experiments with atomic clocks that confirm this also. 0: 02 Clock at higher elevation runs faster. 0: 01 NSCI 122 Part VI 12

Time Travel To the Future? YES! How? • Time Dilation • Worm Holes? NSCI 122 Part VI 13

Time Travel To the Past? Have we seen evidence of it? Is it physically allowed? If it is allowed, how do you do it? • Worm Holes? NSCI 122 Part VI 14