Announcements Reading Chapter 22 Observations Prepare target list

Announcements Reading: Chapter 22 Observations: Prepare target list for third session! April 10 – 12 Midterm: Check for errors; if not satisfied with where you stand – do something now! Lyrid Meteor viewing April 21 4/6/11 1

The Theory of Relativity To appreciate and understand modern astronomy we’ll need some ideas from modern physics We’ve met quantum mechanics now it’s time for relativity Focus on ideas, use equations when they help Today: Special Relativity. Can be done. 4/6/11 2

The Principle of Relativity The laws of Physics are the same for two observers moving at constant velocity relative to each other Newton’s second law F = ma a is the same for the two observers Physical observations can’t determine “absolute motion” – it is meaningless. Motion is relative. 4/6/11 3

Gedankenexperiments You can look at same situation from two inertial reference frames. Details differ but physics is the same 1. You see Jackie move at 90 mph. Jackie sees you move at 90 mph 2. You see ball move at 100 mph catch up to Jackie sees ball move 10 mph while you move 90 mph away V = v 1 + v 2 4/6/11 4

Same, with light You see Jackie move 0. 9 c. Jackie sees you move 0. 9 c 4. You see light move at c catch up to Jackie sees light move at c Nothing can move faster than light! No matter how fast you move, light will catch up at c. 3. 4/6/11 5

Space and Time Ball on moving train goes farther, moves faster as seen from outside than from inside 6. Same with light but speed the same so time dilates Time in a frame moving relative to you moves slower. NB Your time seems slower to them! 5. 4/6/11 6

Simultaneity 7. 4/6/11 Jackie’s ship lights flash simultaneously as she passes you (ie you see simultaneous flashes). But green flash reaches Jackie first because she is moving. In Jackie’s reference frame, green light flashed first Simultaneity at a distance is relative 7

Length 8. Jackie measures length of your ship by measuring time she takes to pass it. Since her time is slow she’ll pass it in shorter time so think it is Lorentz contracted Objects moving relative to you are contracted in direction of motion 4/6/11 8

Mass and Energy 9. 4/6/11 As Jackie passes you, you push her. You give her twin, at rest near you, an identical push. But Jackie feels it for a shorter time so accelerates less. You think her mass is greater Moving objects appear to have greater mass than when at rest 9

Spacetime We live in a threedimensional space. A point can be represented by three numbers Looking at a 3 D object from different directions gives different 2 D images Different coordinate frames split East, North differently but agree on distance 4/6/11 10

Combining Space and Time 4/6/11 11

The point: Moving observers’ reference frames in spacetime are like coordinate frames. They split space and time differently Agree on invariant interval Disagree on simultaneity like coordinate frames disagree on equal latitude Length contraction is like perspective 4/6/11 foreshortening 12

Natural scale of axes is seconds and light-seconds Worldlines of stationary objects are vertical Worldlines of light beams are inclined 45 o Worldline of inertial observer is a straight line inclined less Future and past lightcones contain events that you can influence or can influence you Curved worldline means acceleration. Newton 1’: In absence of external forces worldline is straight 4/6/11 13

4/6/11 14

General Relativity So moving fast makes things weird but we understand it What if you accelerate? Acceleration is not relative, has physical effect of inertial forces We already mentioned key to answer in The Equivalence Principle. Acceleration is same as gravity A theory of relativity with acceleration will include gravity We can forget gravity if we say that standing still on Earth is really accelerating up 4/6/11 15

Gravity is Curvature So near a massive objects straight lines in spacetime are different from straight lines in deep space. What does that mean? Straight lines are weird in curved space In general relativity a massive object distorts spacetime near it Content of theory is an equation relating curvature to mass (energy) Note – we draw 2 D sheets inside 3 D space but should be 4 D spacetime that warps Strength of gravity is curvature 4/6/11 16

So what? 1. 2. 3. 4. 4/6/11 Where curvature weak Einstein agrees with Newton as must be. First evidence found: Lightbeams are deflected Eddington (1919) Precession of Mercury’s perihelion (old) Gravitational redshift Gravitational waves Hulse and Taylor (1974) 17

Light Bent by Gravity 4/6/11 18

Gravitational time dilation You in front, Jackie in rear of accelerating ship set clocks flashing Acceleration makes you see Jackie’s flashes farther apart – her clock looks slow to you. Your clock looks fast to Jackie Equivalence Principle says downward lightbeam blueshifted, upward beam redshifted Measured by Pound (1960) 4/6/11 19

Binary Pulsar PSR 1913+16 is a millisecond pulsar with period 59 ms Period oscillates with oscillation period 7. 8 hr Hulse, Taylor (1974): pulsar in close binary with a neutron star Orbit found from Doppler shift and pulse delay 4/6/11 20

Since orbit so eccentric see gravitational redshift when stars near Also measure precession of orbit Finally, orbiting stars emit gravitational waves lose energy. Should be spiraling down, and are 4/6/11 21

4/6/11 22