Relativity. Astronomy 101

Transcription

1 Lecture 29: Special & General Relativity Astronomy 101

2 Common Sense & Relativity Common Sense is the collection of prejudices acquired by the age of 18. Albert Einstein It will seem difficult at first, but everything is difficult at first. Miyamoto Musashi

3 Newton s Universe In Newton s view: The universe keeps absolute time. Objects move through absolute space. Universe looks the same to all observers, regardless of how they move through it. Result was a set of laws formulated from the perspective of an absolute God s Eye View of the Universe.

4 Einstein s s Challenge 1905: Albert Einstein challenged Newton: We cannot take a God s eye view of the Universe. We can only compare our view with that of other observers. All information we have is carried by light. But, light moves at a finite speed. Result: Irreducible relativity of perspective.

5 Seeing the world All information about the Universe is carried by light. Speed of Light: c 300, km/sec Compared to everyday scales: 65 mph = km/sec = 9.3x10 8 c light travel time across this room ~30 nanosec Human Reflexes: ~0.1 sec (~10 8 nanosec)

6 1 st Postulate The laws of physics are the same for all uniformly moving observers. ( Uniformly (Uniformly = with a constant velocity ) ) Implications: No such thing as absolute rest. Any uniformly moving observer can consider themselves to be at rest.

7 2 nd Postulate The speed of light in a vacuum is the same for all observers, regardless of their motion. Implications: The speed of light is a Universal Constant. We cannot send or receive information faster than the speed of light. Experimentally verified in all cases.

8 Essential Relativity Two observers moving relative to each other experience the world differently: Both measure the same speed of light Both find the same physical laws relating distance, time, mass, etc. But, both measure different distances, times, masses,etc. etc. when applying those laws. The key is the role of light.

9 The Relativity of Time A Thought Experiment Consider a simple photon clock: Laser fires to a mirror 1.5m away Light bounces to a detector Photon Path Length = 3 meters One Tick = Time of Flight = 3 meters c = 10 seconds 1.5 meters Lase r Mirror Detector Tick!

10 Relativity with Dick & Jane Dick & Jane fly past each other in rockets: Constant Relative Speed = 0.8 c Jane is carrying a photon clock Each measures how long it takes between ticks of Jane s photon clock. What do they see?

11 Jane s clock as seen by Jane: Photon Path = 3 meters Tick!!

12 Jane s clock as seen by Dick: Photon Path = 5 meters 0.8c Tick!!

13 He Said, She Said... Jane s s Observations: Jane s Speed = 0 Dick s Speed = 0.8c 08c Photon Speed = c Path Length = 3 m Tick = 3 c = 10 s My Clock Runs OK Dick s s Observations: Jane s Speed = 0.8c Dick s Speed = 0 Photon Speed = c Path Length = 5 m Tick = 5 c=1.67x10 s YourClock runs slow

14 Relative Time This result is true for all kinds of clocks. Conclusion: There is no absolute time. Times passes at different rates for observers moving relative to each other. At speeds small compared to c, the difference is very small. Verified experimentally using atomic clocks on Verified experimentally using atomic clocks on airplanes and satellites.

15 Consequences of Relativity Observers moving relative to each other: Do not measure the same times. Disagreeon what events occur simultaneously. Do not measure the same lengths. Do not measure the same masses. Other Consequences: Mass and Energy are equivalent: E=mc 2 Massless particles must move at speed of light

16 Spacetime Newton s View: Space & Time are separate and absolute. Universe looks the same to all observers. Einstein s View: Space & Time are relative. United by light into Spacetime. Only spacetime has an absolute reality independent of the observer.

17 Light the Unifier Because all information is carried by light at a finite speed: All observers see the same physical laws. All observers measure the same speed of light. We must unify otherwise disparate ideas: Space & Time are unified into Spacetime. Matter & Energy are equivalent (E=mc 2 )

18 What about Gravity? Special Relativity is restricted to uniformly moving (unaccelerated) observers. But, objects are accelerated by gravity. (Newton: They feel a gravitational force. ) Einstein took 8 years to generalize relativity. Ldt Led to a completely ltl new theory of gravity.

19 Key Ideas: General Relativity: Modern Theory of Gravitation Matter tells spacetime how to curve. Curved spacetime tells matter how to move. Tests of General Relativity: Perihelion Precession of Mercury Bending of Starlight near the Sun The Binary Pulsar (Gravitational Waves)

20 Newtonian Gravity Matter tells gravitation how to exert a Force. A Force tells matter how to accelerate. A mass m is accelerated by another mass M: Force Acceleration GMm R 2 Force m GM R 2

21 Einstein s s Discontents Einstein had twoobjections: objections: The force law (line 1) implies instantaneous knowledge of the distance, R, but information is only transmitted at the speed of light The same mass, m, appears in both the force and The same mass, m, appears in both the force and acceleration laws (lines 1 & 2), but disappears from the final acceleration (line 3). This seems to be coincidental.

22 I frame no hypothesis. Newton could not explain physically what gravity was. He asserted that Gravity is an action at a distance. He had no hypothesis for what agent communicates the gravitational force across empty space.

23 The Principle of Equivalence The first postulate of Special Relativity states: The laws of physics are the same for all uniformly moving observers. In 1907, Einstein generalized this statement: The laws of physics are the same for any freely falling observer. There is no distinction between gravitational There is no distinction between gravitational and inertial accelerations.

24 General Relativity Gravitation binds matter to matter. But how does matter know that the other matter is out there? The Goal: Generalize Relativity Special Relativity used light to unify space & time into spacetime, but left matter separate. Need to unite matter & gravity with spacetime.

25 Enter Geometry Newton s laws lead to a geometric description of motion: Least Action Principle: An object moves between two points along the path that takes the least amount of time. Use geometry to describe the paths of objects moving through h space.

26 But, Einstein showed: Space & Time are not absolute but relative. Only spacetime is observer independent. Modified the Least Action Principle: An object moves along the shortest path between two points in spacetime. Need to describe the geometry of spacetime.

27 The Shortest Path... On a flat surface: The shortest path between two points is a straight line. Parallel lines stay parallel always. On a curved surface: The shortest path is a curved line. Lines that t start tparallel l can converge or diverge at some distance away.

28 Geometry the Unifier In empty space, spacetime is flat: The least paths are straight lines. Moving objectsfollow straight lines. Newton would have said: It moves in a straight line because it feels no external force to change its motion.

29 Curved Spacetime Matter curves the spacetime around it: The least paths are curved lines. More mass = Greater spacetime curvature. Closer = Greater spacetime curvature. A freely falling object follows a curved path. Newton would have said: It feels a force deflecting it from a straight line path.

30 A New Theory of Gravity General Relativity may be summarized as: Matter tells spacetime how to curve. Curved spacetime tells matter how to move. Replaces the Newtonian idea of a force with the curvature of spacetime. GR has so far withstood all experimental tests.

31 The Precessing Orbit of Mercury The major axis of Mercury s orbit precesses slowly by 574 arcseconds/century: Earlier Later

32 Einstein 1, Newton 0 Newtonian Gravity: predicts precession of 531 arcsec/century ~43 arcsec/century smaller than observed. General Relativity: Spacetime curvature changes as Mercury gets closer to the sun on its orbit. Gives the orbit a little twist. t This adds an extra 43 arcsec/century!!

33 Bending of Starlight Light travels on the shortest path through spacetime. Prediction: Gravity bends light passing a massive object. Confirmed: 1919 Solar Eclipse Gravitational Lenses (1980s)

34 Bending of Starlight (side view) Apparent Position Earth Sun True Position Scale is exaggerated

35 View from Earth 2 o Data from 1922 Eclipse 2 o 1 o 1 o 2 o Deflection (arcsec)

36 Gravitational Lens around a massive galaxy cluster

37 The Binary Pulsar 1975: Hulse & Taylor discover a binary pulsar GR Prediction: Accelerating masses emit Gravity Waves. Loss of energy from Gravity Waves should make the pulsars orbit closer. Confirmed precisely! Hulse & Taylor won the 1994 Nobel Prize.

38 What About Newton? Newton s laws are approximations of GR. Conditions: weak gravitational ti fields speeds much slower than the speed of light. Newton s Laws: Work accurately in the everyday world. Are mathematically much simpler.

39 Summary: Postulates of Special Relativity: The laws of physics are the same for all uniformly moving observers. The speed of light is the same for all observers. Consequences: Different observers measure different times, lengths, and masses. Only spacetime is observer independent.

40 Summary: General Relativity: Modern Theory of Gravitation Matter tells spacetime how to curve. Curved spacetime tells matter how to move. Tests of General Relativity: Perihelion Precession of Mercury Bending of Starlight near the Sun The Binary Pulsar (Gravitational Waves)