# Duke Physics 55 Spring 2005 Lecture #31: Experimental Tests of General Relativity

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1 Duke Physics 55 Spring 2005 Lecture #31: Experimental Tests of General Relativity

2 ADMINISTRATIVE STUFF - Friday: Quiz 6, 15 minutes at beginning of class Material: BDSV Ch. 22,S2,S3 (focus on lecture WUN2K) Homeworks 11, 12 Astronomy Place tutorials for above (Dark Matter in Galaxies, Black Holes) - Partial solar eclipse on Friday, about 5:45 pm! I will arrange a viewing (if weather permits)

3 OUTLINE BDSV Chapter S3, Experimental Tests of General Relativity - precession of Mercury - bending of light; gravitational lensing - gravitational time shift and redshift - gravitational waves - More on Black Holes - Some Speculations - wormholes and warp drives

4 PRS Question Which of the following best describes the relation between Newton's theory of gravity and general relativity? a. General relativity applies at the subatomic level, but Newton's does not. b. Newton's theory and general relativity give the same answers, but the former tells us to think of gravity as a force, and the latter tells us think of it as curvature of spacetime. c. Newton's theory of gravity is an approximation to general relativity that works when gravity is relatively weak, but breaks down when gravity is strong. d. Newton's theory is now know to be false, and we were previously misled by measurement errors.

5 PRS Question Which of the following best describes the relation between Newton's theory of gravity and general relativity? a. General relativity applies at the subatomic level, but Newton's does not. b. Newton's theory and general relativity give the same answers, but the former tells us to think of gravity as a force, and the latter tells us think of it as curvature of spacetime. c. Newton's theory of gravity is an approximation to general relativity that works when gravity is relatively weak, but breaks down when gravity is strong. d. Newton's theory is now know to be false, and we were previously misled by measurement errors.

6 Review PRS Question According to general relativity, why does the Earth orbit the Sun? a. Earth is following the straightest path possible through spacetime, but this path happens to go around the Sun. b. Because a mysterious force that we call gravity holds the Earth in orbit. c. Because the Earth and Sun are connected by a 'rope-like' set of invisible, subatomic particles. d. Earth orbits the Sun because a spacetime diagram shows the Sun to be a bowl-shaped dip in a rubber sheet.

7 Review PRS Question According to general relativity, why does the Earth orbit the Sun? a. Earth is following the straightest path possible through spacetime, but this path happens to go around the Sun. b. Because a mysterious force that we call gravity holds the Earth in orbit. c. Because the Earth and Sun are connected by a 'rope-like' set of invisible, subatomic particles. d. Earth orbits the Sun because a spacetime diagram shows the Sun to be a bowl-shaped dip in a rubber sheet.

8 Basic Ideas of General Relativity An object floating freely has a worldline that follows the straightest possible path through spacetime. If you feel weight, then you are not on the straightest possible path What we feel as gravity arises from the curvature of spacetime. Mass causes spacetime to curve, and the curvature determines the paths of freely moving masses. 'Matter tells space how to curve; space tells matter how to move'

9 Spacetime and gravity movie /animations.html

10 Caveats for rubber sheet analogy - masses are really part of the universe, not on top of it - we can only see orbits in 2D; for instance orbits at the same radius can be in different planes - time part of spacetime not shown... for instance Earth never returns to the same point in spacetime NNevertheless, it's extremely helpful for visualization

11 What evidence do we have that these ideas are valid?

12 Precession of Mercury's orbit Newton's theory predicts that Mercury's orbit will precess, due to the influence of the other planets (one cycle per 20,000 yr) (exaggerated precession) Einstein's theory predicts a small discrepancy, because space is more curved near the Sun time runs slower at perihelion: this is measured (observed before Einstein!)

13 PRS Question Suppose Mercury's orbit were more elliptical than it is... the discrepancy with Newtonian gravity would be a. greater b. smaller c. the same d. impossible to tell

14 PRS Question Suppose Mercury's orbit were more elliptical than it is...the discrepancy with Newtonian gravity would be a. greater b. smaller c. the same d. impossible to tell Greater difference in perihelion and aphelion means greater difference in clock rate from gravitational time dilation

15 Another prediction of GR: gravity bends light Light always travels along the straightest possible path in spacetime Inertial reference frame equivalent to

16 When the light passes through the curved spacetime from a strong gravitational field, it follows a curved path The apparent position of a object may shift due to the curved path of light This is observed! First observation of this effect: Eddington observed the Hyades near the Sun during the eclipse of 1919

17 Multiple images of the same star are possible Gravitational lensing (strong lensing) Einstein cross Einstein ring

18 Another test: check gravitational time dilation with precise clocks Measurements with clocks on spacecraft: do clocks slow as the gravitational field increases, as predicted by GR? So far, no deviations from predictions found Primary Atomic Reference Clock in Space for International Space Station Gravity Probe A, 1976

19 Can use spectral lines as clocks: they correspond to specific frequencies of light GRAVITATIONAL REDSHIFT: time runs slow near a strong gravitational field, so lines emitted near large objects will be redshifted (not same as Doppler shift) This is observed, and results agree with GR predictions

20 Gravitational Waves Ripples in spacetime caused by a disturbance The waves carry energy; they compress and expand objects as they pass

21 Gravitational Wave animations rotating asymmetric object rapidly rotating pulsar black hole merger from galaxy collision

22 Gravitational waves have so far been observed only INDIRECTLY Hulse-Taylor binary pulsar, 1974 Energy lost to gravitational waves causes the orbits to decay... observed!

23 Ongoing search to observe gravitational waves directly LASER INTERFEROMETER Passing wave causes tiny displacements of masses ~km apart, as spacetime is stretched and squashed... this is detected by laser beam interference

24 LIGO: Laser Interferometer Gravitational Wave Observatory currently searching for gravitational waves (requires tremendously good noise reduction) Hanford, Washington Livingston, Louisiana Several similar projects around the world are also searching... none yet found, but prospects are good

25 Possible future project: LISA laser interferometer in space

26 Let's revisit black holes in the context of general relativity... We saw black holes as compressed stars: collapse as neutron degeneracy pressure can no longer counteract gravity Escape velocity 2 GM v e= r If r is really small, ve gets really big Inside the EVENT HORIZON nothing can ever get out, not even light! Schwarzschild radius 2 GM R s= 2 c

27 When objects compress, the curvature increases nearby them (no change outside) In our rubber sheet analogy, a black hole really is a 'hole in the universe'

28 Meaning of the event horizon in this picture: Light always takes the straightest possible path: inside the event horizon, the path is curved such that light can never exit Schwarzschild radius: radius the event horizon would have if spacetime were flat

29 PRS Question Suppose you drop a clock toward a black hole. As you look at the clock from a high orbit, what will you notice? a. The clock will fall faster and faster, reaching the speed of light as it crosses the event horizon. b. The clock will fall toward the black hole at a steady rate, so that you'll see it plunge through the event horizon within minutes. c. Time on the clock will run faster as it approaches the black hole, and light from the clock will be increasingly blueshifted. d. Time on the clock will run slower as it approaches the black hole, and light from the clock will be increasingly redshifted.

30 PRS Question Suppose you drop a clock toward a black hole. As you look at the clock from a high orbit, what will you notice? a. The clock will fall faster and faster, reaching the speed of light as it crosses the event horizon. b. The clock will fall toward the black hole at a steady rate, so that you'll see it plunge through the event horizon within minutes. c. Time on the clock will run faster as it approaches the black hole, and light from the clock will be increasingly blueshifted. d. Time on the clock will run slower as it approaches the black hole, and light from the clock will be increasingly redshifted.

31 Due to gravitational redshift/time dilation, time runs slower the closer you get to a black hole If your friend Jackie dives towards the black hole, you will see her clock come to a stop... it takes an infinite time for her to cross from your point of view! (she sees your time running fast!)

32 But in fact, Jackie may get squished before she crosses, due to the gravitational force pulling her feet harder than her head!

33 What's inside the black hole? An infinitely dense point? A SINGULARITY We do not know what happens there: information cannot get out! - GR predicts infinite curvature - Quantum physics predicts fluctuations Is information really lost from the universe? Stephen Hawking thought yes... now has changed his mind...

34 Some speculations: Take a short cut through spacetime with a WORMHOLE?? 3D analogy: it takes less time to travel through the Earth than across the 2D surface if you tunnel through

35 What if you could tunnel through hyperspace? You could travel at a speed effectively greater than c This would work if space is conveniently curved...

36 Or, might we curve space ourselves with WARP DRIVE? We have no evidence this would work... but it's also apparently not strictly prohibited But this allows travel in time, too Problem: violate causality? Well explored in science fiction...

37 WUN2K General relativity has so far passed all experimental tests Precession of Mercury Gravitational time dilation and redshift Bending of light; gravitational lensing

38 WUN2K GR is still under test! (Does it break down somewhere?) Gravitational Waves: ripples in spacetime caused by a disturbance GW observed indirectly from orbital decay of binary pulsars Current attempts to observe GW directly using giant laser interferometers

39 WUN2K Black holes revisited Region of infinite curvature? (singularity) Time slows to a stop at the event horizon; objects squeezed by tidal forces

40 WUN2K Speculative ideas (not known if they work, but not strictly forbidden) Wormhole: shortcut through hyperspace; travel at speeds effectively >c Warp drive: curving spacetime at will?

41 Minute Questionnaire Please take a minute to fill it out. I will answer try to answer all (well-posed) questions on the web as soon as I can Please use this to give me feedback

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