How Einstein s Theories of Relativity. Define Our Universe

Transcription

1 How Einstein s Theories of Relativity Dr. Mike MacCallum Long Beach City College mmaccallum@lbcc.edu Define Our Universe Public Lecture - March 1, 2013

2 A Word from Our Sponsors Astronomy at Long Beach City College

3 The Special Theory of Relativity

4 Speed of Light You are standing on the top of a train traveling 60 miles an hour. You throw a baseball toward the front of the train. The baseball leaves your hand at 40 miles per hour. To a stationary observer standing on the ground, How fast does the baseball travel?

5 Speed of Light You are standing on the top of a train traveling 60 miles an hour. You throw a baseball toward the front of the train. The baseball leaves your hand at 40 miles per hour. To a stationary observer standing on the ground How fast does the baseball travel? Answer: 100 miles per hour

6 Speed of Light You are standing on the top of a train traveling 60 miles an hour. You throw a baseball toward the back of the train. The baseball leaves your hand at 40 miles per hour. To a stationary observer standing on the ground, How fast does the baseball travel?

7 Speed of Light You are standing on the top of a train traveling 60 miles an hour. You throw a baseball toward the back of the train. The baseball leaves your hand at 40 miles per hour. To a stationary observer standing on the ground, How fast does the baseball travel? Answer: 20 miles per hour

8 James Clerk Maxwell Developed the four classical electromagnetic field equations (1860s) Explained all previous experiments: optics, electricity, and magnetism Showed that light and electric and magnetic fields travel as waves His equations implied that the speed of light must be a constant The second great unification of physics, after Newton

9 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your headlights. The light from the headlights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the headlights travel?

10 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your headlights. The light from the headlights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the headlights travel? Answer: 186,000 miles per second (the speed of light)

11 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your headlights. The light from the headlights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the headlights travel? Answer: 186,000 miles per second (the speed of light) The light becomes shifted (Doppler shift) To the red, if moving away from the observer To the blue, if moving toward the observer

12 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your taillights. The light from the taillights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the taillights travel?

13 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your taillights. The light from the taillights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the taillights travel? Answer: 186,000 miles per second (the speed of light)

14 Speed of Light You are in a spaceship traveling at 1,000 miles per second. You turn on your taillights. The light from the taillights travels at 186,000 miles per second. To a stationary observer out in space, How fast does the light from the taillights travel? Answer: 186,000 miles per second (the speed of light) The light becomes shifted (Doppler shift) To the red, if moving away from the observer To the blue, if moving toward the observer

15 Why is the Speed of Light Constant? Physicists became distracted trying to answer this question They reasoned that there must be a physical explanation If that reason could be discovered, perhaps we would discover the circumstances under which the speed of light could vary The consideration of this topic was further complicated by the concept of the luminiferous ether Physicists thought that there must be a substance through which light travels, similar to sound waves traveling in air

16 The Alternative... If light always moves at a constant speed, Then two observers can see the exact same thing, but interpret it differently And from different frames of reference Time cannot be constant Length cannot be constant Mass cannot be constant

17 Albert Einstein Most famous for his Special and General Theories of Relativity Published over 300 papers Won the Nobel Prize for his law of the photoelectric effect, which laid the foundation for the understanding of particles of light, called photons

18 1905: Annus Mirabilis (Miracle Year) Received his PhD in physics from the University of Zurich Published four ground-breaking papers on: Brownian motion Equivalence of mass and energy (E = mc2 ) Photoelectric effect Special relativity

19 Special Relativity Key postulates There is no absolute or preferred reference frame The laws of physics are the same no matter what reference frame is used What is observed in one frame of reference may be observed differently in another frame of reference Observations in each reference frame, even if different, are correct for that reference frame Within all reference frames, the speed of light is constant

20 The Right Place at the Right Time All components of special relativity were in place Einstein simply put them together in a single theory Had the vision and the guts to accept the consequences of a constant speed of light and work from there

21 Consequences If light always moves at a constant speed, two observers can see the exact same thing, but interpret it differently Time depends on the frame of reference Length depends on the frame of reference Mass depends on the frame of reference

22 The Lorentz Transformation! " =! 1!! 1-(v 2 /c 2 ) Speed of light: 186,000 miles/second 670,000,000 miles/hour

23 Time Dilation As a spaceship nears the speed of light, the clocks on board slow down to an observer outside the spaceship To the people inside the spaceship, the clocks appear to be moving just fine t = " t

24 Mass and the Speed of Light As a spaceship nears the speed of light, to an observer outside the spaceship, the mass increases and approaches infinity at the speed of light To the people inside the spaceship, the mass appears to be normal m = " m

25 Length Contraction As a spaceship nears the speed of light, to an observer outside the spaceship, the length gets smaller and approaches zero at the speed of light To the people inside the spaceship, the length appears to be normal x = x/"

26 The Twins Paradox One twin stays on Earth The other travels to the nearest star at near the speed of light When the traveling twin returns to Earth, that twin is younger (less time has passed) than the one who stayed home

27 The Speed of Light 186,282 miles per second 670,615,200 miles per hour 10% of the speed of light = 67,061,520 miles per hour 1% of the speed of light = 6,706,152 miles per hour 0.1% of the speed of light = 670,615 miles per hour 0.01% of the speed of light = 67,062 miles per hour 0.001% of the speed of light = 6,706 miles per hour % of the speed of light = 671 miles per hour (jet plane)

28 The Most Famous Equation! E = mc 2 A direct consequence of the special theory of relativity Derived from relativistic energy considerations Represents the kinetic energy of a particle at rest

29 The General Theory of Relativity

30 The General Theory of Relativity Space and time cannot be separated from each other The universe is made up of spacetime Gravity: A warping of spacetime To an observer, indistinguishable from acceleration

31 All on His Own Unlike the special theory of relativity, which was the culmination of work done by many other scientist, the general theory of relativity was conceived by Einstein alone

32 Implications The acceleration by an applied force and the acceleration of gravity are indistinguishable from each other By warping space-time, massive objects will cause light itself to bend around them To an outside observer time will slow down in a gravity well Gravitational time dilation A rotating, massive object affects the surrounding space-time, an effect called frame dragging A massive gravitational disturbance, such as the merger of two neutron stars or black holes, can produce gravity waves

33 First Confirmation Eddington s photograph of stars near the sun during a total eclipse May 29, 1919 Island of Principe, of the coast of West Africa Compared to photos taken previously Star positions had changed as Einstein s equations predicted

34 Subrahmanyan Chandrasekhar Applied Einstein s theory of relativity equations to the interior of stars Stars more massive than about 1.44 the mass of the Sun will become neutron stars at the end of their lives This became known as the Chandrasekhar limit Won the Nobel Prize for this work Chandrasekhar taught at the University of Chicago

35 The Chandrasekhar Limit

36 More Confirmations Mercury s orbit 43 discrepancy in precession Deflection of light by gravity Einstein rings Gravitational redshift Satellites--motion and time Pairs of accurate clocks Airplanes Jefferson Lab Tower, Harvard

37 Einstein Rings A massive foreground galaxy lenses and magnifies the light from a more distant, blue galaxy Can observe the distant galaxy Supports the predictions of general relativity

38 The Theories of Relativity

39 Relativity and Our Universe

40 Nothing Can Travel Faster Than Light Light defines the distance to the nearby stars Nearest star: Proxima Centauri light years away Fastest spacecraft to date: New Horizons (Pluto flyby in 2015) 36,373 miles per hour One light year = 6,000,000,000,000 miles Proxima Centauri: 25,000,000,000,000 miles from Earth At 36,000 miles per hour 79,000 years to get to Proxima Centauri

41 Nothing Can Travel Faster Than Light Communication with other civilizations--if they are out there The Milky Way 100,000 light years in diameter and 1,000 light years thick About 400 billion stars Perhaps tens of billions of earth-like, rocky planets How close would a civilization have to be for a meaningful dialog? 20 light years (40-year round trip) stars 50 light years (100-year round trip) - 1,875 stars 100 light years (200-year round trip) - 15,000 stars 500 light years (1,000-year round trip) - 1,875,000 stars

42 Communications Communication with other civilizations--if they are out there Targeted communication Tightly focussed beam of radio waves Precise aiming is problematic because of the great distances General communication (We are here!!) Prohibitive amount of energy Signal strength falls off according to the inverse square law

43 Communications Communications from Earth Pioneer 10 and 11 spacecraft Voyager 1 and 2 spacecraft--golden record

44 Communications Arecibo message - November 16, 1974 Transmitted toward globular cluster M13 25,000 light years away

45 Communications The SETI Institute - The search for extra-terrestrial intelligence Searching for intelligent signals from outer space SETI@Home - help process data on your own computer

46 The Search for Gravity Waves Laser Interferometer Gravitational Wave Observatory (LIGO) Searching for gravity waves caused by neutron stars and black hole mergers - help process data on your computer

47 Other Implications of Relativity Expansion of the universe Cosmological constant, the Greek letter lambda % Added to general relativity to create a stable, balanced universe But, Hubble found that the universe is expanding The cosmological constant was thought to be unnecessary because the universe is not stable--einstein called it his biggest blunder From recent observations of type Ia supernovae, lambda is now thought to represent the vacuum energy of empty space and is related to the expansion of the universe

48 Other Implications of Relativity The Einstein-Rosen bridge (wormhole) Mathematical solution to Einstein s general relativity equations No observational evidence of their existence May be only associated with black holes May allow travel in time as well as space May lead to other universes May only be one way The presence of a traveller may collapse the wormhole May require exotic matter (negative energy densities)

49 Questions or comments?

50 Thank you for coming tonight!

51 Credits

52 Image Credits 4-7: Smithsonian.com - Annual photo contest 8: Wikipedia commons : Swinburne University presentation 17: Wikipedia commons 22: Wikipedia commons 26: Time Travel Research Center

53 Graphic Credits 27: Wikipedia commons 30: Wikipedia commons 33: American Scientist 34: Wikipedia commons 35: Wikipedia commons 36: NASA/JPL Cassini Solstice Mission

54 Graphic Credits 37: Wikipedia commons 38: University of Alaska-Fairbanks 43: Wikipedia commons 43: NASA Voyager--golden record 44: Wikipedia commons 44: Arecibo Observatory

55 Graphic Credits 45: Allen Telescope Array, the SETI Institute 46: Wikipedia Commons 47: Discovering the Quantum Universe 48: Star Trek: Deep Space 9