Einstein 101.» Surrey U3A Network Study Day» The Menuhin Hall, Stoke d Abernon» Friday June 16 th 2017» Dr Roger Luther - Sussex University

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1 Einstein 101» Surrey U3A Network Study Day» The Menuhin Hall, Stoke d Abernon» Friday June 16 th 2017» Dr Roger Luther - Sussex University

2 Acknowledgements Chris Mason GMU Natalia Kuznetsova Fermilab

3 Einstein The Man

4 March 14, 1879 Albert Einstein was born in Ulm, Germany

5 Einstein saw a wonder when he was four or five years old: a magnetic compass. The needle's northward swing, guided by an invisible force, impressed him. The compass convinced him that there had to be "something behind things, something deeply hidden." 1884

6 Einstein knew, from then on, that he wanted to teach math and Science at a University someday. The problem was, he wasn t a very good test-taker and could not get a job at a University because of it. Rumor has it that he had even failed a Math test, but some people question that because of the way grades were assigned back then. Albert as a Student

7 Einstein, age 17, enters ETH in Zurich in 1896

8 Wedding photograph of Albert Einstein and Mileva Marić, January 6, 1903

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10 Einstein s Annus Mirabilis, 1905

11 Einstein in 1905 Einstein uses the idea that light exists as tiny packets, or particles, that we now call photons. His work anchors the most shocking idea in twentieth century science: we live in a universe built out of tiny bits of energy and matter.

12 Photoelectric effect received March 18 and published June 9

13 Photoelectric effect 1. Increasing the frequency of the light increased the energy of the ejected electrons but not their number. 2. Increasing the intensity of the light increased the number of ejected electrons but not their energy.

14 Photoelectric effect Q1. Increasing the frequency of the light increased the energy of the ejected electrons but not their number. A. Increasing the frequency of the light increases the energy of each photon and so the ejected electrons would have more energy but the number of ejected electrons would not increase.

15 Photoelectric effect Q1. Increasing the intensity of the light increased the number of ejected electrons but not their energy. A. Increasing the intensity of the light increases the number of photons but does not change the energy of each individual one so more electrons are ejected with the same energy.

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17 Einstein Continued his Genius in Next, in April and May, Einstein publishes two papers. In one he invents a new method of counting and determining the size of the atoms or molecules in a given space. In the other he explains the phenomenon of Brownian motion. The net result is a proof that atoms actually exist - still an issue at that time. 1905

18 Brownian motion

19 Paper on Brownian motion received May 11 and published July 18 Here D is a constant called the coefficient of diffusion and t is the time.

20 the straight-line distance travelled from its starting point in one minute would be six thousandths of a millimetre or six times the width of the particle

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22 Einstein s Special Theory of Relativity Relative to who is watching, space and time are transformed near the speed of light: distances appear to stretch; and clocks tick more slowly.

23 Special Relativity received on June 30 and published September 26

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25 Einstein - more on Relativity in And of course, Einstein isn't finished. Later in 1905 comes the most famous relationship in physics: e=mc 2. The energy content of a body is equal to the mass of the body times the speed of light squared. At first, even Einstein does not understand the full implications of his formula. 1905

26 Energy and mass received September 27 and published November 21

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30 In 1907, Einstein begins to apply the laws of gravity to his Special Theory of Relativity. In 1911, he finally gets a job as a Professor of Physics at the German University. 1907

31 Einstein completes his General Theory of Relativity. Einstein challenged the way the world thought about gravity and Sir Isaac Newton himself - by describing gravity as the warping of space-time, not a force acting at a distance. 1915

32 1919 A solar eclipse proves Einstein right, and he becomes an overnight celebrity. An experiment had confirmed that light rays from the sun were deflected by the gravity of the sun in just the amount Einstein had predicted in his theory of gravity, General Relativity.

33 » Einstein and his wife/cousin Elsa, 1919

34 1921 Albert Einstein is awarded the Nobel Prize "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect"

35 Einstein and his wife, Elsa, escape Nazi Germany and set sail for the United States. 1933

36 Einstein- Podolsky-Rosen paradox spooky action at a distance" 1935

37 1935 Einstein-Rosen bridge worm-holes through spacetime

38 World War II begins. Einstein writes a now famous letter to President Franklin D. Roosevelt urging nuclear research and warning him of Germany s building of an atomic bomb. 1939

39 Albert Einstein dies of Heart Failure. This is a picture of his last blackboard. April 18, 1955

40 Special Relativity 40

41 What is relativity about? There are actually two kinds of relativity theories: special and general, both created by Einstein. Why do we need special relativity? Well, here at Fermilab, we accelerate particles to very nearly the speed of light, and the way things move at such high speeds is very different from what we are used to in everyday life. Special relativity allows us to describe what happens at very high energies Fundamentally, both special and general theories of relativity deal with the concepts of space and time March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 41

42 Aristotle's space and time z (x,y,z) There exists a Prime Mover, a privileged being in the state of Absolute Rest y The position of everything else is measured with three numbers (x, y, z) with respect to the Prime Mover, who sits at (0,0,0). x The time is measured by looking at the Prime Mover's clock This point of view prevailed for almost 2,000 years March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 42

43 Galileo's challenge Galileo Galilei Galileo argued that there is no such thing as "Absolute Rest". In his view: The mechanical laws of physics are the same for every observer moving with a constant speed along a straight line (this is called "inertial observer" for short). March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 43

44 Galileo's space and time z z' v (x,y,z) (x',y',z') Every inertial observer could declare themselves "the Prime Mover", and measure the position of everything with respect to their own set of (x, y, z) y y' The time is still measured by looking at the Prime Mover's clock! x x' March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 44

45 Galileo's transformations x z K vt z' K' y x' v y' A y y' We have two frames of reference, K and K', and K' is moving along axis y with some constant speed v. Something happened at point A. According to Galileo, there is no one special reference frame -- if we know where A happened in one frame, we are done! That's because: Galilean transformations: know what happened in one frame, can tell what happened in another March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 45

46 Newton's laws of mechanics Newton's laws of mechanics are in agreement with Galileo's relativity 1. A body, not acted upon by any force, stays at rest or remains in uniform motion, whichever it was doing to begin with 2. To get an object to change its velocity, we need a force Sir Isaac Newton Force = mass x acceleration (acceleration = change in velocity) March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 46

47 Common Sense Physics 60 mph 90 mph 30 mph v new = v old + v train 29 January 2005 Einstein: A Century of Relativity 47

48 The clouds start to gather For more than two centuries after its inception the Newtonian view of the world ruled supreme However, at the end of the 19th century problems started to appear The problematic issue can be reduced to these questions: What is light? How does it propagate? March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 48

49 Here comes Maxwell Maxwell brought together the knowledge of electricity and magnetism known in his day in a set of four elegant equations known as Maxwell's equations In the process, he introduced a new concept: electromagnetic waves, and found that they traveled at the speed of light Light is an electromagnetic phenomenon! James C. Maxwell March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 49

50 Electromagnetic waves electric field magnetic field March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 50

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52 Waves in general The waves we are all familiar with require something to propagate in Sound waves are compressions of air (water, etc.) Spring compressions in a slinky What about light? The most natural assumption would be that it requires a medium, too! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 52

53 Aether This mysterious medium for light was called aether What would its properties be? We see light from distant starts, so aether must permeate the whole universe Must be very tenuous, or else the friction would have stopped the Earth long ago Aether would be like a ghostly wind blowing through the Universe! Michelson and Morley attempted to detect aether by measuring the speed of light in two different directions: upwind and downwind with respect to aether. March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 53

54 Michelson-Morley experiment Michelson and Morley used a very sensitive interferometer to detect the difference in the speed of light depending on the direction in which it travels. NO such dependence was found! So NO aether? Or an error in the measurements? March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 54

55 Another problem Maxwell's equations introduce the speed of light, c But they don't say with respect to what this velocity is to be measured! So what can we conclude? That light must move at speed c in all reference frames? But this contradicts Newtonian mechanics! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 55

56 Common Sense Physics 60 mph 90 mph 30 mph v new = v old + v train 29 January 2005 Einstein: A Century of Relativity 56

57 Maybe that s fine? Suppose that addition of velocities does work for light, too. Then imagine the following experiment: v If the car is moving with speed v, and light from the rear of the car is moving with speed c, we should measure speed of light = v + c. Then if we know c (and we do from other experiments), we should derive v. Numerous experiments tried to measure the speed of Earth based on this general idea -- with NO results whatsoever!!! Speed of light seemed always to be the same! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 57

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59 What do we know so far? Newton's mechanics based on Galileo's relativity All laws of mechanics are the same in different inertial reference frames Maxwell's electrodynamics There is a fundamental constant of nature, the speed of light (c) that is always the same The fact that there is such a constant is inconsistent with Newton s mechanics! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 59

60 Einstein's choices Einstein was faced with the following choices: Maxwell's equations are wrong. The right ones would be consistent with Galileo's relativity That's unlikely. Maxwell's theory has been so well confirmed by numerous experiments! Galileo's relativity was wrong when applied to electromagnetic phenomena. There was a special reference frame for light. This was more likely, but it assumed light was like any other waves and required a medium for propagation. That medium was not found! There is a relativity principle for both mechanical and electromagnetic phenomena, but it's not Galileo's relativity. March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 60

61 Einstein's relativity postulates Albert Einstein March 2, 2002 It required the genius and the courage of Einstein to accept the third alternative. His special relativity is based on two postulates: All laws of nature are the same in all inertial frames This is really Galileo's relativity The speed of light is independent of the motion of its source This simple statement requires a truly radical re-thinking about the nature of space and time! Natalia Kuznetsova Saturday Morning Physics 61

62 Some consequences: time dilation The time dilation formula can be shown to result from the fundamental postulates by considering a light clock. Ticks every time a light pulse is reflected back to the lower mirror Stationary clock: tock! Moving clock: tock! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 62

63 Some Time Dilation Factors

64 2.7: Experimental Verification Time Dilation and Muon Decay Figure 2.18: The number of muons detected with speeds near 0.98c is much different (a) on top of a mountain than (b) at sea level, because of the muon s decay. The experimental result agrees with our time dilation equation. 64

65 Atomic Clock Measurement Figure 2.20: Two airplanes took off (at different times) from Washington, D.C., where the U.S. Naval Observatory is located. The airplanes traveled east and west around Earth as it rotated. Atomic clocks on the airplanes were compared with similar clocks kept at the observatory to show that the moving clocks in the airplanes ran slower. 65

66 Twin Paradox The Set-up Twins Mary and Frank at age 30 decide on two career paths: Mary decides to become an astronaut and to leave on a trip 8 lightyears (ly) from the Earth at a great speed and to return; Frank decides to reside on the Earth. The Problem Upon Mary s return, Frank, now 50, reasons that her clocks measuring her age must run slow. As such, she will return younger, aged 34. However, Mary claims that it is Frank who is moving and consequently his clocks must run slow, so she is 50 and he is 34. The Paradox Who is younger upon Mary s return? 66

67 The Resolution 1) Frank s clock is in an inertial system during the entire trip; however, Mary s clock is not. As long as Mary is traveling at constant speed away from Frank, both of them can argue that the other twin is aging less rapidly. 2) When Mary slows down to turn around, she leaves her original inertial system and eventually returns in a completely different inertial system. 3) Mary s claim is no longer valid, because she does not remain in the same inertial system. There is also no doubt as to who is in the inertial system. Frank feels no acceleration during Mary s entire trip, but Mary does. 67

68 Fitzgerald Length Contraction Just as relativity tells us that different observers will experience time differently, the same is also true of length. In fact, a stationary observer will observe a moving object shortened by a factor of Gamma which is the same as the time dilation factor. Thus, if L is the length of an object as seen by a stationary observer and Lo is the length in the moving frame then: L= Lo/Gamma March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 68

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70 Why length contraction? Suppose that a rocket moves from the Sun to the Earth at v=0.95c (Gam According to an observer from Earth, the trip takes 500s. By time dilation, only 500s/3.2=156s pass on the ship. The crew observes the Earth coming at them at 0.95c This means that the sun-earth distance according to the crew must be re March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 70

71 Lorentz transformations These are Lorentz transformations They show how space and time are related for two different inertial observers in special relativity They are reduced to Galilean transformations when v << c Maxwell's equations are invariant under these transformations March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 71

72 Weird Physics v light v light 30 mph v new = v old + v train v new = v old + v train v old v train /v light 29 January 2005 Einstein: A Century of Relativity 72

73 Mass is not preserved anymore! It can be shown from first principles (conservation of energy and momentum) and relativity postulates that mass becomes dependent on velocity at large speeds: m 0 = rest mass faster means heavier! If velocity v is very small comparing to c, then this formula becomes kinetic energy Such considerations led Einstein to say that mass of an object is equal to the total energy content divided by c 2 March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 73

74 The world s most famous equation The equivalence of energy and mass has been confirmed by numerous experiments -- in fact, we at Fermilab test it every day! m 0 m 0 An electron and an anti-electron (positron) of mass m 0 collide and annihilate, and two photons, each with energy = m 0 c 2, come out! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 74

75 The world s most famous equation One consequence of this formula (and of the others) is that nothing can travel at the speed of light, since that would give it infinite mass. In fact, from the other equations, time would stop, and distances would become zero, at the speed of light. Hence, c is a natural speed limit in the universe March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 75

76 Traveling faster that light: a catch! Notice, however, that special relativity only precludes things from traveling faster than light in vacuum. In media (e.g., water or quartz) particles can travel faster than light can in that medium. This results in the so-called Cherenkov radiation, which is a very beautiful phenomenon widely used by physicists BaBar experiment's DIRC: Detector of InternallyReflected Cherenkov Radiation March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 76

77 Tachyons Special Relativity says that you need infinite energy to reach the speed of light (unless you have zero rest mass) However, going faster than light requires less energy - but an imaginary rest mass! Time slows down to zero at the speed of light- going faster would make time go backwards. This gives plenty of scope for time travel! March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 77

78 Experimental verifications of special relativity Special relativity has been around for almost 100 years, and has brilliantly passed numerous experimental tests Special relativity is a "good" theory in the sense that it makes definite predictions that experimentalists are able to verify. Things like time dilation, length contraction, equivalence of mass and energy are no longer exotic words -- they are simple tools that particle physicists use in their calculations every day. Our Tevatron couldn't function a day if we didn't take into account special relativity! One should remember that special relativity was not something that Einstein just came up with out of the blue -- it was based on existing experimental results. March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 78

79 Is there anything left of Newton s laws, then? Einstein himself felt obliged to apologize to Newton for replacing Newton s system with his own. He wrote in his Autobiographical notes: Newton, forgive me. You found the only way which, in your age, was just about possible for a man of highest thought and creative power. However, special relativity does not make Newton s mechanics obsolete. In our slow-moving (comparing to the speed of light) world, Newton s mechanics is a perfect approximation to work with. March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 79

80 Conclusions Special relativity revolutionized our understanding of space and time There is no "space" and "time" by themselves -- there is only four-dimensional space-time! It describes the motion of particles close to the speed of light No massive particles can ever exceed the speed of light Massless particles move at the speed of light Special relativity has been extremely well-tested by experiment. At everyday speeds, Newton's mechanics is a good approximation to work with. General relativity is an extension of special relativity to the effects of gravity Reconciling gravity with quantum mechanics is one of the major goals and dreams of modern theoretical physicists March 2, 2002 Natalia Kuznetsova Saturday Morning Physics 80

81 Paradoxes in Special Relativity Pole Vaulter Twin Paradox

82 Pole Vaulter & Barn 15 ft 10 ft

83 Pole Vaulter & Barn v 7.5 ft 10 ft

84 Pole Vaulter & Barn v 15 ft 5 ft

85 Front door opens Pole Vaulter Paradox Barn View

86 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn

87 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn

88 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes

89 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn

90 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens

91 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn

92 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn Back end of pole leaves barn

93 Pole Vaulter Paradox Barn View Front door opens Forward end of pole enters barn Back end of pole enters barn Front door closes Pole entirely inside barn Back door opens Front end of pole leaves barn Back end of pole leaves barn

94 Front doors opens Pole Vaulter Paradox Pole Vaulter View

95 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn

96 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens

97 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn

98 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously

99 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn

100 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes

101 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes Back end of pole leaves barn

102 Pole Vaulter Paradox Pole Vaulter View Front doors opens Forward end of pole enters barn Back door opens Front end of pole leaves barn Both ends of pole never in barn simultaneously Back end of pole enters barn Front door closes Back end of pole leaves barn

103 Pole Vaulter Paradox Resolution Use Lorentz transformation, carefully Careful analysis of the events of front door opening and back door closing shows that there is no paradox Lorentz transformation correctly predicts both views correctly from both the barn and pole vaulter frames. Both observers are correct, but they have different views of what simultaneous means.