RELATIVITY. The End of Physics? A. Special Relativity. 3. Einstein. 2. Michelson-Morley Experiment 5

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1 1 The End of Physics? RELATIVITY Updated 01Aug30 Dr. Bill Pezzaglia The following statement made by a Nobel prize winning physicist: The most important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplemented in consequence of new discoveries is exceedingly remote. Albert Abraham Michelson 1903 (before relativity and quantum mechanics were invented) A. Special Relativity 1. Galilean Relativity. Michelson Morley experiment 3. Einstein s postulates 3 1. Galileo s relativity 4 Motion is relative (Galileo) there is no experiment one can do to determine absolute motion relative to space. Velocity Addition Formula: Laws of physics must hold in all reference frames which differ only by a constant velocity. Michelson-Morley Experiment 5 It was thought that light needed a medium in which to propagate, called the Luminferous Æther, and that the speed of light was relative to the Æther. Hence if the earth is moving relative to the Æther, the speed of light would appear different (i.e. obeys the Galilean velocity addition formula). Michelson-Morley experiment (1881, 1887) instead showed speed of light was unchanged by motion of earth, and there was NO Æther. 3. Einstein 6 Einstein Questioned: If you were moving at the speed of light, could you see yourself in a mirror held out in front of you? He concludes: Speed of light is the same for all observers How is this possible? Nature conspires to distort space and time 1

2 3b Einstein s Relativity Einstein (6 years old) publishes theory of special relativity It has postulates: 1. Motion is relative (Galileo) there is no experiment one can do to determine absolute motion relative to space. 3c Relativistic Addition of Velocities 8 Speeds add: V= Adding anything to speed of light gives speed of light. The speed of light (in vacuum) is the same for ALL observers At face value, these two statements seem inconsistent. To make it work he has to propose some changes 3d. Time Dilation 9 (Einstein) A moving clock will appear to run slower t t v 1 c Paradoxically, two observers each moving with a clock, sees the OTHER clock running slowly Muon Decay Muons don t live long: half of any group decay after about a millionth of a second Frisch (one of my professors!) and Smith, 1963, on Mt. Washington in NH: measure rate of cosmic muons at the top and bottom of the mountain: Far more survive from top to bottom than lifetime should allow Traveling at close to c, the muon s internal clock : runs slowly compared to the physicist s clock its time is stretched out e Lorentz Contraction 1 GPS: Relativity and You 4 Global Positioning Satellites, each with an atomic clock Each always transmitting its precise clock time Position found by times and known satellite positions Times must be known to within 0 to 30 billionths of a second. Viewed from Earth: moving clocks run slowly, losing about 7 millionths of a seconds per day. General Relativity: clocks run slowly near a massive object. Farther from Earth, satellite clocks run faster, gaining about 45 millionths of a seconds a day. Without accounting for Relativity, GPS would not work! 1889 FitzGerald, 189 Lorentz Propose a moving meter stick will appear to shrink in length L = L [1-v /c ] 1/ 1905 Einstein deduces this from his postulates of relativity.

3 3f. Mass 13 (Einstein) A moving mass will appear more massive m0 m v 1 c Famous Equation: E=mc "It followed from the special theory of relativity that mass and energy are both are but different manifestations of the same thing a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal (to) m c squared, in which energy is put equal to mass, multiplied with the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 193, experimentally." 14 Making E=mc More Correct 15 Is Mass Equivalent to Energy? 16 pc m 0 c E Energy E in two forms: Rest mass m 0 Momentum p (Kinetic) Total energy is a Pythagorean sum: E m0c pc Photons have no rest mass energy, only momentum energy Consider a deuterium nucleus, composed of a proton and a neutron: M d = amu The proton and neutron have mass M p = amu M n = amu Something s funny! It Doesn t Add Up! 17 Mass IS Equivalent to Energy! 18 M p + M n : amu amu = amu That s MORE than the mass of the deuterium nucleus M d = amu! The proton and neutron are heavier separately than when they re together! amu amu =.0039 amu Energy equivalent to the mass difference is that energy required to bind the proton and neutron together. The equivalent energy is 0 times higher than that of x-rays used by your dentist 3

4 3g Where to find E = mc? 19 B. General Relativity 0 Our Sun, in which fusion reactions exchange the mass of Hydrogen for energy in the form of light and solar wind 1. Equivalence Principle. Bending of light The conversion of food mass into energy to make your body run The conversion of the mass of gasoline into energy to make your car run 3. Bending of space, black holes 1. Definition of Mass There are 3 ways to think about mass 1. Inertial Mass F=ma 1 1b. Galileo s Experiment at Pisa 1590 Galileo s Principle: All bodies fall at the same rate, regardless of mass. Passive Gravitational Mass F=mg 3. Active Gravitational Mass GM g r 1907 Weak EEP (Einstein Equivalence Principle) All bodies will follow same path, independent of internal structure (e.g. mass or composition) The Weak Equivalence principle says that inertial mass equals passive gravitational mass 1c. The Equivalence Principle Reference at rest with Gravity is indistinguishable to a reference frame which is accelerating upward in gravity free environment. 3 a. Bending of Starlight (Date?) Newton: Light is NOT affected by gravity Einstein: Elevator example shows light must be affected by gravity. Predicts starlight will be bent around sun! 1919 Measured by Eddington! 4 The apple accelerating downward due to gravity looks the same as an apple at rest in space, with the floor accelerating upward towards it. 4

5 b. Gravitational Redshift Time is distorted by gravity 1. Time runs slower in a gravity field (your feet are aging slower than your head). Photons leaving the sun lose energy pulling away and are redshifted GM rc 3. If the mass is big enough, the escape speed becomes the speed of light, which means light cannot escape, i.e. it is redshifted out of existence ( black hole ) 5 3a. Curved Space 6 Einstein argued that mass curves space, and gravity is simply particles following the curves of space 3b. Curvature and Black Holes 7 Einstein s General Theory of Relativity Gravity is curved space Big curvature makes a Black Hole that you can fall in and never get out 3c. Schwarzschild Radius If any mass is compressed into a size smaller than the Schwarzschild Radius, it will become a black hole This can happen during a supernova explosion, or later by additional mass falling on a neutron star. Anything that comes closer than the Schwarzschild Radius, will fall in and never escape. Or, light from a black hole is redshifted out of existance 8 For example, when people throw things into my tuba, they are never seen again. 1 GM 1 rc 1 3d. Observing Black Holes They are black, how do we see them? 9 3e. Jets Not all the material falls into Find one in a binary system. As mass falls into the black hole there will be some radiation released the hole. Some is ejected at very high energies out jets along the axis of the black hole. 30 5

6 3f. Galactic Jets Chandra X-Ray Telescope Sees jets coming out of galaxy M87, suggesting there is a BIG black hole at the center. 31 3g. Radio Lobes from galaxy Centaurus A 3 Again, suspect a big black hole in the center 6