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- 1. Chapter 26 Relativity
- 2. Introduction <ul><li>Newtonian Mechanics has been found not to be valid at speeds close to the speed of light </li></ul><ul><li>Albert Einstein (1879 – 1955) </li></ul><ul><ul><li>Published special theory of relativity in 1905 at the age of 26! </li></ul></ul><ul><li>Newtonian mechanics was found to be a special case of Einstein’s theory </li></ul>
- 3. Theory of Relativity <ul><li>Special theory of relativity based on two postulates: </li></ul><ul><ul><li>Laws of physics are the same in all coordinate systems either at rest or moving at velocity with respect to one another </li></ul></ul><ul><ul><li>The speed of light has the same value, c = 3×10 8 m/s, regardless of the speed of the observer or of the velocity of the source of light </li></ul></ul>
- 4. Galilean Relativity <ul><li>Frame of reference </li></ul><ul><ul><li>Coordinate system at rest with respect to something </li></ul></ul><ul><ul><ul><li>For example – your frame of reference can be the school, which is at rest with respect to the ground but moving with respect to the sun </li></ul></ul></ul><ul><li>Galilean Relativity – laws of mechanics are the same in all inertial frames of reference </li></ul>
- 5. Speed of Light <ul><li>Suppose you are traveling on a boxcar that is moving with velocity v </li></ul><ul><ul><li>You send a light pulse with velocity c relative to the observer in the boxcar </li></ul></ul><ul><ul><li>Common sense would suggest that the speed of the light pulse to an observer outside of the boxcar would be c + v </li></ul></ul><ul><ul><li>However, Einstein’s theory says that the velocity should be the same for an observer both on the train and outside of it </li></ul></ul>
- 6. Speed of Light, cont. <ul><li>One of two conclusions must be drawn: </li></ul><ul><ul><li>Either the addition law for velocities is wrong </li></ul></ul><ul><ul><li>The laws of electricity and magnetism are not the same for all reference frames </li></ul></ul><ul><ul><ul><li>If this is true then there is one reference frame for which the speed of light is c but all other reference frames would have a velocity greater or less than c </li></ul></ul></ul>
- 7. Electromagnetic Theory <ul><li>Says that speeds travel through empty space with speed equal to c </li></ul><ul><li>Mechanical waves require a medium to support the wave disturbances </li></ul><ul><li>In the 19 th century, physicists thought light waves would have to also have a medium through with to propagate </li></ul><ul><ul><li>This was called luminiferous ether </li></ul></ul>
- 8. Ether <ul><li>This was assumed to be everywhere, including in open space </li></ul><ul><li>Because planets travel through it, it has to be massless and have no effect on the motion </li></ul><ul><li>Absolute frame – frame of reference at rest with respect to the ether </li></ul><ul><li>The ether had to be moving through the labs on Earth as “ether wind” </li></ul>
- 9. Michelson-Morley Experiment <ul><li>Albert A. Michelson (1852 – 1931) </li></ul><ul><ul><li>Won the Nobel Prize in 1907 </li></ul></ul><ul><li>First performed the experiment in 1881 and then was later repeated with Edward Morley (1838 – 1923) </li></ul><ul><li>Experiment designed to calculate the velocity of earth with respect to the ether </li></ul>
- 10. Michelson Interferometer
- 11. Michelson Interferometer, cont. <ul><li>Should observe different fringes depending on the orientation of the interferometer </li></ul><ul><li>Experiment resulted in negative results </li></ul><ul><ul><li>No fringe shift was observed </li></ul></ul><ul><ul><li>This contradicted the ether hypothesis </li></ul></ul><ul><li>Light is an electromagnetic wave that requires no medium </li></ul>
- 12. Einstein’s Principle of Relativity <ul><li>Two postulates of special relativity </li></ul><ul><ul><li>Principle of Relativity – All laws of physics are the same in all inertial reference frames </li></ul></ul><ul><ul><li>Constancy of the speed of light – the speed of light has the same value, regardless of the velocity of the observer or the source </li></ul></ul>
- 13. Time Dilation <ul><li>A result of special relativity </li></ul><ul><li>Consider a beam of light on a spaceship moving at a speed close to the speed of light </li></ul>
- 14. From the spaceship…
- 15. From the earth…
- 16. Time Dilation
- 17. Time Dilation, cont. <ul><li>On the spaceship, the time it takes to go from the source to the receiver is given by </li></ul>
- 18. Time Dilation, cont. <ul><li>For someone observing from outside of the spaceship, the time is found by: </li></ul>d
- 19. Time Dilation, cont. <ul><li>Solving for the time, you get </li></ul><ul><li>From before, </li></ul><ul><li>So </li></ul>
- 20. Time Dilation, cont. <ul><li>From this equation, the time interval observed by a person outside of the spaceship is longer than the interval for the person on the spaceship </li></ul><ul><li>Proper time – the time interval as observed by someone who sees both events at the same position </li></ul>
- 21. Twin Paradox <ul><li>Consider two twins. At some point, one of the twins decides to travel to a planet 20 lightyears from earth. </li></ul><ul><ul><li>His speed is 0.95 c </li></ul></ul><ul><ul><li>When he returns, the twin that stayed behind has aged 42 years. </li></ul></ul><ul><ul><li>However, the twin that traveled has only aged 13 years </li></ul></ul>
- 22. Length Contraction <ul><li>Proper length, L p , of an object is the length measured by someone at rest with respect to the object </li></ul><ul><li>For an observer on earth, the distance traveled by a spaceship is L p , and the time it takes to travel is L p / v </li></ul><ul><li>Because of time dilation, a person on the ship thinks that the time is smaller; therefore, the distance traveled is shorter </li></ul>
- 23. Length Contraction, cont. <ul><li>Therefore, </li></ul><ul><li>This only takes place along the direction of motion </li></ul>

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