Albert Einstein ( )

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1 Einstein s Special Theory of Relativity Imagination is more important than knowledge Albert Einstein ( ) Contributions: The man who rewrote physics Photoelectric Effect major importance to Quantum Mechanics Theory {Nobel Prize in Physics} Special & General Theory of Relativity Strong Advocate for World Peace Spent the last few years of his life for the Unification Theory a theory that allows all the laws of nature to be placed under one set of equations

2 Special Theory Of Relativity First, a throwback. v A = 24 m/s v B = 10 m/s How fast is Car A going relative to brick wall? How fast is Car A going relative to Car B? How fast is Car B going relative to brick wall? How fast is Car B going relative to Car A? (24 m/s) (14 m/s) (10 m/s) (-14 m/s) Special Theory Of Relativity Since all motion is relative maybe TIME is relative too!! What occurs in one reference frame, may occur in a different order in another reference frame!!! Simultaneous in one reference frame is NOT always simultaneous in another reference frame.

3 Special Theory Of Relativity 2 postulates of Special Relativity: All the laws of nature are the same in all uniformly moving reference frames. Speed of light is a constant, independent of the motion of the light source or the observer. Special Theory Of Relativity Albert Einstein's Gedanken Experiment Imagine yourself inside a closed compartment in a high speed train. There is no experiment that you can do to prove that the train is moving or is at rest, if the train exhibits true uniform motion. How does this apply to light?

4 Does light wave follow Galilean law of addition of velocity? Frame S travels with velocity v relative to S. If light waves obey Galilean laws of addition velocity, the speeds of the two opposite light waves would be different as seen by S. Michelson-Morley experiment on Œther In the pre-relativity era, light is thought to be propagating in a medium called œther - a direct analogy to mechanical wave propagating in elastic medium such as sound wave in air If it exists, œther could render a measurable effect in the apparent speed of light in various direction However Michelson-Morley experiment only found negative results on such effect A great puzzlement to the contemporary physicist: what does light wave move relative to?

5 Michelson-Morley Experiment on the Existence of Œther Using an interferometer they attempted to measure the difference in the speed of light coming from a distant star. Michelson-Morley Experiment on the Existence of Œther Earth moving away from star light Earth Moving towards star light Their interferometer should have been able to measure the difference in speed of the star light!

6 Michelson-Morley Experiment on the Existence of Œther They could not measure any difference in the speed of light coming from the distant star. They thought they had completely failed! Einstein later on said that they hadn t failed but had actually proved his second postulate! Space - Time Einstein thought of these two ideas (Space & Time) as one entity! Light travels so fast that it does all of its moving through space and NONE through time! You and I are turtles and move so slowly that we do most of our moving through time and very little through space! Low Speed Humans spend all their time moving through time they only experience time! Space-Time line High Speed Light spends all of its time here moving through space it experiences no time!

7 Consequences The constancy of the Speed of light has some very special ramifications. One of these is called Time Dilation. A Gedanken Experiment (German for thought) Since light speed c is invariant (i.e. the same in all frames), it is suitable to be used as a clock to measure time and space Use light and mirror as clock light clock A mirror is fixed to a moving vehicle, and a light pulse leaves O at rest in the vehicle. O is the rocket frame. Relative to a lab frame observer on Earth, the mirror and O move with a speed v.

8 A Gedanken Experiment (German for thought) In the rocket frame The light pulse is observed to be moving in the vertical direction only The distance the light pulse traversed is 2d The total time travel by the light pulse to the top, get reflected and then return to the source is = 2d/c In the lab frame However, O in the lab frame observes a different path taken by the light pulse it s a triangle instead of a vertical straight line The total light path is longer = 2l l 2 =(c t/2) 2 (c t/2) 2 =d 2 + ( x/2) 2 l= (c t/2) 2 =d 2 + (v t/2) 2

9 Light triangle We can calculate the relationship between t, and v: l 2 =(c t/2) 2 =d 2 +(v t/2) 2 (lab frame) = 2d/c (Rocket frame) -> d = c /2 Eliminating d, we get: YUCK! Time Dilation Equation Relativistic factor = time as measured by a observer moving with the clock t = time as measured by a stationary observer c = the speed of light v = the speed of the object

10 A clock flies by us at 0.780c. How much time will it take the moving clock to register 60.0 seconds? A clock flies by us at 0.780c. When a clock in our reference frame has registered 60.0 seconds, how much time has registered on the moving clock?

11 Time Dilation - Consequences Remember these effects only become noticeable near the speed of light! Imagine that in the distant future being able to ride on a spaceship that can travel close to the speed of light. You embark on a 2.0 year journey to the distant stars travelling at C. Upon your return everyone that has been left behind has aged by 45 years! You are now younger than all your friends and your children! This is known as the Twin Paradox