K.V.S Prasadh

1. SPECIAL THEORY OF RELATIVITY (විශේෂ සාපේක්ෂතාවාදය ) sandanuwan@phy.ruh.ac.lk 0713324594 K.V.S Prasadh

2. References • Physics for scientist and engineers with modern physics – chapter 39-----Serway Jewett • Fundamentals of Physics – David Halliday, Robert Resnick ,Jeal Walker --- Chapter 38 • Special Relativity -----A.P French

3. CAN WE WAILK THROUGH TIME ????? What is the ultimate speed in world ???? Is time relative ???? Answer

4. 20 HOURS = 16 LECTURES + 4 TUTORIALS. • 3 ESSAY QUESTIONS AND 8-9 MCQS • Topics : • Einstein , classical relativity ,Galilean transformations and either hypothesis • Michelson Morley Experiment • Einstein Postulates (අයින්ස්ටයින්ගේ කල්පිත) • Lorentz transformation. • Length contraction(චපල කෝදු සහ චපල ඔරලෝසු) • Time dilation and twin paradox • Velocity transformation • Space time diagrams • Minkowiski space • Four vectors and tensors • Conservation of four momentum • Relativistic dynamics

5. Classical Physics • At the end of the 19th century it looked as if Physics was pretty well “wrapped up”. • Newtonian mechanics and the law of Gravitation had explained how the planets moved and related that to how ordinary objects here on earth responded to forces.

6. Classical Physics (Cont) • Kinetic theory explained the behavior of gases. • Maxwell’s Theory of Electromagnetism explained the phenomena of electricity and magnetism, predicted electromagnetic waves.

7. Classical Physics (Cont) • All this came to be known as classical physics. • what was in store during the next 100 years, when the ideas, theories, and results of modern physics were developed.

8. Twentieth Century Physics • Special Theory of Relativity • General Theory of Relativity • Quantum Theory

10. Amazing relativity !!!!!!!!!!!!! Probably the most mind boggling lesson you may ever learn ,

11. New Concepts in 20th Century-A Theoretical view point QUANTUM MECHANICS CLASSICAL MECHANICS SMALL SCALE HIGH SPEEDS RELATIVISTIC QM SPECIAL RELATIVITY

13. Classical view of relative motion Galilean relativity

14. A RELATIVE VELOCITY Think you are a passenger in a car on a straight road, moving at a constant velocity. Your velocity relative to the pavement might be 50 Kmh-1. Your velocity relative to the driver of your car is zero. Your velocity can be measured relative to any reference frame.

15. N2 N1 CASE 1 f1 f2 y W x INERTIAL REFERENCE FRAMES A frame of reference is a coordinate system with respect to which we measure motion. For the cart, we measured motion with respect to the screen, across which the cart could be seen moving. This is the most obvious frame of reference. But there is no rule which says we must use the screen as our frame.

16. N2 N1 CASE 1 f1 f2 y W x INERTIAL REFERENCE FRAMES We can use the cart itself as our reference frame, if we want: Now if we are measuring the progress of the cart against our coordinate system, the cart appears to be at rest, all the time!

17. y x V0 CASE 2 INERTIAL REFERENCE FRAMES  Consider a coordinate system connected to the cart which is moving in a constant velocity if we are measuring the progress of the cart against our coordinate system, the cart appears to be at rest, all the time! Any reference frame moving at a constant velocity with respect your IRF is also an IRF.

18. Galilean-Newtonian Relativity

19. Galilean-Newtonian Relativity • Straight vertical path in the car. • Parabolic path when reference frame is the earth. • The laws are the same, but the paths are different because of different initial conditions. • But both observers would agree and understand the situation.

20. v' vb GALILIAN TRANSFORMATION If your friend switched on a flashlight instead of throwing the ball, we would expect the speed of the light to be v = v' + c according to the addition of velocities. Suppose you are on the shore infront of the university, and a boat traveling at a speed v' to your right:  Your friend is on the boat, holding a ball: If you measure the speed v of the ball relative to you (on the shore) it will be v = v'. • If your friend throws the ball with speed vb, then the speed you see the ball moving is v = v' + vb.

21. (S) to (S') (S') to (S) The Galilean Transformations y y' v (S) x (S') x' vt x' = x - vt x = x' + vt y' = y y = y' z' = z z = z' t' = t t = t' THE GALILEAN TRANSFORMATIONS Now let's get a little more precise: Consider two IRFs, (S) and (S')shown below: Note that (S') is moving at velocity vto the right with respect to (S): For a point located at (x, y) in the (S) frame, it will have coordinates (x - vt, y) in the (S') frame: We can write the complete set of transformations from one IRF to another like this:

22. Up to now , nothing looks trouble But , here comes the one !!!!!! The great Maxwell equations ????

23. In the 1860s James Clerk Maxwell derived equations which predicted that light was a wave and that it traveled through space at c = 3×108 m/s. At the time of Maxwell, scientists thought that all waves traveled through a medium: sound through air, water waves through water, earthquake waves through the crust. The medium acted as the vehicle for energy transfer. A particle of air or water bumping another particle of air or water, caused a wave to propagate through the medium. The medium scientists postulated for light was called the luminiferous ether. A lot of effort was put into finding out properties of the ether.

24. Either hypothesis, speed of light and Michelson Morley experiment !!

25. The Michelson-Morley Experiment • This experiment was designed to detect the speed of the earth through the ether. • The earth’s speed around the sun is 3x104m/s. • Predicted fringe shift

26. luminiferous ether It was postulated that this ether permeated space, and anything else that light could travel through. Experiments were devised that tried to measure how fast the earth was moving through the ether. Vorbital sun

27. Vat of liquid mercury Finally two highly skilled experimental physicists named Michelson and Morley made a device that was sensitive enough to detect the small effects of the ether. The apparatus they made was an interferometer. Michelson Mirrors Floating table of heavy marble Detector Beam splitter Source vedio

28. The Michelson-Morley Experiment M&M EXPERIMENT

29. vorb Control beam Squished beam Mirrors Region of interference Detector Vat of liquid mercury Beam splitter Source The interferometer was to be slowly rotated through 90°, and each dark/bright observation in the detector would correspond to a half-wavelength difference between the rejoined beams.  The basic idea behind the device was that as the floating table was rotated, the beam parallel to the earth's orbital velocity would squish. Michelson The beam perpendicular to the earth's orbital velocity would act as the control - it would not be squished. In the region where the beams rejoined, interference would be detected. Destructive interference would result in seeing dark in the eyepiece of the detector. Constructive interference would result in seeing bright in the eyepiece of the detector.

30. The results of the experiment showed that as the device was rotated, there was no evidence of interference. Because of the complexity of the earth's motion through space, Michelson and Morley thought that perhaps they had conducted their experiment at a time when the earth's relative motion through the ether was zero. But whenever they conducted their experiment, the obtained "null results." The Michelson-Morley experiment is probably the most famous NULL EXPERIMENT.

31. ???????? • Are Maxwell’s equations wrong? • They correctly predicted so many observations that physicists were reluctant to give them up. • Ether is “dragged” along by the earth? • Got the same results when the M&M experiment was carried out in balloons and on mountaintops. • Each attempt to determine a way to find a preferred reference system seemed to be doomed to failure

32. Speed of light -------C SPEED LIMIT . The speed of the light is the speed limit of the universe . It is the maximum possible speed of energy transfer and for information transfer . Any object with mass must move at a lower speed.