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Special relativity

Special relativity. Physics 123. Outline. Inertial frames of reference Michelson Morley experiment Universality of speed of light Simultaneity 4-dimentional time-space: Time dilation, twin paradox Length contraction.

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Special relativity

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  1. Special relativity Physics 123 Lecture VIII

  2. Outline • Inertial frames of reference • Michelson Morley experiment • Universality of speed of light • Simultaneity • 4-dimentional time-space: • Time dilation, twin paradox • Length contraction Lecture VIII

  3. Newton’s 1st law (actually first formulated by Galileo Galiley)– definition of inertial frame of reference F=0  a=0 , means no change in speed, no turns – objects continue moving with constant speed in a straight line All laws of physics look the same in any inertial frame of reference. Newtonian mechanics Lecture VIII

  4. Inertial frames of reference • Spaceship is going to Neptune away from Earth = Neptune is going toward ship and Earth is going away from it. Lecture VIII

  5. Maxwell’s theory of Electromagnetism • Changing electric field creates magnetic field • Changing magnetic field creates electric field • Change propagates with a finite velocity c=2.99x108m/c • Electromagnetic wave Lecture VIII

  6. Combine mechanics and EM What do you see when you are riding the wave? • E is not changing in time – does not generate B • B is not changing in time – does not generate E • This paradox lead scientists to think that • There is a preferred reference frame (ether) where physics laws for EM are different Lecture VIII

  7. Michelson-Morley experiment • This hypothesis was experimentally tested in 1887 by Albert Abraham Michelson, Edward Williams MorleyUsing Michelson interferometer • Measure difference in the speed of light along the motion of the earth (c+ v, or c- v) and perpendicular Lecture VIII

  8. Michelson-Morley experiment • Michelson interferometer: precision Dl~300nm • Dt~3x10-7m/3x108m/s=10-16s! • the speed of the earth v=3x104m/s • What base (L) do we need to observe an effect to the precision limit? doable! No difference in c was observed!!! Lecture VIII

  9. Special relativity theory • Formulated by Einstein in 1905 • 1st postulate: The laws of physics have the same form in all inertial frames of reference. • 2nd postulate: Light propagates through empty space with a definite speed cindependent of the speed of the source or observer • The speed of light c is the ultimate speed. No objects (and no information) can travel faster than c. • Only objects with zero mass can (and always do!) move at the speed of light Lecture VIII

  10. Simultaneity • Einstein’s “gedanken” (thought) experiment: • Observer O1 – v • Lightning strikes at A1=A2 and B1=B2 simultaneously • In O2’s frame of reference O1 first sees light from B1 then from A1 • In O1’s frame of reference O1 first sees light from B1 and light from A1 simultaneously (light travels with the same speed in his frame of reference) Simultaneity is relative to the frame of reference Lecture VIII

  11. Space and time are relative to the frame of reference Lecture VIII

  12. Distance between two points – A and B In one coordinate system X - |AB|=x In two coordinate system (X,Y) Coordinates depend on the choice of the coordinate system, but the length does not – rotation invariant Add time to space metric x1=x, x2=y, x3=z x4=ict 4- dimensional “length”=interval Does not depend on the frame of reference – Lorentz invariant Lorentz transformations – rotation in 4-dimentional space-time 4-dimensional space – time A x x B y y Lecture VIII

  13. Lorentz transformations System (x’,y’z’,t’) is moving with respect to system (x,y,z,t) with velocity v • Lorentz • x=g(x’+vt’) • y=y’ • z=z’ • t=g(t’+vx’/c2) • Galileo • x=x’+vt’ • y=y’ • t=z’ • t=t’ Lecture VIII

  14. Time dilation • Clocks moving relative to an observer are measured by the observer to run more slowly ( as compared to clocks at rest) • Dt – measured in v=0 frame, Dt0- measured in moving frame Hendrik Antoon Lorentz Derived time and space transformations before Einstein Lecture VIII

  15. Twin paradox • Two twins: Joe and Jane. Joe stays on Earth and Jane goes to Pluto at v<~c • Joe observes that Jane's on-board clocks (including her biological one), which run at Jane's proper time, run slowly on both outbound and return leg. He therefore concludes that she will be younger than he will be when she returns. • On the outward leg Jane observes Joe's clock to run slowly, and she observes that it ticks slowly on the return run. So will Jane conclude that Joe will have aged less? And if she does, who is correct? Lecture VIII

  16. Length contraction • No change in directions perpendicular to velocity • The length of an object is measured to be shorter when it is moving relative to the observer than when it is at rest Lecture VIII

  17. Lecture VIII

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