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MSTC Physics B

MSTC Physics B . Chapter 26 Relativity. Branches of Relativity. Special relativity – deals with steady motion at high speeds General relativity – deals with accelerated motion and the effects of gravity. First postulate of special relativity.

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MSTC Physics B

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  1. MSTC Physics B Chapter 26 Relativity

  2. Branches of Relativity • Special relativity – deals with steady motion at high speeds • General relativity – deals with accelerated motion and the effects of gravity

  3. First postulate of special relativity • All the laws of nature are the same in all uniformly moving frames of reference. • Based on this postulate, 2 observers in 2 different reference frames will discover the same mechanical laws - both could prove Newton’s laws

  4. Second postulate of special relativity • The speed of light in empty space will always have the same value regardless of the motion of the source or the receiver. speed of light, c = 300,000 km/s

  5. Michelson-Morley Experiment • 1887 proved that light has only one speed • Michelson-Morley experiment

  6. Space-Time • “I don’t know what light is and I don’t care what it is. The problem is not with light; the problem is with speed.” • But what is speed? Speed is a measure of space divided by time. So if the idea of speed is in trouble, it is because the underlying ideas of space and time need alteration.

  7. Space-Time • Einstein decided that the reason for light’s unexpected behavior was some defect in the concept of speed, hence in the concept of space and time.

  8. Space-Time • Space and time are two parts of the same thing • If at rest, still moving through time • If walk across the room you are moving through space and time • If time stood still you’d still be moving through space Space time

  9. Time dilation • Observable stretching, or slowing, of time in a frame of reference moving past an observer at high speeds • 2 observers will never agree on the time it took if in different frames of reference but would always agree on the speed of light

  10. Twin Paradox • 2 identical twins • 1 goes on high speed journey at ½ c for 1 year according to his clock • When he returns he finds that 1.15 years have passed on earth • Twins are no longer the same age

  11. Time Dilation Δt = Δto / (1 – (v/c)2)1/2 Δto = proper time interval

  12. Length contraction • At high rates of speed length contracts in the direction of motion • Faster the motion – the faster the contraction

  13. Length Contraction L = Lo ( 1 – (v/c)2)1/2 Lo = proper length (length at rest)

  14. Relativistic Mass • At high rates of speed mass increases m = m0 /( 1 – (v/c)2 )1/2 m0 = rest mass

  15. Question A train moves past you so fast that you measure the engineer’s clock running at half speed. The engineer measures your clock at • Half speed • Normal speed • Double speed

  16. Question If a gun is fired forward from an onrushing locomotive, the bullet travels forward with the speed of the train added to the bullet’s normal muzzle velocity. Is the speed of light that is fired forward from the headlight of an onrushing locomotive also increased by the locomotive’s speed?

  17. Question You are inside a spacecraft that is a mile long. An alien spacecraft flies past you. When the passing alien is alongside you, you note that the alien craft is exactly as long as your own craft. That is, the alien nose is abreast of your tail when the alien tail is abreast of your nose. Are the two craft identical in length?

  18. Question You measured the passing alien craft to be exactly as long as your craft. Let’s consider what the alien measures: a. the alien measures its craft to be as long as yours b. the alien measures its craft to be longer than yours c. the alien measures its craft to be shorter than yours

  19. Question A square box is falling on a conveyor belt moving to the left. How will the box be measured by aliens who are riding the belt? a. b. c. d. e.

  20. E = mc2 • According to Einstein, when something gains energy it gains mass • Even if it is not matter (ex – light) it has mass because it has energy • Based on this way of thinking, 1 g of matter is greater than the energy used daily by the population of our largest cities

  21. General Relativity • Gravity bends light • Since the light at the top of the curve has to travel more distance than the light traveling at the bottom of the curve but arrive at the same time, the time at the bottom is slower than the time at the top

  22. General Relativity • Speed of time near the earth or in any gravity field has to decrease and keep on decreasing as the light goes lower in the field

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