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PHYSICS 002C Lecture 20

# PHYSICS 002C Lecture 20 - PHYSICS 002C Lecture 20 Serway...

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PHYSICS 002C Lecture 20 May 15, 2009 Serway and Jewett Chapter 9 – Relativity Review Einstein’s principle of relativity All the laws of physics are the same in any inertial frame. Implies the speed of light is the same in any inertial reference frame. This principle is reasonable but totally incomprehensible. It means that space and time are not separate as they would be in a Newtonian or Galilean world. Chap 9.3 Amazing consequences of Special Relativity: 1 A. The Relativity of Time. The boxcar experiment. Lightning strikes both ends of the boxcar. O sees light from both ends at the same time and concludes that events and are simultaneous. In the previous lecture I stated “But, O’ saw the light from before O did and will see the light from after O.” without explaining why. An observant student asked “How do you know this?”, and I said that a quantitative answer requires the stuff coming next (summarized in the Lorentz transformation). The answer you needed was simply that O sees O’ is moving toward B so the light from event has a shorter distance to travel till it reaches O’, than the light from A. Thus O knows that O’ does not receive the signals simultaneously. O’ must agree, since the order of events occurring at the same point cannot be reversed or we could do time travel! A more quantitative analysis is that O can measure that the light from event travels to the left at speed c while O’ is moving to the right at speed v . The light reaches O’ (O concludes) after a time B t such that O B L v c t 2 1 ) ( O L , where is the length of the car as observed by O. Similarly, O concludes that the light from event reaches O’ after a time such that A t O A L v c t 2 1 ) ( . The difference between these two times is [with 2 / 1 2 2 / 1 c v ] c L c v v c v c L t t t O O B A NET 2 1 1 2 1 ) ( ) ( , Thus for any non-zero value of v , O concludes that the light signals from the two events that he/she thought were simultaneous are reaching O’ at times differing by a time . 0 NET t If O perceives the events are not simultaneous at O’, then O’ must perceive them so also or there will be impossible contradictions.

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