Time Dilation and Lorentz Contraction Physics 11 Adv

Time Dilation  We have seen that time is a relative measurement dependant on the frame of reference of the observer taking the measurement. The observer will see proper time as measured by clocks in their frame and dilated time measured by clocks in moving (non-accelerated) frames

Time Dilation  While this is an interesting theory, it appears so strange that without experimental evidence, it would be hard to accept this as a valid theory  A common experimental result that is used to demonstrate is the behaviour of slow muons and muons that have been accelerated to close to the speed of light

Muon  Muons are particles that are created high in the atmosphere due to UV radiation  These particles are created about 9000m above the surface of the Earth and travel at about 0.998c  Slow muons have a half life of approximately 2μs which would mean that most would not reach the surface of the earth

Questions  How long does it take muons to travel to the surface of the earth?  How many half lives have passed in this time?  Assuming that 10 6 were formed initially, how many would arrive on earth?

Questions  Since the previous result does not match experimental results, let us consider time dilation effects on the muon. If the muon measures its half life to be 2μs while moving at.998c, what would an observer at rest measure this half life to be?  How many of the initial muons now arrive at the surface?

Questions  At what speed does the muon measure the earth to travel toward it? Is this a problem?  How could we fix this problem?

Question  Assuming the muon is travelling at.998c for 1.90μs, how far can it travel?  What happens to the distance measure in the rest frame (that of the earth) if the gamma term is applied to it (either multiplied or divided)?  What does this tell us about length?

Problems – Time Dilation  An airplane flies from Vancouver to Halifax (4443km) at a steady speed of 330m/s. How long is the plane in the air according to an observer on the ground? How long is the plane in the air according to an observer on the ground? How long is the plane in the air according to an observer in the plane? How long is the plane in the air according to an observer in the plane?

Problems – Time Dilation  Mavis boards a spaceship, then zips past Stanley on earth at a relative speed of 0.600c. At the instant she passes, both start timers. At the instant when Stanley has measured Mavis to have travelled 9.00x10 7 m, what does Mavis’s timer read? At the instant when Stanley has measured Mavis to have travelled 9.00x10 7 m, what does Mavis’s timer read? At the instant when Mavis reads 0.400s on her timer, what does Stanley read on his? At the instant when Mavis reads 0.400s on her timer, what does Stanley read on his?

Problems – Lorentz Contraction  A spaceship flies past earth at a speed of 0.990c. A crew member on the spaceships measure its length, obtaining the value 400m. What length do the observers measure on earth?  Two observers are separated by 56.4m on earth as a spaceship flies past at a speed of 0.990c. How far are these observers separated according to the crew of the ship?