Time Dilation and Time Dilation and Lorentz ContractionLorentz Contraction

Physics 11 AdvPhysics 11 Adv

Time DilationTime Dilation

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

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Time DilationTime Dilation

While this is an interesting theory, it While this is an interesting theory, it appears so strange that without appears so strange that without experimental evidence, it would be hard to experimental evidence, it would be hard to accept this as a valid theoryaccept this as a valid theory

A common experimental result that is used A common experimental result that is used to demonstrate is the behaviour of slow to demonstrate is the behaviour of slow muons and muons that have been muons and muons that have been accelerated to close to the speed of lightaccelerated to close to the speed of light

MuonMuon

Muons are particles that are created high Muons are particles that are created high in the atmosphere due to UV radiationin the atmosphere due to UV radiation

These particles are created about 9000m These particles are created about 9000m above the surface of the Earth and travel above the surface of the Earth and travel at about 0.998cat about 0.998c

Slow muons have a half life of Slow muons have a half life of approximately 2approximately 2μμs which would mean that s which would mean that most would not reach the surface of the most would not reach the surface of the earthearth

QuestionsQuestions

How long does it take muons to travel to How long does it take muons to travel to the surface of the earth?the surface of the earth?

How many half lives have passed in this How many half lives have passed in this time?time?

Assuming that 10Assuming that 1066 were formed initially, were formed initially, how many would arrive on earth?how many would arrive on earth?

QuestionsQuestions

Since the previous result does not match Since the previous result does not match experimental results, let us consider time experimental results, let us consider time dilation effects on the muon. If the muon dilation effects on the muon. If the muon measures its half life to be 2measures its half life to be 2μμs while s while moving at .998c, what would an observer moving at .998c, what would an observer at rest measure this half life to be?at rest measure this half life to be?

How many of the initial muons now arrive How many of the initial muons now arrive at the surface?at the surface?

QuestionsQuestions

At what speed does the muon measure At what speed does the muon measure the earth to travel toward it? Is this a the earth to travel toward it? Is this a problem?problem?

How could we fix this problem?How could we fix this problem?

QuestionQuestion

Assuming the muon is travelling at .998c Assuming the muon is travelling at .998c for 1.90for 1.90μμs, how far can it travel?s, how far can it travel?

What happens to the distance measure in What happens to the distance measure in the rest frame (that of the earth) if the the rest frame (that of the earth) if the gamma term is applied to it (either gamma term is applied to it (either multiplied or divided)?multiplied or divided)?

What does this tell us about length?What does this tell us about length?

Problems – Time DilationProblems – Time Dilation

An airplane flies from Vancouver to Halifax An airplane flies from Vancouver to Halifax (4443km) at a steady speed of 330m/s. (4443km) at a steady speed of 330m/s. How long is the plane in the air according to How long is the plane in the air according to

an observer on the ground? an observer on the ground? How long is the plane in the air according to How long is the plane in the air according to

an observer in the plane?an observer in the plane?

Problems – Time DilationProblems – Time Dilation

Mavis boards a spaceship, then zips past Mavis boards a spaceship, then zips past Stanley on earth at a relative speed of Stanley on earth at a relative speed of 0.600c. At the instant she passes, both 0.600c. At the instant she passes, both start timers.start timers. At the instant when Stanley has measured At the instant when Stanley has measured

Mavis to have travelled 9.00x10Mavis to have travelled 9.00x1077m, what does m, what does Mavis’s timer read?Mavis’s timer read?

At the instant when Mavis reads 0.400s on At the instant when Mavis reads 0.400s on her timer, what does Stanley read on his?her timer, what does Stanley read on his?

Problems – Lorentz ContractionProblems – Lorentz Contraction

A spaceship flies past earth at a speed of A spaceship flies past earth at a speed of 0.990c. A crew member on the 0.990c. A crew member on the spaceships measure its length, obtaining spaceships measure its length, obtaining the value 400m. What length do the the value 400m. What length do the observers measure on earth?observers measure on earth?

Two observers are separated by 56.4m on Two observers are separated by 56.4m on earth as a spaceship flies past at a speed earth as a spaceship flies past at a speed of 0.990c. How far are these observers of 0.990c. How far are these observers separated according to the crew of the separated according to the crew of the ship?ship?