IB Physics – Relativity Relativity Lesson 2 1.Time dilation 2.Lorentz Factor 3.Proper time 4.Lorentz contraction 5.Proper length 6.Twin paradox and symmetric situations 7.Muon decay; evidence for time dilation

IB Physics – Relativity Time dilation

IB Physics – Relativity Time dilation Think about what this means? ????

IB Physics – Relativity Proof of formula The proof of the time dilation formula is a standard requirement in the exam. Carefully work through the proof using Pythagoras’ Theorem. Make sure you understand each step. Hints The “prime” notation refers to measurements in the ‘moving’ frame The speed of light is the same for all observers.

IB Physics – Relativity The Lorentz factor v 0.1c0.2c0.3c0.4c0.5c0.6c0.7c0.8c0.9cc  For what values of v is  significant ? Work out  below

IB Physics – Relativity Example of time dilation If the train passengers measure a time interval of  t 1 = 6 s and the train moves at a speed v = 0.80c, calculate the length of the same time interval measured by a stationary observer outside the train standing on the ground

IB Physics – Relativity Atomic clocks prove time dilation!

IB Physics – Relativity Proper time A proper time interval is the time separating two events that take place at the same point in space observed time interval =  x proper time interval Note that the proper time interval is the shortest possible time separating two events

IB Physics – Relativity Examples of proper time 1.The time interval between the ticks of a clock carried on a fast rocket is half of what observers on Earth record. How fast is the rocket moving with respect to the Earth? What are the two events here? 2.A rocket moves past an observer in a laboratory with speed = 0.85c. The lab observer measures that a radioactive sample of mass 50 mg (which is at rest in the lab) has a half life of 2.0 min. What half-life do the rocket observers measure? Again, what are the two events? 3.In the year 2010, a group of astronauts embark on a journey toward Betelgeuse in a spacecraft moving at v = 0.75c with respect to the Earth. Three years after departure from the Earth (as measured by the astronaut’s clocks) one of the astronauts announces that she has given birth to a baby girl. The other astronauts immediately send a radio signal to Earth announcing the birth. When is the good news received on Earth (according to the Earth Clocks)? In each case first suggest in which frame the proper time is directly measured Tsokos, 2005, p562

IB Physics – Relativity Length Contraction Another consequence of the invariance of the speed of light is that the distance between two points in space contracts according to an observer moving relative to the two points. The contraction is in the same direction as the relative motion. Measured by observer who is stationary with respect to the object Measured by observer in a moving frame with respect to the object A paradox on length contraction

IB Physics – Relativity Proper Length The proper length of an object is the length recorded in a frame where the object is at rest Any observers moving relative to the object measure a shorter length (Lorentz contraction);

IB Physics – Relativity Examples 1.An unstable particle has a life time of 4.0 x s in its own rest frame. If it is moving at 98% of the speed of light calculate; a)Its life time in the lab frame b)The length traveled in both frames. 2.Electrons of speed v = 0.96c move down the 3 km long SLAC linear accelerator. a)How long does take according to lab observers? b)How long does it take according to an observer moving along with the electrons? c)What is the speed of the accelerator in the rest frame of the electrons? Tsokos, 2005, p566 Kirk, 2003, p145

IB Physics – Relativity The twin paradox Link to twin paradox Read about this in Kirk p 146. The paradox arises because both twins view a symmetrical situation. Explain why? Explain why it is not a paradox.

IB Physics – Relativity The muon experiment This offers direct experimental evidence of time dilation Key points Muons have an average lifetime of 2.2 x s in their own rest frame. They are created 10 km up in the atmosphere with velocities as large as 0.99c. Show that without special relativity muons are unlikely to be detected on Earth. Muon decay explanation