Consequences of Relativism SPH4U

Wind Back the Clock Two consequences of relativism discussed: To a stationary observer, time appears to slow down in a moving frame. Two events that appear simultaneous to a stationary observer may not appear so to a moving observer.

Time Dilation

If the equation for time dilation is true (and experiments have conclusively shown that it is), why have we not noticed time dilation before now? We will do an activity in class to grow our understanding and other info can be found on

Time Dilation Problem Time Alvi is travelling with a speed of 0.850c relative to Frances. Alvi travels for 30.0 s as measured on his watch. (a) Determine who measures the proper time for Alvi’s trip, Alvi or Frances. Explain your answer.

Time Dilation Problem Time Alvi is travelling with a speed of 0.850c relative to Frances. Alvi travels for 30.0 s as measured on his watch. (b) Calculate the elapsed time on Frances’s watch during this motion.

Time Dilation Problem Time A tau (J) particle has a lifetime measured at rest in the laboratory of 1.5 x s. If it is accelerated to 0.950c, what will be its lifetime as measured in: (a)the laboratory frame of reference? (b) the J particle’s frame of reference?

Time Rewind on How We Know Time is Relative Please work on the group assignment provided by Mr McCormack to deepen our understanding of why time dilates according to special relativity

We can find the formula for  by considering a ‘light’ clock, which sends light up and down between mirrors once every time t.

Suppose that this clock is on a rocket ship moving at a speed v to the right. We observe that the light travels farther in our frame. To keep c constant, it must also take more time, c =  x/  t. Therefore, our time interval is larger than the rocket’s. Their clock runs slower..

How much more slowly can be found by applying Pythagoras’ theorem to the diagram below. Write the equation and solve for t. ct ct’ vt  = 1/ 1 – v 2 /c 2 t = 1/ 1 – v 2 /c 2 t’ c 2 t 2 = v 2 t 2 + c 2 t’ 2 (c 2 - v 2 ) t 2 = c 2 t’ 2

This formula does not depend on the fact that we used a ‘light’ clock. Anything that ‘ticks’ will do. If you were on a rocket ship and sent a signal to Earth every time your heart beat, doctors on Earth would say that your pulse was slow.

If the Earth doctor sent you a signal every time that her heart beat, you would say that her pulse was a) faster b) normal c) slower

Length Contraction To a stationary observer, the length of a moving object (along the direction of motion) appears to decrease. Check out the animation at: crel/lc.cfm Hewitt Tutorial

Extra Mentions Length contraction only occurs along the direction of motion. For example, a cylindrical spaceship moving past the Earth at a very high speed would appear shorter from tip to tail (but of the same diameter) due to length contraction.

Example Problem A spacecraft passes Earth at a speed of 2.00 x 10 8 m/s. If observers on Earth measure the length of the spacecraft to be 554 m, how long would it be according to its passengers?

Example Problem An asteroid has a length of 725 km. A rocket passes by parallel to the long axis at a speed of 0.250c. What will be the length of the asteroid as measured by observers in the rocket?

Example Problem How fast is the car travelling when its contraction is one-half its normal length

Reality Check #1: The cyclotron at Triumf can form pions moving at 0.96 c which decay by emitting muons and neutrinos.

Many of these emitted particles go faster than 0.96 c, but none go faster than light.

Reality Check #2: At CERN, neutral pions were accelerated to c. When these pions decayed, they emited light.

All the light emitted by the pions traveled at c.