Time Dilation

Question 1

For an object travelling close to the speed of light, why does the observer moving relative to the spaceship look as if the object slowed down

Answer 1

-The observer sees the time in the space ship as slower, ticks slower
-The spaceship passenger sees the earth clock as ticking slower

A stationary observer in their reference frame views clocks as running slower in the moving reference frame. We’re back to disagreeing

Question 2

The train situation shows time dilation

Answer 2

-for a person who’s on the train, they view the light as going up and down in a given time interval..
-but for someone outside the train they see the light travel 2l and also an extra distance horizontally.. this means that the speed of light travelled a greater distance.. and this means that time has to be dilated and has increased so c is constant

Question 3

Explain the time dilation formula

Answer 3

t = gamma x t0

t = time interval measured by observer moving relative to the time interval being measure
Gamma always > 1
t0 : proper time

So that means t > t0 so t is the time for the observer from earth

Question 4

Muon lifetime experiment

Answer 4

Remember that it is the observer on Earth that viewed the muons’ lifetime or half-life as longer (time dilation), whilst it is the muons’ reference frame that views the distance needed to travel as shorter (length contraction).

Question 5

What does Muon lifetime experiment give evidence for ?

Answer 5

provide experimental evidence for time dilation and length contraction

Question 6

What is the speed of Muon and half life?

Answer 6

0.98c and 1.6x10-6 seconds

Question 7

For T = gammaT0 what does it show about muon half life

Answer 7

-it shows that the half life in reference to the Earth (person) is long (T) compared to the proper time in the muon inertial frame

Question 8

Summarise Length contraction

Answer 8

-Observer H, in their rocket moving close to the speed of light, measures the length of their pencil to be 14 cm
Observer G, at rest on Earth, would measure (with remarkable eyesight) the length of the pencil to be shorter

Question 9

Explain the length contraction formula

Answer 9

L = L0/gamma

L = the length measured by an observer moving relative to the length being measured (m)
L0 = the proper length (m)

Question 10

Why does length contraction show Einsteins 2nd postulate ?

Answer 10

Both observers G and H must measure the speed of light to be c
-Since the time for observer H (L0) (T) will run slower, according to observer G (L) (T0) (i.e. t increases), then for c to stay the same, the length of the object, L must decrease

Question 11

Explain the relativistic mass equation

Answer 11

m = gamma x m0

m0 = proper mass (rest mass) by person who’s at rest relative to the object
m = intertial reference frame