Time dilation

Question 1

In a ‘thought experiment’ about relativity, a student stated that a twin who travelled from the Earth to a distant planet and back at a speed close to the speed of light would be the same age on return as the twin who stayed on Earth. Explain why this statement is not correct. –

Answer 1

the time between two events depends on the speed of the observer; traveller’s journey time is the proper time between start and stop; journer time measured on Earth > journey time measured by traveller; traveller younger than twin on return to Earth

Question 2

A student claims that a twin who travels at a speed close to the speed of light from Earth to a distant star and back would, on return to Earth, be a different age to the twin who stayed on Earth. Discuss whether or not this claim is correct. –

Answer 2

space twin’s travel time = proper time < time on Earth so space twin ages less than Earth twin – travelling in non-inertial frame of reference.

Question 3

Derivation:

Answer 3

Consider observer on a moving train (constant v), with a light clock timing pulses between two mirrors in the carriage, at distant L apart
The light pulse travels a distance 2L at a speed c over a time t0=2L/c
The platform observer sees the light pulse travel a distance 2S at speed c over a time t=2S/c

Using Pythagoras, S^2 = L^2 + (vt/2)^2
Eventually gives time dilation equation

Question 4

Lorentz factor, y =

Answer 4

(1 - v^2 / c^2 )^-0.5

Question 5

What is bigger, t or t0

Answer 5

0 < 1/y < 1
Therefore y > 1
As t = yt0 then t > t0

Question 6

Time dilation equation

Answer 6

t=t0 * (1 - v^2 / c^2 )^-0.5

t=t0 * y

Question 7

What is t0

Answer 7

t0 = proper time = time between two events as measured by an observer in the reference frame at which they occur at the same point = 0000wn frame of reference

Question 8

What is t

Answer 8

t = time between the two events as measured by an observer in a frame which moves with a constant velocity, v

Question 9

A moving clock runs ____ relative to…

Answer 9

a moving clock runs slow relative to an external observer

Question 10

Why do moving clocks run slow relative to an external observer?

Answer 10

1) Time runs at different speeds for two observers moving relative to each other
2) a stationary observer measures the time interval between two observers as the proper time t0
3) an observer moving at constant velocity measures a longer interval, t

Question 11

A consequence of the invariance of the speed of light in free space is that moving clocks…

Answer 11

moving clocks run slow

time runs slower when moving at relativistic speeds

Question 12

What absolutes exist?

Answer 12

The speed of light is the only absolute

Time and distance can vary

Question 13

What happens to time as speed increases

Answer 13

t = t0 (1 - v^2 / c^2 )^-0.5

as v–>c
y –> 1/0 ~ infinity
therefore t –> infinity
So time moves slower as speed increases

Question 14

What happens to half-lives at relativistic speeds

Answer 14

Half lives increase when a particle is moving due to time dilation

Question 15

What is meant by a stationary observer

Answer 15

someone that is stationary relative to the reference frame that events are happening in

Question 16

What does a graph of Lorentz factor on y axis, v/c on x axis (speed parameter) look like a show about time dilation

Answer 16

Origin = (0,1)
Usual reflected 1/x shape

Shows difficulty testing time dilation and length contraction. The value of y only becomes significantly greater than one at speeds approaching c so speeds must be close to the speed of light to test for special relativity

Question 17

Twin thought experiment: One twin leaves on a space flight travelling close to c while the other remains on Earth. What does time dilation predict will happen?

Answer 17

Predicts that time will move slower for the space twin so upon return the Earth twin will be much older than the space twin

Space twins time is the proper time
Time on Earth is greater than in space so space twin ages less

Question 18

Twin thought experiment: One twin leaves on a space flight travelling close to c while the other remains on Earth. What does the time between both events depend on?

Answer 18

Speed of observer

Question 19

Twin thought experiment: One twin leaves on a space flight travelling close to c while the other remains on Earth. What is an opposing view?

Answer 19

The space twin would have had to accelerate to achieve a speed close to c and then change direction and decelerate on return to Earth which could alter the effects of time dilation.

Question 20

Kinetic energy reminder -

Answer 20

don’t use 0.5mv^2 at relativistic speeds