Time dilation Flashcards
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. –
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
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. –
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.
Derivation:
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
Lorentz factor, y =
(1 - v^2 / c^2 )^-0.5
What is bigger, t or t0
0 < 1/y < 1
Therefore y > 1
As t = yt0 then t > t0
Time dilation equation
t=t0 * (1 - v^2 / c^2 )^-0.5
t=t0 * y
What is t0
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
What is t
t = time between the two events as measured by an observer in a frame which moves with a constant velocity, v
A moving clock runs ____ relative to…
a moving clock runs slow relative to an external observer
Why do moving clocks run slow relative to an external observer?
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
A consequence of the invariance of the speed of light in free space is that moving clocks…
moving clocks run slow
time runs slower when moving at relativistic speeds
What absolutes exist?
The speed of light is the only absolute
Time and distance can vary
What happens to time as speed increases
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
What happens to half-lives at relativistic speeds
Half lives increase when a particle is moving due to time dilation
What is meant by a stationary observer
someone that is stationary relative to the reference frame that events are happening in
What does a graph of Lorentz factor on y axis, v/c on x axis (speed parameter) look like a show about time dilation
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
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?
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
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?
Speed of observer
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?
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.
Kinetic energy reminder -
don’t use 0.5mv^2 at relativistic speeds
