Time dilation
A moving clock runs slow as seen by a stationary observer, by the factor gamma = 1/sqrt(1 - v squared / c squared).
Last updated
Analogy
Time stretches for fast travellers.
Example
gamma = 1/sqrt(1 - 0.64)= 1.6673 yr x 1.667 = 5 yr
In practice
At 0.8c, gamma is 1.67, so 3 years on a spaceship is 5 years on Earth.
Practice
Flashcards
- Write the time dilation factor gamma.gamma = 1/sqrt(1 - v^2/c^2).
Interview questions
- Describe time dilation and calculate the Earth-time for a trip that takes 3 years on a spaceship at 0.8c.
- gamma = 1.67
- Moving clocks run slow
- 3 years x 1.67 = 5 years on Earth
Questions people ask
Has time dilation been measured?
Yes. Fast-moving muons made in the upper atmosphere survive long enough to reach the ground, which is only possible because their clocks run slow. Atomic clocks flown on aircraft also showed tiny shifts. GPS satellites correct for relativity every day.
Does the moving observer notice their own clock running slow?
No. Everyone sees their own clock run normally. Time dilation only appears when you compare clocks in relative motion. Each observer sees the other's clock slow, and the so-called twin paradox is resolved by noticing which observer accelerates or changes frame during the trip.