# Time dilation

A moving clock runs slow as seen by a stationary observer, by the factor gamma = 1/sqrt(1 - v squared / c squared).

Physics (university) · Part 10: Relativity and quantum physics · Card 2 of 11 · Last updated 2026-10-19

## Analogy

Time stretches for fast travellers.

## Example

**Spaceship at 0.8c**

gamma = 1/sqrt(1 - 0.64)
= 1.667
3 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.

## Related concepts

- [Postulates of relativity](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-1)
- [Length contraction](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-3)
- [Mass-energy equivalence](https://studyvisually.com/learn/science/physics-university/physics-university-part-10/physics-university-part-10-concept-4)

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