What the Result Means
In special relativity, a moving clock ticks slower when viewed from a stationary frame. If a stationary observer measures a trip lasting 10 years, the moving traveler can experience less than 10 years of proper time.
The Formula Used
The Lorentz factor is:
If Δt is the time measured by the stationary observer, then the moving observer’s proper time is:
This is the version used by the calculator. It answers: “How much time does the moving observer experience while the stationary observer measures Δt?”
Common Relativistic Speeds
| Speed | Lorentz factor γ | Moving time for 10 stationary years |
|---|---|---|
| 0.1c | 1.005 | 9.95 years |
| 0.5c | 1.155 | 8.66 years |
| 0.9c | 2.294 | 4.36 years |
| 0.99c | 7.089 | 1.41 years |
Why the Original Wording Can Be Confusing
Time dilation formulas are often written from different viewpoints. One formula gives the stationary-frame time when the moving proper time is known. The other gives the moving proper time when the stationary-frame time is known.
Step-by-Step Example
Velocity = 0.9c Stationary observer time = 10 years γ = 1 / √(1 − 0.9²) γ = 2.294 Moving proper time = 10 / 2.294 Moving proper time = 4.36 years
Common Mistakes
- Using a velocity equal to or greater than the speed of light.
- Mixing up stationary time and moving proper time.
- Forgetting that everyday speeds give extremely tiny effects.
- Using the formula without checking which observer’s time is known.
- Confusing special relativity time dilation with gravitational time dilation.
Frequently Asked Questions
What is time dilation?
Time dilation is the effect where different observers measure different elapsed times because of relative motion or gravity. This calculator focuses on special relativity time dilation due to velocity.
Can velocity be exactly the speed of light?
No. A massive object cannot reach the speed of light. Mathematically, as velocity approaches c, γ increases without limit.
Why is the moving time smaller?
From the stationary observer’s frame, the moving clock ticks more slowly. Therefore, less proper time passes for the moving observer during the same stationary-frame interval.
Does this apply at normal car or airplane speeds?
The effect technically exists, but it is extremely small at everyday speeds. It becomes noticeable only at speeds that are a significant fraction of the speed of light.