免费时间膨胀计算器
根据相对论效应计算高速运动物体的时间膨胀。
Dilated Time (observer)
2.294157 s
Dilated Time (observer) vs Proper Time (moving frame)
公式
Time Dilation
Special relativity predicts that time passes more slowly for objects in relative motion.
Formula
t = t_0 / sqrt(1 - v²/c²) = gamma * t_0
where t_0 is the proper time (measured in the moving frame) and gamma = 1/sqrt(1 - v²/c²) is the Lorentz factor.
计算示例
1 second of proper time at 90% the speed of light.
- 01gamma = 1 / sqrt(1 - 0.9²)
- 02gamma = 1 / sqrt(1 - 0.81)
- 03gamma = 1 / sqrt(0.19)
- 04gamma = 1 / 0.4359 = 2.294
- 05t = 1 * 2.294 = 2.294 s (observed from outside)
常见问题
Is time dilation real?
Absolutely. It has been confirmed by comparing atomic clocks on jets to ground clocks, by muon lifetime measurements, and by GPS satellite corrections.
What is the twin paradox?
If one twin travels at high speed and returns, they will have aged less than the stay-at-home twin. This is not a paradox but a real prediction confirmed by experiment.
Why does GPS need relativity corrections?
GPS satellites move fast (time dilation) and are in weaker gravity (gravitational time dilation). Without corrections, GPS would drift by about 10 km per day.
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