免费时间膨胀计算器
计算狭义相对论中的时间膨胀效应。
Dilated Time
2.293433 s
Dilated Time vs Proper Time (t0)
公式
## Special Relativistic Time Dilation A moving clock runs slower as observed from a stationary frame. ### Formula **t = t0 / sqrt(1 - v^2/c^2) = gamma * t0** - *t0* = proper time (time measured by the moving clock) - *v* = relative velocity - *c* = speed of light (2.998 x 10^8 m/s) - *gamma* = Lorentz factor At 90% of c, time passes about 2.3 times slower for the moving observer.
计算示例
1 second of proper time at 0.9c.
- 01beta = v/c = 2.698e8 / 2.998e8 = 0.8999
- 02gamma = 1 / sqrt(1 - 0.81) = 1 / sqrt(0.19) = 2.294
- 03t = gamma * t0 = 2.294 * 1 = 2.294 s
常见问题
Has time dilation been experimentally confirmed?
Yes, many times. Muons created in the upper atmosphere reach the ground because their decay time is dilated. Atomic clocks on aircraft and satellites also confirm it.
What is the twin paradox?
If one twin travels at high speed and returns, they age less than the stay-at-home twin. The apparent paradox resolves because the travelling twin accelerates, breaking the symmetry.
Does GPS use time dilation corrections?
Yes. GPS satellites move fast enough (and are in a weaker gravitational field) that both special and general relativistic corrections are essential for accuracy.
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