免费长度收缩计算器
根据相对论效应计算高速运动物体的长度收缩。
Contracted Length
43.5890 m
Contracted Length vs Proper Length (rest frame)
公式
## Length Contraction Objects in relative motion appear contracted along the direction of motion. ### Formula **L = L_0 * sqrt(1 - v²/c²) = L_0 / gamma** where L_0 is the proper length (measured at rest). This is only along the direction of motion; perpendicular dimensions are unchanged.
计算示例
A 100 m spaceship traveling at 90% the speed of light.
- 01L = L0 * sqrt(1 - v²/c²)
- 02L = 100 * sqrt(1 - 0.81)
- 03L = 100 * sqrt(0.19)
- 04L = 100 * 0.4359
- 05L = 43.59 m (56.4% shorter)
常见问题
Does the object actually shrink?
The object does not physically compress. Length contraction is a consequence of the geometry of spacetime. In its own reference frame, the object retains its proper length.
At what speed is contraction noticeable?
The effect is negligible below about 10% of c. At 86.6% of c (gamma=2), length is halved. At 99.5% of c, length contracts to 10%.
Is length contraction related to time dilation?
Yes. Both are consequences of the Lorentz transformation. Length contracts while time dilates, keeping the speed of light constant in all frames.
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