Length contraction

To measure the length of a given body that is at rest in our frame of reference, we can calmly measure the coordinates of the extremities of this body using a ruler.

But when we try to make this measurement when the body is in motion, we have to simultaneously observe (in our frame of reference) the coordinates of the extremities of the body for the result of our measurements to be valid.

In his postulates, Einstein proposed that: the laws of physics are the same for any inertial frame of reference, and the speed of light in a vacuum has the same value in all directions and in all inertial frames of reference.

Thus, it has been proposed that the length of a body, measured in another frame of reference relative to which it is moving (in the direction of the dimension being measured), is always less than the length initially measured.
Let’s see the figure below:

Let’s suppose that in the figure above the body is at rest, having length L’ in relation to an observer. In a second moment, the body has velocity V (relative to the same observer) in the same direction in which the initial length was measured. Einstein stated that this body will have a length L, with L < L’, keeping the value of height h constant.

In such a way, we can say that there was a contraction of length, being the equation below the one that makes a direct connection between these lengths:


L = length of the object in motion
L’ = length of the object at rest
u = relative speed between the reference frame
c = speed of light in vacuum

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