Answer to Question #106431 in Quantum Mechanics for Nikita Koladiya

Question

Two rockets of rest length L approach each other with equal speeds of 0.4c. How long would one rocket appear to the other?

Answer 1

Rockets move with sublight speeds, therefore, they should be applied to the concept of the special theory of relativity. Transformations of coordinates and time in this theory during the transition from one reference frame to another are called Lorentz transformations. Lorentz studied Maxwell's equations for electromagnetic fields and showed that they are invariant with respect to such transformations. If you determine how the distance between two points located along the direction of movement changes, then you get

$l=L\cdot \sqrt{1-(\frac{v}{c})^2}$ , where $L$ - the distance in the rest system, $v$ - speed of moving system and $l$ - the distance in moving system.

$l=L\cdot \sqrt{1-(0.4)^2}=0.916\cdot L$

In the direction perpendicular to the movement, the reduction in size and length does not occur.

Answer: one rocket appear to the other with length $l=0.916\cdot L$