In relativity, perpendicular motion does not show contraction... Isn't the whole concept lost? I read in HC Verma's Concept of Physics that a body moving in direction perpendicular to length, doesn't show Length Contraction. And Length Contraction, they said, is to maintain the velocity of light constant, while still in relative motion to it. If a body doesn't show contraction (which is in this case), how is the speed of light kept constant? ( I am still a beginner in Relativity with no teacher as I am a Pre-Med and just excuse me if this is an idiotic question, but please clarify it anyway).
 A: A body with finite dimensions will always contract in the direction of motion. A square sheet will contract in either direction by a factor of $L = L_0/\gamma$ where $\gamma = 1/\sqrt{1-\frac{v^2}{c^2}}$. A sheet moving in both directions will experience contraction in both dimensions.
Length contraction is motivated, as you say, by a need to keep the speed of light (the velocity of the propagation of interaction) constant in all reference frames. The most common derivation involves a moving train car and a light bulb, where the velocity of light from the bulb must be constant in the rest and comoving reference frame. Length doesn't contract in the direction perpendicular to the velocity, since there is no motion relative to the rest frame.
A: I think you misunderstood something.Length contraction in a moving body,does not occur in the perpendicular direction of its velocity (not length as you mentioned). Length contraction occurs in the direction of its motion.
A: The measured length of an object along the line of relative motion is contracted while measured lengths perpendicular to the motion are not.

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