Why is Normal Area to Light Rays Invariant?

[center o bass]

It is a fact that all inertial observers would measure the same area normal to a beam of light rays in relativity. You can prove this by considering the displacement vector connecting a light ray to its neighbouring light rays. But I wondered if there were some intuitive explanation of why this must be true?

 

[BiGyElLoWhAt]

Not really sure what you're looking for. Length dilation/time dilation?