Yet another SR "paradox". A spaceship is moving w.r.t someone on earth. From the POV of a ship observer standing in the middle, he shines a laser beam in both directions. Assume that the part of the ship the laser touches explodes, and that the explosion imparts some force to the ship (normal to the surface at the point of explosion pointing towards the inside of the ship).
From the ship guy's perspective, both ends of the ship explode at the same time. So the same force is imparted at both ends of the ship in opposite directions - no acceleration. But from the earth guy's perspective, the rear end explodes first. So the ship will get some boost in one direction - hence some acceleration.
How can this apparent contradiction be resolved?
Following Will's comment, I tried to resolve it with a spacetime diagram but I still can't figure it out. Sorry if I sound dense but i'm new to the subject.
This is a spacetime diagram from the pov of earth guy. The 45 degree lines represent worldlines for the laser beams sent by rocket guy in both directions. The "mid" worldline is that of rocket guy. $t_1$ and $t_2$ are the times of the events corresponding to rear and front side explosions.
Initially I was thinking that earth guy could just take a photograph of the rocket between $t_1$ and $t_2$, in which the rear end of the rocket would be destroyed and the front end intact. Based on your comments, I also have to consider these events - "light from the rear explosion reaches earth guy", "light from the front explosion reaches earth guy".
Obviously I'm doing something so obviously wrong that it's painful for people familiar with the subject to look at. So at this point I'd be grateful for pointers on how to resolve the contradiction, because even these two events of light reaching earth guy are not simultaneous.