Pole-barn paradox, one question

[mentors’ note: moved from another thread because it’s a different question]
Preface: I'm an idiot who occasionally watches science videos and has questions.

If it's not inappropriate to tag on to this post, as I too have questions regarding relative simultaneity and apparent contradictions, I'd like to explore the ladder and barn thought experiment a bit.

This stems from watching a Don Lincoln video about the barn paradox where a ladder larger than the barn can fit into it because of length contraction and the simultaneity of the doors, etc. I think I actually understand everything he said while explaining it but wondered about a situation in which the doors activated a mechanism.

Knowing that the barn observer can see the ladder fully fit into the barn and close both doors while the ladder is inside, what happens if we have a high powered laser suspended from the barn ceiling that is turned on when both doors are shut simultaneously. I know it can't be instant but if each door shot a photon at the laser when the door closes, and the laser only switches on when it gets hit by two photons at the same time wouldn't we have a scorched ladder for the barn observer and a pristine ladder for the ladder observer?

Thanks, and like I said I'm an idiot so be nice lol.

Thanks for moving my comment, sorry about that

[Mentor replies “no problem, no apology needed”]

FIL said:

if each door shot a photon at the laser when the door closes, and the laser only switches on when it gets hit by two photons at the same time wouldn't we have a scorched ladder for the barn observer and a pristine ladder for the ladder observer?

Actually, you would get a scorched ladder for both observers. You already specified what happens for the barn observer.

For the ladder observer the back door closes first and sends a photon towards the laser. But the laser is moving away, so the distance the photon must travel is larger than half the ladder and takes a long time. Then later the front door closes and sends a photon towards the laser. The laser is moving towards, so the distance is shorter and takes less time. The photons wind up both reaching the laser at the same time, turning on the laser and scorching the ladder

Dale said:

Actually, you would get a scorched ladder for both observers. You already specified what happens for the barn observer.

For the ladder observer the back door closes first and sends a photon towards the laser. But the laser is moving away, so the distance the photon must travel is larger than half the ladder and takes a long time. Then later the front door closes and sends a photon towards the laser. The laser is moving towards, so the distance is shorter and takes less time. The photons wind up both reaching the laser at the same time, turning on the laser and scorching the ladder

Hey thanks, just to be clear if the ladder is moving from left to right, the back door is the first door it encounters?

Ohh nevermind it's the right most door. I think I got it now

FIL said:

Hey thanks, just to be clear if the ladder is moving from left to right, the back door is the first door it encounters?

If the ladder is moving left to right then the back door is the right door. I was describing a ladder going in the front door and out the back door of the garage.

Dale said:

If the ladder is moving left to right then the back door is the right door. I was describing a ladder going in the front door and out the back door of the garage.

Okay sorry one follow up question. If the ladder is 90ft and barn is 30ft long, the ladder frame sees the barn as contracted right? And the photon from the left door can't be sent until it closes. So wouldn't that result in only like the last 5ft of the ladder getting scorched, but perhaps more for barn observer?

If you work it out you will always get the exact same fraction of the ladder is scorched. You can add more complications, it just makes the analysis more complicated.

Yeah that makes sense. There's a lot to keep track of when you first learn about this stuff. Thanks for your time

FIL said:

Yeah that makes sense. There's a lot to keep track of when you first learn about this stuff. Thanks for your time

This is why you need a systematic way to describe the coordinates of events in one frame and transform them to another frame. This takes the sting out of these so-called paradoxes. Once you understand how to apply the Lorentz Transformation, it all becomes rather straightforward!