It takes time for the light to pass through the barn. Even if they are opened out of sync, if that time difference is less than L/c, light will get through.

Could you simplify this for me considering just the barn's time frame. If you have two synchronized clocks, one at each door, what are the doors doing relative to each other.

 

It seems that when you consider what you would observe due to the time it takes light to reach your eyes, the event is unnecessarily complicated.

In the rest frame of the barn, the doors close at the same time, while the ladder is inside.

Could you simplify this for me considering just the barn's time frame. If you have two synchronized clocks, one at each door, what are the doors doing relative to each other.

 

It seems that when you consider what you would observe due to the time it takes light to reach your eyes, the event is unnecessarily complicated.

 

Assume that light passes through one door just as it closes. In the Barn frame, the other door closes at the same time and the light does not pass through the barn.

 

In a frame in which the Barn is moving in the same direction as the light, the second door remains open for some time after the first door closes. But it still takes time for the lght to cross the width of the Barn, especially since in this frame the second door is actually moving away from the light and the light has to catch up with it.

 

The point is that the time delay due to the non-simultaneous closing of the doors in this frame will always be smaller than the time it takes light to reach the seconf door in this frame. IOW, the seconf door will always close before the light leaving the first door reaches it.

 

 

Now let's use the bomb example.

 

There is a bomb sitting halfway between the two doors. It is set to go off if, and only if light from both doors hit it at exactly the same time.

 

In the barn frame, both doors are opened at the same time, the light strikes the bomb at the same time and it explodes.

 

In the frame the bomb barn is moving, the bomb is running towards the light from one door and running away from light coming from the other door, so it takes more time for light from one door to reach it than from the other.

 

So, the only way for the bomb to go off is for the trailing door to open first, and then some time later, the leading door. That way, the light reaches the bomb at the same time it goes off in this frame too.

 

This is exactly what the Relativity of Simultaneity says happens. In fact, it is the Relativity of Simultaneity that makes sure that the same events happen in both frames (e.g. the bomb exploding)

I believe an event is viewed in all frames as it occurs (adjusting for signal transfer). Only its time may not be agreed on. The exploding bomb depends on the signal reaching it, not on the event occurance.

What, in your view, exactly is the difference???

The barn door movement is the event.

From the time frame of the barn the ladder length contracts and will fit in the barn. From the time frame of the ladder the barn length contracts and the fit will be worse. From an outside time frame both will length contract. All this with respect to the same barn and ladder. What trust one must have?