How can you apply the philosophy of the Gita to a modern person’s responsibility in time of war?

This is an interesting question. Arjuna was a fantastic mythic war hero while Oppenheimer was key to facilitating the atom bomb which ended WW2. Both brought devastation to the "enemy" but both asked the fundamental question, "What good can come from killing so many people?" Oppenheimer lamented on why he should only do his duty as a physicist while ignoring the consequences of the horrific results of his efforts. Similarly Arjuna states that what happens in the world must be significant in our political and moral thinking. To both, destruction exacted a terrible price. For Arjuna, the "significance of human life" was of great concern. So was the case with Oppenheimer who once told the president that he has so much "blood on his hands".

dear friend.teachings of bhagwadgita are faraway from frame of timeline.it is an all time thought or knowledge. there is no comparison of Oppenheimer with Arjna . because Oppenheimer was simply atom bomb provider in world war 2 while Arjuna was directly responsible for mahabharat. there was killing of common innocent persons in world war 2 while in mahabharat sin persons wear killed.