Grammar
N2AI-drafted〜ないものか/〜ないものだろうか
isn't there some way to ~?; I do wish ~ could happen
Formation
V-ない形 + ものか/ものだろうか(可能形が多い:〜できないものか)
Usage
A rhetorical question expressing the speaker's strong wish that something difficult could somehow be realized. It is often used with potential verbs (〜できないものか) and frequently appears in editorials, letters and thoughtful speech. 〜ないものだろうか is softer and more reflective. Note it is quite different from 〜ものか (=strong denial, 'as if I would!').
Examples
この問題を早く解決できないものか。
このもんだいをはやくかいけつできないものか。
Isn't there some way to solve this problem quickly?
もっと安く海外旅行に行けないものだろうか。
もっとやすくかいがいりょこうにいけないものだろうか。
I wonder if there isn't some way to travel abroad more cheaply.
事故を減らすために、何か対策が取れないものだろうか。
じこをへらすために、なにかたいさくがとれないものだろうか。
Couldn't some measures be taken to reduce accidents?