I agree that the current 404 page is relatively boring, but I quite dislike the idea of having a formula, and particularly one with such localized meanings as those. The reason for my dislike is that it can only ever speak to a very narrow population, and it will bug other physicists and alienate non-physicist visitors.
Moreover, as was mentioned in the comments, it is by default not possible, and should not be something to aim for, to have different error pages depending on what happened to the post. The point of the 404 page is that it's what you get when the page isn't there, i.e. when you've put in a corrupted address, and this should be the main thrust of the design.
That said, the system does provide a custom page when the page exists but has been deleted; indeed it will go as far as giving you the question title even if you ask only by numeric ID: physics.se:99313. This page does distinguish between questions "removed for reasons of moderation" (automatic and moderator deletions) and posts removed by their author (e.g. this one). However, this should be seen as a secondary feature; altering the design only adds stigma to deletions. I'm not even sure that it can be done; finding deleted posts is nigh-impossible, by design, unless you're 10k+ on that site.
Regarding the design, here are some interesting ones from across the network to see if anyone comes up with ideas:
