How to implement "bullet time" in a multiplayer game?

I have never seen such a feature before, but it should provide an interesting gameplay opportunity.

So yes, in a multiplayer/real-time environment (imagine FPS), how could I implement a slow motion/bullet time effect?

Something like an illusion for the player that's currently slo-mo'ed. So everybody sees him "real-time", but he sees everything slowed down.

Update

A sidenote: keep in mind that a FPS game has to be balanced in order for it to be fun. So yes, this bullet time feature has to be solid, giving a small advantage to the "player", while not taking away from other players.

Plus, there is a possibility that two players could activate their bullet time at the same time.

Furthermore:

I'm going to implement this in the future no matter what it takes. And, the idea is to build a whole new game engine for all this. If that gives new options, I'm more then interested in hearing the ideas.

Meanwhile, here with my team we're thinking about this too, when our theory will be crafted, I'm going to share it here.

Is this even possible? So, the question on "is this even possible" has been answered, now it's time to find the best solution.

I'm keeping the "answer" until something exceptionally good comes up, like a prototype theory with something close to working pseudo code.

What the physicists and philosophers say:

The links are for you interest, because topics are closed.

https://physics.stackexchange.com/questions/17118/time-traveling-and-time-dilation-within-a-multiplayer-videogame

https://philosophy.stackexchange.com/questions/1704/seeing-everything-in-slow-motion-but-being-real-time

The conditions I thought about when writing the question on physics site (copied):

1. The player under the effects of slow motion has an advantage to make more precise actions (shooting, movement etc.), due to seeing everything in a much slower pace.


2. His actions should affect the other players in real-time.


3. The players looking upon our affected player, do not see any difference, except they can experience the actions he have done (like, player gets shot/affected dodges a rocket).


4. When the player comes out of this effect, he simply continues in the same pace as usual. (If this is not possible, then I guess he'll have to suffer until the time gets synced back)

References on bullet time (slow motion):

Sadly, most of implementations are single-player only

http://www.gamesradar.com/a-videogame-history-of-bullet-time/

Answer

It has been done before. :) Check out the specialists, a half life mod that has two different bullet time powerups.

EDIT to include zzzzbov's info below

The way bullet time worked in "The Specialists" from a gameplay perspective was that the player could get powerups that would give limited amounts of "bullet time". When used, a bubble around the player would have its physics slowed down.

Players far away would move at normal speed, but anything in the bubble (bullets, players, explosions) would slow down. The player that used the power-up would move slightly faster, allowing them to run away or use stunts to dodge bullets.

Anyone else caught in the "bullet-time" bubble still has the advantage of being able to see what's about to happen, but the relative speed difference between a caught player and bullets remains the same, so that the ability to react is practically nonexistent.