Probably with a gigabit in bandwidth, it's possible that OnLive could use some kind of predictive modeling based on what you're currently doing and what you've done in the past to see what actions in the future are likely. It could then run (in parallel) all the likely actions and send them down simultaneously (example: simultaneously send what would be displayed if you panned right, left, up and down one or more frames before the user has given input and the client caches these frames and renders the one that the user ends up doing).
Sure it would be a "waste" of compute power and network, but that's certainly one way to, in a sense, "push data across distances faster than the speed of light". That's exactly the kind of approach which would be unimaginable in a scenario where you have to worry about compressing media in order to get a single stream across in a timely manner (read: now), but might actually fall within the realm of possibility when gigabit bandwidth is ubiquitous.
I think computing power would be a much bigger issue than bandwidth. You'd need to run many instances of the game for each user, and continuously kill and fork them.
And frankly, a $500 computer today can already display quite good graphics. Maybe by the time gigabit bandwidth is ubiquitous, computers will be usable enough that installing and running a game locally will be as seamless as clicking a link on a web page, so we won't need cloud gaming amymore.
And then a cheating client will be developed that uses the information in these "alternate timeline" frames to alert you of enemies around the corner, etc.
I'm not saying that's catastrophic, but I think the impossibility of cheating is one of OnLives clear advantages. Sure you can write a bot, but it will only have access to the same information a human player does.
Sure it would be a "waste" of compute power and network, but that's certainly one way to, in a sense, "push data across distances faster than the speed of light". That's exactly the kind of approach which would be unimaginable in a scenario where you have to worry about compressing media in order to get a single stream across in a timely manner (read: now), but might actually fall within the realm of possibility when gigabit bandwidth is ubiquitous.