the PS4 won't have backwards compatibility per-say, but it will have the ability to stream PS1/2/3 games using sony's Gaikai service. (Although this meant huge input lag)
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Streaming the Cloud will also produce input lag.. I don't understand why Microsoft doesn't understand this? Unless your internet is like 50 download or something crazy good.
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You realize not everything done in a game needs to be super fast right? It is okay and unnoticeable for certain aspects to have a 100 ms input lag while the small and fast calculations get taken care of on the console itself. One quick example I can think of is skyrim's map feature. From my simple understanding of it, when you look at the map it takes a real time rendering (of relatively low quality) of the entire map of skyrim which is why there is a second pause. With the cloud, you can have a map of 1000x the accuracy and resolution rendered in the same amount of time. There are plenty more possibilities other than the trivial one I presented.