Sometimes people on forums speak a lot, maybe more than they should. Nowadays, Neo-GAF is one of the best sources to produce rumors, because there are insiders of different companies camouflaged as ordinary users.
Gaikai will be a star feature for PS4, this tool could provide backward compatibility to the system, among other functions. Thought if we consider the Neo-GAF’s rumor, Gaikai will be on PS3 too. We will only need to update our console. Of course, we are speaking about a rumor, so, this function could never arrive to PS3.
I would like to highlight this comment, extracted from Neo-GAF:
Hopefully playable PS4 demos via remote play for E3. (Thanks, StuBurns)
I reckon myself playing PS4 games through PS3 months before the system reaches the selves. This is not going to happen, but it would be the best way to sell a new system. Try before buy.