if a person has a ps3 and wants to multiplayer with someone who has a ps4. Is this possible?
No because no one has a PS4 .
I think it would be, if they have that PS3 game playable on PS4 (via Gaikai or whatever). But no one will know until Sony says anything about it.
I'm hoping they allow PS3/PS4 owners to play online together in upcoming games like "Destiny", "Watch_Dogs", and "Assassin's Creed IV." But, as far as older PS3 games being streamed on a PS4, I'd assume they will have the MP taken out. Much like PS2 classics on PS3 don't have online multiplayer.
The games will be built around different architectures. So I would say no.
It sounds to me like you're thinking of the same game having a PS3 version and a PS4 version, and I would agree with you on that. OP didn't specify what kind of situation he was thinking of which is why I replied as I did. If the PS4 was able to run an actual PS3 game (not a PS4 port) via Gaikai, for example, I don't really see why it could not be compatible, although lag could be an issue.