To the people claiming that it's impossible to run PS3 games on PS4, you're really not providing any reasons why, you're just making unsupported claims.
In reality the issues involved are the programming languages used by PS3 (RISC in PPC and ISA on it's SPEs) and location where certain tasks are processed.
Translating RISC/ISA to CISC isn't impossible, it's no different than translating one language to another.
PS3's Power PC unit in the Cell Broadband Engine is only a single 2 threaded core, the 360's is 3X more powerful than PS3's PPC, yet XB1 has no issues in handling that code, this would be even easier for PS4, because it's only a single core's worth of work.
Code that runs on SPEs can be moved over to PS4's GPU using a virtual machine, translated from ISA to CISC.
Microsoft has already shown with their 360 BC that an NVidia GPU can be emulated easily by an ATI GPU, since RSX is a very weak NVidia GPU roughly a decade old at this point it could easily be emulated by modern AMD GPU technology.
Designing a virtual machine to do all of this isn't impossible, it would just require Sony to dedicate the programming resources to tackling each problem.
You can say anything is impossible if you're unwilling to try to tackle the task, but really when you break down each issue it becomes perfectly feasible that they can be resolved.
