>Relativity does not forbid anything from moving faster than light, only stuff
>that has mass or energy or carries information.
As you point out later, this isn't true. Relativity doesn't say things
can't move faster than light; it only says they can't move AT the speed
of light. (Actually, it doesn't even say *that*; it just says that it
takes an infinite amount of energy to accelerate a non-zero-mass object
to c. And experiments bear this out to several decimal places. But of
course relativity could some day be proved wrong...)
>It's been proven experimentally that some quantum effects propagate
>instantly and for unlimited distances.
No, it's been proven experimentally that some quantum effects propagate
without measurable delay over a few meters. That's a big difference.
The effects definitely propagate faster than light, but it may only be,
for example, 100c. As methods for measuring time get better, we may be
able to put better bounds on that (say, >10^6 c), but I doubt we'll
ever be able to prove the effect is precisely instantaneous. And the
experimental apparatus (I assume you're referring to Alain Aspect's EPR
experiments) is only a few meters big, so saying "unlimited distances"
is far too strong a claim for what's been actually verified
experimentally.
And before anybody gets any ideas about "definitely faster than light",
remember that (as John correctly points out later in his post) these
effects can not be used to transmit information, because the correllations
can only be seen *after* you compare the data using conventional information
transfer methods (eg., walking across the room to the other end of the
apparatus :-).