Okay so now that we have an entangled pair of particles, an interesting thing about being entangled is that, the particles stay entangled as a system even if we move them away from each other.
Even if we move the individual particles apart to vast distances in the universe, they keep behaving like a system in superposition of multiple states.
So consider we have such an entangled pair separated by a huge huge distance (light years away) in the universe. The moment we make a measurement of the system, let's say by measuring one of the particles, it obviously collapses the superposition of the system to one of the possible states, like it should as per quantum mechanics. This implies, that instantaneously both the particles collapse to one defined state (spin up or spin down).
Think about this for a moment!
The particle which was put under our measurement device collapsing to a defined spin immediately when measured sounds fine, but the other particle also collapsing to a defined spin immediately at the same time is crazy!! It means that the collapsing effect, was transmitted from the measurement end to the other far away particle instantaneously without any delay.
Violation Of The Most Fundamental Principle - Causality
The effect from a cause cannot travel faster than the speed of light is the fundamental principle called 'Causality'. Most of our classical physics, involving Einstein's Theory of Relativity is based on this fundamental assumption, that nothing can travel faster than the speed of light, even the effect from a cause.
But in the case of entangled particles, the collapsing effect is transmitted to the other end faster than even light - instantaneously. This is the EPR Paradox.
Einstein called it "Spooky action at a distance."
With this thought experiment, Einstein believed that he had proved that the Copenhagen Interpretation was incomplete in thinking that particles could be in a state of superposition of multiple possible states, because as per the EPR Paradox, that would mean that even our most fundamental principle of Causality would be violated.
Experimentation However Proved That Bohr Was Right!
You'd be surprised to know, that much later, in multiple experiments, it was indeed observed that Causality is violated in the case of entangled particles and that the collapsing effect is transmitted instantaneously.