This is where lay people -- and some great physicists -- fail in their conceptualization. There is no "instantaneous."
The closest we could come is a proof that the wave function of one particle collapses simultaneously with the measurement on the other. Simultaneity in Minkowski space is well defined. "Instantaneous" means nothing at all.
No one [except people making conceptual errors] has ever claimed that the collapse of the wave functions of entangled particles satisfy a spacelike connection. However, there is no experiment one could devise that would prove the spacelike connection existed. This is because all of the entanglement experiments designed to test causality violations are measuring quantities which have no measurement along any space-time dimension. The easiest to see is intrinsic spin. The basis vectors in Hilbert space for "spin" don't have any space or time components. They don't project onto spacetime axes at all. This is why the no communication theorem applies.
People find the invocation of nonlocality [which is not the same thing as simultaneity] astonishing and weird -- except when they overlook it, which is most of the time; but it's already present in the classical physics of Newton and Maxwell, as well as the quantum physics of Schroedinger, Dirac and Klein-Gordon Equations -- as metaphysics.
In Newton's world, F=ma holds throughout the universe. That's about as nonlocal as you can get. And the laws of classical and quantum physics both have that kind of nonlocality or they would not be useful for getting any answers.
Isn't this more or less what the Aspect experiments did?