[Doctor Stochastic]

...a paradox exists because the measurement itself instantaneously determines the partner as well.

That's not really a good description. The measurement on one of a pair of entangled particles tells you what a measurement on the other pair would give. It does not force that measurement to be made. The tricky part is that this is true for all measurements.

[Alamo-Girl]

Thank you so much for your reply!

The measurement on one of a pair of entangled particles tells you what a measurement on the other pair would give. It does not force that measurement to be made.

I didn't mean to imply that measuring the one forces the other to be measured.

The point Penrose made was that if such measurements were made simultaneously, there would exist a paradox.