The issue is not so much with the word "determine" as it is with the word "instantaneously". You could say "Entanglement lets the measurement of one particle instantaneously frob the state of a partner particle" without knowing or specifying what the word "frob" means and you'd have the same problem: you're claiming that measuring one particle
does something to the other particle, and does it
instantaneously and, moreover, that this is mysterious because the two particles are far apart (hence the slogan "spooky action at a distance"). All this is wrong. There is no "spooky action at a distance" because there is no
action. Whether that action is "determining" or "frobbing" the state of the other particle is irrelevant.
The correct story is that measurement and entanglement are the same physical phenomenon. The creation of an EPR pair is the first step in any measurement process. The correlations in EPR measurements derive from exactly the same physical process as the correlations in "ordinary" measurements (I put "ordinary" in scare quotes because, as I said, even "ordinary" measurements start with the creation of an EPR pair). When you "measure" the two halves of an EPR pair what you are really doing is performing two measurements on whatever system produced the EPR pair to begin with. When you look at it that way it is not at all surprising that the measurements should be correlated.
For more details see:
https://www.youtube.com/watch?v=dEaecUuEqfc
http://www.flownet.com/ron/QM.pdf
