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When have I stated the process is supernatural? I have laid out specific facts very clearly. What specific physical mechanism is involved in creating what Einstein called "action at a distance."
It's clear that entangled particles act as one system, but whatever the connection that causes that is "outside time and space" as Zeilinger put it, and there is a reason he and other quantum physicists say that. Physical things have properties such as location (time and space), energy and matter. If you want to quibble with that, go ahead, but at least address the picture here.
There is no way that physical particles travel faster than the speed of light, or at least that's the current thinking, and to do so these particles would have to adjust their speed to create instant action at a distance, as Einstein put it.
So whatever medium is connecting the different particles is not something within space and time. It can be described mathematically as a wave-function, but that doesn't mean it has physical properties such as being limited to the speed of light, or definite locations within space-time.
You say, well, the field connects it. Ok, let's go with that. Why is the action instant?
Why does Zeiliner say it's "outside time and space"?
So, if the entangled particles are able to move simultaneously at such great distances apart, then practically T(time)=0. That, in turn, would mean that we are en route to create a time travel machine and change events that have already ocurred.