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If we take two balls that change colours white and black, if we set that change in colours is always opposite one from another, for sure if we take one ball to the end of universe, if that ball will have black colour and second will have white colour..

How we know that spin (black and white balls) are not set from start when two entangled photos are made?

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What OP is suggesting is not entanglement. In OPs case the properties of both the particles that shoot in opposite direction is predefined albeit unknown to the observer due to lack of full knowlegde so to say.

Bell famously showed that one can experimentally test if thay is really the case in nature.

[Partly quoting from wikipedia] He showed that if measurements are performed independently on the two separated particles of an "entangled pair", then the assumption that the outcomes were predefined (also see Einstein–Podolsky–Rosen paradox) implies a mathematical constraint on how the outcomes of the two measurements (i.e., performed on each particle) are correlated. This constraint is called Bell inequality. Bell showed that quantum mechanics predicts correlations that violate this inequality.

In other words quantum mechanics (with its definition of entanglement) predicts a different correlation for the output of measurement then what one might expect from OPs proposal.

In addition experiments have shown that quantum mechanics description is correct. The 2022 Nobel prize was awarded for this verification.

S.G
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