How Was Quantum Entanglement Theoretically Predicted?

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San K
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Schrödinger had proved/predicted QE theoretically prior to experimental (though not loop-hole free) verification.

the theory also firmly predicted that QE could not be used to send instantaneous signals.

the theoretical understanding/prediction of QE was there prior to experimental observation (?)

Question- What knowledge/logic was used to prove/predict QE theoretically? - explain in layman's terms/language

i.e. what body of QM knowledge, rudimentary observations were known prior to bell's tests?
 
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Nothing is ever "proved" theoretically - QE was first shown to be a consequence of the Schrödinger equation as "Bell's Inequality" (iirc)... which you know. Presumably, therefore, you know the history - so your question does not make sense.

Perhaps you imagine that QE theory must have been predicated by some sort of observations? afaik this is not the case - rather it came about as a result of attempts to disprove or find limits to QM. (I think the earliest was in the EPR paradox).