Questioning Bell's Theorem

Imagine that you blindly place a pair of shoes into two boxes with one shoe in each. Once it is done, you send one box to John; and another to Bell without knowing which is send to whom. John and Bell live in different cities with some hundreds of miles apart. Before any of the boxes is opened, no one, including you, knows who got which shoe (either left or right). Being a pair, the shoes are called entangled in terms of quantum theory. Entanglement means that the object on either side contains some or complete information of another. Revealing one's reality would reveal another. Since there is no way to tell which shoe is in either box without opening them, both shoes, in this case, are in a dual states i.e. either shoe is both right and left. The above analogy is similar to Schrodinger's cat.

When either John or Bell opens one of the boxes, the reality is revealed and the outcome of the first opened box would instaniously affect the outcome of the second one with no time interval i.e. the impact is faster than the speed of light. This is what Bell's theorem is trying to imply.

However, this instantaneous interaction between the two boxes has no physical meaning. There is no information or matter been transferred faster than speed of light. It only states that the realities on both sides are unveiled simultaneously when one side makes an observation as long as the both sides are entangled together.

In case of electron spin experiment, used to prove Bell's theorem, the situation is a bit more complicated than the popularized story above. My concern is that the time difference between the two observations. if one side of observation occurs earlier than another, we still have to say that the realities on both sides are unveiled at same time even if the observation on the second side has not happened. At mean time, when the first observation occurs, the entanglement between the two sides is destroyed. Therefore, it is extremely important to observe both sides at exact same time. Otherwise, any arguments concerning the entanglement is not valid. Once the entanglement is destroyed, the status of the second particle is once again uncertain. For this reason, I am questioning if any Bell's theorem related experiment has put this fact into consideration. It is worthwhile to arrange an experiment with different distances on two sides.

Assuming that the time difference between the first and the second observations is noticeable (not zero). Once the first observation occur, as mentioned earlier, the entanglement is no longer exist. Therefore, the outcome of second observation should be same as any other non-entangled tests, I.e. 50% wrong. If the result still agree with what Bell's theorem predicted, then we have to agree that once reality is unveiled, the status of that reality would be kept the same until it is altered. However, this would against the current QM principles. If, on other hand, the outcome does not agree with Bell's prediction, then what are the allowed time intervals between the two observations that all current experiment has been using?

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Another thing worthwhile to try is to introduce the time factor into Bell's inequality.