Idea of entanglement and EPR Paradox

Let’s try to understand this hyped word ”entanglement” by considering an example. Say you have two objects: one black and the other white. You put them into boxes and shuffle them around. Now if you open one of the boxes, and see it’s black, then you know without having to check that the other box has the white object in it. We say that these two objects are ”entangled” which means knowing something about one causes you to know something about the other, without having to look at it. However, what makes ”quantum” entanglement interesting is the idea of superposition. Let’s go back to our example. While the boxes are closed, we don’t know which state the object in each box is in. If it were truly impossible to know which one is which -which isn’t actually the case in everyday life, but let’s say it was this time, then quantum mechanics tells us, that each object must be both black and white at the same time. This is called superposition. There are only two possibilities, either, the A is black, and B is white, or the other way around. But superposition tells us, that all possible things happen at once, so the state of the two objects is both A is black, B is white and A is white, B is black which is a strange superposition. What happens if Alice checks her box? She not only collapses the state of A but also of B, which she didn’t even touch. In the classical case, measuring one of the particles, say finding out that its black has nothing to do with the other one. The objects already had a colour beforehand. But quantum mechanically, the objects have affect on each other. The EPR paradox exploited this difference between the classical case and the quantum one and showed that quantum mechanics cannot explain these results. Two assumptions were made by EPR:
i) The objective reality principle states that the values of physical quantities have physical reality regardless of whether or not they are measured. The internal state of each particle contains enough information to decide the results of either measurement
ii) The local determinism principle states that the result of one system’s measurement cannot impact the outcome of another system’s measurement.

These two assumptions together are known as the assumptions of local realism. So for now we just assume that if we have an entangled pair A and B, then measuring A really does affect B. Now, if the boxes get shipped to the other sides of the universe to Alice and Bob. Alice opens hers a second before Bob opens and finds her object is black, so Bob must find that his is white. During this difference of a second, A must tell B that its been measured and what result it decided to be or else B won’t know what to do. But that message has to go a long way in a very short time. In fact even light couldn’t go that.From Einstein’s theory of relativity nothing can go faster than the speed of light. This means quantum mechanics is wrong.