The equivalence is between an accelerated reference frame and a gravitational field, not between the two twins. The principle of equivalence is one of the foundations of general relativity. It states that the laws of physics are the same in an accelerated reference frame as they are in a gravitational field. That's why one way of providing "artificial" gravity in a spacecraft is to continuously accelerate.

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind." - William Thompson, 1st Baron Lord Kelvin

"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

This isn't right. This isn't even wrong. - Wolfgang Pauli