Common! Haven't you realize by now that the concept of "dimension" in physics, including Einstein's four, is a fallacy? The fallacy of misplaced concreteness.
Indeed, it all started with Descartes' two "mathematical" data of planes, to which a third one was added to situate an object in space.
However, this "third "dimension" was already present in Descartes' plane, since, without a third dimension, there is no room for the two first ones to exist. One and two-dimensional realities only exist in mathematics as the 10 of String Theory.
"Dimensions" exist in reality, but they are "domain" possessing different laws and properties.
Energy is such a dimension with its laws and properties; so are matter, life, and human consciousness. These are the "four dimensions," which the General Theory of Relativity "mathematically explain. (I say "human" for the "fourth dimension" because our domain is the only dimension comprising elements (ourselves) conscious of living in space and time. (That is why Einstein's had it right, but from our point of view!)
Everything happens in space and time, but we are the only living entities that had to conceptualize these elements to "objectify" reality to survive in the Savannah. It is these notions of space and time, indeed, that has allowed us to create the tools we needed to survive the millions of years we lived in the African Savannah.
Without this "extra somatic" conceptualizations, which have been transmitted to us as infants for eons while developing our "minds" in "post-fetal" social wombs, we would not be here to talk about them. Without this essential post-fetal period of development, we never become complete human beings (cf. feral children).
You are telling me that "dimensions" in physics well explain reality? So were the crystalline spheres, the epicycles, the equant, and the deferent that we were using to explain the behavior of the planets' motion when we believe that the Earth was the center of the universe for two thousand years. The Ptolemic system did indeed explain reality for two thousand years, but he did not have it right.
The same will happen to science when we realize that we are 100% made of elementary particles, all "entangled" with the whole universe and that space and time do not matter for them as they should not for us either.
Hard to believe? So was the mention that "we are not at the center of the universe" for our forbear academicians discussing how many angels could stand on the head of a bin. As these "savants" were irrelevant for the advent of science, so is modern science for our survival.