If you projected our four dimension space onto the 2d surface of a balloon you can see an analogue. As the balloon inflates galaxies on the surface of the balloon get further apart. Light can travel forever around the surface of the balloon and never “hit” what the balloon is “expanding into”. And from the perspective of all the 2 dimensional creatures living on the surface of the balloon their universe isn’t expanding *into* anything, they just see everything moving farther apart. In this analogy the space inside and outside of the balloon can be thought of as time. The balloon was smaller earlier, and will be bigger later. But the balloon is not expanding into physical space like you or I (or our 2 dimension friends) experience. Now convert that flat balloon surface+time existence to our three dimensions + time and you have a sense of how our universe can expand but not expand into anything. That requires an imagination better than mine.
This analogy does break down however because as far as our observations have shown the universe is most likely “flat” (or has a curvature so small our observations can’t detect it yet) and likely doesn’t curve into (like a balloon) or away from itself. As far as our experiments show, based on the error range of our observations measuring the curvature, the universe must be *at least* 23 trillion light years in diameter (we can only see 93 billion light years in diameter) or 15 million times bigger than what we can currently observe. Consider we estimate there are 2 trillion galaxies within our 93 billion light year sphere and you can imagine the massive number of galaxies that likely exist in the full universe.
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