How can we see something that’s 32 billion light years away when the universe is only 13.8 billion years old?

The short explanation is that the Universe is expanding, not static. Light from a clump of matter that left 13.8 billion years ago, and started heading towards (what is now) us, has been traveling for 13.8 billion years.

Therefore, you would think that that light has traveled 13.8 billion light years, and therefore this must be the distance between us and that distant clump of matter (or whatever objects it has now formed into).

This would be true in a static Universe, but not in an expanding one.

The reason is that, in the meantime, while the light was traveling, the clump that it left from has been continuously expanding away from us, so that its present-day distance is much farther than what you would infer from the light travel time.

It’s not a simple calculation, but if you work it out using the Friedmann Equations, taking into account the full history of the expansion rate of the Universe, you find that light arriving at Earth just now from 13.8 billion years ago is coming from points in space that are now a distance of approximately 46 billion light years away.

Thus, this is the farthest distance out to which we can see at the present day.

To emphasize: this distance is the distance to these points of origin now, at the present day. Obviously these points of origin were much closer to us at the time when the light left.

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