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Distant galaxies are rushing away from us without moving. It is the space between that grows.

Astronomy Facts, sourced to NASA Imagine the Universe.

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What it means

The light from a far galaxy arrives stretched toward the red end of the spectrum, and the further away the galaxy, the greater the stretch. The natural reading is not that we are at the center of an explosion. It is that space itself is expanding everywhere at once, carrying the galaxies with it, so every observer anywhere sees the same thing. Run the expansion backward and everything was together about fourteen billion years ago.

The claim comes from NASA Imagine the Universe.

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