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drnickbone comments on Belief in the Implied Invisible - Less Wrong
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I'm pretty sure the spaceship doesn't actually seem to bleep out of existence. It's just that, from your point of reference, time passes slower and slower for it.
I could be wrong, though.
I think this is right... Crossing a cosmological horizon is very similar to crossing a black hole event horizon.
In the reference frame of an observer outside the black hole, the spaceship would never enter the black hole. Rather it just hovers on the edge of the horizon, getting more and more red-shifted. If the black hole evaporates (due to Hawking radiation) then the spaceship's state is returned in scrambled form by the radiation, so there is no net loss of information from the region outside the black hole.
The same applies to a spaceship crossing our cosmological horizon... From the reference frame of an Earthbound observer, it never does, but (probably) a scrambled ghost image of the spaceship eventually returns in Hawking radiation from the horizon.