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The universe is a big place – and getting bigger all the time – so at a large scale all unbound structures are all moving away from each other. So when we look out at distant objects, we need to remind ourselves that not only are we seeing them as they appeared in the past, when the light that hits our eyes first left them, but also that they are no longer in that location where they appear to be.

This issue reaches an extreme when we consider observations of the first luminous stars and galaxies – with the galaxy UDFy-38135539 currently holding the record as the most distant object observed and one of the youngest, existing 13.1 billion years ago – although UDFj-39546284 may be the next contender at 13.2 billion years old, subject to further spectroscopic confirmation.

UDFy-38135539 has a redshift (z) of 10 and provides no measurable light at visible wavelengths. Although light from it took 13.1 billion years ago to reach us – it is not correct to say that it is 13.1 billion light years away. In that intervening period, both it and us have moved further away from each other.

So not only is it now further away than it appears, but when the light that we see now was first emitted, it and the location that we now occupy were much closer together than 13.1 billion light years. For this reason it appears larger, but much dimmer than it would appear in a static universe – where it might genuinely be 13.1 billion light years away.

So we need to clarify UDFy-38135539’s distance as a comoving distance (calculated from its apparent distance and the assumed expansion rate of the universe). This calculation would represent the proper distance between us and it – as if a tape measure could be right now instantaneously laid down between us and it.

This distance works out to be about 30 billion light years. But we are just guessing that UDFy-38135539 is still there – more likely it has merged with other young galaxies – perhaps becoming part of a huge spiral galaxy similar to our own Milky Way, which itself contains stars that are over 13 billion years old.

It is generally said that the comoving distance to the particles that emitted the cosmic microwave background is about 45.7 billion light years away – even though the photons those particles emitted have only been traveling for almost 13.7 billion years. Similarly, by inference, the absolute edge of the observable universe is 46.6 billion light years away.

However, you can’t conclude that this is the actual size of the universe – nor should you conclude that the cosmic microwave background has a distant origin. Your coffee cup may contain particles that originally emitted the cosmic microwave background – and the photons they emitted may be 45.7 billion light years away now – perhaps just now being collected by alien astronomers who will hence have their own 46.6 billion light year radius universe to infer – most of which they can’t directly observe either.

All universal residents have to infer the scale of the universe from the age of the photons that come to us and the other information that they carry. And this will always be historical information.

From Earth we can’t expect to ever come to know about anything that is happening right now in objects that are more distant than a comoving distance of around 16 billion light years, being the cosmic event horizon (equivalent to a redshift of around z = 1.8).

This is because those objects are right now receding from us at faster than the speed of light, even though we may continue receiving updated historical data about them for many billion of years to come – until they become so redshifted as to appear to wink out of existence.

Further reading: Davis and Lineweaver. Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe.