A question concerning the act of observing distant galaxies

The comoving radius of the observable universe is currently put at $46$ to $47$ billion light years. Source wikipedia.

When we observe galaxies at great distance, such as the Hubble Deep Field at $13$ billion light years, how do we know we are observing very young galaxies in the very early universe, rather than galaxies that have entered our observable universe at a time when the comoving radius of the observable universe was $13$ billion light years and are therefore older than we might otherwise expect.

• Are you suggesting, that an alternative explanation may be, that galaxies may pass trough the event horizon at T_cosmological=0 (i.e. that there is no such event horizon)? Sep 3 '14 at 19:31
• @CuriousOne I hope not. I think that I am suggesting that we may observe a galaxy at a distance of 13 bn light years whose age is more than a couple of billion years.
– user57876
Sep 3 '14 at 19:39

The comoving radius of the observable universe is currently put at 46 to 47 billion light years.

We need to be precise about what this means. The comoving distance is the value of the proper distance at the current time, and this is calculated using the FLRW metric with the current values of the various cosmological parameters (NB that link is a 15MB PDF). So the statement is based on the assumption that the universe is well described by the FLRW metric.

So what we are seeing when we look at something 13 billion light years away? The way to answer this is to calculate the trajectory of a light ray that has been travelling for 13 billion years. More precisely we need to calculate a null geodesic for the FLRW spacetime (if you're interested the procedure for doing this is discussed in the question Photon on null geodesic). If we do this we find the light ray must have started at a spacetime point 0.7 billion years after the Big Bang. It couldn't have started at an earlier or later time, or it wouldn't be intersecting our position right now.

So if we believe the FLRW metric is a good description of the universe then we can be sure the distant galaxies we are seeing 13 billion light years away really are 0.7 billion years old. The only way they could be younger or older is if the FLRW metric is not a good description of the universe. But in that case we wouldn't know the galaxies are 13 billion light years away, because the calculation of their distance assumes the FLRW metric is valid.

• My technical background is modest at this stage, but I think I understand what you are saying here. When we calculate the trajectory of 13bn year old light according to FLRW, we must necessarily conclude that the light originated 0.7bn years after big bang. Hopefully I will be better able to fully understand all of the assumptions when I have a more mature understanding of the subject. Thanks for taking the time to answer my questions.
– user57876
Sep 4 '14 at 17:33

If string theory is reasonably accurate there would seem to be no real need for more than one string, since Planck level items are not restricted by time and space. Therefore, associative laws and macro distances would be essentially moot.

• I'm having a hard enough time naively understanding the classical view. I fear I may have to leave String Theory to a time when I'm too old to understand it. Does the topology of String Theory not include a measure of distance, or does String Theory not have a topological interpretation.
– user57876
Sep 3 '14 at 22:47
• @PaulStuart, can you relate this to the original question? Sep 3 '14 at 23:43
• @HDE 226868, yes, I am suggesting that time and space in classical observations may be similar in some sense to the square root of -1, providing us convenient terms to describe observations, but terms that have no demonstrable mathematical substance. Sep 4 '14 at 0:36