Cosmic microwave background radiation: why did it take so long to get here?

I understand that the universe after the big bang was a super dense cloud of elementary particles, and because of this high density was "not transparent" to light. Then, roughly 400.000 years (380.000 to be exact) after density and temperature lower enough for the first hydrogen atoms to form. Thanks to the lower density, now photons were free to travel. Theoretically the Cosmic Microwave Background Radiation (CMBR) should be this light that "became free" 400.000 years after big bang. Let's reason in 2d for simplicity. If the universe was a circle, the maximum radius could have been a bit less than 400.000 light years (it's probably an exaggeration, but let's simply assume that matter can't travel faster than light). So, if we imagine that the matter that eventually generated the earth was on the border of this circle (and somehow we are still close), the most far photon at that time should have been at 800.000 light years.

If my reasoning is correct, I can not understand how it is possible that we see that photon after 13 billion years. It should have reached us long long time ago.

• When the CMB was emitted, the Universe was much, much larger than 400,000 ly in radius (quite possibly infinite). Although nothing can travel through space faster than light, space itself can expand at any rate. Plenty of answers cover this, e.g. Big Bang did not happen at a point. The observable Universe, defined by the distance that light has had the time to travel since Big Bang, is not equal to the age of the Universe times $c$, but much larger since space expands between the time of emission and detection.
– pela
Oct 15 '16 at 20:10
• "should be this light that "became free" 400.000 years ago." How do youwork this out - it seems to be your main problem. The CMB photons have been travelling for the time since the big bang minus 400,000 years. Oct 15 '16 at 20:47
• While your numbers are off, the simplest answer to this conundrum is, If you imagine the universe at it was 13 billion years ago and take 2 objects 1 billion light years apart, or (or other large distance if you like, but much smaller than the current size of the observable universe). one of those objects emits a light ray towards the other. It takes quite a bit longer than 1 billion years for that light to reach the other object because the space between the objects is expanding the entire time. Oct 16 '16 at 0:27
• Hi @user3555654 - in your terms, that ball is expanding. Oct 16 '16 at 15:11
• @Rob Jeffries I meant 400.000 after big bang. Corrected in the text Nov 11 '16 at 18:29

Here's a very, very simple explanation:

"why did it take so long to get here?"

There's two aircraft carriers, A and B, fifty miles apart on the ocean. You've got a helicopter that flies 50 mph. Of course, it takes one hour to make it from A to B.

Now, imagine A and B are both moving - they're steaming away from each other at a good speed.

Of course, it now takes longer than an hour for the chopper to make it between A and B.

Regarding the many, many mysteries of the metric expansion of space, this trivial observation is just one thing to bear in mind. Note that of course this is not a full and complete analogy, and the analogy is indeed utterly wrong / totally irrelevant to many aspects of the broader discussion.

"I thought that the photons were "trapped" in an expanding ball" sure, the chopper can only move at 50 mph over the water underneath it meaning that at any given time it can only have moved so far over the water underneath it (a sort of "circle of achievablity", if you will). But you can see with the carriers moving the hell all over the place, it's just an open question whether the chopper reaches B in much less than an hour, much more than an hour, or can never reach B at all.

• Thanks for your explanation. My problem was that I thought that universe was expanding way slower than light speed. So for me the light should have reached us long time ago. Nov 11 '16 at 18:31