I like this cosmology calculator: https://www.astro.ucla.edu/~wright/CosmoCalc.html Enter redshift z=1100 (which is the observed redshift of the CMB) and hit the “general” button, which calculates the distances using the currently-accepted general model and Hubble parameter/dark matter/dark energy values. This gives the “comoving radial distance” of 45.5 Gly (giga light years). That means that if right now, at this very instant, you put down a meter stick in front of you, and the buddy next to you put down a meter stick, and the buddy next to them, and so on through the next galaxy, and every galaxy, all the way to the place where the CMB in that direction originally came from (the place is still there and there is probably a galaxy there now though there wasn’t one back then), there will be 45 billion light years worth of meter sticks.
The other values of note are the light travel time of 13.72 Gyr (travel time is how distances are usually reported in news articles, as opposed to scientific articles that only report the redshift z), and the age of the universe at the time the light was emitted: 0.37 My = 370000 years, which is the age when recombination happened. The total age of the universe (13.721 Gyr) is the sum of these two.
The value you probably want is the “angular size distance” in the calculator, which is the meter-stick method done in the moment when the light was emitted rather than at the moment right now. In this case the distance is 0.0413 Gly. Only 41 million light years, really close by! There was a lot of stuff packed together, but it has stretched out since. The relationship between the two distances is:
comoving distance = angular-size distance * (z + 1)So redshift of 1100 means the spacing has been made 1101x times wider.
Of course if the universe were literally stationary then your question wouldn’t make sense because the universe would never cool down and CMB would not happen. If the universe expansion had stopped at the moment the CMB happened, then the distance to the CMB you want is the 13.72 Gly travel time distance, but it wouldn’t be our CMB anymore, it would be some other last scattering surface much farther out away.
Thank you! You got what I was trying to ask, but I didn’t know exactly how to put it into words.
Put another way, now that you have landed on the number I was missing:
Each elastic yardstick of 41 million light years, has stretched to 45.5 billion light years, and it took 13.7 billion years to do it. Trying to visualize this type of abstract math borders on the surreal.
EDIT: maybe something like this famous dolly zoom?But wait, there’s more…!
I’ve heard it said often, in print and video, that inflation took the universe from subatomic size to the size of an orange, or to the size of the solar system, or even several light years, in an instant. That’s quite an error range in the narratives.But when the CMB flashed, what we call the visible universe was barely 380,000 years old, but already 41 million light years across. And the geometry of it seems flat, so if it is actually curved, it must be have been gigantically larger than that already.
Like I said, trying to visualize this borders on the surreal for a fragile primate mind barely out of the grassy steppes, in a much more placid place and time of the life of the cosmos.
if the universe was stationary The Big Bang theory would be false and the microwave radiation measured would not be a cosmic background.
in this scenario we would need another origin to explain it.
Without such an alternative theory for its origin, we could not say from what distance it is.It’s roughly evenly distributed throughout the universe. So if you imagine the universe Big Banged into existence at the current size, no expansion, it would be emitted in all parts of space, out of the primordial energy soup, before condensing into matter.
But that doesn’t really make sense because if you increase the volume you decrease the density, therefore you wouldn’t have the big bang or any background radiation at all.
But to strictly answer your question, if you picked any one CMB photon you received right now, that photon would probably have been from the edge of the visible universe, ~46.5 billion light years away. The distance would probably be slightly less because our theoretical static universe would not have expanded in the intervening time.
The early universe before cosmic inflation, was nothing but high energy sub atomic particles. Cosmic inflation kicked in, and dispersed that matter and energy. Cosmic background radiation is the remnants of that process. It comes from all directions in the universe, because it predates inflation.
Which is to say, your question can’t be answered, because cosmic background radiation exists only because of inflation. It was created before inflation kicked in, as part of a singularity, with no spatial dimensions. As a result, today, it’s everywhere, all the time, from all directions. It wasn’t far away when it was created, because far away didn’t have any meaning in a singularity without spatial dimensions.
