I understand that we see the cosmic background in microwave(CMB)because, due to the expanding universe and great time/distance, the light has shifted through red and infrared all the way to microwave.
My question is, how then can we view stars in visible light that are 13.2 billion light-years away, nearly as old as the CMB itself?
ANSWER: The amount of redshift depends upon how close to the CMB you are looking. At well over 13 billion light years' distance you can only observe things at infrared and microwave wavelengths, so only space telescopes will serve; but at distances that aren't that much closer the redshift is substantially smaller and you can "see" light that was originally in the ultraviolet part of the spectrum. This means you are only seeing the radiation from very hot very bright stars, but that's all you'd see at such distances, anyway.
As an example, suppose that we were to observe something with a redshift "z" equal to 5, meaning that the wavelengths of its radiation is shifted to five times longer than normal wavelength by the time it reaches us. That means that the peak radiation from a star with a temperature 4 times hotter than the Sun (about 25000 Kelvins), which is normally about 1250 Angstroms, would be red-shifted to about 6250 Angstroms (5 times longer than normal), which is at the red end of the visible spectrum. That value of z corresponds to a light-travel time of about 12.5 billion years, which is what we actually mean when we say that we see something at a distance of 12.5 billion light years. The object wasn't really that far away when the light by which we see it was emitted, and it is now much further away than that. The details depend upon what "shape" you assume the Universe has, but a typical guesstimate of a "flat" Universe would place the object about 4.5 billion light years away at the time it emitted the light we now see, and about 26 billion light years away now (putting it so far away that we will never see the light it is now emitting).
The most important thing involving your question is the fact that even "at" 12.5 billion light years "distance" (meaning that the light took 12.5 billion years to reach us) we can still see stars using visible light (even though it wasn't visible light when it was emitted). The objects we see with light that took that long to reach us were much closer when the light was emitted, but since the space between here and there was rapidly expanding, the light had to cover a lot more distance than you might expect, to reach us (namely the 4.5 billion light years' original distance, plus an additional 8 billion light years caused by the expansion of the space the light passed through). Meanwhile, the object was being carried away from us faster and faster because as it moved outward there was more and more space between us, and the expansion of that space increased as its total distance increased (in this example, by an additional 21.5 billion light years during the 12.5 billion years it took the light to reach us).
I think that's pretty clear, but I have the advantage of knowing what I meant to say. Experience as a teacher tells me that it isn't necessarily as clear as I would like to believe. If there is any part of this answer that isn't reasonably clear, please let me know and I'll give it another try.
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That was the perfect answer for me, a very curious non-scientist, and hit my level of understanding just right. It explains to me that Hubble can see (in visible light, I think) something 13.2 ly away because the light had been shifted down to there from higher frequencies.
The added information about past and current location of light sources due to expansion was also very interesting to me, as I have wondered some about that. You mentioned flat or curved space impacts your figures, but I thought that estimations about the rate(s) of expansion is the most important factor for such estimates. In fact, don't all of our estimates of the age of the universe depend upon how fast we think the universe expanded, or do we have other ways to say the universe is 13.75by old?
If the Universal rate of expansion was a constant, then all we would need is that Hubble Constant. But that number is actually a "constant" throughout the more or less visible Universe only at a given time, and slowly changes with time in a way that depends upon the density of the Universe. Near the beginning of time the Universe was expanding much faster than now, in the sense that the rate of expansion of a given amount of space was much larger (and therefore, so was the Hubble "constant"). Right now, 300-some million light years of space is expanding at about 700 km/sec (the ratio of the two numbers being the Hubble constant, which is about 70 km/sec/Mpc, or 700 km/sec/326-million-light years). Very early on the rate of expansion was considerably faster, because the initial "Inflationary" expansion was nearly infinitely fast, and even after Inflation ceased the outward motion per unit of distance was very, very fast compared to now.
However, at that time the Universe was much "smaller" (things were closer together, not having been carried as far away from each other as they now are) and denser, and as a result the rate of expansion per unit of space was rapidly decreasing. If the mass-density of the Universe were a "critical" value, the gravitational effect of the mass would have gradually slowed the expansion in such a way that at each moment in time the current rate of expansion of space and the current rate of slowing of the expansion by the mass of the Universe would eventually result in a very slow expansion, but also a very small rate of reduction of that expansion, that would just go on forever and ever without ever quite stopping. (This is like a rocket that is fired upward just fast enough to escape the Earth's gravity, but not fast enough to have any significant speed left by the time it is far away from the Earth; in other words, at exactly the escape velocity.)
However, as the Universe expanded its density decreased (the mass in a given part being spread out more and more), and since the actual density is less than a quarter of the "critical" density, the ability of the mass to slow down the expansion decreased faster than the rate of expansion. By about 6 or so billion years ago the tendency of the empty space in the Universe to expand became equal to the ability of its mass to slow the expansion, and instead of decreasing its rate of expansion, the expansion "coasted" for a while. Then as the density decreased still further, the tendency of space to expand became larger than the ability of its mass to slow the expansion, and ever since then the expansion per unit of space has been going faster and faster. (In other words, the Hubble Constant started off much larger, gradually decreased, stayed roughly constant for a while, then gradually increased, and the currently quoted value is only what it happens to be at the current time.)
How this (past, present and future) change in speed works depends upon the "shape" of the Universe. I prefer a "simple" theory of expansion in which totally empty space has a fixed intrinsic rate of expansion that is faster than the current rate of expansion (perhaps two to three times faster as a very rough guess), meaning that as the density of the Universe approaches zero the rate of expansion will approach a constant value (namely the just-mentioned ratio of two or three). This corresponds to a more or less "flat" Universe (as discussed in the paragraph at the end of this reply). But there are many cosmologists who believe that the rate of expansion has no limit, and that as the Universe continues to expand it will do so at an ever increasing rate, until it is expanding at an infinite rate. This is the most extreme version of an "open" Universe (namely, the one called "The Big Rip").
The reason that the "shape" affects the calculations is that since the rate of expansion (the Hubble "constant") is changing with time (less if the Universe is nearly "flat" and more if the Universe is more "open"), the amount of expansion that the light had to overcome to reach us (and hence the time it took) is different in different theories/guesses of how the rate of expansion has changed. Insofar as we can determine distances of very distant objects independently of their recessional velocities, we can tell how the Universe has slowed in the distant past and sped up in the recent past; but the accuracy of redshift-independent distance estimates, although much better than just a decade or three ago, is still not good enough to tell exactly how things have changed (and in any event can't tell us what's going to happen in the future without a correct theory of how the expansion works). That's why some assumptions are needed to get "accurate" numbers for things such as how far away distant galaxies once were, or now are. Specifically, when we see that light from a given object has been red-shifted by a certain ratio "z", we can more or less confidently say that the space through which it traveled to reach us expanded in a certain way compared to its original distance, and based on that, calculate the age of the Universe, the original distance of the object, and its current distance (as I did in my initial reply). But if the space expanded faster than we believe, then the same value of "z" would involve less past time and yield a smaller age for the Universe, a closer initial distance for the object and a further current distance. And although current limits on the expansion rate at various times are amazingly accurate compared to what would have been thought possible when I was a student, they still aren't good enough to rule out a distressingly wide range of possible futures.
(And now for the "last" paragraph referred to above:)
There is a bit of slop in the terms used above due to changes in the way things have been described during the 50+ years I've been following this field. Early on a constant eventual rate of expansion other than nearly zero would have been called an "open" Universe, and only a near-zero asymptote would have been called "flat". However, in comparison to an eventually infinite rate of expansion, a constant expansion rate only a few times larger than now is "essentially" flat, so in the discussion above (and in the calculations in my prior answer) I said that the Universe is nearly flat. This means that comparing what I've written to other discussions may not be as simple as it should be; but the whole field is rapidly changing, as new data come in and are trumpeted in the press as spectacular improvements to our understanding on a seemingly daily basis. (This doesn't mean that the new discoveries aren't important, just that how important they are will be more accurately determined at some unknown future date.)
I hope that the above doesn't muddy the waters more than it clarifies them, and that this takes care of this question for now. I will be busy the rest of today and tomorrow and most of Friday, so I won't be able to do much to improve on this answer until the weekend. But you are welcome to send a follow-up at any time, and if you do, I'll get to it as soon as I can.