I understand that the further you look out into the universe, the further back in time you see. Is it then theoretically possible that we could see the primordial light itself with powerful enough telescopes? (I mean the first light that came into being through the process of the Big Bang.)
And, drawing our telescope back, and coming forward a little, could we see the formation of the first galaxies, etc?
Or is there some limit, some physical law which in effect says, you can see thus far back, and no further?
The early universe was composed of a “soup” of free elementary particles (primarily neutrons, protons and electrons), and was opaque to light, since these particles would immediately absorb and randomly re-emit any stray photon. About 380,000 years after the Big Bang, the temperature of the universe had fallen sufficiently for hydrogen atoms to exist, and became transparent to most wavelengths of radiation. This point is called the “decoupling” of light and matter, and the Cosmic Microwave Background is radiation from that era, redshifted into microwave wavelengths. So in a sense we already see as far back as we possibly can, because the universe was opaque before that period.
The current age of the universe is generally accepted to be around 13.7 billion years, and objects as old as 12.7 billion years old have been observed. We aren’t that far from the limits of the ultimately visible.
It depends on what you mean by “the primordial light of the Big Bang”. The furthest back we can see is to about 300,000 years after The Beginning, using microwave telescopes such as MAP (images of that first light are available on that webpage). This is not the first light that ever existed, because before that time, the Universe was essentially opaque to light: You’d have light, but it would only travel a short ways before it would be absorbed by some particle and re-emitted. At about 300,000 years, the Universe cooled down enough that it de-ionized, and at that point, abruptly became very transparent, so any light that was around at that time just kept on going and going, and some of it is reaching us now. This was significantly before the formation of galaxies and other interesting structures in the Universe, so yes, we can and do see very early galaxies being formed in telescopes.
Note that the limitations I mentioned above apply only to the various sorts of light. There are other ways to “look” at the Universe which are less limiting. Neutrinoes, for instance, interact much less with matter than light does, so the Universe became effectively transparent to neutrinoes earlier than for light. That takes us back to about 200,000 years after The Beginning. And gravity interacts far more weakly yet; we have not yet been able to directly detect gravitational radiation, but it’s believed that once we build good enough detectors, we’ll be able to “see” gravitational waves which originated a mere 10[sup]-20[/sup] seconds, or even earlier, after The Beginning. If, that is, NASA ever gets the funding to build the durned things, which at the moment looks somewhat unlikely.