We can not even see all the way to the Big Bang, but we do get pretty close. The problem is that you can only see through space that is transparent. However if you put enough matter and energy in a small enough space, like the conditions were after the Big Bang, then it forms opaque plasma. So this is the limit to how far we can see in space, and therefore how far back in time we can see.
There is a limit mainly because our universe is expanding.
The further apart two points are, the further it expands. In small distances this doesn’t matter, forces like gravity and electric forces easily compensate, your atoms say don’t get ripped apart because forces pull them back together. But over longer distances, the universe expands more meaningfully.
At some point the universe expands faster than the speed of light relative to us. So we will never see these parts of the universe because the light will never reach us.
Light isn’t infinitely fast. The maximum distance we can see is a function of how far away an object is, and how long it takes for the light to reach us. The universe is growing bigger faster than the speed of light. The longer time goes on, the less of the universe we will be able to see, since we will be getting further away from those objects faster than light travels towards us.
We also can’t see back to the big bang because there was a period after the big bang where the universe was opaque, rather than transparent, so light couldn’t travel through it. Eventually the universe cooled down enough that it became transparent. The faint light echos of this time period are now observable as the cosmic microwave background radiation.
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