How old is Earth? It's an interesting question. What does it mean to be old? It means to have survived long in time. So in order to ask what it means to be old, we must first ask, "What is time?"
Good luck with that question.
Wikipedia, I notice, has taken a highly controversial position on the subject. "Time," it says, "is a dimension... and also the measure of duration of events and the intervals between them." That's not what we usually think of when we talk about time. If it is a dimension -- usually the fourth -- then things within it are static. There is no change in the fourth dimension: everything, past, present and future, is ordered and obvious, like looking at a graph.
That is not obviously right, although some contemporary physicists really like the idea of time as a dimension. Those of you who read my Arthurian novel were introduced to the concept of thinking about time that way: but of course I didn't stop with that approach, whereby there is no real possibility or potentiality, but only a determined single time. That doesn't seem right, and it doesn't seem real. We are aware of unrealized potentials all around us. I know in my heart that I could have had beans for breakfast instead of eggs, for instance. The beans were there. The eggs were there. I was there, and I was hungry. I made a choice.
Traditionally there are several answers to the problem that have made sense to people. Three of the leading answers are Aristotle's, Proclus', and St. Augustine's.
Aristotle's is a reasonable answer: time, he says (in Physics VIII) is the measure of motion. But there are only things and their qualities in Aristotle, which means that every thing must have its own time, each separate and different. Time is a quality that belongs to the thing.
That aspect of Aristotle's theory has been a problem for a lot of people, because our experience of time is that it is the same for everything. An hour for me is an hour for you: that's why we can meet for lunch. How could I have one time, and you another, my horse a third, and so on?
But we learn from relativity theory that there is something to this matter. Time is not the same for everyone and everything. And yet it is not really a quality of the thing, either: it is relative, for example, not to my speed, but to the difference between your speed and mine. So it is, in a way, a quality of mine; but in another way, you are indispensable also. It's a fact about us, even though it is not the same for us. (See here.)
So Aristotle is not right, not quite; but we still aren't there.
Proclus has a theory that time is atomic, in the ancient Greek sense of being finally indivisible. You can divide a minute into seconds, and seconds into parts of seconds, but there comes a time -- he thought -- that is really the smallest length of time that can practically exist. This, I suppose, might be an analog to the Planck length: and that's useful, if we believe as Aristotle did that time and motion are geared together. For those of you who have JSTOR access, there is a good article on the subject here.
Augustine, though, has what I take to be the most interesting account. He points out that the past and the future do not exist in the same way that the present moment does. As much as you enjoyed going to the fair yesterday, it's gone: and as much as you are looking forward to Christmas morning, it's not here.
So what we have is the now. But how long is now? So short that it is gone before you can name it.
That's a problem, because it means that we are doing things with our minds that involve times that do not exist. When we begin a sentence (for Augustine it is a prayer), we are somehow aware of a desire to say something in a time that doesn't exist: and when we are saying it, we remain aware of how much has been said in the past that no longer exists, and how much remains to be said in the time that has not come to be.
If we couldn't do that, we couldn't speak or think at all.
So for Augustine, time is a kind of extension of our soul into the realms of things that do not exist. How we do that is a mystery, but our common experience suggests that somehow we do in fact do it.
Of course one way of responding to the Augustinian answer is to suggest that the past and future do exist -- that they are, as the physicists have it, a kind of dimension whose existence is sustained. But the physicists can't explain freedom; they are left to declare it something of an illusion, even though I am quite sure that I could have had beans and not eggs for breakfast.
So we are back at the beginning of the question. What does it mean to be old? It means to have lived long in time. What is time? Is it the same for all things, and from all perspectives? It seems not to be, though it also seems to sustain a relationship between all things, while managing to be different from different perspectives.
Which means that there is no answer to the question -- no final answer. How old is Earth? It depends on whom you ask, and how they stand in relationship to it. Perhaps that relationship is physical, and perhaps it depends on where they are in their prayer.