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Is there no way to prove

that the earth is young or old?

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At first glance, it would seem that if the world and the rest of the universe was created less than 10,000 years ago, that there should be some way to absolutely prove its approximate age. If the universe evolved due to natural forces or as a result of God's interventions for the past 10 billion years, it would seem that there should be some way of proving that.

An all powerful, all intelligent God might have chosen to create the world, its life forms and the rest of the universe in such a way that they all look as if they developed naturally. For example, God may have created the universe in 4004 BCE, and:

bullet Created trees containing tree rings which give the impression that the trees were in existence for hundreds or thousands of years previous to the date of creation.
bullet Created worn-down mountain ranges that look as if they once had had tall peaks millions of years previously, and had gradually eroded away since.
bullet Created stars millions and billions of light years away from earth, and then created light radiating from each star to earth so that an astronomer would conclude they look as if the rays had left their stars millions or billions of years ago.
bullet Created fossil-bearing rocks in layers so that each layer contained only the remains of certain specific species of animals. Paleontologists would later observe that a particular species was only found in a certain rock layer around the world. Thus they would conclude that the species did not exist before or after that layer of rock was laid down. The would assume that only those species found in a specific rock layer actually existed together on earth during the same era. They would not realize that all species were created along with the earth and lived together, only to be carefully sorted by God during the flood into separate layers of sediment that later became rock.

In other words, God created the universe in such a way as if it appears to have been evolving over billions of years. There is no test that a scientist could design that would differentiate between:

bullet a universe specifically created to look as if it had a evolved over multiple billion of years in response to natural forces, and
bullet a universe that actually evolved over billions of years in response to natural forces.  

We suspect that there is probably no way to resolve these differences in belief through reason or scientific investigation, unless:

bullet A time machine could be created that would let a person go back to 10,000 BCE, look around, and determine first-hand whether the universe existed at that time. Unfortunately, time machines do not exist and are probably impossible to construct. Even if one could be built, there is no way in which it could be calibrated and its proper functioning verified.
bullet If the universe was created by God, and if God were still active in the world, then He might wish to inform humanity directly in such a spectacular way that skeptics, atheists, agnostics and others would accept his word. For example, he might rearrange a few hundred stars to spell out the phrase "I AM" in the sky. This would be a trivial task for an all-powerful deity. No communications of this type have happened in the past millennium. If there had been, then the number of atheists and agnostics would have shrunk to zero.

There is thus no way to prove that the earth and the rest of the universe is either young or old. However:

bullet If you assume that the Bible is inerrant, and that it is to be normally interpreted in a literal manner, then the beginning of the book of Genesis shows conclusively that the earth is obviously less that 10,000 years old.
bullet If you assume that God does not exist, or that God exists but did not take part in creation, then the only logical way to interpret the geological, fossil, and other evidence is that the earth is billions of years old, and that most of the rest of the universe is even older.

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