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In short, it depends on who you ask. Answers range from as little as 4,000 years to as much as 4.5 billion years old.
The age of the earth is a topic of great controversy with people aligned into two basic camps. It is important to note, that as with most things, there are people with beliefs that bridge the two sides, but dividing the beliefs into two disparate camps will help in a cursory discussion of the age of the earth. The two differ basically on whether religion plays a role in the analysis, and with that we get two groups — the traditional scientists and the creationists.
On the one hand, we have the traditional scientists who base the age of the earth on scientific proofs and theories. They point to things like carbon dating, evolution, radiometric dating, and the big bang theory. This group, sometimes referred to as the secular-, evolution- or science-based group, generally believe that the earth is about 4.5 billion years old. What the traditional scientists or secularists generally do not consider in their analysis of the earth’s age is something the other group does consider — religion.
This religion-based group, which also includes scientists, is commonly referred to as the creationists. It’s important to note that when we speak of this religious-based camp we are referring primarily, but not only, to the Judeo-Christian religions. Hindus for example generally believe the earth is billions of years old and has a cycle of existence and non-existence. The creationist camp, like the traditional scientists, includes a variety of beliefs, but the majority of creationists provide dates for the age of the earth in the range of 4,000 to 10,000 years old. This group bases the age of the earth on the literal interpretation of religious texts, namely Genesis in the Old Testament.
Creationists may point to the flaws in carbon dating as inaccurate for deciding the earth’s age. Traditional scientists, however, note that carbon dating is only one way to gauge the age of rocks and fossils. Several types of radiometric dating methods are employed to determine the age of the earth. These methods evaluate the half-life of radioactive isotopes present in rocks and minerals and other material. Typically, traditional scientists may look at the half-life of substances like argon, lead, potassium, and uranium, in addition to carbon.
To support arguments that the age of the earth is much younger, creationist scientists argue the young earth theory not only based on biblical evidence, but scientific theory. Some creationist scientists, for example, suggest that the accumulation of dust on the moon should be significantly higher if the earth was billions of years old. Further, creationists suggest that the amount of helium currently in the atmosphere suggests that the earth must be younger. If it were older, there would be more helium in the atmosphere. Creationist scientists may also challenge the validity of radiometric dating methods. They believe that such dating may easily be contaminated, voiding the tests.
Are you working as a scientist? Scientific society tries to be objective in observations and findings, even though I can promise from practice that it is regularly not, but this is a topic for science philosophy. Nevertheless, it's always good to bear in mind the problems with science and the dominant paradigm we're living in.
If you objectively/critically look at the topic (do literature research), you will find sufficient studies which explored enough controversial observations where interpretations of a 4.5 billion years old earth just doesn't make sense. (extremely different dated age of skeletals in sedimentary layers with same radiometric dating methods, etc.)
Young earth creationists (6,000 years old earth) is, scientifically speaking, very unlikely also. I would advise
people search good sources of dating methods and the critics on it as well as looking at explanations of the Taphonomy to understand more about it
But stating that it is crystal clear that the earth is 4.5 billion years old is not different (scientifically objective) than the young earth creationists talking about 6,000 years. Sadly enough, this is the current paradigm since (macro)evolutionary processes etc. need that much time to interpret their findings. Do research, think critically and find out for yourself whichever interpretation(s) make the most sense.
"The age of the earth is a topic of great controversy..."
There is no controversy. But there are may who are scientifically illiterate. The Earth is 4.5 billion years old.