For the age of the Earth people look at many different sources, some of which are debatable. To bump the age range into the hundreds of thousands of year one claim is that the answer can be found in the layers of ice in the Antarctic - which have been drilled through. The thought process is that within each individual layer is a precise summer-through-winter passing... from what I have heard is that the amount of layers found in said ice is somewhere around 160,000 thousand (suggesting that the earth is at
least that old). I haven't actually researched the claim out or tried to disprove it, but it's a place to start.
Where you hear about the millions and billions of years age range is based on radiometric dating (which has been performed on asteroids as well as Earth) and the claim of billions of stars that are millions of lightyears away. The speed of light, however, isn't constant... and it's something you can also try to research. In my mind, it is quite unfathomable to imagine a single star that is just ONE lightyear away. Multiplying the proposed speed of light (which is said to be 186,000 miles per second) by 31,563,000 (the amount of seconds in a year) equals a ginormous 6 trillion miles!
Carbon-14 dating which is something I've done a little research on is particularly interesting on how it relates to fossils.
Keep in mind this this explanation is very lengthy and incredibly technical... so if you can... bear with me. Carbon-14 happens when the sun's radiation mixes with our atmosphere, exciting the nitrogen and carbon molecules, and radiates a small portion of them, turning them into... Carbon-14. Now when I say small amount I mean VERY tiny. One out of every trillion carbon cells is Carbon-14. It is estimated that 21 pounds of Carbon-14 is produced by the sun every year, in our atmosphere, being spread across the globe. These Carbon-14 cells gets absorbed into our plant life, then the animals eat the plants, the Carbon-14 gets absorbed into the bones and once the animal dies. POOF! The fossils will no longer absorb anymore Carbon-14... it's finished... all that's left now is for the Carbon-14 to very slowly decay. This is what Carbon-14 dating means... it's a measurement of decay within the fossils. How fast does Carbon-14 decay? Well it's half-life is 5,730 years... but hold on, what's a half-life?
A half-life is the amount of time by which HALF the atoms will decay. I will give you an example. Say that when the animal died he had within him 16 atoms of Carbon-14. This means that after 5,730 years the animal will only have 8 atoms of Carbon-14 in it's bones. After 11,460 years it will have 4 atoms, after 17,190 years it will have 2 atoms, and so on and so forth. So what does this mean? It means, for the scientists, they only Carbon-14 date something that's assumed to be in the range of 20,000 - 40,000 years old - anything older and it's impractical that any Carbon-14 would still exist in the bones. This is some heavy science, but some assumptions are prominent through out it. The first is the assumption that the said animal partook Carbon-14 that's roughly proportionate to the amount of Carbon-14 that it's in the air - to give an analogy it would be similar to walking inside a room, seeing a candle, and then measuring with great accuracy how FAST the wax was melting, but having no prior knowledge of how TALL the candle was before it began burning. The second assumption is that our atmosphere was the same today as it was back then. And so... we take a journey to Genesis...
My theory lies in the "waters above the waters" mentioned in the first chapter of Genesis. The idea is that a mist (or barrier of water) existed prior to the flood. Supposing that this water did in fact, exist, then it could very well be connected with Carbon-14 dating. The "waters above the waters" severely diluting the radiation from the sun, thus,
producing much less Carbon-14.
Looking at it from this perspective gives it a whole new light. For example, if the average amount of Carbon-14 intake for any living creature TODAY is 16 atoms, and the average Carbon-14 intake for any living creature PRIOR TO THE FLOOD is 4 atoms, you would get immensely different results. Your base model for the average animal is 16 atoms, you measure the decay of Carbon-14, and you get the results of fossils that are much OLDER than they really are.
So to conclude, because this dating system is only practical with things assumed to be within the 20,000 - 40,000 year old range, it's interesting that dinosaur bones are NEVER Carbon-14 dated because of the assumption that they are
60 million+ years old. However, this hasn't stopped some archaeologists from doing it anyway. In Georgia, on one expedition of dinosaur bone hunting, a group of archaeologists had about ten sets of dinosaur fossil specimens. They went in to the Carbon-14 dating science lab - being sure to encase the bones in foil so as not to contaminate them - and then proceeded to Carbon-14 date them,
not telling them that they were dinosaur bones. Once the results came in they were none other than, fascinating. They ALL ranged within the 20,000 - 40,000 year old range. They told them, rather off-handedly, "Oh and by the way, these were dinosaur bones." And do you know what happened next? They said, flabbergasted, "Oh then these results can't be right! Here, let me Carbon-14 date these again!"... did you see what happened there? Using their own scientific methods they severely damaged their own hypothesis.
So is Carbon-14 dating a hokey science? Well not
exactly, but to be sure it is based on some very fundamental assumptions.
One last thought, before I conclude, is to look at Dendrochronology: tree-ring dating. Some assert that the oldest living tree is around 4,000 years and others have claimed it's a little over 8,000... we're talking much, much tinier age-ranges when compared to 4.5 billion years, but it's nonetheless worth looking into.
Best of luck on your quest!