1.
It assumes that all of the daughter atoms were derived from the parent atoms.
No one knows the history of the sample being tested.
2.
Noah's Flood or some other geological event could have contaminated the sample.
It assumes that uniforitarianism is true and there was no possibility of contamination.
3.
It assumes that the slow rates of radioactive decay as measured today were always the same.
No one can prove that the rates of decay have been constant since the beginning of the world because there is no observation or record that old.
(Based upon comments by Dr. Andrew Snelling in an AiG video entitled "Age of the Earth.")
Even if all three of your suggestions were theoretically possible, there is no actual scientific evidence of them being true.
On the other hand, we have decades of directly observable evidence of radioactive decay of all types having a constant rate and the physics models that predict that decay based on forces between subatomic particles.
So should we make scientific assumptions based on observed scientific data or should we make them based on what ifs that have no observable data to back them up?
That's just it.
We have decades and we have no knowledge of what happened before our research.
There is no chain of custody.
We know that uniformitarianism is not true because of the global flood of Genesis and perhaps the following Ice Age.
I remember reading an article years ago in Scientific American "C is not a Constant" (The speed of light is actually variable).
Heresy of course but the idea was given that at the "moment" of the expansion of the Singularity (the Big Bang) the laws of creation of time, space and matter were and are different than the laws of the maintenance of time space and matter.
So Carbon dating (or whatever) is useless.
Think about it. You purchase a new car. The rules for the use and maintenance of the car (fuel, oil, tires, brakes) are all together different than the rules to put it together on the assembly line.
Assuming of course you have that frame of mind concerning the presence of the material universe.
Yes.
Our understanding of physics currently cannot make sense of what happens at a singularity where the math of quantum physics (for very tiny things) and special relativity (for very big things) collide and it is possible that c is not how we understand it in that moment.
But very soon after that moment the universe would take on characteristics that quantum physics and special relativity would make complete sense in where c is a constant.
None of this has anything to do with carbon dating which is not related to c or cosmology.
Again, creation and maintenance are intimately related but we cannot know the legal details of the one (creation) from observing/participating in its maintenance.
A child comes home from school and says "Mommy where did I come from?"
Then the mother tried very hard to tell the child in words he could understand the process of procreation mingled with a simplistic theology.
When she was all through she said "why do you ask?".
Oh, I met a new friend today and he said he came from New York City.
Exactly.
Just like creation ex nihilo.
That is why atheists didn't like the Big BangTheory originally proposed by a Catholic priest.
It sounded too much like Genesis.
It is ironic now that some Christians are trying so hard now to discredit the Big Bang theory because they think it doesn't sound like Genesis which is the opposite of the truth.
This is tribalism.
Christians attacking the Big Bang theory because they see it as belonging to the tribe of atheist when we should actually be celebrating it as one of the strongest scientific supports for Genesis 1 and was discovered by someone from our tribe (the theistic creation one).
What? shall we redefine and re-categorize every pursuit of differences of the truth under tribalism?
We need to discuss it with atheists/agnostics. Many accept intelligent design; time compression - perhaps that's how the light from stars billions of "light years" away can be seen in the night sky.
rather than traversing the distance for billions of decompressed years.
It shouldn't stop discussions even spirited discussions. I have a cousin with whom have been debating for decade.
Not every difference.
But when we attack and twist the truth about something just because we think it belongs to the other side of a different view, that is tribalism.
When we do this, it is very difficult to see that we are doing it.