The only way we know our observations were the same last week as they are today is if we have an eyewitness testimony from someone who made the same observations last week.
Actually, the latest estimates suggest a date of 4.57 billion years.
But this figure wasn’t established by radiometric dating of the earth itself. The truth is that the age of the earth has been established by dating meteorites, which are not earth rocks.
If you did, you'd know about radiometric dating and how it is used as irrefutable proof that the Earth by itself is approximately four billion years old. Yes, we are well aware that there are different radioactive isotopes and that they can be used via the technique of radiometric dating to date materials from bone fragments to rocks. From the way you are using the word, it does not seem that you understand its meaning.
In a courtroom, the “proof” that is sought by the judge and the jury is corroborated testimonies from eyewitnesses who were present at the scene of the crime and who saw the accused perpetrate the crime.
They have come from somewhere else in the solar system, and their source is assumed to have formed at the same time as the earth.
Therefore, the age they supply is an interpretation based on that assumption and is emphatically not “irrefutable proof.” How do we know for sure that the meteorites came from another body in the solar system that was formed at the same time as the earth?On the other hand, the court testimonies of forensic scientists are subjected to intense scrutiny, because they do not constitute proof.Rather, the evidence of scientists who were not there to witness the event is open to alternate interpretations.In our three article series on radiometric dating, we discuss in depth the assumptions that scientists must make.For example, it has to be assumed that all the daughter isotopes found in rocks today have been derived by radioactive decay of the parent isotopes.That’s an assumption, not “irrefutable proof.” As for the idea that “there is a great amount of proof…that dinosaurs lived millions of years ago,” you should check out the dating of dinosaur bone fragments.