Hello, MisterOpus.
The first three of the alleged assumptions are
not assumptions that need to be made in all cases of radiometric dating. If the unit to be dated is heterogenous (for example, it contains crystals of different minerals) then
isochron dating can be used. Isochron dating completely eliminates the need for the first two assumptions. Furthermore, it also puts into place a diagnostic that allows the investigator to tell whether assumption 3 is warranted.
In regards to the third assumption, it is currently, and has been in the past, to discover when and how the sample may have been contaminated by the parent or daughter materials, or when some of the daughter materials may have been lost. There is a body of knowledge now that allows a researcher to determine which dating methods will not be accurate based on the composition and physical state of the sample in question.
Also, several different dating methods are often employed. Each isotope has a different half-life, the decay mechanisms are often different, and, most importantly, each of the parents and each of the daughters have different chemical properties, making it unlikely that each of them will be added or lost in just the right amount to make the different dating methods give consistent results. So consistency of dates by different methods is an indication that there has been little or no addition or subtraction of the parent or daughter materials.
Finally, as far as your fourth assumption, there is no reason to believe that decay rates have changed. Decay rates are constant despite any change in chemical or physical environment -- the only exception is that for some nucleotides beta decay is
slightly affected by physical conditions (like complete ionization of the atom) that are simply not met in a terrestrial geologic setting.
To change decay rates would require changes in the laws of physics themselves. But there is no indication that the laws of physics, particularly the ones involved in radioactive decay, have ever substantially changed. This is born out by astronomical observations -- the further we see in distance, the further back in time we observe. We see no evidence that the laws of physics have changed -- such an assumption is not warranted by physical data, but by a need to preserve certain
a priori religious beliefs.
Furhermore, quantum mechanics shows us that certain conservation laws are tied to the invariance of physical laws. If the laws of physics change, then energy would not be conserved. So far, we have never seen a violation of the law of conservation of energy.
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