Lord Kelvin dated the age of the earth at 20 to 400 million years old. He based this on a starting point of a molten earth at 7000 degrees centigrade and the amount of time it would take to reach its current temperature given today's rate of heat dissipation. He did not take radioactivity into account.
He did later concede that it was much older than he estimated.
What age could be determined if you believed in a cold start to the earth? IOW, an earth formed instantaneously and miraculously?
You mean with an "appearance of age", including all the elements already differentiated, as though they had been sorted by gravity? If you take away the latent gravitational heat from that sorting, and the heat from impact of accretion of solid bodies to form the Earth, then it would be really, really old.
The primary heating source would then be radioactive breakdown in the core and mantle. I don't remember hearing how long that takes to get to the lithosphere, but it takes about a million years for it to get out of the sun, a fluid body, and convection works a lot faster than conduction in rock. And that means it would go a lot slower in the Earth, but the distance would be a lot less.
I should know that, but I don't. I'll see what I can find.
Does anyone have an estimate of the original amount of radioactive materials in the primordial earth? If this information could be obtained, a calculation could be made of how much heat in total was generated from 4.5 billion years worth of decay(assuming today's decay rate). A person could take that total amount of heat over that time and imagine it was released all at once. You could take today's rate of heat dissipation and calculate the amount of time it would take to reach the temperature of the earth today. If that amount of time is less 450 million years(10% of accepted age), then the 4.5 billion year figure is without support in my opinion. Why? A heat dissipation age close to 4.5 billions years would have to depend on a primordial earth that was molten and made by plantoid accretion. IOW, it would be based on an assumption that is no more valid than an instantaneous, miraculous creation.
There's considerable evidence for that in the form of crater data, meteorite data, and of course the physics of system formation (we are now discovering more about that in other systems)
Poofing is not merely an insult to God, it's contrary to the evidence we do have.