On: Computation as a universal and fundamental concept

[RandomLensman]

How to build a Turing machine to tell which one of ten atoms of a radioactive element decays next?

[peter_m1 → RandomLensman]

That would be a quantum Turing Machine as radioactivity is a quantum process.

[RandomLensman → peter_m1]

How would that work as current understanding from quantum theory is that we cannot predict which atom decays next? Is there a quantum algorithm that can do that?

[GoblinSlayer → RandomLensman]

The decay process is calculated as

sqrt(1-exp(-t/T))|1> + sqrt(exp(-t/T))|0>

[RandomLensman → GoblinSlayer]

How do you use that to predict which atom decays next?

[GoblinSlayer → RandomLensman]

The decayed state exists, it's the second term sqrt(exp(-t/T))|0>

[RandomLensman → GoblinSlayer]

How do you predict which atom decays next from there?

[GoblinSlayer → RandomLensman]

Since the decayed state exists, then any. Your question tries to assume sqrt(exp(-t/T))=0, which is false.

[RandomLensman → GoblinSlayer]

My point was that we cannot predict which atom decays next.

If you want to claim that we could predict which specific atom decays next, I'd really like to see a lot more explaintion and exposition as it would upend current understanding.

[GoblinSlayer → RandomLensman]

The trick is that you can't predict something that doesn't happen even if you feel otherwise.

[RandomLensman → GoblinSlayer]

Atoms don't decay? Radioactive decay isn't a thing?

But at least we agree there is nothing we can predict.

[GoblinSlayer → RandomLensman]

We can predict decay process as

sqrt(1-exp(-t/T))|1> + sqrt(exp(-t/T))|0>

[RandomLensman → GoblinSlayer]

If I were to give you ten atoms of Po210, could you tell me which one will be next to turn into Pb206. What's your algorithm to do that?

[GoblinSlayer → RandomLensman]

My algorithm is at least to not predict it as not what it is. All ten atoms decay according to the formula above.