Perhaps a tough question for a physicist here

@Arbitrageur

That quite a good read.

Thank you.

Use a random number generator...

a reply to: Steffer

You cannot. There are no random number generators. The pathetically closer you can get is using pseudorandom generators.

Might pi ever be used in an equation on random sequencing since the exact value of that number is infinite?

Pi is not infinite. It is a finite number. Actually, there is nothing infinite in this Universe. Nothing. There are theoretical constructs that are infinite, indeed, but to make a practical use of them you need an infinite time of computation, and an algorithm as large as the infinite sequence you wish to generate. And long before your computation is done, the Universe will collapse and your random sequence will be meaningless... and only pseudorandom.

a reply to: Steffer

You asked for a physicist's approach so you're going to get a physicist's answer: in the Bose-Einstein coherent state of a laser, all of those photons are literally identical.

Then there's the question: "why are elementary particles identical in the first place, when all the big stuff we see is always slightly distinguishable from one another?"

Turns out that's a pretty non-trivial thing: it's because every particle of a given type is really an excitation of some fundamental elementary particle field, and there is only one of those per type in the Universe. (In truth, it's a little bit more complicated how the elementary fields map to particles). Universe really is just those fields of the Standard Model which has all the 'stuff'.