[x3n0ph3n3]

One thing worth pointing out is that our universe operates on the integers rather than the real numbers, and the Banach-Tarski requires operating on the reals.

[Smaug123]

Is that known? It's an appealing idea, but bearing in mind that general relativity is very resistant to quantisation, I'm not sure I'd be comfortable to declare it as fact.

[x3n0ph3n3]

It's implied by quantization. There is a minimum divisibility of space (plank lengths) and objects (fundamental particles).

[Smaug123]

I specifically said that the resistance of GR to quantisation is why I'm not very happy saying that it's fact.