For example, there's probability 0 of worlds where charge isn't conserved.

Aren't you really just talking about the level of abstraction being applied? If there are infinite possibilities between zero and one, then it's just our way of relating to it that imposes the perception of a limitation.

And can't one do all of mathematics without 3...(just map all the numbers > 1 to points inside the interval 0-1)?

That's true for theoretical physics.

Experimental physics takes it one step back: it's all about setting bounds on what is potentially possible. A model of the universe might say that the numbers are between zero and one, but there's some other model that says there could be 3s.

Note that this epistemic uncertainty is not the same thing that the article is focused on. The article is mostly about one specific model, which itself has some randomness baked on.

Yes, and in a more general way Noether thm applies in QM/QFT as well (energy conservation is just a special case). Symmetries become operators acting on the Hilbert/Fock space (ie representation).

With the caveats: - anomalies-> symmetries/conservation broken by quantum noise (has to be cancelled in valid theories) - Heisenberg’s incertitude

In quantum mechanics? Energy conservation is not as strict as you might think.

It just somehow always balances out in the end.

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I love this podcast. The solo or very physics focused episodes go over my head sometimes but they're always a fun listen. I enjoyed "Jody Azzouni on What Is and Isn't Real" where they (among other things) argue about what it means for a thing to be "real"/"exist", and extend that to mathematical concepts, fictional characters etc.

Surprising that he could have that intuition in 1935, before the Unruh effect was known of, before AQFT was invented, and really before most of QFT was formulated.

But then again, he was John von Neumann.

Not according to many worlds! I think nowadays many physicists think many worlds/an everettian view is most plausible

Yes! But at some level, doesn’t it kind of get blurred?

That is, we are trying to come up with rules describing the underlying rules, right? The world isn’t made of stuff, it’s made of rules, right? Or math? Just not the same notation, at least.

Help! I feel like I’m falling off a metaphysical cliff!

No. The Hilbert space is the territory. Our perceived classical world is the map.

The nice additional reading is that you could even know what a Hilbert space is, but not what is a Hilbert space.

Or, there is no time. Awareness traverses the grand graph of possibility.

Disclaimer: total armchair philosophy.

Given infinite time, is it possible to randomly draw a rational (instead of an irrational) from the interval [0, 1]? And if so, is it possible infinite times?