Not all things are possible, only potentially possible ones.
If you take all the numbers between zero and one, you will find an endless supply of distinct numbers but none of them are 3.
We don't know the mechanism which generates the gauge symmetry that makes charge discrete or generates conservation laws from symmetries, so it's risky to be too prescriptive about what is and isn't possible.
In the limit you can imagine a meta-technology which manipulates the mathematical structures that generate reality instead of just assuming the rules are fixed. That might or might not be possible, but the rules have to come from somewhere and there's no absolute guarantee they're hardcoded.
However, my post sucked and I didn't get around to emphasizing that. In quantum mechanics, it's possible for some state to have zero probability, and it's those probabilities that we're talking about everything being possible.
There's also the epistemic side where we know that there's a chance our theories are wrong in any given way. Those can't go to zero based on our model since the whole point is we're not restricting to a model. BTW, I really like your example as a good, clean limiting case.
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I'm sure people have come up with theories that violate conservation of charge, but they'd have to break U(1). I don't know what conservation CPT would break, if any; Noether's theorem shouldn't apply to it as a discrete symmetry.
The C in CPT is not only a change f charge but also a change of electron <---> positron, and quark <---> antiquark, and ...
The conservation or charge comes from the U(1) gauge symmetry. That is almost obvious if you ignore the mixing with the weak interaction, but after the mix you still have a U(1) gauge symmetry anyway.
In an expanding universe, energy isn't conserved. (Unless we do the trick we always do with energy and just define it to be conserved https://youtu.be/lCgKTpIzjRk?t=174 )
I don't know exactly why you think this applies to charge conservation. The U(1) symmetry is where charge conservation comes from and it isn't affected by an expanding universe.
There is "rest mass" and "relativistic mass". The GP is talking about "rest mass" that is not conserved even in simple examples.
Most modern books try to eliminate "relativistic mass" because it's misleading, for example is good to calculate acceleration perpendicular to the movements (for example in a cyclotron) but it's not good to calculate acceleration in the direction of the movement.
So most modern books they call the same idea just "energy" and use that "energy" to calculate gravitation. "Energy" is conserved in special relativity and almost conserved in general relativity.
But the "relativistic mass" is useful in some problems and is widespread in popular culture and don't ask about the weird parts of the mass of the proton, so it's difficult to kill the idea.
Either the baryon number started non-zero and was conserved; or non-conservation of baryon number (protons vs antiprotons etc) have to be paired with equivalent non-conservation of lepton number (electrons vs positrons etc); or it can happen without simultaneously balancing the lepton number, and charge isn't conserved.
Unfortunately (for me) those implications are above my level. I can't usefully converse with an LLM about it, as this isn't a domain I know well enough to detect if it's making stuff up.
Now, on logistical level, the mapping procedure is not free, it does have a physical/energetic/mental cost to handle it, and a more trivial representation of integer has a lower cost on this regard.
But the simpler integer representation can represent less many situations. If all one need to deal with in a certain frame is covered by a simpler shipper representation, from an economical perspective it can be argued it worth the risk of hitting a point where the representation will be insufficient as the situation evolved with cases it can't handle.
My impression is that your underlying premises are conflating all of this distinguishable aspects. But of course my impression is limited by my own narrow representation of the world, no matter how open and curious I can be about learning from experiences it makes me go through.
I sometimes wonder how much we allow the map to become the territory.
That said, I accept that literally, 3 never occurs between the ∞ of 0-1 -- unless, we are assuming symbolically, rather than actual, that in our particular ∞, something does not transcend entirely, which we really cannot know, because the closest we have ever come to a real infinity is a representation or symbol of it.
Edit: I realized that the question appears, or is, stupid. But when I see 0.3, I tend to see the 0.0, 0.1, 0.2 between. This is not what 0.3 is supposed to mean though. But on the testability of any real infinity, I do not budge.
on edit: maybe should say infinite set instead of infinite sequence.
What leads you to claim that you can't encode infinite information given an infinite set to work with?
I don't have a formal education in QP so this comes from my engineering perspective of working on quantum computers.
If spacetime is infinite in extent yet discrete at the Plank scale, it would be ℵ₀; the Hilbert space is real-valued and therefore (a vector of) ℵ₁.
The Bekenstein bound, in practice, would do limit how much information can be actually encoded, even if all quantum states have an underlying real value and therefore even just one quantum value of one particle is ℵ₁ all by itself.
But cardinality of real numbers might not be ℵ₁. It's literally unprovable in ZFC.
Infinity is an abstraction that simplifies a lot of maths, it isn't real though.
There's a possible future where you're President, but no possible future where you're a talking cucumber. This intuitive fact gets overlooked in pop culture explorations of Many Worlds, such as Everything Everwhere All At Once, which has ridiculous parallel universes which obey the rather more relaxed rules of "anything the writers can think of that looks silly", rather than "anything which can conceivably happen".
Ignoring that you have to give up a sense of personal identity at this point, there is nothing in the laws of physics that says the matter that makes up what we're presently calling me can't morph into a talking cucumber with a brain with my memories in it. It's just absurd number of extremely specific things that have to happen out of an ever more absurd number of possible things to happen.
If talking cucumber was too pedestrian for you, we could add stipulations until your intuition collapses. Perhaps, starting next week, the Earth begins to spontaneously turn into raspberry custard on Tuesdays. Perhaps the entire universe turns to custard! Just think of it - billions of lightyears of custard in every direction. Whoops, did I say billions? Too grounded! Let's make it a googolplex. And a single lone piece of rhubarb, floating somewhere in the middle of it all...
...sorry, couldn't resist. Joking aside, while we can quibble about the boundaries of the possible, the fact remains that there are boundaries - at least, if we're still talking about known physics. No evolution of the universal wave function will lead to a world where pi suddenly equals 3.
It reminds me of that scene where the guy is upset about the ratio of ingredients in his wife's dessert:
(Note that the author many times is not the person that choose the title.)
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.