It's a standard assumption, in anthropic reasoning, that effectively, we simultaneously exist in every place in Tegmark IV that simulates this precise universe (see e. g. here).

How far does this reasoning go?

Suppose that the universe's state is described by $n$ low-level variables $x_{1}, \dots, x_{n}$ . However, your senses are "coarse": you can only view and retain the memory of $m$ variables $y_{1}, \dots, y_{m}$ , where $m ≪ n$ and each $y_{i}$ is a deterministic function of some subset of $x_{1}, \dots, x_{n}$ .

Consider a high-level state $Y^{*}$ , corresponding to each $y_{i}$ being assigned some specific value. For any $Y^{*}$ , there's an equivalence class of low-level states $X^{*}$ precisely consistent with $Y^{*}$ .

Given this, if you observe $Y^{*}$ , is it valid to consider yourself simultaneously existing in all corresponding low-level states $X^{*}$ consistent with $Y^{*}$ ?

Note that, so far, this is isomorphic to the scenario from Nate's post, which considers all universes that only differ by the choices of gauge (which is undetectable from "within" the system) equivalent.

Now let's examine increasingly weirder situations based on the same idea.

Scenario 1:

Consider two Everett branches, $A$ and $B$ . They only differ by the exact numbers of photons in your room: $A$ has an extra photon.
Suppose that we gave the entire history of your observations over your lifetime to AIXI, which simulates all universes consistent with your observations. Suppose that, in the end, it's only able to narrow it down to " $A$ or $B$ ".
Does that mean you currently simultaneously exist in both branches?
Importantly, note that the crux here isn't whether you, a bounded agent, are able to consciously differentiate between $A$ and $B$ .
- That is: Suppose that, in $A$ , the extra photon hits your eye and makes you see a tiny flash of red. If so, then, even though you likely won't make any conscious inferences about the photons, that'd still create a difference between the sensory streams, which AIXI (an unbounded computation) would be able to use to distinguish between $A$ and $B$ .
- Similarly, if the existence of the extra photon causes a tiny divergence ten years down the line, which will lead to a different photon hitting your eye and your seeing a tiny red flash, this will likewise create a difference that AIXI would be able

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