What we would say is that in the world-split that occurs when that potassium isotope in your stomach decays, the likelihood that the *measurement* of that decay has an effect on your propensity to choose the cheeseburger has an infinitesimally small amplitude.

I think the problem you're having here, is you *are* using fictionalizations of the multiverse from movies and such to back into your understanding.

When a world split happens, it doesn't cause a roll of the dice into ad infinitum outcomes. It creates two branches two branches of the wave function which can be described as:

1. There is a branch of the wave function where the potassium isotope in your stomach has decayed, and was observed to be decay; and

2. There is a branch of the wave function where no decay occurred.

The only *mechanism* that the random decay of that isotope would have to cause you to choose chicken nuggets rather than a cheeseburger, would be if somehow the alpha particle managed to hit some part of your brain in *exactly* the right way, at *exactly* the right time, to cause you to have a change in your cognitive processes in such a way that you act upon a different preference.

But you seem to be thinking that Carroll et. al. are saying is that every time one of these decays occurs, that a world-spit occurs where you make *every* *possible* *choice*. And that's just absolutely not what Carroll or Everett were saying.

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... which actually brings us back to how this thread started. This is fundamentally about probabilities. Extremely low probability outcomes, have a *low* *amplitude* and thus represent a much smaller fraction of the multiverse in Hilbert space. It does not say that every possibility is equally likely to occur. The probability of an outcome, and in the case of Everettian quantum interpretation, is the amplitude of a world in the multiverse is *proportional* to the square of the wave function. That's a probabilistic distribution. Not a isotropic one.

To say that every possible thing, within all degrees of freedom, happens at every moment in time, is to say that the probabilities of the wave function are *isotropic*. But we know they're not. When you describe many-worlds in such a naive way, and you consider what the mathematics of that must be, you see it has no resemblance to Born's rule, or Schrödinger's equation.

So you're trying to impose an intuitive understanding about what the multiverse must be like onto this picture. The problem is, it's not intuitive at all.

In fact, even the insistence of thinking about these branches of the wave function as separate universes is a mental shortcut. They're not like different dimensions, with 100% copies of our entire universe. They're different branches of the wave function. That's it. Now, does that mean that there are different branches where your life turned out very differently? Yes. There's an exorbitant large number of such worlds. But your macroscopic considerations, such as whether to put milk in your coffee or drink it black, are *emergent* descriptions of the world of decohered quantum systems. These are not branching points. That's a silly Hollywood trope.

The branching happens at the quantum level, as described by the Schrodinger equation. And there is no wave function collapse. What we observe as the collapse of a wave function is where we find ourselves on a new branch of the wave function that is decohered from other branches. That's it. That's all it says. Human choices, and human-scale decisions are not really relevant to this world. To understand many-worlds, you have to understand the math, and stop trying to use mental images of what branching worlds look like.