Why doesn't that apply to photons and electrons, then? At what scale do things stop interacting with the other worlds and stay in their own world only?

This is exactly the measurement problem, essentially identical between Copenhagen and MWI.

It does apply to photons and electrons.

As I understand it, it becomes ever more difficult to maintain a coherent quantum state among larger and larger collections of particles (this is why making large quantum computers is difficult), so for most practical purposes large aggregates of particles behave like a single "world". But there is no sharp dividing line, and the same math applies at all scales.

Unfortunately, this is where the imperfect mapping to which I referred above — between the math and our intuition — becomes misleading, and why I don't like the term "world" to begin with.

MWI actually postulates that coherence of the system is always preserved, even up to the level of the entire universe. It's only locally that decoherence seeps in, at some scales.

But still, the problem I was questioning was different: you are saying "there is one of us in each world". In fact, that is not what QM predicts: in QM, there is only one of us in the entire system described by the wave function, with different amplitudes in different states. A system with 1 electron with some amplitude < 1 in state A and some amplitude < 1 in state B is not the same as a system with 2 electrons, one with amplitude 1 in state A and another with amplitude 1 in state B.

So, if we took a detector that could measure state A or state B, we should expect that it detects state A with some amplitude and, simultaneously, state B with some other amplitude. Instead, MWI postulates that there are 2 detectors, one which measures state A with amplitude 1, and the other state B with amplitude 1 (in fact, it postulates an infinity of detectors, out of which some number measure state A and some measure state B, such that the Born rule predictions by "counting" detectors).

This is the part that remains unexplained.

"One of us in each world" is shorthand for "one of us in the entire system described by the wave function, with different amplitudes in different states".

There is only 1 detector, and it, along with the detected particle, is in a superposition of states.

Again, this is where the language of "worlds" becomes misleading, and why I don't like it.

It applies to photons and electrons: when superposition consists of valid solutions of the schrodinger equation, these components evolve independently as if the other components didn't exist. It's possible to measure them in a rotated basis because a single elementary particle doesn't have inner structure. If you want to analyze the structure, you will have difficulty measuring in a rotated basis, this starts with two particles.

Different worlds interact by interference. To interfere they must be in some sense "adjacent" so that they can both evolve into the exact same world - but with opposite phase. If you have a huge object like a human it's very hard to get every single atom to line up with those of the other world.

Define "sees."

That's just one of the many problems that MWI fails to solve.

In MWI, the problem doesn't exist to begin with.

In e.g. the Copenhagen interpretation, observation plays a special role, because it's the moment of wave function collapse.

In MWI, there is no wave function collapse, so there's no need to identify certain special events called "observations" which are somehow different from the rest of physics. It's just our eyes, and brains, and instruments, interacting and becoming entangled with the other things in the world.

When we "observe" Schrödinger's cat, we entangle ourselves with the cat just as the cat was already entangled with the cesium atom. Now the world is in a superposition of two states: in one, the cat is alive and we see it as alive; in the other, the cat is dead and we see it as dead. This is exactly what the equations say should happen. Nothing special.

And yet, photons can keep interacting with both versions, while we are forever unable to see the other version of the cat. The problem doesn't go away.

Even more interestingly, say you want to predict the outcome of a quantum experiment. In the MWI, that outcome is deterministic, and it is a superposition in Hilbert space. However, in your own space, you still need to compute a probability for that outcome.

What is this a probability of in the MWI? The concept of probability across worlds is not really rigorously defined, especially since you need to arrive at very specific results to be consistent with observations.

I address your first point here: https://news.ycombinator.com/item?id=25999766 (in brief, photons are treated no differently than people).

I agree that the meaning of probability in the MWI context is an interesting open question. Mathematically, it's the squared amplitude of part of the wave function. But why this corresponds to our personal experience of frequency is something I'm unclear on.

The local wavefunction part corresponding to each world has a configuration in it that involves a human being with eyes and optical nerves and a brain registering neural impulses in response to light stimuli to perceive its world.