[loup-vaillant]

Generally, when you know everything there is to know about an experiment, it makes you quite certain about the outcome you will observe.

Yet this is not the case when you send a single photon through a half-sieved mirror. Even when you know everything there is to know about this experiment, you just don't know which sensor will go off, and if you repeat the experiment, you will find that previous results tells you nothing about the next one. Perfect independence.

When total knowledge of the setup yields only partial knowledge about future observations, one is very tempted to look for "probabilities" in the setup itself. But it's a cop-out, a non-explanation. The fact that there is no hidden variable does not mean amplitudes (or their squared norm) are probabilities.

So, what to make about our uncertainty about the perceived outcome of quantum experiments? Well, it's simple: the laws of physics as we know them are deterministic. When you send a photon through a half-sieved mirror, the actual result is always the same: the world splits in half. There will be one blob where the photon hit the first sensor, and one blob where the photon hit the second one. Subjectively, the result is the same: we still observe the Born statistics. But step further from the amplitudes as probabilities cop-out: the Born statistics are now more of an anthropic problem.