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If there would be a distribution of dark matter that explains the poltergeist, we could measure that distribution of dark matter.

We can measure the mass distribution on astronomical scales. We "see" the dark matter. Just not with light.

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We don't measure dark matter, we measure some anomaly and then we say "it must've been dark matter".

It's not crazy different from saying the same about that poltergeist.

We measure the matter distribution by its affect on light (strong/weak lensing). We also measure the matter distribution by the amount of light coming from it. The results are not the same. The simplest explanation is that there is matter which does not produce or reflect light via e/m, i.e. it is dark. Dark Matter.

We know of particles which behave the same way. Neutrinos for example.

You're saying the same thing, we see some anomaly in measured light and we say "the simplest explanation is dark matter".

We are not measuring dark matter, we are measuring something that is not what we expect and we decided it's dark matter.

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