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This question is probably far above my current understanding of physics but how do you explain why sterile neutrinos wouldn't keep falling into each other since gravity is the only force working on these particles.

Maybe you can just say pauli as an answer but don't you need a fundamental force that enables the pauli exclusion principle to be possible? Many thanks

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Ordinary matter tends to clump into things like galaxies, stars, and various detritus like dust, planets, orange peels and humans because it interacts with itself.

It's pretty much been determined by the behavior of dark matter around galaxies that it doesn't interact with itself or with ordinary matter (or if it does, it does so to a vanishingly small degree).

Imagine two big clouds of stuff, motionless with respect to each other but big enough to gravitationally attract. Now let them go.

In one case, let them be ordinary matter, released to fall into each other via gravity. They will do so -- and when they hit, the particles will interact, and heat up, and collide and turn momentum into heat or radiation or whatnot. That will drive clumping. Pretty soon you'll have one big cloud of hot, clumpy matter, very possibly on its way toward forming stars.

In the other case, let them be dark matter. If they act as dark matter is believed to act, will fall through each other. They won't hit each other, because that's an interaction. They won't heat each other up because they won't hit. Because they don't interact, the clouds would fall through each other. If you arranged the starting conditions just right, they'd fall through each other, change places, then fall through each other again and end up at their starting positions, motionless and poised to do it all over again.

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  • $\begingroup$ I can follow it would act like an oscillator but how do you make sure the pauli principle isn't broken in this scenario? when they "pass trough" each other, both in the same quantum states this would be against pauli, wouldn't it? I always thought you needed a force to make sure pauli's principle wasn't broken, am i just thinking to much in classical terms? $\endgroup$
    – da maro
    Nov 21 '19 at 21:19
  • $\begingroup$ OK, you're starting to stretch my understanding of quantum mechanics, but if two particles have different positions or different momentums then their quantum states are distinct. So two particles heading in opposite directions won't occupy the same state, and the Pauli exclusion principle doesn't come into play. $\endgroup$
    – TimWescott
    Nov 21 '19 at 21:45

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