Physicists have the premise that nothing just appears out of nowhere or vanishes without a trace. Much like balancing a chemical formula, the interactions of tiny particles must balance when something decays. In the case of beta decay a particle was theorized would need to be emitted, the neutrino, but due to the properties it must have it would be very difficult to detect.
We know beta decay is happening in the sun in huge quantities so if this particle was being emitted we would expect huge numbers of them to be passing through us, and only very rarely interacting in ways we can detect.
It turns out that we can build detectors to find those very rare interactions. Since we expect them to be extremely rare even if there are huge numbers of them around, even our small number of observed interactions is enough to prove their existence and their high volume. If there weren’t trillions passing through us then not only would beta decay in the sun be unexplained, we also wouldn’t know why the neutrinos that we did detect were inexplicably interacting far more frequently than expected.
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