So the Boltzmann brain (BB) is a thought experiment. First let’s clarify what a thought experiment is,then we go on.
A thought experiment is an experiment that you do not perform, but you think what would happen. It’s basically a tool to test ideas (if this were true then this would happen), or to explain/describe an idea.
There are a lot of popular thought experiments. For example the trolley problem is one. Or Scrödinger’s cat. The common thing is that using such an “experiment” you can think about the world: how it works, how it should work.
Now the BB is also a thought experiment in a way. Boltzmann said that if the universe exists for ever, then eventually a fully formed human brain will pop up out of nowhere. Why? Because forming a human brain from atoms (just by random assembly of atoms) is very unlikely but not impossible. And every unlikely things happen if you have enough time for it.
Boltzmann used a brain in his example, but it could have been any complex thing: a car, a mobile phone (if it had been invented). Then it would be the Boltzmann-car or the Boltzmann-phone.
So the BB is basically a toolkit to think about the universe for physicists. If they come up with a new theory, they can test it by asking a question: if this theory is true, would it allow forming brains (or cars or phones) out of nothing? And how likely? Once in every hundred years? Once in every trillion years? And because in the real universe we do not see brains popping out of nowhere, a theory that would allow it frequently is a bad theory and ruled out.
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