I was watching a video about black holes, and when they mentioned that Einstein proved black holes exist with maths, it hit me.
I’ve never asked myself that question, how do numbers tell you that something exist in outer space and what to expect from it? especially things that we never knew they existed in the first place (exp black/white holes) ?
In: 407
We proved that black holes exist by observing that objects with all the properties we expect from black holes (as described by the math) exist.
What Einstein did was make a mathematical model that explained the discrepancies between Newton’s gravity and astronomical observations at the time, using some unique insights. The math threw up black holes and would require reworking (or at least explaining why it’s actually not physically possible even if the pure math works as intended) if it turned out that was some sort of error that needed eliminating. But it also worked really well in all other experiments where all alternatives (which existed) failed, so astrophysicists just said “hey, lets assume it’s correct”, and then decades later it turned out to be correct.
The problem with using math predictions is that you can “predict” ANYTHING. You can make the math do anything you like.
So what science does is sort of that. Make mathematical models that explain what you want them to explain, but which also have some yet undiscovered consequences which you could test for. And then you go test them. If your predictions are correct, brilliant, your model reflects reality (until it doesn’t anymore because you got new, more precise data, any model is only an approximation of reality). If your predictions are wrong, your model is wrong.
This is actually a big problem in particle physics at the moment. All the clean, neat hypotheses that would expand our current model (the Standard Model, which we know for a fact is incomplete) turned out to be just flat out wrong, again and again. And theoreticians are really struggling to come up with something new, because so many logical options were disproven.
Note that “not being proven” and “being DISproven” are two different things. Absence of evidence is not evidence of absence. But a contradiction IS. If you don’t see a mountain, it doesn’t mean mountains don’t exist. But if you expected to see a mountain and it’s not there, whatever told you to expect a mountain is wrong.
This brings us back to General Relativity. As well as Black holes, it predicted White holes. Those are not thought to ge able to exist in our universe. But it doesn’t disprove GR. The reason for that is that the maths predicting White holes is in itself correct, it just requires an arrangement of circumstances (matter, forces, energy) that are not expected to exist in our universe. Let me stress that: not EXPECTED. But not impossible/disproven.
To simplify it, “white hole” is a solution to an equation if you put in -1 into it, but our universe seems to be only positive numbers. The math is correct, and it’s on you to be careful not use it in an “unphysical” way.
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