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) ?
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He didn’t simply do math – he did science. Science like physics really has three steps: experiment (or observation), phenomenology, and theory. In the first step, you look at what’s going on around you and take lots of notes. If you’re studying something that you can easily play with (like what colors things glow when you heat them up), you do that. In the second step, you look at all the data you’ve gathered and look for patterns. You do some math here, often writing an equation to describe the shape of those patterns. Finally in the third step, you ask “what could be going on here that would lead to that?”
For example, people have been observing the movement of stars and planets in the sky for thousands of years, and keeping really good records. There were all sorts of really complicated tables and bits of math that described the patterns – and you could use them to predict where the planets would be, which was great, but they were *really* messy and unintuitive. Then starting in the 15th century, some people started to notice that if you imagined that the Sun was standing still, and all the planets were going around it in very simple curves – ellipses – then that would explain the motion that we saw and be WAY simpler than the math you need to explain what we now realized was an ellipse viewed from another moving ellipse. Not long after that, some other people realized that if the Sun and all the planets were being pulled towards each other by gravity, just like rocks were towards the Earth, and if gravity followed a certain simple math rule, then that would explain why all the planets moved in ellipses, and even other weird things like the motion of comets.
The final step is to go back to where you started. The theory is a very simple statement, and hopefully explains what you saw, but if it’s a useful theory you can ask it what happens in a case you *haven’t* seen yet. It makes a prediction, and you can go test it out. If it starts predicting things you didn’t know about, you know you’re on to something.
So back in 1905, Einstein worked out some pretty amazing theory about how light works that turned into the special theory of relativity, and it was quickly confirmed. But the “special” in its name was because the theory had a big limit: it could only explain the motion of objects that were moving at constant speed. He decided to see what the math would predict if you removed that restriction – and the short answer to that is “about 14 years of really hard work, because the math it turned out to require was WAY more complicated and half of it hadn’t even been invented yet.”
The reason it was complicated is that he quickly realized that if you allowed things to change speed, the math started describing gravity. Like, you literally couldn’t make the math work *unless* you also let it predict that gravity would exist.
Now, his new theory of gravity was similar to the old one, in that when things aren’t *too* heavy it gives almost the same predictions – almost, but not quite. For example it predicted some small differences in the orbit of Mercury.
And the amazing thing was, the predictions were *right.* Mercury actually does move like Einstein predicted, not like Newton did.
So that made people very curious about the other predictions – including one very weird one about black holes. A lot of people thought that one was totally nuts, and just evidence that general relativity wasn’t _actually_ correct, but we’d have to find a better theory still that didn’t have these weird predictions in it.
That is, until 1971, when we actually observed one for the first time.
Turns out Einstein was right, and the universe was weirder than we thought.
So that’s a short version of how doing science lets you guess that things like black holes exist. You observe, measure, make models, make theories, make predictions, and if your theory is right, you’ll have predicted something true that nobody knew before.
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