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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If I show you a box that has 3 apples in it, close it so that you can’t see inside, I then show you my hand putting an apple in, then my hand again as it pulls 2 apples out, you can use mathematics to predict that when I open the box, there will be 2 apples inside. You made a real-world prediction using math.
Physicists do the same thing, but on a larger scale. Observe what you can, invent an equation to fit what you see, apply the equation to something else and see if it makes a successful prediction about it.
Edit: As pointed out, the premise of 3 apples being in the box could be faulty, which breaks your entire prediction. This happens in Physics too, which is why multiple observations and finding links between phenomena are so important, like a Sudoku puzzle. By ruling out impossibilities, you get closer to the truth.
Einstein didn’t prove the existence of black holes. What he did was propose a set of generalized equations and conceptualization of space-time and gravity.
One of the possible solutions of those equations was an “object” that we now called a black hole. First, Einstein was not the one who discovered this – it was another scientist working on Einstein’s equations that generated this particular solution. His name was Schwarzchild.
At the time, it was not known if such a solution was simply a fancy mathematical outcome of the equations and if such an object actually existed in the universe. There was no “proof” of anything, to be precise. It was only later that actual observations of the motion of stars etc gave evidence that black holes actually exist.
Ironically, the existence of black holes actually points to a “failing” in Einstein’s theory. The mathematical singularity in the equation that “predicts” the black hole is strong indication that the theory is incomplete and insufficient.
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It doesn’t. A lot of things could be solutions to equations. In our case we are talking about Einstein’s equations. (The solutions to the equations is sapcetime geometry given some matter distribution.)
Now just because something is a valid solution doesn’t mean its physically realistic. A black hole in the simplest form is the solution for a point mass. Cool but if there is no mechanism that can compress matter below isn’t Schwarzschild radius, black holes won’t exist.
Now in our case we have mechanisms creating black holes. But that doesn’t mean that any valid solution must exist. Of course the point of these equations is to allow us to work out any scenario. We just assume everything we are able to work out is valid, and if we get something familiar we are happy, and when we get something new/weird we are excited. Then we can do experiments to see if the predictions are correct. If yes its good, if no its great because we found new physics.
The point of models is to quantify physics. The models don’t tell what exists, but what can exist. What ends up existing depends on what mechanisms are available.
Was it Dirac who had that antimatter solution from his equations about particles?
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.
Our understanding of the universe gets better from year to year. What happens is we try something, or look at something, and we realize that the math we have doesn’t give us the same answers as what we see in real life. So people come up with a better model for how we think the universe works, and we write better math that we think gives us better predictions based on that model.
And once we find math that seems to match what we see better, people then start using the math to see what would happen in the universe in situations that we haven’t been able to see yet.
Einstein came up with some better equations that describe gravity better than the ones we had before. He and Swartzchild started trying to see what those equations would say about situations where gravity was very very strong, and the equations gave them some really weird answers suggesting that there would be these bubbles in space that light can’t escape from.
A lot of science is taking better math like this, finding new things that the math predicts that we haven’t seen yet, and then searching for those things. Once we verified that black holes were real, this gave us a lot of confidence that the math Einstein and others have come up with is the best description of reality.
But we also know it’s still not complete. Quantum physics teaches us that a lot about the universe is actually about probability at small scales, but we can see that gravity doesn’t behave probabilistically, so there’s a lot more room for people to come up with better math, and then we can start using that math to see what other strange things might exist that we don’t know about today.
Ancient pacific islanders could tell that there were landmasses beyond the horizon by patterns in currents. This is similar. Black holes have gravitational effects that can be noticed.
As soon as you understand how something works, you can make predictions and test those predictions.
This is what is being done.
Sometimes your predictions don’t work out and it generally means you don’t understand something completely. It doesn’t necesarily means it is wrong, but it could be incomplete.
In our solar system, this is how many outer planets were discovered as those interefered with the orbits of the known planets and those orbit predictions didn’t work out exactly.
Black holes can’t be seen, but were predicted due to observations of other things in space.
The hard part is not detecting something is wrong, but coming up with a hypothesis that explains this behaviour while it still matches with everything else we know.
Einstein didn’t prove the existence of a black hole.
He defined a theory (general relativity) that showed that if something is massive enough in a small enough radius, there is a radius for which light orbits it, and we can call those objects black holes, and it defined most of the properties of black holes.
There was no guarantee that those objects actually exist. We proved that by observation afterward. However, they were likely to exist since they didn’t need anything exotic. Just high density or high mass (the bigger the black hole, the less density is required to make it a black hole).
Even without general relativity, you could have black holes if you assume that light is accelerated the same way than anything else by gravity, but most other properties of black holes require general relativity: how they cause time dilatation, how their rotation affects space-time, how they cause gravitational wave while absorbing matter including colliding with another black hole, etc.
Black hole radiation comes from quantum mechanics, though.
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