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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math can only prove things about math. for physics math gives you a model or theory, which let’s you make predictions, but you need experimental evidence to actually prove the model fits reality.
A good example of math finding something is Neptune. When Uranus was found, it’s orbit was calculated but the actual observations showed it was off from the calculated orbit. Astronomers thought that there must be another larger planet out there throwing off the orbit from their calculations that had yet to be discovered. They calculated how big the planet would have to be and where it would be using math. They then looked where the math calculated where this mystery planet would be and holy shit there it was.
I’m sure the full story is a tad more complicated but it’s the basic story.
This is why I love math. My background is math, well at least before I went into IT. Math is the language used to construct the universe. Math is everywhere.
It is sort of the other way around. We humans try to describe the way things work using equations. We make those equations based on what we observe. When the equations are useful for predicting how things work, then we use them to predict. Toss them or modify them if they do not quite work, or do not work at all.
Sometimes an equation, or the many different secondary equations (functions) that follow logically/mathematically from the first one, indicate something ought to happen but we have never seen it. Of course, being curious humans, we then look for it, to see if it really exists.
Sometimes, we find new things that way. For example, Einstein’s equations said that light ought to “bend” when passing close to a massive object like a star. That “bending” was confirmed a few years later during a solar eclipse. This meant that the equations were actually predicting real world behavior. What else could be true, then? What do the equations indicate will happen when mass gets huge and distance gets very small? Well, eventually, when mass gets high and distance (volume) gets small, the function blows up toward infinity (becomes undefined, “breaks”).
The black hole situation is what the equations predict will happen when mass gets very high and volume goes very small. So, people looked to see if it really happens. Turns out it does. Apparently.
We observe things in the real world. Those things work according to laws of physics. We then create equations that describe these laws of physics as math equations.
If equations are good enough, then when we put in parameters of things we observe (mass, velocity, etc.), they predict effects we observe.
But then we can put some funky stuff in like very big mass and see if the equation hold up. If it does, then there technically could be an object out there with very big mass. Or our equation is actually not goid enough.
One thing to add to the various explanations.
One of the biggest assumptions (though we can, to some extent, prove it) we make in astronomy and cosmology is that the observable universe is relatively homogenous. What we mean by that is that on Earth, we can experiment with things like physics, chemistry, studying matter or forces like gravity – and we *believe* that those observations, those laws, are the same on Venus, or Callisto, or in the Andromeda Galaxy.
So that means it’s possible for us to experiment with something on Earth, and use that information to predict stuff that we’ve never seen.
Now of course, the universe being homogenous is an assumption; but it’s one that’s borne out by everything we know (for example, we don’t any any evidence that gravity works the opposite way in the Andromedia Galaxy).
You can prove certain things are always true.
Very smart people looked at the sky and measured how planets and the sun moved, they noticed patterns in the movement.
They used maths to describe the pattern and noticed they were able to predict where things would be.
If a maths equation is always right, its proven, it becomes a fact thats always true ( until we find out its not because its actually way more complicated!)
Equations are cool because they mean you can use reason to infer facts about the universe. If it’s always true x = y +1, and you know x, you will always know y.
You need to do this with outer space because we can’t go and see for ourselves! We can go weigh a planet to see its mass. But we can work out an equation that means if we know where a planet is in the sky we know a bunch of other stuff too!
An easy example is gravity. We understand gravity pretty well. But we can’t see gravity. Not directly.
But we know as a mathematical fact that gravity effects light. And light we can measure! And we know a bunch of facts about light too! We know a lot about orbits and can measure those too (using light to see em!).
We can’t see the black hole at the center of the milky way, but we can see all the stars moving around it. We can _infer_ its there because all our equations that explain the universe say it has to be there.
The math alone didn’t “prove” the existence of black holes. What it did was help provide a framework for making testable predictions.
If someone did the math that proved that unicorns made of diamonds were orbiting around the sun, you’d naturally be skeptical. But if you found sparkling light sources orbiting the sun at the right distance and spectroscopy (analysis of the light) showed the presence of carbon crystals, that’d be stronger evidence.
Point is, the math let astronomers and astrophysicists know what to look for and it explained a host of other previously anomalous events. Sure, some people won’t be satisfied until they see one with their own eyes and they’ll spin endless amounts of pseudoscience, but their guessing doesn’t make any testable predictions.
Physics is governed by math, much like a game of checkers is governed by the rules of checkers.
If you study the rules of checkers, you may realize that a quadruple jump is possible even if you have never seen one before. You might predict that given all the things that occur in games of checkers, there are probably games where quadruple jumps have occurred.
Einstein did something similar. He looked at the laws of gravity and used some math to show that a black hole is possible within those laws.
The same way you use language to describe it with the term “black hole”. That is, the term “black hole” is a stand-in (an analogue) for the real thing. The same works with math, except math is way more precise than your usual language.
Using analogues, all it takes is a human to go “what if…” to come up with all sorts of crazy ideas. We then check those against our current theories and see how they play out. Even if it’s a dead end, we can learn a lot from exploring ideas.
All math is only as good as the assumptions it starts with. So, it’s not enough to just do math, you also have to pick a good place (a good set of assumptions) to start doing the math. Einstein picked a great starting place (at large distances / masses / energies, at least), so his results are very good (for large distances / masses / energies).
Fwiw, his assumptions turn out to be very poor for very small distances / masses / energies, so his results are not at all accurate at these scales.
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