I’ve been reading the Wikipedia page for wormholes to kill some time.
The theatrics of a wormhole I understand somewhat through the diagrams and visualisation, but how do math equations represent the theory itself? To me it comes across as… well, just maths.
**Please do actually ELI5, I hardcore sucked at physics and maths in school.**
Link for context: https://en.wikipedia.org/wiki/Wormhole
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Math is just a way of explaining things using statements that are not false. Wether or not they apply to an object is unknown without measuring inputs and outputs. But it’s our best predictor. For example we did not have the ability to compute many machine learning algorithms on the scale we do today but the models/theories were developed in 1950s (the true foundations for hundreds of years before!). Now come 70 years later they hold up.
I do not have the full context to why each variable holds up to be true and what conditions they expect which will imply what equation is true but the idea is to use existing work and model things the best they can using known information.
Math is a language, just like any other language people use. Math equations are “math sentences” and they describe things just like “this dog has red fur and a bushy tail” is a sentence to describe a dog.
All of physics is math. It’s not that math is used to explain how things behave, it’s that things behave in a way that is best explained through mathematics. This is as true of wormholes (if they actually exist) as it is of tracing the trajectory of a golf ball. The words and diagrams we use help with visualizations and sometimes useful analogies, but those words and diagrams are imprecise and paint an approximate picture at best. Useful for the layperson, but not rigorous enough for modern physics.
Discoveries like black holes and wormholes emerged FROM the math – physicists developed equations that precisely (or nearly so) described what they could see, and through the process of extending and solving those equations, things like black holes and wormholes emerged. For a long time, we weren’t certain black holes actually existed or whether we were just extending the equations to a realm where they didn’t apply (or were just missing some key part of the equation(s).
Max Tegmark, a physicist at MIT, postulates that the universe (actually the multiverse) fundamentally IS mathematics. Not that math is a useful tool to help describe the universe, but rather it is the math itself that is fundamental and all that we see (and touch, taste, hear, etc.) somehow emerges from the existence of the math, almost as if the universe is somehow solving the equations through its existence (and that’s why it exists – to solve the fundamental equations that are the true essence of reality). Heady stuff, and there’s no way I can do it justice.
Math is a language. When you think of a wormhole, you can write it in words, and you can also write down some properties that you think a wormhole should have — such as how things behave when they go through that wormhole. At this point, everything is in words and any additional aspect of the wormhole needs to be written down.
Instead of writing down everything your wormhole can do, you can write a rule or give a prescription for how your wormhole behaves. Then, when people think about your wormhole, then just look at your rule and can determine if it has the properties they like. This rule takes the form of a math equation, for example the first one under “Metrics.” In some senses, the diagrams that you see are just math equations. Instead of writing an equation, we can plot a function and see, visually, what is going on. The two are interchangeable, as are the words we use to describe the wormhole and its diagrams.
Once the metric is defined, someone can then ask what happens when an object falls into the wormhole. Instead of you needing to answer them, they can solve the equation themselves, and the result will fit according to how you defined your wormhole. This object can be anything, whereas if it was just in words, you’d have to specify how each object behaves. The math can also be quicker and easier to understand when trying to incorporate other physics like black holes, planets, light, gravity, etc. which already have well defined mathematical forms.
With physics, they attempt to use math to explain what is happening in the world. Like say mass in relation to gravity comes out as some mathematical equation.
And once you have that equation, you can take the math to extremes and ponder what might happen when say signs flip.
It’s how you end up with the concept of a black hole before we were able to ever observe them in nature. The math equation when you take mass to an extreme implied even light wouldn’t be able to escape from an object so massive were they to exist.
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