When James Clerk Maxwell turned his attention to the stability of Saturn’s rings, he did not rely too much on observations. He began with a series of mathematical models. He responded to the following questions.
Can solid rings be stable? Can fluid rings be stable? Can rings composed of distinct solid particles be stable?
He let the mathematics lead the way. The only way for a solid ring to be stable was if it was more like a moon. There was no way for a fluid ring to be stable. A ring composed of particles, on the other hand, could be stable!
Why should mathematical models represent reality?
This is a deep question. I have no idea why mathematics seems to be the language of physics. I don’t know why mathematical truths should correspond to reality. It’s bizarre! But that’s the beauty of physics!
When the Voyager and Cassini satellites took pictures of Saturn’s rings, Maxwell’s ideas were confirmed. The rings are composed of many small solid objects orbiting the planet.
Theoretical physics is based on the exploration of mathematical models. We don’t know why mathematics is so good at describing our physical world; we just know that it works!
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