Well, for one, classical mechanics don't work at the particle level, and we're not entirely sure they work at grand macro levels. We've noticed that galaxies behave in a way that suggests they have way, way more mass than is visible, so we invented Dark Matter to fill the missing mass.
Anyways, in quantum mechanical terms: I'm not a math guy so I can't provide the equations, but the foundation of quantum mechanics came from some very smart people doing a lot of math, and realizing that the solutions for particle position/momentum don't make sense unless you view them as statistical probabilities, not real values. So any particle you care to choose is in fact not deterministic as far as we can tell, and instead behaves probabilistically.
This has real world applications beyond weird math shit. For instance, quantum tunneling. Sometimes a particle will spontaneously move through a physical barrier it wouldn't be able to cross in classical mechanics, without expending energy to do so. This is actually a problem for CPUs. As transistors get increasingly smaller, the probabilities that electrons will decide to teleport out of a transistor and into a different place go up. And a CPU that can't control electron flow stops being a useful object and starts being an impure silicon crystal desk toy.
When we look at the movement of the planets in our solar system, we see that they all match our equations of orbital mechanics. They all have a balance between gravity and centripetal acceleration, so they follow stable orbits. If we discovered an exact copy of our solar system, but with planets that moved twice as fast in the same orbits, that wouldn't make sense with our equations. They would predict that gravity could not be strong enough to balance the centripetal acceleration, and the planets should fly apart as we watch. If that doesn't happen, it means one of our assumptions is wrong. It could be that the sun is actually much more massive than our sun, or something stranger is going on.
When we look at a galaxy, plug in the positions and velocities of all the stars we see, and try to simulate how it will behave, the simulation typically predicts that the galaxy is going to fly apart immediately. Since that's not happening, we know something is wrong with our explanation. The simplest fix is if there's a lot of mass that we can't see, but if that's not true, then we're in the much more uncomfortable situation of our equations being wrong or incomplete.
Well, for one, classical mechanics don't work at the particle level, and we're not entirely sure they work at grand macro levels. We've noticed that galaxies behave in a way that suggests they have way, way more mass than is visible, so we invented Dark Matter to fill the missing mass.
Anyways, in quantum mechanical terms: I'm not a math guy so I can't provide the equations, but the foundation of quantum mechanics came from some very smart people doing a lot of math, and realizing that the solutions for particle position/momentum don't make sense unless you view them as statistical probabilities, not real values. So any particle you care to choose is in fact not deterministic as far as we can tell, and instead behaves probabilistically.
This has real world applications beyond weird math shit. For instance, quantum tunneling. Sometimes a particle will spontaneously move through a physical barrier it wouldn't be able to cross in classical mechanics, without expending energy to do so. This is actually a problem for CPUs. As transistors get increasingly smaller, the probabilities that electrons will decide to teleport out of a transistor and into a different place go up. And a CPU that can't control electron flow stops being a useful object and starts being an impure silicon crystal desk toy.
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Their behavior doesn't follow our model of gravity. If we add a bunch of extra mass it follows it perfectly, however.
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When we look at the movement of the planets in our solar system, we see that they all match our equations of orbital mechanics. They all have a balance between gravity and centripetal acceleration, so they follow stable orbits. If we discovered an exact copy of our solar system, but with planets that moved twice as fast in the same orbits, that wouldn't make sense with our equations. They would predict that gravity could not be strong enough to balance the centripetal acceleration, and the planets should fly apart as we watch. If that doesn't happen, it means one of our assumptions is wrong. It could be that the sun is actually much more massive than our sun, or something stranger is going on.
When we look at a galaxy, plug in the positions and velocities of all the stars we see, and try to simulate how it will behave, the simulation typically predicts that the galaxy is going to fly apart immediately. Since that's not happening, we know something is wrong with our explanation. The simplest fix is if there's a lot of mass that we can't see, but if that's not true, then we're in the much more uncomfortable situation of our equations being wrong or incomplete.