But there are forces even in our 3d world that do not follow inverse square law (strong/weak nuclear forces). That kind of proves that all forces do not need to follow this intuition?
In particle physics, fundamental forces are generated by the exchange of virtual particles (I have been reading a quantum field theory textbook for the last few months to try to understand precisely what this means, among other questions, but this is accepted fact in the field). The Coulomb force comes from the exchange of photons. So this 1/r^2 argument for intensity leads to the Coulomb force falling off like 1/r^2.
This argument doesn't obviously apply to gravity (though presumably it would for a quantum theory of gravity), but the equations for gravity (general relativity) give the same result.
At a higher level, it turns out that when you try to combine quantum mechanics with special relativity, the resulting theories are highly constrained. It's not like classical mechanics, where you can just say 'suppose there's a 1/r^12 force.' You get mathematical inconsistencies if you stay too far. Weird stuff
All long-distance forces seem to follow it though. I think it's related to the energy conservation law.
It proves nothing of course. When we speak of these N+T universes, we try to imagine a system that follow the same "fundamental laws" but with different N and T. What exactly is fundamental is up to debate. You can even imagine a system that has different math, but it will be very hard to reason about it.
Those forces are also mediated by particles (called gluons, W, and Z bosons). But these particles are massive, charged and interacting, which caused them to behave quite differently and only act on short length scales.
qnleigh|2 years ago
This argument doesn't obviously apply to gravity (though presumably it would for a quantum theory of gravity), but the equations for gravity (general relativity) give the same result.
At a higher level, it turns out that when you try to combine quantum mechanics with special relativity, the resulting theories are highly constrained. It's not like classical mechanics, where you can just say 'suppose there's a 1/r^12 force.' You get mathematical inconsistencies if you stay too far. Weird stuff
alexey-salmin|2 years ago
It proves nothing of course. When we speak of these N+T universes, we try to imagine a system that follow the same "fundamental laws" but with different N and T. What exactly is fundamental is up to debate. You can even imagine a system that has different math, but it will be very hard to reason about it.
qnleigh|2 years ago