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Rev

So, Laws only describe the regular features of reality? Gosh, that's disappointing!
– Scott Rowe
Commented Dec 21, 2023 at 20:37
1

@ScottRowe The regular parts and the manner in which the irregular parts differ. I could have a law that gives the gravitational force pulling me towards the Sun right now, one for the force pulling me towards the Moon 3 hours ago, one the force pulling me towards the dog next door 30 nanoseconds ago, etc. Or I could have one law that says "That force is different in each of those cases, but if you know the mass of the objects and how far away they are, you can figure it out for any case you care to like so: $F = G m_1 m_2 / r^2$.
– Ray
Commented Dec 21, 2023 at 20:46
The only way we can't have a law at all is if things differ for literally no reason whatsoever, and even then, we could potentially describe it probabilistically. (Or if it's just really really complicated and we can't figure it out.)
– Ray
Commented Dec 21, 2023 at 20:49
2

I think gravity is a terrific example: we have P = m g as a first law, and we can notice that g differs by a few percents between ocean level and the summit of Mount Everest; and then when that law is no longer enough we have F = G m1 m2 / r^2, which can be thought of as a generalisation or complexification of P = m g. This directly answers the OP's question: it wasn't a coincidence that things were following law P = m g on Earth, even though P = m g wasn't the fundamental natural law behind gravity.
– Stef
Commented Dec 22, 2023 at 11:16
1

@Stef And then we notice Mercury's orbit is funny and it's actually G_{μν} ≡ R_{μν} − 0.5 R g_{μν} = κ T_{μν}; ∂^2 x^μ/∂s^2 + γ^μ_{αβ} ∂x^α/∂s ∂x^β/∂s = 0, at which point we start to wonder if maybe P = m g wasn't such a bad approximation after all. :-)
– Ray
Commented Dec 22, 2023 at 16:37

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