Sometimes I just can't go back to sleep
This is a physics thing: if you don't recognize the equations, you can safely skip this post.
F = ma
That's fine in S.I. units, but in English Imperial units you need F = kma with a constant k to work out the proportionality of the units. S.I. just defined the units so that k was equal to 1.0, so there really is always a constant present. But wait, we defined those units based on experiments performed on earth, relatively recently. What if k isn't constant, what if it is a function of some variable that changes relatively little in our recent, nearby experience? What if k is a function of gravitational curvature - then the force needed to accelerate an object would vary with distance from massive objects (planets, stars, etc.). What if k is a function of time - then acceleration of objects would change as the universe gets older. And if k isn't constant, that throws some serious kinks into special relativity. Have we proved that k is a constant across the universe? Can we prove it?
Or is treating k as constant just an approximation, only useful until we move farther out from our home?
F = ma
That's fine in S.I. units, but in English Imperial units you need F = kma with a constant k to work out the proportionality of the units. S.I. just defined the units so that k was equal to 1.0, so there really is always a constant present. But wait, we defined those units based on experiments performed on earth, relatively recently. What if k isn't constant, what if it is a function of some variable that changes relatively little in our recent, nearby experience? What if k is a function of gravitational curvature - then the force needed to accelerate an object would vary with distance from massive objects (planets, stars, etc.). What if k is a function of time - then acceleration of objects would change as the universe gets older. And if k isn't constant, that throws some serious kinks into special relativity. Have we proved that k is a constant across the universe? Can we prove it?
Or is treating k as constant just an approximation, only useful until we move farther out from our home?