In "Gravitation" by Misner et. al., in chapter 1, it says in box 1.6,
|[O]ne can "look at the separations between these nearby [two]
|test particles and from the second time-rate of change of
|these separations and the 'equation of geodesic deviation'
|(equation 1.8) read out the curvature of spacetime."
. To me, a "force" is something that is causing an acceleration
(thinking of "F = ma"). So, I'd be inclined to say that the
curvature of spacetime is a /force/ that is accelerating the
two test particles relatively to each other.
If someone thinks that this curvature is /not/ a force, maybe
he could explain why the curvature of spacetime should not
be called a "force" although it causes an acceleration?
And while I'm at it: Wikipedia says: "Most fermions decay by
a weak interaction over time.". This weak interaction also
is called "weak force"; so, this weak force does not seems
to cause accelerations, but decays. Why is it still called a
"force"?
What is a force?
[[Mod. note -- Applying the same force to different-mass test bodies
results in different accelerations, as per Newton's 2nd law $a = F/m$.
But spacetime curvature induces the *same* relative accelerations
between different-mass test bodies. So to call spacetime curvature
a "force" you have to posit that's really a "force-proportional-to-inertial-mass", which is a funny sort of beast.
It seems cleaner to just call it "spacetime curvature".
As to the weak interaction, I think particle physicists usually call
it the "weak interaction". Calling it a "force" is colloquial usage.
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