What is a force?

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Stefan Ram

Apr 25, 2022, 3:49:49 AMApr 25
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

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.

As to your general question... there's a rather extensive discussion
of "what is a force" and the operational definition of same, in the
context of teaching introductory physics courses, in the excellent
Arnold B Arons
"A Guide to Introductory Physics Teaching"
Wiley, 1990, ISBN-10 0-471-51341-5
-- jt]]

J. J. Lodder

Apr 25, 2022, 8:10:48 AMApr 25
This is all fine for gravitation, but not for 'real' forces. [1]
The electromagnetic force for example remains a force,
and it causes accelerations satisfying F = ma.
(Avoiding non-flat complications, and with F and a 4-vectors)

As for the weak interaction, of course it produces real forces too.
It doesn't matter whether electrons scatter elastically
through exchange of a virtual photon or a virtual Z-boson.
In both cases their momentum is changed,
so a real force must have acted somewhere in between.
(speaking classically)

For the rest, the use of 'force' is just folklore,
like in the never-ending discussions about a 'fifth force',
which is really a fifth interaction.


[1] Unless you linearise, invent gravitons,
and start exchanging those in the by now flat spacetime.
No experience with actually doing it,
beyond the lowest order divergencies are known to be nasty.

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