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

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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.

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

book

Arnold B Arons

"A Guide to Introductory Physics Teaching"

Wiley, 1990, ISBN-10 0-471-51341-5

-- jt]]

|[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.

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

book

Arnold B Arons

"A Guide to Introductory Physics Teaching"

Wiley, 1990, ISBN-10 0-471-51341-5

-- jt]]

Apr 25, 2022, 8:10:48 AMApr 25

to

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.

Jan

[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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