The questions is not sufficiently well defined - I vote to put this on hold until there are further clarifications. Is the questions asking whether: 1. There is a test particle that - in the Classical sense - experiences zero acceleration at some point. 2. There is a particle that - in the Quantum sense - couples only to fields that are locally identically zero at a given spacetime point. 3. As above but with locally zero spacetime curvature.

@Marius Ladegård Meyer, the former, but out of curiosity I wouldn't mind hearing about the latter as well

@Akerai, I meant (1) but I'm not familiar enough with some concepts you mention in (2) and (3) - I'm not a physicist

I think it's a rather tricky question to ask as you will get drowned in inconsistent answers depending on what framework people work in. For all intents and purposes force-free motion will always be only an approximation to something much more involved and complicated that in the end does not matter. At the end of the day physics is here to describe the world as we can currently measure it - not to explain it.

To my knowledge any answer that will claim exactly force-free motion to exist (or not) will do so in the context of a particular mathematical framework.

@Akerai you second comment above is an interesting answer in and of itself. Could you however give examples of such frameworks in which the answer might differ?

Eh

Do you have any physics background?

@acros

Sadly no, i'm a computer scientist by training whose math/physics date back 15 years now...

Alright, I think the question, and my uncertainty about the answer comes down to definitions really.

Essentially there are two tricky things here to define one of them is "force" and the other is "motion".

Now physics should never be understood as the 'truth' or as the way 'the world works'. It is simply a descriptive model that given some input data about a physical system should lead to some output data about the same physical system at a later time / different position.

It turns out that we have just such descriptive models - and we use different models for different approximations. For example for human length and time scales the best approximation might be the classical Newtonian physics.

In Newtonian physics a particle is something that has a position uniquely defined by three coordinates (x,y,z) at a time 0. Then it's easy to define the 'motion' as the pace at which these coordinates change with time.

Force is simply something that causes acceleration - and there are many ad-hoc equations for different forces. i.e. the gravitational force, the coulomb force. (Weak and Strong force don't appear in the Newtonian description as they can be approximated to be zero).

Now in the Newtonian sense to have a particle with exactly zero force on it you essentially need all of the force components acting on the particle to cancel.

for example if you have three massive bodies like this:

o ---- o ---- o

then the body in the middle will feel exactly no force as the forces cancel by symmetry.

In that formalism you can have exactly force-free motion for the body. If you speak of our universe, then there is too many bodies and it is highly unlikely they conspire to be in exactly the kind of configuration that would give exactly zero force somewhere.

Now in the Quantum case things get a little fuzzy, as the 'motion' cannot be particularly well defined and nor can the 'force' be.

It is however the correct approximation to use if you are speaking of an extremely small particle.

Essentially the formalism does not know "particles" as dynamical entities, particles are simply something that is measured.

the entities that are physical and change in time are fields, i.e. some 'probability densities' that a particle is somewhere (don't take me too literally here) that are a function of (x,y,z,t)

It gets rather involved, but essentially it is nearly impossible to get a real particle (such as the electron) that would not interact with any other force field.

It's all quite complicated, but in short it's something you shouldn't care about. It's enough that things don't feel 'forces' to the extent we care about. For all intents and purposes it is a valid statement to say that the paperweight on my table feels no net forces.

ok, there's a lot for me to unpack here

but when you say: "If you speak of our universe, then there is too many bodies and it is highly unlikely they conspire to be in exactly the kind of configuration that would give exactly zero force somewhere.", it's kind of where I was approaching my question from

You are right then, it is unlikely

but then again, the gravitational force falls off as 1/r^2

so if you are sufficiently far away in the empty space out there you will feel effectively no force.

The real question is, do you care about feeling effectively no force or exactly no force in the particular framework you work in.

i mostly care about "exactly"

basically i thought to myself that if there is mass in the universe, and the warping from has had time to catch up to me, then i can't be in "force-free" motion

There are things worse than gravity.

but that is until it was pointed out to me that gravity isn't a "force" per se in GR

the nice thing about gravity is that it does not interact with itself.

but that does not then have a feedback on the particle itself.

now just one thing you mention that intrigues me: "Now physics should never be understood as the 'truth' or as the way 'the world works'.", I mostly agree but wouldn't you say that a few things such as the speed of light may qualify for an accurately descriptive feature of the universe?

In what sense

we could call it differently and use different units to measure it, but it would have a counterpart in reality (that is, would not be a "theoretical-only notion"

there are indeed particles that "move" at the speed of light: photons

That's fair enough, it seems to be a reasonable assumption that the space as-is has a finite limit to the speed of a particle.

Nonetheless, it does not explain why.

It's simply a descriptive model, and it clashes with many things in other branches of physics.

also there are many technical nitpicks I could make when it comes to that statement as well, it would probably be more true if one formulated it as

yes, why is an even deeper question

'If you average over a sufficiently long time then it is not possible to send information at a speed faster than light.'

Yeah, physics is imperfect.

where is it from?

(that quote)

I just wrote out a more sensible definition when it comes to some speed of light constraints.

because things can move faster than light

but i was under the impression that it wasn't the case for information, eg a boolean value

Information cannot be sent faster than light is the rule, there is no particular reason why.

as far as I know anyway.

also regarding clashes in other branches, do any clash actually arise from c being the upper limit? or do the clash arise from other properties we derive indirectly from c?

It doesn't matter what the upper limit is, as long as there is an upper limit the physics is going to be the same.

The clashes arise from GR setting a fixed upper limit.

while quantum field theory implies that one can get particles that move faster than light (for very short periods of time).

I didn't realize that

and only if one averages them over sufficiently (macroscopically) long times then one gets the GR rule

that nothing is faster than light

could it be observed, or is it too statistically unlikely (any time soon)?

Not sure, that is way beyond the area of my expertise.

but here you have a whole list of things that propagate faster than light

without transmitting information

hmm I see, it's still about information

anyway, thanks for the write up, always nice to get more context from someone who actually knows what he's talking about :)

he or she I guess

I think it wouldn't shock me if someone managed to measure superluminal virtual particles at some point.

In an indirect way anyway.

I absolutely can't wait for that!!

It would be way less exciting than you think though :D

it would be for me :)

There is a whole new world of interesting physics to be measured with the advent of ultraintense lasers.

Lasers intense enough to actually force electron-positron pairs out of the vacuum.

so I guess they'd just annihilate right away, but we could actually observe it?