How does inertia, a property of mass, arise?

[paradisePhysicist]

If you rotate two objects of mass #m# joined by an inextensible string in a circular orbit, the string will not lose or gain tension due to the tidal force of the Earth's mass, only with the passage of time it will shorten due to the gravitational attraction of the masses #m# of the objects themselves.

Ran it in the simulations, it just collapses.

Instead of just putting a stationary object, I then put some planets into orbit. The planets orbited for hundreds of years fine without collapsing. Then when I connected the planets together they all just collapsed before one orbit. Maybe the precision isn't precise enough. Maybe a higher precision simulation is needed. In Kerbal do planets automatically have synchronous rotation or are they asynchronous at spawn, then slowly become synchronous over time?

Think about if there was no property called inertia. We couldn't do anything. Maybe that's why.

I thought inertia was the concept of objects in motion staying in motion, or rather, the concept of objects with no motion having no motion, ie. no activity happening.

 

[Richard R Richard]

Instead of just putting a stationary object, I then put some planets into orbit. The planets orbited for hundreds of years fine without collapsing. Then when I connected the planets together they all just collapsed before one orbit. Maybe the precision isn't precise enough. Maybe a higher precision simulation is needed. In Kerbal do planets automatically have synchronous rotation or are they asynchronous at spawn, then slowly become synchronous over time?

First of all I want to thank you for taking the trouble to answer me and publish the animation.
My criticism of this model continues to be that you have not simulated circular rotation, it is inertia, which will keep the "arc of segments" in balance, if you do not introduce movement, I share with you that the mere fact of approaching the center of the Earth is enough for the material to sag.
Or may be I do not understand what you want to demonstrate, the acceleration of two small bodies for hundreds of years in the absence of resistance, will appreciably shorten the distance between them and the rope will buckle as anticipated, the idea is that the collapse occurs almost instantaneously when freeing the extremes, this happens with zero speed but not with speed

$$v_{orbit}=\sqrt{\dfrac{GM}{h+R_E}}$$

 

[paradisePhysicist]

My criticism of this model continues to be that you have not simulated circular rotation, it is inertia, which will keep the "arc of segments" in balance, if you do not introduce movement, I share with you that the mere fact of approaching the center of the Earth is enough for the material to sag.
Or may be I do not understand what you want to demonstrate, the acceleration of two small bodies for hundreds of years in the absence of resistance, will appreciably shorten the distance between them and the rope will buckle as anticipated, the idea is that the collapse occurs almost instantaneously when freeing the extremes, this happens with zero speed but not with speed

$$v_{orbit}=\sqrt{\dfrac{GM}{h+R_E}}$$

The animation only shows a stationary object. I did do a sim with orbit but didn't upload the gif (was sleepy). The stationary object wouldn't stay in orbit so I just made a new sim with planets, the planets orbited for hundreds of years until I connected the planets, then they collapsed into the gravity circle. The Kerbal question was to see what happens when you put a planet with 0 angular momentum into orbit around a bigger planet. Will there be synchronous rotations or will it take a while for the synchronous rotations? One of the reasons the planets collapsed and the strings warped was because the planets did not have synchronous rotations. But the planets collapsed even when I just put a string in the middle and no strings on the outside, which idk could mean the simulation is not precise enough. I thought about it more last night and imagined the space station instead as a bunch of cubes orbiting the earth, at least in my imagination in a perfectly circular orbit, the cubes should, as you said, maintain the same string length between each cube. Except if there are strings on the outside, if there is no synchronous rotations on the cube, then no. So the answer of if a space station experiences any bend would depend on if there are synchronous rotations on cubes inherently or not imo. Also the planets should be called moons but I was sleepy when posting, when I say planets around a big planet this just means moons around a planet.

 

[jbriggs444]

The animation only shows a stationary object. I did do a sim with orbit but didn't upload the gif (was sleepy). The stationary object wouldn't stay in orbit so I just made a new sim with planets, the planets orbited for hundreds of years until I connected the planets, then they collapsed into the gravity circle. The Kerbal question was to see what happens when you put a planet with 0 angular momentum into orbit around a bigger planet. Will there be synchronous rotations or will it take a while for the synchronous rotations? One of the reasons the planets collapsed and the strings warped was because the planets did not have synchronous rotations. But the planets collapsed even when I just put a string in the middle and no strings on the outside, which idk could mean the simulation is not precise enough. I thought about it more last night and imagined the space station instead as a bunch of cubes orbiting the earth, at least in my imagination in a perfectly circular orbit, the cubes should, as you said, maintain the same string length between each cube. Except if there are strings on the outside, if there is no synchronous rotations on the cube, then no. So the answer of if a space station experiences any bend would depend on if there are synchronous rotations on cubes inherently or not imo. Also the planets should be called moons but I was sleepy when posting, when I say planets around a big planet this just means moons around a planet.

It is far from clear what setup(s) are being described here. But it is well known that a rigid ring (e.g. Rimworld) does not orbit in a way that is stable against small perturbations. So it is immediately obvious that a ring of satellites, each tethered to the next with taut strings will not be stable against small perturbations if they are set to moving in an orbit centered on the Earth.

 

[paradisePhysicist]

It is far from clear what setup(s) are being described here. But it is well known that a rigid ring (e.g. Rimworld) does not orbit in a way that is stable against small perturbations. So it is immediately obvious that a ring of satellites, each tethered to the next with taut strings will not be stable against small perturbations if they are set to moving in an orbit centered on the Earth.

In a system with total vacuum, perfect circular orbit and zero particles in space, would the ring of satellites be stable (with no forces besides gravity, the satellite's inertia, and the strings), with just a string in the middle and no outside strings? What about with outside strings?

 

[jbriggs444]

In a system with total vacuum, perfect circular orbit and zero particles in space, would the ring of satellites be stable, with just a string in the middle and no outside strings? What about with outside strings?

I am not sure that I know what you mean by "a string in the middle" or by "outside strings".

One could hazard a guess that "string in the middle" would run a string (e.g. a "beanstalk") from each satellite down to an anchor point at the center of the primary. Such an arrangement would not be stable against small perturbations. Two satellites nudged a bit nearer to one another would gravitate toward each other until they collided.

If, instead, one anchors the beanstalks to the surface of the primary then stability against small perturbations can be achieved. Perturbations away from a vertical angle for a beanstalk will result in a restoring force (if the rotation rate of the primary is high enough and matches the orbital period of the satellites).

 

[paradisePhysicist]

I am not sure that I know what you mean by "a string in the middle" or by "outside strings".

One could hazard a guess that "string in the middle" would run a string (e.g. a "beanstalk") from each satellite down to an anchor point at the center of the primary. Such an arrangement would not be stable against small perturbations. Two satellites nudged a bit nearer to one another would gravitate toward each other until they collided.

If, instead, one anchors the beanstalks to the surface of the primary then stability against small perturbations can be achieved. Perturbations away from a vertical angle for a beanstalk will result in a restoring force (if the rotation rate of the primary is high enough and matches the orbital period of the satellites).

Oh, I don't know what a primary is. String in the middle referred to a string at the center of mass of each satellite connecting it as a link to the others. Outside string is some string which is offset from the center of mass, also forming a linkage to another satellite offset from center of mass.

 

[jbriggs444]

Oh, I don't know what a primary is. String in the middle referred to a string at the center of mass of each satellite connecting it as a link to the others. Outside string is some string which is offset from the center of mass, also forming a linkage to another satellite offset from center of mass.

A "satellite" is an object in orbit around another object. A "primary" is the object about which it orbits.

So the moon is a satellite with the Earth is its primary.
And the Earth is a satellite with the Sun as its primary.

If you have an "outside" string, as I understand your description, we would still have a ring of satellites, each tethered to the next in line. But the attachment point for all of the strings would be somewhere somewhere on the far side of the satellite -- the side facing away from the primary.

That means that each satellite will, if nudged a bit, tend to flip over to the outside of the tether instead of remaining down on the inside.

With strings in the middle, you do not have this sort of instability. But you have a different kind. The problem is that if the ring as a whole remains in a circular arrangement and one side gets a little closer to the primary than the other, the closer side will get closer still and the farther side will get farther away. That is the Ringworld instability difficulty.

 

[synch]

Anything that affects the mass will collapse it's wavefunction which exists from pre-event. Applying a force is not altering the mass, it is altering the existence of the mass. The observed inertia is not from the mass, it is from the previous existence of the mass.

 

[PeterDonis]

Anything that affects the mass will collapse it's wavefunction

First, this is the classical physics forum, not the quantum physics forum; there are no such things as wave functions in classical physics.

Second, even if we were in the quantum physics forum, your claim here is only true on one speculative interpretation of QM (which has been advanced by Penrose and others but which is still speculative), and hence would only be on topic in the QM interpretations forum.

Applying a force is not altering the mass, it is altering the existence of the mass. The observed inertia is not from the mass, it is from the previous existence of the mass.

I don't know where you are getting this part from, but it has nothing to do with Newtonian physics, which is the theory on which this thread's discussion should be based. Personal speculations are off limits here at PF.

 

[synch]

mea culpa ! my apologies..

 

[timmdeeg]

If I understand this correctly B. Haisch attempts to derive the origin of inertia due to the interaction of matter with the quantum vacuum.

https://arxiv.org/abs/physics/9807023
In this ZPF-inertia theory, mass is postulated to be not an intrinsic property of matter but rather a kind of electromagnetic drag force that proves to be acceleration dependent by virtue of the spectral characteristics of the ZPF. The theory proposes that interactions between the ZPF and matter take place at the level of quarks and electrons, hence would account for the mass of a composite neutral particle such as the neutron.

 

[PeterDonis]

If I understand this correctly B. Haisch attempts to derive the origin of inertia due to the interaction of matter with the quantum vacuum.

You have understood the proposed model correctly, yes. That proposal goes back to, IIRC, the 1970s, but has never gotten any traction outside its few proponents. Nor has it made any experimental predictions that are both different from mainstream theories and confirmed by experiment. (Note that the paper you reference is from 1998, and refers to "investigations" currently in progress; to the best of my knowledge, they never panned out.)

 

[Vanadium 50]

That paper was part of an "explanation" of paranormal powers. One of the authors claimed to have them. I would pay it no mind.

 

[timmdeeg]

(Note that the paper you reference is from 1998, and refers to "investigations" currently in progress; to the best of my knowledge, they never panned out.)

Thanks for clarifying that. It seems to confirm that "why" questions don't make too much sense in physics.

 

[saddlestone-man]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe. Therefore to change the motion of any object you have to overcome the forces applied by all the others. That's why there can't be an immediate change in motion.

 

[timmdeeg]

This reminds me of Mach's principle which is about rotating objects though. As far as I can tell today it is assumed that inertia is a local phenomenon.

 

[weirdoguy]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe.

No.

 

[PeterDonis]

Doesn't inertia have to do with the fact that all objects in the Universe are being attracted by all the other objects in the Universe.

Not in GR. In GR gravity (which is the only "attraction" that could be in play here) is not a force, it's spacetime geometry. One could say that spacetime geometry determines inertia in GR (and at least one whole textbook, Gravitation and Inertia by Cuifolini and Wheeler, has been written about this), but what that actually means is that spacetime geometry determines which trajectories through spacetime are inertial (geodesics, freely falling) and which are not, and what the path curvature is of the ones that are not. But it doesn't explain why path curvature is felt as weight, which is part of "inertia" as commonly understood; that part just has to be accepted as an axiom, without explanation.

There have been attempts to explain inertia along the lines you describe (for example, Sciama in the 1950s tried it), but these attempts did not use standard GR; they used other theories of gravity. In Sciama's case, he used a simple idealized scalar field model, which is known to be incorrect but which he picked in order to illustrate the basic idea. He planned to write a follow-up paper to try to extend his idea to a tensor theory of gravity, which would have been much closer to GR, but unfortunately it appears he never did.

 

[Paige_Turner]

Well, this university physics dept seems to think that the inertial reaction force is reverse-time gravity from all the galaxies in the distant future reaching backwards in time and pushing back at you.

THE ORIGIN OF INERTIA​

By Dr. James F. Woodward, Fullerton University

It's thought by some folks these days that the cause of inertial reaction forces isn't yet really understood, or that they have just succeeded in figuring out the explanation for these forces with their "new theory." These views are mistaken.

The cause of inertial reaction forces has been understood to be the action of gravity for quite some time now.

Back in 1953, Dennis Sciama showed that gravity could account for inertial reaction forces as long as the interaction of local stuff with the gravity field of distant matter was like the interaction of electric charges and currents with the electromagnetic field. (Monthly Notices of the Royal Astronomical Society, 113, 34-42 [1953]).

It turns out, as a matter of fact, that this is true in general relativity theory, but it took a while to show this. (It was done by D.J. Raine in 1981: Reports of Progress in Physics, 44,1151-1195 [1981]).

The full-blown argument is rather formal and a bit daunting, but it's easy to see that gravity causes inertia in a simple little argument modeled on that presented by Sciama back in 1953.

Full text here.

 

[PeterDonis]

Well, this university physics dept seems to think that the inertial reaction force is reverse-time gravity from all the galaxies in the distant future reaching backwards in time and pushing back at you.

As you were already told in another thread, the article you refer to is the personal opinion of one particular physicist, not a "university physics dept", much less an actual peer-reviewed paper.

Of the two actual papers the article links to, one (the paper by Sciama) was an attempt to account for inertia using a simplified model of gravity (a scalar field) that is known to not be correct. Sciama said he planned to write a follow-up paper extending his idea to a tensor theory of gravity (which GR is), but never actually did so.

The other paper (Raine) does not actually show what the article you quote claims. It does not show that Sciama's idea works in General Relativity (the abstract explicitly says that Mach's principle, which is what Sciama's idea embodies, is not contained in GR). What it does do is propose additional structure that could be added to GR to make it Machian (at least in the author's view). AFAIK this proposal has not gained any traction in the GR community (possibly because many relativists do not share the author's opinion that GR is not Machian; at least one GR textbook, the one by Cuifolini & Wheeler that I referred to in post #54, has been written to justify and expand on the view that it is).

 

[Paige_Turner]

Ahh, thank you! I wondered why I hadn't seen this anywhere else.

> As you were already told in another thread,

I haven't seen it yet.

--lkt

 

[PeterDonis]

I haven't seen it yet.

https://www.physicsforums.com/threads/need-sr-beliefs-integrity-filter.1005129/post-6515561

 

[Paige_Turner]

> Mach's principle, which is what Sciama's idea embodies, is not contained in GR

Yes, but it's not inconsistent with GR.

> What it does do is propose additional structure that could be added to GR to make it Machian

By Machian, I assume you mean that local inertia is determined by faraway mass.

Well, I'm glad you think it's false. I thought I had to believe it because that physics prof said so in the inertia paper.

I never did see what the problem is with the only object in the universe rotating.

...Or do you believe Mach was right? I'm confused. You'd think I'd get used to it.

 

[PeterDonis]

it's not inconsistent with GR.

Agreed.

By Machian, I assume you mean that local inertia is determined by faraway mass.

That's what the references you gave appear to me to mean by it. For example, that's the view that the Sciama paper was proposing.

I'm glad you think it's false.

I didn't say I thought GR wasn't Machian. I only said the abstract of the second paper referenced in the article you quoted said so.

I thought I had to believe it because that physics prof said so in the inertia paper.

This is not a good reason to believe anything. You don't "have" to believe things just because some physicist in some paper says so. At the very least, you should be reading more than just one paper; you should have some sense of the overall literature and where that particular paper fits in. That's one of the biggest advantages of a good textbook (like MTW or Wald for GR): the authors have already done a huge survey of the literature for you, and will put various claims in their proper context.

Or do you believe Mach was right?

Mach himself only had a preliminary and very tentative version of the whole conceptual scheme in question. So the things he himself said weren't really right or wrong; they were initial gropings towards understanding and should not be taken as definite anyway.

My personal view on GR is closer to that of the Cuifolini and Wheeler textbook I referenced, whose tag line is "mass there governs inertia here", i.e., GR is Machian to the extent that such a question even matters. The Einstein Field Equation says that the spacetime geometry at any event is determined by the distribution of stress-energy in the past light cone of that event. That seems pretty Machian to me. The only issue I see with that viewpoint (and I'm certainly not the only one to see it, many physicists have discussed this in the literature) is that many solutions of the EFE require some kind of boundary condition or initial condition, and those conditions can be viewed as something separate from the distribution of stress-energy and hence a non-Machian element.

 

[timmdeeg]

My personal view on GR is closer to that of the Cuifolini and Wheeler textbook I referenced, whose tag line is "mass there governs inertia here", i.e., GR is Machian to the extent that such a question even matters. The Einstein Field Equation says that the spacetime geometry at any event is determined by the distribution of stress-energy in the past light cone of that event. That seems pretty Machian to me.

Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?

 

[PeterDonis]

Doesn't "mass there governs inertia here" imply that the inertial mass of a body depends on the spacetime geometry?

No. A more precise phrasing would be that mass there governs inertial motion here. Mass there determines the spacetime geometry here, and the spacetime geometry here determines which worldlines here are inertial, and what the path curvature is of worldlines here are not inertial. But path curvature is only proper acceleration; what you feel as weight is proper acceleration times inertial mass. The spacetime geometry does not determine what the inertial mass of a body is.

 

[timmdeeg]

No. A more precise phrasing would be that mass there governs inertial motion here.

Yes this way it makes sense to me and I would prefer to call it just Einsteinian.