Why does a body has inertia and from where does it get that

[nouveau_riche]

why does a body has inertia and from where does it get that inertia,theoretical explanation will suffice?

 

[Dale]

I think that the theoretical explanation would be Noether's theorem and the translation-symmetry of the Lagrangian of an isolated system.

 

[Ken G]

Actually, that to me seems like the explanation for conservation of momentum of an isolated system. To get inertia, you have to open the system up, and ask how much can you get its parts to accelerate, given that the whole will conserve momentum. Inertia must have something to do with the ratio of F/a that you see on the different parts of the system, that tells you the ratio of the inertia of those parts (there is no absolute scale for inertia, only ratios are meaningful, because the numerical value of the inertia simply depends on the scale of force, or some other convention). The concept of inertia must result from the fact that when you look at all the F/a on all the parts, and allow forces to simply add, then you find you also get an additive property to inertia-- a part that combines two parts has the inertia of the sum of the two parts, where we have that the net force on the sum of the parts is the sum of the net forces on each part. Within Newtonian physics anyway, that's what makes inertia a useful notion, I would say.

 

[nouveau_riche]

Actually, that to me seems like the explanation for conservation of momentum of an isolated system. To get inertia, you have to open the system up, and ask how much can you get its parts to accelerate, given that the whole will conserve momentum. Inertia must have something to do with the ratio of F/a that you see on the different parts of the system, that tells you the ratio of the inertia of those parts (there is no absolute scale for inertia, only ratios are meaningful, because the numerical value of the inertia simply depends on the scale of force, or some other convention). The concept of inertia must result from the fact that when you look at all the F/a on all the parts, and allow forces to simply add, then you find you also get an additive property to inertia-- a part that combines two parts has the inertia of the sum of the two parts, where we have that the net force on the sum of the parts is the sum of the net forces on each part. Within Newtonian physics anyway, that's what makes inertia a useful notion, I would say.

I think that the theoretical explanation would be Noether's theorem and the translation-symmetry of the Lagrangian of an isolated system.

i thought it was mach's principle?

 

[Ken G]

Mach's principle relates to the origin of inertia, not what inertia is, which is what I was talking about (but you're right the OP also asks where it comes from, and one idea is that of Mach). Mach felt that an object that was alone in the universe could never have inertia, no matter how massive the object was, so inertia must come from "the rest of the universe". This is equivalent to saying that an entire universe cannot exhibit proper acceleration, only parts of it relative to other parts. Often this is framed in terms of rotation of the whole universe, and indeed our universe does not appear to have any global rotation, but it's not clear that is because of Mach's principle. I think we'll need to know what mass is before we can assess where inertia comes from!

 

[Dale]

i thought it was mach's principle?

I would disagree with this. Inertia seems to be something that applies in this universe, and this universe appears to be non-Machian. At least as far as Brans-Dicke gravity formalizes Mach's principle into something testable.

 

[nouveau_riche]

I would disagree with this. Inertia seems to be something that applies in this universe, and this universe appears to be non-Machian. At least as far as Brans-Dicke gravity formalizes Mach's principle into something testable.

if you could please justify for disapproval?

 

[nouveau_riche]

Mach's principle relates to the origin of inertia, not what inertia is, which is what I was talking about (but you're right the OP also asks where it comes from, and one idea is that of Mach). Mach felt that an object that was alone in the universe could never have inertia, no matter how massive the object was, so inertia must come from "the rest of the universe". This is equivalent to saying that an entire universe cannot exhibit proper acceleration, only parts of it relative to other parts. Often this is framed in terms of rotation of the whole universe, and indeed our universe does not appear to have any global rotation, but it's not clear that is because of Mach's principle. I think we'll need to know what mass is before we can assess where inertia comes from!

i know what mach's says but if it's true then inertia will vary according to observation setup

 

[Ken G]

Not necessarily-- this is what I mean by the difference between what inertia is, and how we can trace its origin. I think Mach's principle is often mischaracterized-- to me, we have two very different issues: the issue of what is the inertial path, and the issue of how easy or hard is it to get a particle to deviate from the inertial path. I would say the existence of an inertial path is "what inertia comes from", because without a concept of an inertial path, there is no concept of how hard it is to deviate. But the numerical value of the inertia, what I meant by "what inertia is", is more about how hard it is to deviate from that path. Mach doesn't need to be talking about the latter issue, only the former. I think he is often confused as talking about the latter, and that would just seem to me to be a much weaker claim than what he actually said, though I'm no Mach expert. But if "mass there" determines "inertial path here", then it might require a whole lot of mass-- like the mass of the rest of the universe-- to do that.

 

[Dale]

if you could please justify for disapproval?

Brans Dicke theory is more "Machian" for lower values of its dimensionless parameter, w. Current observation puts a lower bound on w of about 40000, so it seems that the universe is decidedly not Machian.

http://en.wikipedia.org/wiki/Brans–Dicke_theory
http://prola.aps.org/abstract/PR/v124/i3/p925_1

I wouldn't recommend using Mach's principle to explain anything.

 

[nouveau_riche]

Not necessarily-- this is what I mean by the difference between what inertia is, and how we can trace its origin. I think Mach's principle is often mischaracterized-- to me, we have two very different issues: the issue of what is the inertial path, and the issue of how easy or hard is it to get a particle to deviate from the inertial path. I would say the existence of an inertial path is "what inertia comes from", because without a concept of an inertial path, there is no concept of how hard it is to deviate. But the numerical value of the inertia, what I meant by "what inertia is", is more about how hard it is to deviate from that path. Mach doesn't need to be talking about the latter issue, only the former. I think he is often confused as talking about the latter, and that would just seem to me to be a much weaker claim than what he actually said, though I'm no Mach expert. But if "mass there" determines "inertial path here", then it might require a whole lot of mass-- like the mass of the rest of the universe-- to do that.

what you call inertial path is not the intrinsic property of matter,the setup for an experiment will decide it