What causes the inertia of an object in classical physics?

[Edward Solomo]

Hello!

My name is Edward Solomon and I have found a very particular concept in classical physics to be more mystifying and puzzling than even more advanced topics covered in modern physics. This is the theory of "inertia."

Although there is much literature covering the effects of inertia, I have yet to come across any texts that state the "cause" of inertia. The best answer I've come across is that it is an "inherent property of mass."

What is interesting is that inertia cannot be a force. This follows from the very definition of inertia. Here is a simple (and hopefully well-known) proof of this claim.

F = ma

We can interpret inertia to say that an object will not accelerate unless acted upon by some force. In other words inertia preserves scalar and angular momentum, thus the "force" of inertia is equal to zero.

So now for my ultimate question.

Photons carry electro-magnetic radiation, gluons carry the strong force, the predicted-but-yet-unobserved gravitons carry the gravitational force (recall that inertia and gravity are derived from the same quantity "mass"). Is there any hypothesized particle that may carry inertia?

Another question: The centrifugal force, Coriolis Force and the Euler force are known as the three fictitious forces. Is the concept of inertia simply a "fictitious" entity itself to explain what we do not know.

Last question:
Even if inertia is real, its force is equal to zero, so how could we ever detect it? How can it even interact with our universe? For instance if in some strange universe, Newton's Gravitational Constant (G) was equal to 0, then we could hypothesize that gravity exists, but we could never detect it because as far as our universe is concerned, gravity does not exist. The same concept seems to apply to inertia in OUR universe, unless there is a different concept of force that must be invented/discovered in order to adequately explain how it does interact with our universe.

 

[Academic]

Inertia is a property of mass (or perhaps, a definition of mass). Like most fundamental properties, nobody knows what 'causes' it.

In my opinion this kind of question is not a question that we should expect science or physics to answer. Science models and describes our observations, the fundamental 'causes' and 'reality' are forever hidden from us. Perhaps someday we will explain it in light of a more fundamental property, but for now it is seen as fundamental and thus no further explanation is expected.

 

[K^2]

There are two parts to inertia. First, the tendency of things to stay at rest. You don't expect something at rest to suddenly start moving for no apparent reason. That'd be bad. You wouldn't be able to predict anything. Of course, once you establish that, going into a moving frame of reference gives you tendency to move in a straight line. Again, no mystery here. Finally, the the thing that makes it do something other than stay at rest we call a force. That's the definition of force, so asking why a force accelerates mass is pointless. A better question is why effect is linear, and that can also be explained by considering different coordinate system. If you want, I can go into a bit more detail here.

Second part, and probably what you are really thinking of, is the tendency of objects to push back when you push against them. So it's really the Newton's Third Law that makes you think of inertia, not second.

So why must there be a reaction force equal to the applied force? Fundamentally, this is going to be because of conservation of momentum, and that, again, has to do with symmetries in space. But for very simple explanation, think of what causes interaction forces? You normally come across gravitational and electrostatic forces. For both, the particle that's affected by the field, creates a proportional field of its own. So if particle A experiences force F in field from particle B, the particle B is in the field of A, and will experience force -F.

Both of these work within the framework of existing forces, so we really do not need any new particles. If you apply a force via gravity, your reaction force, which you perceive as result of inertia, is also gravitational. No new carrier particles are needed.

Fictitious forces aren't fictitious because they are made up or undetectable or anything of the sort. It's just a name. They are called fictitious because they depend on the choice of coordinate system.

In view of all of the above, I think you'll agree that your last question is a non-sequitur.

 

[Ketman]

I don't think it's a silly question, but it's more a philosophical question than a scientific one. There are certain qualities in the universe which have no apparent cause. Not just inertia, but time and space, gravity, magnetism, etc. These just have to be called "phenomena". They all come into existence with the Big Bang, and we can't investigate that, because at that point in the history of the universe the tools science needs don't even exist yet. The Big Bang is apparently a causeless cause, so ultimately it isn't a rational universe. We just have to accept the phenomena that are presented to us and deduce or infer laws that govern how it all works. That's all science can do. Inertia is just a phenomenon whose cause is unknown.

 

[AlexB2010]

If I give kinetic energy to a body, they will accelerate and this new velocity in the same frame of reference will be an increase in inertial mass. So, energy can be converted in inertial mass. I can increase and decrease inertia given or taken energy to a body.

 

[petm1]

I don't think it's a silly question, but it's more a philosophical question than a scientific one. There are certain qualities in the universe which have no apparent cause. Not just inertia, but time and space, gravity, magnetism, etc. These just have to be called "phenomena". They all come into existence with the Big Bang, and we can't investigate that, because at that point in the history of the universe the tools science needs don't even exist yet. The Big Bang is apparently a causeless cause, so ultimately it isn't a rational universe. We just have to accept the phenomena that are presented to us and deduce or infer laws that govern how it all works. That's all science can do. Inertia is just a phenomenon whose cause is unknown.

Why should the cause be unknown? In my mind just using the little twist we call big bang as the cause explains the motion I still feel today because our continuum was created when the original hot dense state broke into our atoms 300,000 light years after the singularity. Outward motion is the motion of energy, which is the motion we count as time, mass is nothing more than the dilating momentum of matter from the inside out imparted at this break up. A dilating area is all we need from the singularity.

 

[dulrich]

I'm not an expert in particle physics, but isn't the Higgs boson hypothesized to be the source of mass for elementary particles?

http://en.wikipedia.org/wiki/Higgs_boson#Theoretical_overview

 

[mechprog]

There is a book by Amitabh Ghosh (Manufacturing Engineering emeritus professor!) named 'The Origin Of Inertia'. He takes a different and uncommon (but not new) view of inertia and Newtonian Laws.
As of fictitious forces, if we call them fictitious because of their dependence on reference frame (of course non inertial) then what is real (non-fictitious) for every force is dependent on choice of frame- take a frame with acceleration 'a' and force,F[=ma] is gone! No gravity in freely falling lift!

 

[Ketman]

No gravity in freely falling lift!

Sounds like a situation of some gravity to me.

 

[Phrak]

I don't find inertia so odd. Most things in physics are constant, in-and-of-themselves, and change with external conditions, inertia included.

 

[Naty1]

The cause of inertia IS a question we should expect science to answer. The objective of science is to explain what happens (which we are getting pretty good at doing) and why it happens (we are not so strong here.).

Inertia is not necessarily any more strange that electric charge or energy or time. We don't know where any of them originate, but we are lucky they did or we would not be having this discussion.

 

[GRDixon]

Hello!

Although there is much literature covering the effects of inertia, I have yet to come across any texts that state the "cause" of inertia.

A small spherical shell of charge has electromagnetic mass ... an external agent must exert a force on the sphere in order to accelerate it. When the charge is accelerated, its own fields INDUCE an electric field component right at the charge itself. This component is such as to always point opposite to the acceleration. It is helpful to think of the charge as a "conduit" or point of contact between the driving agent and the electromagnetic field. The agent exerts a force on the field (by pushing/pulling on the field source) and the field pushes back, ala Newton 3, via an electric force experienced by the charge in its own field. Using the field solutions for point charges, this can easily be modeled on a computer, and it can be demonstrated that the accelerating charge does indeed experience a self-induced electric field right at its own position. "The Feynman Lectures ...", V2, Sect. 28-4 discuss "The force of an electron on itself."

 

[DaveC426913]

I'm not an expert in particle physics, but isn't the Higgs boson hypothesized to be the source of mass for elementary particles?

http://en.wikipedia.org/wiki/Higgs_boson#Theoretical_overview

Yes, this is the hypothesized particle that imbues objects with mass and thus inertia.

 

[Cleonis]

Although there is much literature covering the effects of inertia, I have yet to come across any texts that state the "cause" of inertia. The best answer I've come across is that it is an "inherent property of mass."

Regarding inertia as an "inherent property of mass", that doesn't work.
If you throw, say, a marble towards a chunk of clay the marble will embed itself into the clay. Penetrating the clay takes considerable force. The fact that the fast-moving marble can penetrate the clay cannot be seen as just an inherent property of the marble; it cannot be the case that the marble is pushing itself into the clay.

For comparison: there is a Baron von Munchhausen story in which he pulls himself out of a swamp by grabbing his own hair and pulling himself up with all this strength! Clearly that is unphysical, and the idea of a marble pushing itself into the clay is just as unphysical.

What is interesting is that inertia cannot be a force.

I agree with that, but it's not a very deep statement. The thing is, the very concept of force is defined as: 'that which causes acceleration'. We have that inertia opposes acceleration, so in order to be consistent with the definition of force inertia cannot be categorized as a force. As I said, this isn't so much physics considerations, it's about using the chosen definition of force consistently.

Photons carry electro-magnetic radiation, gluons carry the strong force, the predicted-but-yet-unobserved gravitons carry the gravitational force (recall that inertia and gravity are derived from the same quantity "mass"). Is there any hypothesized particle that may carry inertia?

Electromagnetism and the Strong Nuclear force are interactions between pairs of particles. The interaction is thought of as being mediated by a field. Each particle is thought of as the source of a field.

Inertia is quite different in nature; it's not interaction between pairs of particles. While you can get away from the source of an electric field, you can't get away from inertia. At present the properties of inertia must be assumed in order to formulate a theory at all. Possibly at some point in the future we'll be able to account for inertia in terms of a deeper theory, but as yet there are no clues as to what such a theory should look like.


About the Higgs field.
What is interesting about the Higgs field is that it is thought of as a field that is uniformly present everywhere. The Higgs field is not attributed to a source, the Higgs field is just there.

It's my understanding that for certain particles interaction with the Higgs field imposes an energy cost. It is the energy associated with that energy cost that gives rise to the mass of those particles. As described by special relativity, Energy has inertial mass. When a quantity of energy is confined to a finite volume of space then that quantity of energy has a corresponding inertial mass. The formula m=E/c^2 expresses the magnitude of the inertial mass in that case.

In other words, the Higgs mechanism does not account for inertia itself; the Higgs mechanisms does not explain why matter and energy are subject to inertia.

 

[DaveC426913]

If you throw, say, a marble towards a chunk of clay the marble will embed itself into the clay. Penetrating the clay takes considerable force. The fact that the fast-moving marble can penetrate the clay cannot be seen as just an inherent property of the marble; it cannot be the case that the marble is pushing itself into the clay.

But if the marble had zero (or negligible) mass, it could not push itself into the clay.


I think inertia is closely related to momentum, which is comprised of its mass and its kinetic energy. You have imbued it with kinetic nergy, but its mass is intrinsic.

 

[Studiot]

I think inertia is closely related to momentum,

Related yes, but different.

IMHO The best non mathematical explanation of inertia is the idea of

"resistance to change"

This can be applied to physical systems other than mechanical which also exhibit such a resistance.

In mechanical systems you need to also consider rotational inertia, which is independant of linear momentum.

 

[Cleonis]

IMHO The best non mathematical explanation of inertia is the idea of
"resistance to change"

I like to think of inertia as opposition to change. Inertia opposes change of velocity, but does not prevent it.

There is an intriguing analogy with with the physics of electric current in a circuit. Electric resistence is analogous to friction. Electric resistence limits current strength. Given a particular electromotive force and a particular resistence there is a corresponding current strength.

Then there is inductance.
Take a current circuit that includes a coil with self-induction. When there is current the coil gives rise to a steady magnetic field. This setup does not resist current. However, when there is change of current strength the magnetic field changes, the change in magnetic field induces an electric field that opposes the change in current strength. In a circuit with high inductance it is hard to get a current flowing, and it is hard to decrease current strength. Starting with zero current: if you apply a voltage the current will steadily climb. The higher the inductance, the slower the increase in current strength.

(Inductance can be quite dangerous. If you have current flowing in a circuit with high inductance then when you break the circuit the current will continue nonetheless, and it will arc between the separated contact points.)

Inductance is a responsive process. The system as a whole responds to any change, with a reaction that opposes the change. Inductance does not prevent change in current strength because it arises in response. For the opposing force to arise there must be change to begin with.

Summerizing the analogy:
- Electric resistence relates to current strength, mechanical friction relates to velocity.
- Inductance relates to change of current strength, inertia relates to change of velocity.

 

[Phrak]

Or we can view matter as field with wave properties. In such a view where we talk waves, a propagating disturbance tends to continue in its propagation. Normally we see this as inertia if the propagation velocity is greater than c (with a group velocity less than c). For particles that propagate at c, and so would always propagate at c, the association with inertia is not made, yet the difference between the two disturbances is somewhat trivial.

In this view, the concept of inertia loses value as a meaningful physical phenomenon. One varies under a Lorentz boost, the other is constant. With this difference in mind, we can ask why one sort of propagation is massive, where the wave velocity must exceed c, but where the natural propagation velocity of Minkowski space is exactly c.

 

[mechprog]

Inertia as resistance to velocity change is a partial story. We must not forget the equivalence principle- Gravitation too has an equally prominent role.
Mass is also defined by gravitation.
Charge is analogous to mass in terms of electrostatic field and gravitational field. And mass has two equivalent forms. But charge still does not have more than one equivalent form. I see a broken symmetry here - quite interesting!

 

[DaveC426913]

Mass is also defined by gravitation.

What? No it isn't.

Weight is defined by gravitation. Mass is defined only by matter.

A 1kg massive object floating in a void between superclusters a billion light years from the next nearest object will have a weight that is incalculably small, but its mass will still be 1kg. If you push on it, it will still react as a 1kg mass. a=F/m.

 

[Phrak]

Inertia as resistance to velocity change is a partial story. We must not forget the equivalence principle- Gravitation too has an equally prominent role.
Mass is also defined by gravitation.
Charge is analogous to mass in terms of electrostatic field and gravitational field. And mass has two equivalent forms. But charge still does not have more than one equivalent form. I see a broken symmetry here - quite interesting!

I'm not sure what you mean by mass defined by gravity. However, we could take

$$G_{\mu\nu} = T_{\mu\nu} \ ,$$

as a definition of mass rather than a relationship between two different entities. The corresponding symmetry in electromagnetism is

$$\rho = \nabla \cdot E \ ,$$

where we could define charge as the divergence of the electric field, rather than giving rise to it.

 

[pgardn]

I think some parts of the following add something to the aforementioned ideas...

http://en.wikipedia.org/wiki/Mach's_principle

 

[mechprog]

I'm not sure what you mean by mass defined by gravity

I am talking about equivalence of gravitational and inertial masses.

we could define charge as the divergence of the electric field, rather than giving rise to it.

such thing can be done with gravity and mass as well
$$\rho_{m}=\frac{1}{4\pi}\nabla\bullet\vec{g}$$
just like
$$\rho_{q}=\frac{1}{4\pi}\nabla\bullet\vec{E}$$
So, whether field defines property (mass/charge) or property defines field, from symmetry point of view it's immaterial. Mathematical transmutations cannot alter the nature!

And one more interesting [broken] symmetry: moving charge creates new effects (or field), but, moving mass seems to be not much different from mass at rest?

 

[K^2]

Only in linearized gravity. But EM could also turn out to be just a linearization. And is that CGS? That 1/4π term looks out of place on E, but I'm used to SI.

 

[Tomsk]

I wonder if inertia can be explained in terms of relativity? I was thinking maybe the Noether current of Lorentz transformations could explain the inertial properties of matter? Apparently Noether's theorem applied to boosts guarantees conservation of the velocity of the centre of mass, but doesn't that imply objects will resist a change in velocity? Surely that is just what inertia is!

Also, we know that Lorentz transformations are made up of rotations and boosts, so I thought it could help explain Mach's principle, which seems to involve both inertia and rotation.

I think it would be great if the inertial properties of matter followed from the structure of spacetime and Noether's theorem.

 

[Taturana]

I understand inertia as a consequence of law of conservation of energy. Any body that has rest-mass resist to the change of motion because to do that we need to transfer energy to that body. If we have energy transfer it implies that we have disequilibrium and in nature everything tends to equilibrate.

Am I wrong?

 

[K^2]

I would say conservation of momentum, personally. Or better yet, conservation of 4-momentum. Then you also get conservation of energy to go along with it.

 

[frish]

We can interpret inertia to say that an object will not accelerate unless acted upon by some force. In other words inertia preserves scalar and angular momentum, thus the "force" of inertia is equal to zero.


1)
Force of inertia is not zero, as explained e.g. here:
http://knol.google.com/k/Newton-s-laws-the-concepts#


2) particle mediatin gravity is called graviton:

http://en.wikipedia.org/wiki/Graviton

 

[pgardn]

Another source:

http://physics.fullerton.edu/~jimw/general/inertia/index.htm

 

[Bob Nesil]

Inertia, i.e., what is in uniform motion remains in uniform motion, is the natural law, because empty space has no absolutely resistance to motion of matter. What is unnatural is retarded motion, because of resistance of several medium that permeate empty space. So, the big problem is...why motion of matter in empty space is so hard to put it on action, and it is harder as its mass increases, if the so called empty space has no resistance at all...

 

[Jonathan Scott]

There's a beautiful paper "On the Origin of Inertia" from 1953 by Dennis Sciama, which can be found online, which provides a specific explanation of inertia by drawing analogies between electromagnetism and gravity, combined with Mach's principle.

In electromagnetism, the electric field isn't just $-\nabla \phi$, but it also contains the term $\partial A / \partial t$ where A is the vector potential. The vector potential due to an individual source is proportional to its velocity times the scalar potential, so the rate of change is proportional to the acceleration times the potential.

This means that if you accelerate nearby sources, this gives rise to an induced field. In corresponding gravitational terms, this means for example that a nearby accelerating mass gives rise to a tiny bit of "linear frame dragging", giving rise to an apparent field in the same direction, which tends to accelerate a test particle very slightly in the same direction.

Sciama points out that this could logically be extended to the whole universe, so if you consider the effect of accelerating the whole universe relative to a test mass, it will produce a significant force on the test mass in the same direction. If you then look at it from the other point of view, this says that if you accelerate a mass relative to the universe, you need to push against the force tending to resist that acceleration, which is what inertia is about. It also means that (in his simplified model) for the force to match $F=ma$ the total potential $\sum Gm/rc^2$ for all sources in the universe must be equal to 1, so G becomes a function of the distribution of masses in the universe.

This is all very neat, and I feel there must be some truth in it, but unfortunately this model doesn't fit very will with the standard relativistic theory of gravity, Einstein's General Relativity. For a start, the electromagnetic analogy is very limited, as gravity is a tensor theory, and at the very least some factors of 2 or 4 are needed to make the equivalence work. I believe that in GR, according to Nordtvedt, it's the sum of $4Gm/rc^2$ which would have to be equal to 1 to make linear frame dragging match inertia. However, as $G$ is a fixed constant in GR, it is not clear how this could be made to work at all.

 

[Bob Nesil]

Thanks Jonathan for reply. I have download the mentioned article and will read it maybe tonight if I can wait it.
Your explanation is reasonable, and I like this way of thinking, even not so mainstream, as youself have said.
Can I go further ? I say on my post that uniform motion is natural. Natural why ? Because Inertia is natural on good sense ? Because Newton said that ? (Im not so sure about the last)
But what is the property of a body that provides it with this property of Inertia. "Vis Inertia" so said Newton , is intrinsic to all matter. Going further, if this property would not be from the matter, but from the medium of space, or whatever you call the space (may be quintessence ??). Then if space not influence matter, you move a mass and it would remains there, no movement after.
But if there is an exterior cause, then the movement of the mass is justified. That is a simple concept of space and matter, for me it would explain the mistery of Inertia, without conecting directly with a electromagnetic resistance kind of.
And I still remain looking for good arguments against and pro...I don't want to be so stuborn that no recongnize a good theory.

 

[mechprog]

The book enlisted in post#8 is basically about the extension of sciama's idea.

 

[Bob Nesil]

What is that inherent property of mass so called inertia? The space, as I may say, the "space-force" itself carry Inertia, the "vis Inertia" from Newton. This invisible, untouchable SpaceForce, yet to be lightened, is the source of the forces os nature. There is no suche particle carrying gravity, no such even so carrying Inertia, there is fictious force that is thinked as "real force". This space-force is the source of Inertia. F=ma never says that F may be vrom Space-force, the quintessence, the so called "aether" by the ancients, what for the heat that they imaged come from an ghost inside the cannons ? And the heay proves to be real only with more detailed experiences. Inertia is real, but not from the mass, but from this universal space-force, that quantum scientist deduct from abstrat maths, and space-force is also corresponsible for gravity, what its names means at least names that was given to classifies them, what is the cause of Inertia, some big and spectacular, beyond any imagination, I may call space-force, you give what name you should, and I go further, Inertia may be detected, not as misteriuous like is today, but with apparatus that take in account the space it self. Country was token from the center of universe by the discovery of the world, world was taken from the center of Universe by Copernicus, Neston gave us the spectacular Theory of Mass, and it is an endless thinking, sorry people, never is permanent, not the sacrosants theories. There is an enormous field of force that surrounds us, and in it there is much more your imagination can dream. And I am going to say more, there is links beyond Inertia and Gravitation that only an concept of Space-force may fill. But and it is a great but, how you equation the unobservable and unknowing ? Copernicus, Newton, Maxwell, Einstein were right, but there is more beyond them. G=m.m/d2, it is geometry, but what kind of interaction may repulse points of same kind on a field ? That what electromagnetic field do. And why the same points called mass can attract one other on the field called gravity ? The concept of Inertia is the same of Gravity, see the Equivalence Principle from Einstein. Sorry for this unaligned text, Iam sure that these gnetlemen at this forum will understand this relief.What I have more in a simple math about these above is not so complete I could exhibit. But Iam trying.

 

[Creator]

accidently deleted.