What causes the inertia of an object in classical physics?

[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.

 

[Creator]

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, .

I also think Sciama makes an excellent, subtle and eloquent (Machian) case of the origin of inertia.

Here is a good simple discussion of his ideas for anyone familiar with the gravitoelectric equation in terms of the grav. vector and scalar potentials...
...in which he shows inertia to be a gravitoelectric field which must result from a changing gravitational vector potential. (see eqn.2 ..which is the EM analog to the gravitational case...which becomes equivilent to eqn. 6)...

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

Its nice to see others who enjoy these "not so commonly known" formulations.

BTW, I have no problem with the linear approximations as long as there are no locally strong field / high velocity sources that can skew the results with post Newtonian terms.

Creator

P.S. I should note that Sciama's formulation provides a natural underlying 'reason' for the local equivalence of inertial and gravitational mass, something Gen. Relativity doesn't address.

 

[cesiumfrog]

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

I don't think this is right. I thought the Higgs was supposed to explain most (not all) of the mass-energy of ordinary matter, but not to explain anything about inertia (e.g., why the resistance to forced acceration should be proportional to mass-energy in the first place).

 

[mohitkapil]

A body keeps on moving in uniform motion in extremely low temperatures of deep space. Doesn't the temperature affect its motion. If the body reaches areas where the temp. is near absolute zero, would it still cotinue as before. If molecules get slowed down why not the body?

 

[DaveC426913]

A body keeps on moving in uniform motion in extremely low temperatures of deep space. Doesn't the temperature affect its motion. If the body reaches areas where the temp. is near absolute zero, would it still cotinue as before. If molecules get slowed down why not the body?

Why would it? Can you think of any mechanism whereby an inertially moving body would slow down (an act that requires energy) if there's less energy around?

 

[mohitkapil]

Why would it? Can you think of any mechanism whereby an inertially moving body would slow down (an act that requires energy) if there's less energy around?

If low temperature can lower the speed (vibration) of the molecules it is composed of, it means that its internal energy is also lowered. This should have an effect on its motion as the body is nothing but an aggregate of all those molecules. The motion that a body possesses has its effect on the molecules it is made of ( especially if the body is traveling at a very high speed). The reverse can also be true.

 

[harrylin]

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."

Self induction may indeed be a clue, related to field theory of matter. Regretfully no full-blown theory has come of it (I think), but as you mentioned, at least for the electron the hypothesis that inertia is caused by self induction works reasonably well.

Thus, one way of interpreting inertia is as a measure of the resistance to change of motion of bound field energy. It is therefore also strongly related to mass, which is a measure of (field) energy content.

 

[epenguin]

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

So this shows it is not a philosophical question.

Except within the framework of a false philosophy.

You might need some better philosophy to get you out of that, better philosophy would do no harm and I have nothing against that but Science does have a habit of doing it anyway without philosophising when the time is ripe.

 

[DaveC426913]

If low temperature can lower the speed (vibration) of the molecules it is composed of, it means that its internal energy is also lowered. This should have an effect on its motion as the body is nothing but an aggregate of all those molecules. The motion that a body possesses has its effect on the molecules it is made of ( especially if the body is traveling at a very high speed). The reverse can also be true.

You've composed a word salad. Lots of words tossed together, but the logic's missing.

You seem to be thinking the object is expending energy to keep moving such that removing some energy would cause it to move less. Not so.

Newton's first law: A body in motion will stay in motion unless acted upon by an external force. So what external force are you proposing?An analogy: If I were floating through space playing music really loud, and then I stopped playing the music really loud, would I slow down? Why?

 

[mohitkapil]

You've composed a word salad. Lots of words tossed together, but the logic's missing.

You seem to be thinking the object is expending energy to keep moving such that removing some energy would cause it to move less. Not so.

Newton's first law: A body in motion will stay in motion unless acted upon by an external force. So what external force are you proposing?


An analogy: If I were floating through space playing music really loud, and then I stopped playing the music really loud, would I slow down? Why?

You should explain what’s wrong in my post rather than calling it a ‘salad’. You have tried to divert the talk with another example. This is tactics but not science.

 

[DaveC426913]

You should explain what’s wrong in my post rather than calling it a ‘salad’.

What's wrong with it is that one sentence does not follow from its previous sentence.

...its internal energy is also lowered. This should have an effect on its motion...

B does not follow from A.I refer you again to http://csep10.phys.utk.edu/astr161/lect/history/Newton3laws.html". Note the especially the phrase "...an external force is applied".

The motion that a body possesses has its effect on the molecules it is made of ( especially if the body is traveling at a very high speed). The reverse can also be true.

This is something you've simply made up that sounds plausible to you. But it sounds like word salad to anyone else. You should not just make up your own ideas.

You have tried to divert the talk with another example. This is tactics but not science.

Tactics? This is not a debate. This is you learning. You need a better grasp on the laws of motion. I'm trying to help you understand a concept you are failing to grasp. Multiple examples are a tried and true teaching method.

 

[AlephZero]

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

They are not at all indepdent. A (theoretical) point particle has no rotational inertia. If you consider a finite sized body as being composed of point particles, then the rotational inertia and angular momentum of the whole body can be found (by integrating over the volume of the body) from the linear momentum and inertia (mass) of each particle.

Angular momentum and rotational inertia are nice mathematical tools to work with, but they don't introduce any new physics into classical mechanics. They can be explained entirely by Newton's laws of motion, even though Newton's laws are appear to be stated only in terms of linear motion.

 

[Andrew Mason]

They are not at all indepdent. A (theoretical) point particle has no rotational inertia. ...
Angular momentum and rotational inertia are nice mathematical tools to work with, but they don't introduce any new physics into classical mechanics. They can be explained entirely by Newton's laws of motion, even though Newton's laws are appear to be stated only in terms of linear motion.

According to classical mechanics, the electron, which is considered to be a point particle, should have no angular momentum. But it has angular momentum, as do quarks. So I don't think you can explain an electron or a quark by Newton's laws of motion.

AM

 

[harrylin]

According to classical mechanics, the electron, which is considered to be a point particle, should have no angular momentum. But it has angular momentum, as do quarks. So I don't think you can explain an electron or a quark by Newton's laws of motion.

AM

I don't follow your logic, especially not in the context of this sub forum of classical mechanics. According to classical mechanics everything that has mass, angular momentum etc. - any material object - must have size. The Earth is approximated as a point particle in astronomical calculations, but that doesn't mean that the Earth is considered to be really a point particle!

 

[DaveC426913]

I don't follow your logic, especially not in the context of this sub forum of classical mechanics. According to classical mechanics everything that has mass, angular momentum etc. - any material object - must have size. The Earth is approximated as a point particle in astronomical calculations, but that doesn't mean that the Earth is considered to be really a point particle!

Nonetheless, the subatomic particles are considered to be point masses.

 

[harrylin]

Nonetheless, the subatomic particles are considered to be point masses.

A true point (infinitely small) implies infinite density, which is not possible in classical physics.

 

[Andrew Mason]

A true point (infinitely small) implies infinite density, which is not possible in classical physics.

What principle or law of classical physics sets an upper limit on the density that a body can have?

AM

 

[Studiot]

I have just appended an (interesting?) additional question about inertia and its causes in this thread:

https://www.physicsforums.com/showthread.php?p=3530129#post3530129

 

[harrylin]

What principle or law of classical physics sets an upper limit on the density that a body can have?
AM

Good one!

Also the electrostatic field energy would be infinite, so that already the creation of an electron would require infinite energy - that does not make any sense. Theorists generally dislike that kind of singularities, but I must admit, that it's a non-binding principle, similar to Occam's razor.

Anyway, I'm pretty sure that electrons were modeled in classical physics as particles with a nominal radius that follows from its charge and its mass, which is assumed to be fully electromagnetic - already before the advent of special relativity.

There even is the label "classical electron radius" which accounts for SR.
- http://en.wikipedia.org/wiki/Classical_electron_radius

What is pertinent for this discussion, is that in classical physics it is rather standard to assume that the inertia of the electron is fully caused by its electromagnetic field.