Where does inertia come from?

[Natan-Augusto]

TL;DR

Where do the inertial properties of matter come from?

We know that, in classical mechanics, the acceleration of a body is inversely proportional to its inertial mass, given a constant resultant force (as expressed by F = ma). However, while this relationship mathematically describes the observed behavior, it does not, in itself, explain why mass fundamentally determines a body's resistance to changes in its state of motion—that is, it does not explain the underlying physical mechanism.

My question is: What is the fundamental physical origin of inertia for an individual particle?

For instance, an isolated electron possesses mass and inertia, even when not bound to any other particles. In the most fundamental description of nature, what is it that causes its velocity to respond in a finite way to the application of a force, rather than changing instantaneously?

While the Higgs mechanism and the dynamics of quantum fields help explain the origin of mass, do they also explain why this mass dictates the dynamic response to a force? Or does this relationship arise from the fundamental symmetries of spacetime, the relativistic structure of momentum and energy, or perhaps some even deeper principle?

 

[Dale]

I would say it is symmetry. The spatial translation symmetry implies a conserved momentum. Then force is simply the transfer of that conserved quantity.

 

[ohwilleke]

Normally, we recognize this as an observed law of Nature and consider any "mechanism" beyond that to be unknowable.

One alternative explanation is known as Mach's principle, which is the conjecture that inertia arises from the gravitational pull of everything in the Universe on everything else, which explains why gravitational mass and inertial mass are identical. This is fairly speculative, however, and has not been demonstrated to be true in a rigorous manner as opposed to a back of napkin conjecture. But there is a moderately large academic literature considering this conjecture.

 

[Andrew Mason]

We know that, in classical mechanics, the acceleration of a body is inversely proportional to its inertial mass, given a constant resultant force (as expressed by F = ma). However, while this relationship mathematically describes the observed behavior, it does not, in itself, explain why mass fundamentally determines a body's resistance to changes in its state of motion—that is, it does not explain the underlying physical mechanism.

It does not explain inertia of a fundamental particle of matter. But if one assumes that matter is made up of fundamental particles each of which are the same and each having the same inertia, as Newton did, it is easy to see why inertia would be proportional to the quantity of matter (mass) (i.e the quantity of such fundamental units of matter).

If one considers the fundamental unit of matter as being either a neutron or proton+electron, Newton was almost right. (He did not conceive of binding energy as contributing to inertia).

In Newton's $\vec{F}=\frac{d\vec{p}}{dt}$ or $\vec{F}=m\vec{a}$ where $\vec{p}=m\vec{v}$, $m$ (mass) is now understood to be the inertia of the body as a whole, rather than the quantity of fundamental particles it contains (ie. that number multiplied by the inertia of a fundamental particle), although the two are very close.

My question is: What is the fundamental physical origin of inertia for an individual particle?

No one really knows. But one could ask the question the other way around: e.g. How would one define "force" without a concept of "inertia" or "resistance to change motion"?

AM