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The Origin of Inertia

The origin of inertia is still somewhat of a mystery. But what is inertia? It is the principle that an object will resist any effort to change its state of rest or motion. This definition does however not reveal its origin.

Albert Einstein also puzzled about the origin of inertia and coined the term 'Mach's principle',[1] loosely described as: "inertia originates in a kind of interaction between bodies".[2] Mach's principle says that the inertia stems from an interaction between a body and the mass of the Universe as a whole. How a body 'knows' its state of motion relative to the Universe at large was not made very clear by Einstein.

The closest Einstein came to revealing the origin of inertia was by means of spacetime geodesics. In his general theory of relativity of 1916, he showed that the mass of the Universe shapes and curves space and time. All bodies, even stationary ones, are always in motion through spacetime, following paths of 'least action'. These paths are called spacetime geodesics.

Spacetime geodesic
The curved vector with length ct in the above figure represents a two-dimensional projection of the spacetime geodesic of particle P through the curved spacetime surrounding the Sun. This is the basis for Einstein's 'origin of inertia'. Bodies resist being pushed out of their spacetime geodesics and hence they show inertia.

Einstein's special relativity of 1905 actually hints at a totally different origin of inertia, although Einstein never considered it as such.[3] When we push an object, it seeks to maintain not only the existing spatial relations between its parts, but also the temporal phase relations between those parts. When an object is accelerated, either the spatial or the temporal (or both) relations must change due to relativistic effects.[4]

The figure below comes from an illuminating presentation by John Mallinckrodt.[5] It shows a rigid flashing rod that is being accelerated lengthwise to a relativistic speed. For an observer in the reference frame, the front of the rod not only accelerates slower than the rear, but the front of the rod flashes faster than the rear, indicating that its clock gains time on the rear clock. This means a change in temporal relations between the front and the rear of the rod.

Relativistic acceleration of rigid rod

This 'new view' of the origin of inertia says that all objects with size will resist any change to these relations (spatial, temporal, or both). In order for the object to be accelerated, it is necessary to overcome the object's intrinsic resistance to changes in these relations. This might be the cause of the resistance that inertial bodies have against being accelerated.

So, maybe Einstein was wrong on the origin of inertia. Maybe it has nothing to do with Mach's principle or the matter in the Universe at large, but just with what's going on within every object's spatial and temporal relations.


[1] Wikipedia: "Mach's Principle".

[2] Einstein's letter to Ernst Mach, 25 June 1923, as stated in Misner, Thorne and Wheeler's textbook: "Gravitation".

[3] Mathpages: "Born Rigidity, Acceleration, and Inertia".

[4] H. Nicolic: "Relativistic contraction of an accelerated rod".

[5] John Mallinckrodt: "Simple, Interesting, and Unappreciated Facts about Relativistic Acceleration".

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