This post was written after fruitful discussion I had at the Hebrew University of Jerusalem with Professor Igal Galili, on the Modern Physics concepts of Weight, Inertia and Gravity.
The more we become conscious of Einstein’s Theories of Relativity (TRs) the more we get amazed with the harmony and the interconnection of the elements in Nature. In the Special Theory of 1905, Einstein showed that an observer “A” at rest perceives the dimensions of space and time of an inertial* material body “B” (* with constant velocity “v” relative to “A”), with a shrinking of space in the direction of “v” and an expansion of time. This happens as a consequence of the invariance of the speed of light “c” for all observers and the attempts in vain to “B” to achieve or even notice any change in “c” due to their relative motion. This is easily demonstrable and any high school student can understand and also deduce the contraction (or expansion) Lorentz’s Factor gamma, γ = {1 / [1 – (v/c)2]1/2}. I take this as known and if you are not familiar to this, you can read any TR introductory text to realize how easy this is. Between 1907 and 1915, Einstein spent eight years building something more complex: the General TR, valid for accelerated referentials. In my post “Understanding What Gravity Is” you can read about the relation between gravity/acceleration and both space contraction and time expansion, using a thought experiment proposed originally by Einstein (a material spinning disc) to explain the space-time effects caused by gravitaty. Such a space-time distortion can be understood as a bi-univocal cause/consequence of acceleration. Under this point of view the acceleration of gravity, in the Earth for instance, must be seen as a space-time radial gradient, with dimentions of m/s2 in its long range neighborhood, proportional to 1/r2, not a force as Newton proposed in the 17th Century.
The connection between gravity and the inertial mass comes as follows: Let´s see the inertia of a resting body as a tendency of a material object to resist being moved (accelerated) out from its rest position in space-time. You can see the planet’s space contraction, perpendicular to g, and the time expansion in the Earth’s vicinity as a kind of “grabbing action” of the planet (actually of any material body) into the Universe’s space-time framework -it creates a dimple or a kind of nest in space-time- in order to keep itself inertially at rest. Like a belt that you fasten to hold yourself in the car’s or in the airplane’s seat. When observed from its own referential, the Earth or any material object shrinks the space and expands the time in its neighborhood as a mechanism of inertia trying to stand still. Note that according to the GTR the reduction of the Earth’s circumference “C” assuming the approximation of a constant density through its ~6,378 Km radius is ΔC=2πGM/3c2 #, that corresponds to only ~ 9.4 mm shrinking, if compared to the circumference of the same planet without inertia (gravity) – this together with the time expansion at the sea level (relative time delay Δt/t = GM/Rc2 # of about 0.69 ns per second if compared with a clock set in a zero gravity referential – at the center of the Earth for example) producing a space-time deformation gradient with metrical units of m/s2 that is enough to generate our gravitational field g = 9.8m/s2. The more massive is the object, the stronger it sets itselg into space-time; this makes absolutely natural the conceptual fusion of “inertial mass ≡ gravitational mass”, with any possibility of questioning. In other words, the larger is the inertial fixation of a body into space-time, the larger is the space-time deformation that means the gravitational field or gravity well. Under this point of view, the energy associated to the “inertia of movement”, corresponding to the tendency of a material body “B” to keep a constant velocity “v” relative to an observer “A”, can be seen as both: kinetic energy of “B” relative to “A” as well as a source of gravitational waves with Doppler Effect forwards (shorter gravitational wavelengths) and backwards (larger gravitational wavelengths) when measured by “A”. As both gravity and inertia are interconnected (actually they are different manifestations of the same thing), this article’s title could be changed to “How Gravity Creates Inertia” or “Inertia is Gravity” without any change in its full meaning.
# G=Gravitational constant = 6.67 x 10-11m3Kg-1s-2 ; R= Earth’s radius = 6.37 x 10 6 m; M = Earth’s mass,=5.97x 1024 Kg; c= speed of light in vacuum = 3 x 108m/s
I would like to thank Professor Galili for suggesting me to write this essay on Modern Physics Concepts and would appreciate the comments of my readers.
Prof . Aba Cohen Persiano
Departamento de Física-UFMG, Brazil








