Part VIII.   Conclusions (Appendices)
3.   Is Gravitational Mass Really Equal to Inertial Mass?

Galileo was primarily concerned with the phenomenon or sensation of a body’s weight (or heaviness). Galileo dropped many different kinds and weights of bodies toward the Earth, and always found their free-fall to be 9.8 m/s/s. However, he did not know what caused this phenomenon. The correct answer is: free-fall or weight of any body on Earth results because a second body (i.e. the Earth) is gravitationally attracting the first body’s mass and pulling it toward the center of the Earth, and vice-versa.

If the first body is a parachutist who jumps from an airplane high above the Earth, his initial sensation will be a rapidly increasing gravitational acceleration as he free-falls through the air toward the Earth. When he pulls the rip-cord and his parachute opens, his free-fall will be partially restrained by the open parachute which creates a much greater resistance through the air, and he will sense part of his normal weight. When the parachutist lands on the Earth his free-fall or gravitational acceleration will be completely terminated by the solid surface of the Earth and he will then sense all of the normal weight or heaviness of his body’s mass.

When the parachutist steps on a balance scale his “weight” in kilograms is the quantity of the Earth’s intensity of pulling force in all directions which is received by the mass of the parachutist, and this quantity of force continues to pull him toward the center of the Earth. The parachutist’s sensation of “weight” or heaviness is the result of the Earth gravitational force pulling him down. But his weight itself is not a force pulling or pushing the parachutist toward the Earth, as is frequently misasserted even by scientists. The phenomenon of “weight” is not a “force,” it is the result of a force, i.e. the Earth’s gravitational force of attraction acting on the parachutist.

The quantity of the Earth’s equivalent and reciprocal pulling force which acts on the parachutist and pulls him toward the Earth (in other words, his “weight”) has been misnamed by Einstein and others, as the parachutist’s “gravitational mass.” These two false concepts (that weight is a force, or is a gravitational mass), which concepts are generally interpreted to mean the same thing, have caused much mischief in physics during the last few centuries.

On the other hand, Newton in the Principia introduced the concept of a body’s “mass,” which he defined as the body’s “quantity of matter,” its “density and bulk” (volume) conjointly, or together. Mass was later given the algebraic symbol (m).

In his second law of motion, Newton impliedly defined mass (m) as a measure of a body’s inertia; in other words, its inertial resistance to the body’s being accelerated or its state of motion or rest being changed: m = F/a. This quantity is now generally referred to as “inertial mass.” The concept of inertial mass is always rigidly correct in the vacuum of free space where there is no resistance (R) of friction. Therefore, inertial mass is a universal constant quantity in free space, whereas gravitational acceleration, weight and heaviness are totally relative concepts.

To make matters somewhat more confusing, Newton also described the gravitational acceleration of inertial masses in terms of weight and heaviness toward other bodies (inertial masses), and he repeatedly confused the phenomena of gravitational acceleration with heaviness and weight, especially in Proposition 6 of Volume 3. Newton also postulated in Proposition 6 (Vol. 3) that the weight or heaviness of any body is proportional to its mass, whereas it is actually proportional to the gravitational force of the Earth which is acting on the parachutist, and it is inversely proportional to the parachutist’s own inertial mass.

The primary relevant question for this section is: Does the quantity of gravitational mass (gravitational acceleration, weight and/or heaviness) of the parachutist always equal the quantity of the parachutist’s own inertial mass as Einstein asserted? The short answer is a resounding: No. As we have already briefly described with respect to the Earth-Moon gravitational system in Section N, the so-called gravitational mass of any gravitating body (that is, its gravitational acceleration, weight and/or heaviness) is always inversely proportional to its inertial mass (its inertial resistance to being moved). The fact that the so-called gravitational mass of the parachutist (his acceleration) is always proportional to the force of the inertial mass of the opposing gravitating body (the Earth) acting upon the parachutist, does not make gravitational mass of the parachutist (his acceleration) equal to inertial mass of the Earth. Proportionality and equality are entirely different concepts. Equality, identity, and unity are all absolute concepts, whereas proportionality is a relative concept.

In addition, gravitational mass and inertial mass are not equal based upon the following empirical examples. A body’s weight on Earth varies substantially depending upon its altitude; that is, its distance from the gravitational center of the Earth. But at any altitude on Earth the inertial mass of such body remains the same. A body in an orbiting space shuttle becomes weightless and floats endlessly about the cabin, but it still takes the same quantity of force to push its inertial mass in a different direction at any distance from the Earth. A body on the Moon only weighs about 1/6th of its weight on the Earth because the surface gravity on the Moon is much less strong (see Section P and Figure 17.1), but it still takes the same force to push or pull it from one place to another on the Moon as it does on Earth. There are endless other examples of the inequality of any form of so-called gravitational mass of a body as compared to its constant inertial mass.

There is no logical reason why the response of one body (i.e. the Moon) to another body’s gravitational force (i.e. the Earth) should be equal to the inertial mass of the first body (the Moon), but there are many empirical reasons why it is not. All of the experiments that were designed or interpreted to confirm that gravitational mass and inertial mass are equal, were either based on false assumptions or were interpreted incorrectly.

The false concept of the equality of gravitational mass and inertial mass was introduced into physics by Albert Einstein around 1916, because he needed the weight, heaviness, gravitational acceleration, and inertia of any mass to be equal or even identical in order to justify his ad hoc General Theory of Relativity; his new abstract mathematical theory of gravity without force. But if all bodies do not gravitationally accelerate equally, if their weight does not also remain the same, and if gravitational mass of a body is not always equal to inertial mass of such body, then were does this leave General Relativity?