After Laplace attempted to describe Newton’s concepts of gravity with the formula
the Newtonian mathematicians of the 19th century began to tinker with it. They decided that the above formula was also a mathematical expression for the weight W of the apple. Therefore, they substituted W for F, and changed mi (inertial mass) to mg and called it “gravitational mass.”
The Newtonian mathematicians justified this change, by asserting that in Laplace’s incorrect formula “m has no obvious connection with the inertial resistance of the body to being accelerated…” The weight of the apple mg became the measure of the apple’s gravitational response to the Earth’s gravitational force of attraction, and “the force pulling it down [became] is its weight W.” For example, Cohen claimed that “[W]hen an apple falls from a tree, the force pulling it down is its weight.” The weight of the apple was even referred to as a “weight force.”
At this point, there were now two equations for the force (or weight) acting on the apple: the dynamical or inertial equation m = F/a, and the gravitational equation
where Me is the gravitational mass of the Earth, and rc is the distance from the Earth’s center to its surface. The mathematical justification for these two artificial equations was inter alia that Newton had described matter (or mass) both in terms of its weight and its quantity. The mathematical conclusion was that gravitational mass (mg) must be equal to inertial mass (mi).
In his 1917 popular book, Relativity, Einstein adopted these artificial and meaningless concepts, and introduced the idea of the absolute “equality of gravitational mass and inertial mass” as a foundational premise for his General Theory of Relativity (his new theory of gravity not based on force). These meaningless concepts have distorted and confused physics and cosmology ever since.
Describing the physical sensation of “weight” as a “force” is not merely an innocuous mistake that can be overlooked. It and Einstein’s General Theory have completely distorted the concept of gravity.
In reality, the physical sensation of weight or heaviness is nothing more than the gravitational acceleration of a body’s mass, if and when it becomes restrained by an atmosphere or if and when such acceleration is terminated by a solid surface. The phenomenon of a body’s gravitational acceleration and/or its weight only occurs when the mass of an opposing body mutually pulls on the body in question with the same force and both bodies resist such force with their inertial masses. To call the weight of a body a force is a perversion of Newton’s concepts of gravity, and to mathematically invent two theoretically different masses for the same body is pseudo-science.