What did Galileo prove with his thought experiment of Pisa?

The famous experiment of Galileo Galilei throwing a ball and a feather from the top of the Pisa tower remains still an interesting matter to me. Well, he didn’t exactly throw anything but he thought of it. Scientists these days however, made his thought experiment a reality. But what does this experiment proves to us? It proves that the ball and a feather despite their different masses will fall on the surface of Earth at the same time. Then, Newton would conclude that the feather and the ball fall into the ground because the force of gravity pulls them toward the Earth. So, at this point we have a force of gravity causing a movement and two objects with different masses falling on the ground at the same time. What does this prove again? This proves that Earth pulls all objects with the same force and based on this we concluded that the constant of gravity G must be the same all over the Earth. But what if we were wrong? The first one to question this concept was Einstein in his theory of Relativity. Einstein argued that we are able to see that the ball and the feather are falling toward the Earth and they indeed can touch the ground at the same time when dropped from the same height, but if we would remove the background we would not be able to see if the ball and the feather are falling at all. Therefore, Einstein concluded that if we are not able to see if the ball and the feather are falling or standing still then there is no force applied to them; there is no gravity. According to Einstein, the gravity, the attraction toward objects in space, occurs due to the bending of the fabric of space around these objects, not due to an actual force of gravity. If the space around an object bends than this creates a whole in which small objects will fall as result of momentum created. So, how can we prove that Einstein is right or wrong? We cannot. All what Einstein says is another thought experiment, which started with the fact that he suggested that if we remove the background we will not be able to see that the ball and the feather are falling or not. And yes, Einstein may be right regarding the ball and the feather; these two may not be falling but instead standing still, but that will be true if we look at them from a different point in the universe. However, from our point of view, from us here on Earth, the background exists, we exist, and we can see that the ball and the feather fall at the same time when the air is removed in order to prevent the friction. So, what can this experiment prove then and why is it still interesting to us? I believe that there is one question we should ask at this point: What if we rushed into conclusion when we decided that the Earth pulls all objects with the same force and because of this we concluded that gravitational constant is the same all over the Earth?

So, let’s look at the formulas we know from mechanical physics. We know that the moment we let the feather and the ball fall free from the same height h, the potential energies of ball and feather will turn into kinetic energy: mgh=(mv^2)/2   . At the end, when the ball and the feather reach the ground their initial potential energy is transformed into kinetic energy. Since height h is the same for both objects, the feather and the ball, and we also ASSUMED that gravitational constant g is the same, after some equivalent transformations that mathematics allows us to perform, we can conclude that the speed at which ball hits the ground is V(ball) = (2*g*h)^(1/2) , and the speed with which the feather hits the ground is  V(feather)= (2*g*h)^(1/2) (Note: sorry this blog does not have a insert equation option, but those who know math and physic will recognize the formulas) . Since height is the same and g is ASSUMED to be constant, then we can conclude that not only the time that it takes the feather and the ball to reach the ground is the same but also the speeds at which they reach the ground are the same   However, this conclusion is based on one assumption, that gravitational constant g is constant. I will go ahead and disagree with this ASSUMPTION, since it is just an assumption anyhow. If we do not consider g a constant, but that instead it depends on the material each object is made of (the structure of their atoms and molecules, to be more precise), then we can conclude that time at which the two objects hit the ground while free falling from the same height, it is the same, yet this doesn’t prove that they fall with the same speed. Instead: V(ball) = [2*g(specific for that ball)*h]^(1/2) and V(feather) = [2*g(specific for the feather)*h]^(1/2). Since the speeds are not the same and g’s are not the same, that doesn’t mean the time is not the same either. The time is still the same while g’s and v’s are not: V= v (at start) + g*t, since v(at start)=0 for both objects, then V(ball) = g(ball)*t  and V(feather) = g(feather)*t therefore: t = V(ball)/g(ball) = V(feather)/g(feather)

By assuming that g is not constant but it depends on the material of the object we do not contradict any of the concepts or formulas known from mechanical physics regarding time and height, or kinetic and potential energies. We are only questioning the assumption that objects are attracted by Earth in the same way and with the same force. So, if we question that g is constant everywhere, then we can conclude that force of gravity at which the Earth pulls objects is not the same everywhere and is not the same for all objects. As why I made this assumption that g may not be a constant for all objects, that will take a little bit longer to explain, and I have laid all the details for this argument in my The Truth In Search of Antimatter book; but, I can leave you now with one simple question to think about: If Earth pulls all objects with the same force of gravity and starting speeds for two objects is zero, the height from where they fall is also the same, and if g, the acceleration was also the same then why would a heavier object always cause more damage to the surface it crashes to than a lighter object? Would density of the object be a more important factor than the mass of an object? Let’s think about it.

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