It looks like you're new here. If you want to get involved, click one of these buttons!
we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.—Einstein, 1907
Can you please and in simple words explain why in your opinion the feather and the hammer will hit the ground almost simultaneously (ignore the 10 to the power minus 21 seconds difference) ?
gravity pulls the hammer with a greater force than the feather since it have more mass
, on the other hand because it havemore mass, it takes more force to move it than the lightweight feather
, so eventually there will be a state of equivalence which will accelerate them equally (in vacuum of course).
Objection 1. You are just playing dirty games: what you have designated as the mass of Earth, M, has different numerical values in the two scenarios with the hammer and the feather.
Objection 2. But we know that the laws and principles of Newtonian mechanics, which you have accepted as valid from the start, are not quite correct and they, in fact, hold only approximately. Therefore, your demonstration is not thorough because it ignores Einstein's corrections of Newton in regards to the second law, F=m*a, as well as to the law of universal gravitation, F=G*m*M/R^2.
Objection 3. The inequality a1≠a2 you are talking about is so indistinguishably near to the equality a1=a2 that discussing it is sheer waste of time.
You combine 2 accelerations in an odd way, but nevertheless the first part necessarily confirms the acceleration as the same. The second part shows that for the hammer and the feather the earth is negligible attracted.
Objection 4. In your demonstration, you have used two identical hammers, and two identical feathers, both pairs symmetrically located with respect to the Earth, instead of using one hammer and one feather in free-fall as you should. Isn't that dishonest?
Objection 6. In all your demonstrations, so far, of the alleged logical inconsistency of Galileo's hypothesis of free-fall acceleration invariance, you have always used three bodies (two hammers and earth; two feathers and earth; a hammer, a feather, and earth) insisting that holistic approach requires that we take into account all three pairs of gravitational interactions. But your insistence on the holistic approach is hogwash because taking into account three bodies is not much more holistic than taking into account just two of them. True holistic approach would require taking into account every possible type of interaction (mechanical, electrical, magnetic, gravitational, and multitude of others we don’t even know about) between all the bodies in the entire universe! Such an approach is obviously untenable; therefore, it is of no use to us. Hence, we have no other choice but to be content with what you have fastidiously called kaleidoscopic, patchwork-quilt-like view of nature. With the gravitational interaction of two bodies alone, you will find no logical contradiction between Galileo's hypothesis and Newton's laws of physics.