What explanation is given under A. Newtonian gravity and B. General relativity for the fact that in the absence of atmospheric influences, bodies of different mass fall at equal rates. It's so counterintuative and I can't seem to locate an answer!
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1$\begingroup$ Have you looked here: physics.stackexchange.com/q/82675 $\endgroup$– user140606Commented Jan 9, 2017 at 1:40
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2$\begingroup$ Possible duplicate of Why do two bodies of different masses fall at the same rate (in the absence of air resistance)?. This was item #2 in a google search of your exact title. Your own question was #1. -1 for lack of effort. $\endgroup$– sammy gerbilCommented Jan 9, 2017 at 2:14
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1 Answer
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Actually, it's very normal for similar materials of different amounts of mass to fall at the same rate (ignoring air resistance, of course). To see that, simply imagine dropping two dimes, once where the dimes are fused together, and once where they aren't. Would you expect them to fall differently in those two situations? Certainly not, so it's obvious that mass should not affect the rate of fall.
What is actually surprising is that the material doesn't affect the rate of fall-- nickel falls just like wood or plastic. That is not the normal state of affairs for other forces, they always depend on the material. Newton's explanation is that it is mass that creates and responds to gravity-- any kind of mass, regardless of material.
Einstein's explanation is that gravity is not a force, it is a geometric effect on spacetime, but even so, the degree to which gravity affects spacetime only depends on mass, and of course the path an object takes through spacetime will not depend on the mass or material that an object is made of.
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$\begingroup$ Apparently, it's not obvious to OP. That's why the question was asked. Saying things are obvious without some physics reasoning (two dimes fused is a different mass) is not an answer. $\endgroup$– Bill NCommented Jan 9, 2017 at 2:01
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1$\begingroup$ @BillN In my undergrad days we used to compile "Prof Quotes" one of my favourites was "Let me explain why this is obvious..." $\endgroup$– M. EnnsCommented Jan 9, 2017 at 2:03
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1$\begingroup$ @Bill N-- my point was that the best possible answers always reduce a question to something obvious. Why objects of the same material, but different mass, must fall at the same rate can indeed be reduced to something obvious. All you have to do is drop any object, lift it back up, saw it in half, and drop it again. If it isn't obvious yet, imagine attaching the halves with a string, or a rubber band, or successively stiffer connectors. When do they fall at the same rate, if not always? $\endgroup$– Ken GCommented Jan 9, 2017 at 2:10
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1$\begingroup$ KenG I understand that. OP was asking about the reasoning of Newtonian theory and GR theory which explain the experimental evidence. An answer to the question asked should involve gravitational fields (Newtonian) or geodesics (GR). $\endgroup$– Bill NCommented Jan 9, 2017 at 15:34
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$\begingroup$ Or, an answer could involve clear reasons why either gravitational fields, or geodesics, or quantum gravity, must all give that objects made of the same material but different mass will have to fall at the same rate, or it won't make any sense from a simple experimental perspective. The best way to say it is, "bccause gravity is one of the body forces." $\endgroup$– Ken GCommented Jan 12, 2017 at 17:24