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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!

Qmechanic
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RaSullivan
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1 Answers1

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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.

Ken G
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  • 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. – Bill N Jan 09 '17 at 02:01
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    @BillN In my undergrad days we used to compile "Prof Quotes" one of my favourites was "Let me explain why this is obvious..." – M. Enns Jan 09 '17 at 02:03
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    @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? – Ken G Jan 09 '17 at 02:10
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    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). – Bill N Jan 09 '17 at 15:34
  • 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." – Ken G Jan 12 '17 at 17:24
  • So, given that it is a body force, what is tricky to understand about gravity is why it produces the same acceleration on all materials. The point is, it is way easier to explain why it is the same on all masses, than on all materials. This key distinction is often missed when people talk about, say, the equivalence principle. – Ken G Jan 12 '17 at 17:30