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In the book "Evolution of Physics" - Albert Einstein and Leopold Infeld, the following explanation is given for two types of masses:

A body at rest gives way before the action of an external force, moving and attaining a certain velocity. It yields more or less easily, according to its inertial mass, resisting the motion more strongly if the mass is large than if it is small. We may say, without pretending to be rigorous: the readiness with which a body responds to the call of an external force depends on its inertial mass. If it were true that the earth attracts all bodies with the same force, that of greatest inertial mass would move more slowly in falling than any other. But this is not the case: all bodies fall in the same way. This means that the force by which the earth attracts different masses must be different. Now the earth attracts a stone with the force of gravity and knows nothing about its inertial mass. The "calling" force of the earth depends on the gravitational mass. The "answering" motion of the stone depends on the inertial mass. Since the "answering" motion is always the same all bodies dropped from the same height fall in the same way it must be deduced that gravitational mass and inertial mass are equal.

There are two things I'm unsure if I'm understanding correctly:

Now the earth attracts a stone with the force of gravity and knows nothing about its inertial mass

I understand this statement to mean that gravity does not affect inertial mass, only gravitational mass. Is this correct?

The "calling" force of the earth depends on the gravitational mass

I assume that the mention of gravitational mass here refers to the stone and not to earth/planet. Is this correct?

And finally the last statement makes absolutely no sense at all to me:

Since the " answering " motion is always the same all bodies dropped from the same height fall in the same way it must be deduced that gravitational mass and inertial mass are equal

How can they be equal? by definition they are different things. Is the value of the gravitational mass and inertial mass of the stone the same? If so, how? Because inertial mass is unaffected by gravity, so why would there even be a connection. What am I missing?

The whole book is available online here for free, (in case the context is needed): https://archive.org/stream/evolutionofphysi033254mbp/evolutionofphysi033254mbp_djvu.txt

Finally, please understand that I'm not asking about what is the "correct" or "current" model that we have of masses or for that matter, of physics. I am simply trying to understand what is being said in the book. Any pointers at all, will be very helpful.

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Imagine a stone in your hand. Shake it. Its resistance to motion is inertial mass. He calls it answering mas because it is how much the stone answers to your force. Now drop your stone. It is pulled by gravity. The force of pull is due to gravitational mass, what he calls calling mass. He calls it calling mass because that is how much the gravity of a body calls the object to it. Now, the answering motion (falling) is proportional to the answering mass (inertial mass). The calling force (desire to fall) is proportional to calling mass (gravitational mass). The pull of gravity seems to ignore inertial mass. What Einstein is non-rigorously stating is that perhaps inertial mass isn't being ignored, but instead is both calling and answering mass. A single mass. If they were the same, it would account for this affect.

  1. This is the classic view which he is about to challenge by saying that inertial mass = gravitational mass

  2. It refers to that of the stone

  3. They are called the same because Einstein points out. Why is one mass simply ignored. Maybe it isn't. Perhaps there is only one mass. This mass is responsible for answering and calling. .

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  • $\begingroup$ Can you specify to which objects you refer to when you mention any form of mass. I am unclear as to when you say inertial mass, do you mean inertial mass of stone or of earth, same for calling, answering, gravitation mass etc. As it stands, I'm still not clear. $\endgroup$ – ˆᵛˆ Apr 20 '15 at 4:36
  • $\begingroup$ @λ- every time that I mention mass, I mean that of the stone. $\endgroup$ – Jimmy360 Apr 20 '15 at 4:41
  • $\begingroup$ Ok. Is that also what Einstein means? Can you look at the three specific questions I ask, and answer those as well. Thanks so much. $\endgroup$ – ˆᵛˆ Apr 20 '15 at 4:51
  • $\begingroup$ @λ- I edited it $\endgroup$ – Jimmy360 Apr 20 '15 at 5:21

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