# Inertial and gravitational mass

StephenPrivitera
What's the difference between inertial mass and gravitational mass?

Originally posted by StephenPrivitera
What's the difference between inertial mass and gravitational mass?

See www.geocities.com/physics_world/mass_concept.htm

n Einstein's words
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By the word “mass” of a body one denotes two things that are very different according to their definitions: on the one hand, the inertial resistance of the body and, on the other hand, the characteristic constant that is the determining factor for the effect of the gravitational field on the body.
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Pete

Originally posted by StephenPrivitera
What's the difference between inertial mass and gravitational mass?
Einstein discovered that there is none. This is called the equivalence of gravitational and inertial mass.

plus
I thought that this was just a hypothesis of einstein.

Anyway, gravitational mass is the number that you plusg into gravity equations. Inertial mass is the number you plug into F = ma

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At the time Einstein was writing, a great experimentalist named Eotvos had demonstrated the numerical equality of inertial and gravitational mass for many materials. Since that time this has continued to interest experimentalists and many measurements have confirmed the equality to high orders of accuracy.

That doesn't prove it is so, of course, but it sets a high bar for those who might try to falsify it.

StephenPrivitera

Originally posted by DavidW
Einstein discovered that there is none. This is called the equivalence of gravitational and inertial mass.
Well, I knew that they are numerically the same. I was wondering actually what they are supposed to measure. The only way for it to be possible that they are numerically different is if they measure different quantities. Why else would a scientist have to conduct an experiment to show they are the same?
In the book I'm reading now, Matter and Motion by Clerk Maxwell, he writes (in Article 50), "the force required to produce a given change of velocity in a given time is proportional to the number of units of mass* of which the body consists"
The footnote reads: "Here mass means the measure of inertia rather than the quantity of matter; at extremely great speeds they would not be proportional, but connected by a law involving the speed, so that the momentum or impulse would then be the primary quantity and inertia a derived one."
That's not where my question came from, but it seems to contain the answer. I would speculate that inertial mass is a measure of inertia, and gravitational mass is a measure of the quantity of matter. Then, from what is written in the footnote, I concluded that at high speeds these two quantities deviate from each other (ie, they would not be proportional). Is that correct?

Originally posted by DavidW
Einstein discovered that there is none. This is called the equivalence of gravitational and inertial mass.

Not quite - That fact was around long before Einstein. GR does not explain the equivalence - it postulates it

Indeed, while so far nobody really disputes the difference (because if there is one, its incredibly small), there still is no real reason why inertial mass should be so close/equal to gravitational mass.

Simply put, Intertial mass is the mass an object has with regards to resisting a force imparted on it (try and push a ball on a horizontal plane). Gravitational mass is the mass an object has with regards to attracting objects with a gravitational force.

Tyger

Originally posted by DavidW
Einstein discovered that there is none. This is called the equivalence of gravitational and inertial mass.

Einstein postulated that there was no difference in principle, and that is what lead him to a theory of gravity based on space-time curvature. And as I brought up in another thread, we can derive the property of inertia from simple considerations of quantum mechanics and special relativity, so that if C2 is constant the gravitation can be associated with the energy as easily as with the inertia.

Any comment on the following?

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Originally posted by Tyger
Einstein postulated that there was no difference in principle, and that is what lead him to a theory of gravity based on space-time curvature. And as I brought up in another thread, we can derive the property of inertia from simple considerations of quantum mechanics and special relativity, so that if C2 is constant the gravitation can be associated with the energy as easily as with the inertia.

What led Einstein to a theory of gravity was not curved spacetime - that was simply something that happened along the way. What guided Einstein was the Equivalence Principle which was based on the equality of gravitational and inertial mass. And this implied that the gravitational force is an inertial force. I.e. According to Einstein

That the relation of gravity to inertia was the motivation for general relativity is expressed in an article Einstein wrote which appeared in the February 17, 1921 issue of Nature [28]

Can gravitation and inertia be identical? This question leads directly to the General Theory of Relativity. Is it not possible for me to regard the Earth as free from rotation, if I conceive of the centrifugal force, which acts on all bodies at rest relatively to the earth, as being a "real" gravitational field of gravitation, or part of such a field? If this idea can be carried out, then we shall have proved in very truth the identity of gravitation and inertia. For the same property which is regarded as inertia from the point of view of a system not taking part of the rotation can be interpreted as gravitation when considered with respect to a system that shares this rotation. According to Newton, this interpretation is impossible, because in Newton's theory there is no "real" field of the "Coriolis-field" type. But perhaps Newton's law of field could be replaced by another that fits in with the field which holds with respect to a "rotating" system of co-ordiantes? My conviction of the identity of inertial and gravitational mass aroused within me the feeling of absolute confidence in the correctness of this interpretation

If you want the original article I got that from then read this

http://www.geocities.com/physics_world/einstein-nature-1.gif
http://www.geocities.com/physics_world/einstein-nature-2.gif
http://www.geocities.com/physics_world/einstein-nature-3.gif

Pete

ObsessiveMathsFreak
I was under the impression that mass was mass was mass.

Isn't mass related to inertia by F = ma.
Since gravity is a force then why should it cause confusion?

Creator

Originally posted by StephenPrivitera
... I would speculate that inertial mass is a measure of inertia, and gravitational mass is a measure of the quantity of matter. Then, from what is written in the footnote, I concluded that at high speeds these two quantities deviate from each other (ie, they would not be proportional). Is that correct?

You sure know how to start an argument, Stephen.
This question has been debated heatedly before in other circles; yet it is a very valid concern.