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

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

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pmb

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

Pete

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DavidW

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

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

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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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selfAdjoint

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

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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?Originally posted by DavidW

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

In the book I'm reading now,

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,

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pmb

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

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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.

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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 C

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ztfthtay

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pmb

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 C^{2}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

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Isn't mass related to inertia by F = ma.

Since gravity is a force then why should it cause confusion?

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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.

Obviously, it hasn't been answered or even addressed here yet.

Your assumption of gravitational and inertial mass deviation at high speeds is predicated on graviatational mass being, as you stated, a function of the'quantity of matter'. However, that is rather nebulous. What exactly is 'a quantity of matter'? Don't we measure the quantity of matter ultimately by inertial reaction? thus making gravitational mass identical to inertial mass? From that standpoint then, like PMB has pointed out with Einstein, they can be considered identical. But can't we measure it gravitationally also?

However, now (and in answer to your question) we have a conceptual problem (hotly debated often) involving gravitational bodies moving at relativistic speeds. Does the increase in inertial mass (due to velocity) mean an increase in gravitation? Moving mass has greater gravity? If so does one observer at rest relative to a body see a gravitational acceleration that is different than an observer traveling quickly with respect to it?

If so would not a moving observer measure planets as having a different orbital period than measured by a person at rest? How can that be? Now you've turned this into a full blown relativistic question. Shame on you.

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