Originally Posted by MBW
Hi Anonymous, long time no posts.
Mass is not only a measure of how an object behaves under acceleration,
it is also a measure of how strongly that object distorts space-time to create a gravitational effect.
The distortion caused by an individual proton or electron is truly minuscule, and is generally barely even considered,
but put several billion, trillion, (etc.) together (as in a planet for example) and it becomes significant.
see wikipedia:Equivalence Principle
The aspect of an object that resists changes in momentum is called inertial mass
. The aspect of an object that acts to generate a gravitational field is called active gravitational mass
. The aspect of a body to respond to a gravitational field (i.e. a body accelerates when placed in a gravitational field) is called passive gravitational field
. Mach's definition utilizes Newton's third law.
Note: Just because there is active gravitational mass in a region of space and it generates a gravitational field which causes bodies in it to accelerate it doesn't mean that the spacetime is curved. The gravitational field may very well be a uniform gravitational field which is defined as a gravitational field which has no tidal gradients in it. And tidal gradients is just the Newtonian way of saying spacetime curvature
. Thinking that Einstein said that gravity is a curvature in spacetime is a common misconception.
Einstein actual defined the gravitational field according to how objects accelerate when placed in a region of space.
Regarding what mass is please see the paper I wrote on it at: http://arxiv.org/abs/0709.0687
Regarding the way that Einstein defined the gravitational field please see the paper I wrote on it at: http://arxiv.org/abs/physics/0204044
Newton defined mass in a circular way. He said that the mass of a body equals the density of it times the volume of the body. He then defined momentum as the mass times velocity and then defined force as the time rate of change of momentum.
Mach's definition of mass is the one most people are familiar with. The one most used in relativity
for inertial mass is the one used by Weyl and utilizes Newton's conservation of momentum.
The former definition utilizes Weyl’s definition of mass (m ” p/v) while the later utilizes Mach’s definition (m ” F/a). 8 It is Weyl’s definition that is used in relativity on both sides of this debate and each is referred to as inertial mass.