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Q & A: Inertial mass and acceleration

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Most recent answer: 07/10/2008
Q:
The impossibility of accelerating an object to the speed of light is often explained by invoking the relativistic increase in inertial mass; for any given force, the acceleration produced by that force will decline as the velocity of that object nears the speed of light But what if the force used to accelerate an object is gravity -- the equivalence of inertial and gravitational mass does away with that objection, doesn't it? My guess is that the answer lies in general relativistic "corrections" to the Newtonian gravitational force law, but I've never seen it explained. -- thank you! PS. Let's take my knowledge of physics at a mathematical level to extend approximately through the classic Feynman's lectures ... somewhat further than that at a qualitative level.
- Steven Bratman, MD (age 53)
Denver, Colorado, USA
A:
There is a problem here in that there are actually two definitions of "inertial mass".   The first comes from  the special relativistic formula Mrel = E/c2, where E2 = p2 c2 + mo2c4.  Frankly, I have never liked this but you see it all the time in elementary textbooks.

The other definition is related to the acceleration of a mass due to a force, such as an electric force or the force of gravity.   The main issue is whether two different types of material, such as gold and aluminum weighing the same amount on a scale, have different values of acceleration under a gravitational force.  The answer, epitomized by the Eotvos experiment, (see is that there appears to be no difference between two different kinds of material.  Hence the term "Equivalence of inertial and gravitational mass".

Yes, general relativity does give corrections to a 1/r2 gravitational force law but it doesn't allow for velocities equal to or greater than c for a particle with a finite rest mass.

LeeH

(published on 07/10/2008)

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