OK, Doc (why do I suddenly crave carrots?), I’ll give this a shot. Bear in mind that I do not claim to really know what I’m talking about–I’m just trying to apply logic to my limited knowledge of the subject. Feel free to poke holes in it as long as you give details–I want to understand what’s wrong with it.
The essential factor in the increased mass bit is the additional energy. If you add energy to something, it effectively gains mass–irrespective of its motion relative to anything. If you heat something up, it gains mass. If you add kinetic energy to something, it gains mass. (Aside: In order to produce a net gain in mass in an accelerated object, the acceleration must be produced without using on-board fuel.) Velocity is unimportant–acceleration is the key.
As for increased mass within the reference frame:
The change in mass can be represented as a coefficient in the gravitational force equation:
F=Gxm[sub]1[/sub]m[sub]2[/sub]/r[sup]2[/sup], where x is the coefficient of mass change.
Which gives us xm[sub]1[/sub]a=Gxm[sub]1[/sub]m[sub]2[/sub]/r[sup]2[/sup] =>
a=Gxm[sub]1[/sub]*m[sub]2[/sub]/(r[sup]2[/sup]xm[sub]1[/sub])
The coefficient x cancels, leaving the same acceleration of m[sub]1[/sub] toward m[sub]2[/sub], despite the fact that both objects have mass increased by a factor of x.
The energy of a system also depends on your reference frame. If I’m in a car going down the freeway at 60 mph, and I use the car as my reference frame, then in my frame, the car has 0 kinetic energy. However, in that same frame, the streetlight I pass has significant energy, so I still don’t want to collide with it.
If objects in the moving train car had higher mass, this could be tested easily. Just put two massive objects close to each other, and measure the force between them using springs, or some other method independent of mass. Since this would then tell you that you’re moving, the mass must not increase, from your frame of reference.
I think the train analogy might have served to confuse things more instead of clarify (par for the course).
Let me try and restate my question:
A) The velocity of an object is dependent on one’s frame of reference.
B) The velocity of an object affects its mass.
Therefore C) The mass of an object also depends on one’s frame of reference.
Is this logic correct? Chronos seems to vote yes, Balance no.
If the logic IS correct, would this imply that two objects moving in the same frame of reference do not appear to each other to be gaining mass as they accelerate?
I’ll take Chronos’s answer on a physics question over mine any day. That gives me one right answer and one wrong one this thread–I can live with that, since the wrong one has been corrected.