My understanding is that the "relativistic mass" of an object means any of the following three quantities (which are all identical):
- The "mass-energy", as defined by the formula $m = E / c^2$.
- The inertial mass: the ratio between the force applied on an object, and the amount of acceleration it undergoes as a result.
- The gravitational mass: the amount of tendency for an object to gravitate towards other objects.
(But the rest mass of an object is something different, and my understanding is that when physicists say "mass" nowadays, they almost always mean the rest mass.)
Now, as an object's speed increases, the object gains kinetic energy. So, it seems like it must gain inertial mass and gravitational mass, too. As the object's speed increases, the object requires more force in order to produce the same acceleration, and it also exerts a greater gravitational force on other objects. Right?
But speed is relative. For every possible speed, there is a frame of reference (an inertial frame of reference, in fact) in which I am traveling at that speed.
Now, I weigh about 100 kg. All of the above seems to mean that there is also a frame of reference in which I weigh 300 kg, and a frame of reference in which I weigh 10,000 kg, and so forth.
So that seems to imply that there must be a frame of reference in which gravity is pinning me down hard and I struggle to move, as well as a frame of reference in which I am instantly crushed flat by the force of gravity, and even a frame of reference in which I collapse into a black hole.
That doesn't happen, of course. I am comfortably sitting in a chair and typing on my laptop, in all frames of reference.
Where's the hole in my understanding? Do the inertial mass and the gravitational mass of an object depend on the frame of reference, like it seems like they would? If they do, is there a simple explanation of how this dependency is consistent with the observation that I can stand up and walk around regardless of frame of reference?