No, you don't. This is where relativity get's more flakey.
Certainly not. It's quite clear on what happens to mass in different reference frames.
Mass increase due to acceleration is not relative. There is a theoretical point where the mass is at it's abolute lowest. In relativity it's one of the few things that is not relative to it's frame of reference.
Mass, in fact, is relative. We give a special name to the mass we measure of an object at rest with respect to us: that's its "rest mass" or its "inertial mass". We can then define its relativistic mass as a function of this mass and the relative speed of the object.
Nothing flakey about it.
In otherwords, as long as the force is constant in my frame of reference, so is the acceleration.
If that was true, then you would not be suject to the psuedo gravity of acceleration, and everything would be in freefall.
Hm, again I'm not sure I'm following you. I know that acceleration is locally indistinguishable from gravitation, and that we are not in freefall as long as the ground is pushing up on us.
What I was referring to is that, in the Earth's frame of reference, if there is a constant force on it, the Earth will accelerate at a constant rate, and every object rigidly attached to the Earth will accelerate at the same rate.
A small fraction is going above 99% light speed, anything lower than that the dimentional changes are miniscule.
In fact, Lorentz contraction and time dilation are noticeable at much slower speeds than that. For example, at sqrt(3)/2*c (approximately 87% the speed of light) objects are reduced to half their rest length. At half the speed of light, objects are reduced to 87% their rest length. I would say these changes are quite the opposite of miniscule.
The first point of paradox is the two object would seem to be able to move in relationship to each other at just below twice the speed of light.
That's not really a paradox. Relativity does not state that this is impossible; only that it is impossible for a signal (information) to travel faster than light. If these two objects were signalling each other, then to them, the signals would appear to be travelling at light speed or less.
The second is that if you could reach 99.9999% of light speed or so, to the point where time dialation occurs, and you were racing a light ray, the closer you go to light speed, the faster the light would seem to be passing you because time for it is going faster than time for you.
No. The speed of light (in a vacuum) is always the same. Under no conditions (says Einstein) will its speed appear to be anything other than c.
-Erasmus