Ok, you have the elevator experiment that Einstein used for his equivalence principle.
You have one elevator in space and one elevator on earth. Both are being affected by force, but they are different forces. The one on Earth is experiencing force (acceleration) by gravity at a rate of [itex]9.8m/s^2[/itex], while the elevator in space is experiencing accelerated forces at a rate of [itex]9.8m/s^2[/itex]. So, on earth, the acceleration is 1-g. The elevator in space is being accelerated at 1-g equivalence. Therefore, you are unable to tell if you are moving or stationary, right?
Ok, here is how it contradicts with SR. In space, your velocity increase by the appliance of this 1-g force, while on Earth it is unoticeable. So, in space, time will allow you to reach close to the speed of light. What happens as your velocity increases? Yes, your mass increases as well. So, you are able to tell that you are moving by an increase in mass overtime. Your velocity in space will never reach the speed of light, but it will come ever so close, like an asymptote. So, your mass will increase forever as long as you are experiencing this 1-g in space. Thus, you are able to tell if a force is applied by acceleration or gravity by the fact if your mass is increasing or not. Or something like that.
I'm sure you people will find something wrong with this. Just an idea I saw while trying to get information on SR and GR.