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## Main Question or Discussion Point

Hello. I have read many of the posts on this forum concerning relativistic accelerations, constant accelerations to exceed the speed of light, etc. and one thing is still bothering me about the concept: why can one not accelerate constantly to achieve any arbitrary velocity as calculated in their reference frame? I have been searching for a definitive answer to this question for a long time and have yet to find one. Allow me to construct the question using the following thought experiment.

I am traveling on a rocket that is powered by a nuclear reactor that works in such a way that it converts matter into energy at some efficiency. On board I have a normal bathroom scale, a clock, and a calculator. The engine is constantly emitting energy in such a way that the ship is constantly accelerated at about 10 m/s2 (1 g). From my perspective aboard the ship, physics should be working exactly as they would on earth due to the general equivalence principle. Since I know that I am in a rocket ship, however, and I can calculate my acceleration by dividing my weight by my mass (which I assume is remaining constant in my reference frame). I can also record the time that has elapsed since I began to accelerate using my clock (the proper time of my reference frame). Though I have no actual velocity in my constantly accelerating frame, using my calculator I should be able to calculate an "extrapolated instantaneous velocity", v, that some distant observer would see, were I not warping spacetime by accelerating. After accelerating at 10 m/s2 for about 350 days I should finally reach an extrapolated velocity of 300,000,000 m/s (speed of light) and can even exceed this to reach any arbitrary velocity, provided I have enough fuel.

Since we assume the laws of relativity work on Earth they should also hold in this spaceship, so how can I have apparently exceeded the speed of light? In my reference frame my mass remains constant so it would never take an infinite amount of energy to cause me to accelerate from my point of view. In fact, even from a distant observer's point of view, even if my mass goes to infinity as my velocity approaches c, the mass of my fuel is also going to infinity. Because the ship converts the fuel's mass into energy to provide acceleration, I would thus have an infinite amount of energy to accelerate my infinitely massive ship. So, regardless of who's reference frame you're in, there does not seem to be any reason why I cannot reach the speed of light, or any velocity for that matter, as long as I am bringing enough fuel with me. How is this possible?

Thanks,

Rexx

I am traveling on a rocket that is powered by a nuclear reactor that works in such a way that it converts matter into energy at some efficiency. On board I have a normal bathroom scale, a clock, and a calculator. The engine is constantly emitting energy in such a way that the ship is constantly accelerated at about 10 m/s2 (1 g). From my perspective aboard the ship, physics should be working exactly as they would on earth due to the general equivalence principle. Since I know that I am in a rocket ship, however, and I can calculate my acceleration by dividing my weight by my mass (which I assume is remaining constant in my reference frame). I can also record the time that has elapsed since I began to accelerate using my clock (the proper time of my reference frame). Though I have no actual velocity in my constantly accelerating frame, using my calculator I should be able to calculate an "extrapolated instantaneous velocity", v, that some distant observer would see, were I not warping spacetime by accelerating. After accelerating at 10 m/s2 for about 350 days I should finally reach an extrapolated velocity of 300,000,000 m/s (speed of light) and can even exceed this to reach any arbitrary velocity, provided I have enough fuel.

Since we assume the laws of relativity work on Earth they should also hold in this spaceship, so how can I have apparently exceeded the speed of light? In my reference frame my mass remains constant so it would never take an infinite amount of energy to cause me to accelerate from my point of view. In fact, even from a distant observer's point of view, even if my mass goes to infinity as my velocity approaches c, the mass of my fuel is also going to infinity. Because the ship converts the fuel's mass into energy to provide acceleration, I would thus have an infinite amount of energy to accelerate my infinitely massive ship. So, regardless of who's reference frame you're in, there does not seem to be any reason why I cannot reach the speed of light, or any velocity for that matter, as long as I am bringing enough fuel with me. How is this possible?

Thanks,

Rexx