Principle of Equivalence and Acceleration in Deep Space

[Calpalned]

Homework Statement

I know that the principle of equivalence states that a person in a window-less box will not be able to tell if s(he) is in a stationary box on Earth or in a box that is accelerating upward at a constant rate. I am assuming that the acceleration of the rocket is 9.8 m/s^2

Homework Equations

F = ma

The Attempt at a Solution

What I don't understand is that for the box accelerating at a constant rate (in deep space), it will eventually reach the speed of light. Therefore, the principle of equivalence doesn't seem to work because eventually the person in the box will stop accelerating (and therefore be weightless). If my logic is wrong, please correct me, thanks

 

[gneill]

1. The Equivalence Principle isn't about indefinite eventualities, it's about whether or not the two cases can be distinguished in principle by experimental tests conducted within the elevators.

2. No matter how long the elevator on the rocket continues, its occupant will still experience the same acceleration regardless of what another outside observer sees. Time, clocks, mass, etc., don't change for the occupant from his own point of view. And he has no view of the outside word so he has nothing to compare his state of motion (or lack thereof) to.

 

[phinds]

What I don't understand is that for the box accelerating at a constant rate (in deep space), it will eventually reach the speed of light. Therefore, the principle of equivalence doesn't seem to work because eventually the person in the box will stop accelerating (and therefore be weightless). If my logic is wrong, please correct me, thanks

No, it would not. Nothing with mass ever reaches the speed of light, even if you keep accelerating it and in any case that really isn't relevant to the equivalence principle which is not intended to be taken to boundary value cases.

EDIT: I see gneil beat me to it.

 

[Calpalned]

Thanks gneill and phinds

 

[Orodruin]

Just to complete with how an inertial observer outside the box would see it: the box would always be accelerating, but acceleration in the observer's frame would be decreasing such that the box never reaches the speed of light. This does not mean the acceleration felt by the occupant of the box is less. Accelerations, just like velocities, are observer dependent.

 

[vela]

What I don't understand is that for the box accelerating at a constant rate (in deep space), it will eventually reach the speed of light. Therefore, the principle of equivalence doesn't seem to work because eventually the person in the box will stop accelerating (and therefore be weightless). If my logic is wrong, please correct me, thanks

You seem to be using Newtonian mechanics where the speed of the box can steadily increase without bound. In relativistic mechanics, you find the speed of the box (to the outside observer) asymptotically approaches the speed of light.

 

[Calpalned]

Thanks everyone, now I understand