# Question about FTL travel vs. FTL acceleration

1. Nov 7, 2011

### JoshWilliard

Hello all, this is my first post everyone!

I've had a curious mind about the limitations faster than light-speed travel ever since I first heard of the concepts involved as a young kid in science class. Ever since I have inquired about this subject to many teachers and professors. I've never been able to have a lengthy, well-thought discussion that's put my mind at rest on this issue. I start thinking about physics and I become quite obsessive trying to wrap my mind around this stuff.

Take an object in a perfect vacuum moving at a constant speed. Let's say this speed could be anything, as long as it is constant, which in a perfect vacuum would be the case. To the occupants of this object, or to the object itself, it would appear to be moving at a speed of zero. Could this not be light speed, or faster than that relative to an area of the space that is stationary? Meaning, if it were to pass an object while moving at this constant speed it would appear to be moving at the speed of light from the occupants who feel like they are moving at the speed of 0.

If this is true, where do the limitations lie as far as achieving this speed incrementally in space? Say the object from that last paragraph is moving at a speed 5 miles per hour lower
than the speed of light. Would it take an occupant an infinite amount of energy to walk in the direction of the objects movement, despite the fact that at this constant speed he appears to not be moving at all while standing still?

What would stop a vessel from moving through space at the speed of light as long it did not accelerate to the speed of light instantaneously?

2. Nov 7, 2011

### Passionflower

Proper acceleration, which is acceleration that an observer can measure, is not the same as coordinate acceleration, which is for instance the acceleration an inertial observer sees when another observer starts his rocket engines.

There is a relationship between the two:
$$\Large a= \left( 1-{v}^{2} \right) ^{3/2}\alpha$$
a is the coordinate acceleration while alpha is the proper acceleration.

As you can see the factor in front of alpha decreases for higher velocities, thus the coordinates acceleration reduces more and more for larger velocities. That is why one can have a constant proper acceleration while never reaching the speed of light.

3. Nov 8, 2011

### Bill_K

Very Frequently Asked Question, Josh. Say your spaceship is moving at c - 5mph, and you walk forward at 10 mph. It does not take an extraordinary effort to do so, and does not feel any different than if the ship were standing still. What does happen is that an observer on the ground still does not see you as moving faster than c. Special relativity has an addition law for velocity which differs from the Newtonian law v = v1 + v2. Rather it is v = (v1 + v2)/(1+v1v2/c2). This guarantees that v can not exceed c, as long and v1 and v2 are individually less than c.