Travel faster than speed of light. According to what reference frame?

[cbell39]

I have been reading Einsteins Relativity and a simple concept in special relativity is tripping me up. I have heard that an object can never reach the speed of light. To which observer is this speed limit seen by. I know your answer will be "By all observers" but that is what I don't get. Wouldn't that have to imply that there is a universal static reference frame by which you could judge whether or not something was traveling faster than the speed of light. If I am not allowed to travel faster than the speed of light by Earths reference frame and therefor I am moving at let's say c-1m/s according to Earth and the Earth is moving away from the Sun at way let's say 10 m/s (really slow, its just to illustrate my question) on the same line I am moving , wouldn't that mean that I am now moving at c + 9 m/s relative to the Sun? I'm sure this is where the intuitive idea of relativity breaks down. I just would like an explanation

 

[darkhorror]

velocities aren't added in the normal way that you think they are. You can check out the velocity addition formula.

http://en.wikipedia.org/wiki/Velocity-addition_formula

 

[ghwellsjr]

If you look up "velocity addition" in wikipedia, you will see this formula for adding two velocities:

Maybe you can see that no matter how close v and u are to c, the resultant speed, s, will still be less than c. Just for fun, let's make v and u equal to c. Then we have:

s = (c+c)/[1+(c²/c²)
s = 2c/[1+1]
s = 2c/2
s = c

But since v and u must be less than c, the resultant speed will also be less than c. If you want you can do the actual calculation knowing that c = 299,792,458 m/s, v = 299,792,457 m/s and u = 10 m/s but the answer will come out less than c.

 

[ghwellsjr]

OK, I did the calculation and got 299792457.0000000667 which you can see is only a tad more than v and still less than c. In other words, it hardly made any difference.