Calculating Beta Factor: Frame of Reference?

[STAii]

In relativity, when it comes to calculating the beta factor, what frame of reference are we supposed to use to measure the speed of the object ?

 

[damgo]

Whichever you want, as long as you're consistent.

Typically you start by picking a useful frame of reference - the lab frame, or the center-of-momentum frame, for example - and do all your calculations in that. If you want to switch to another frame, you have to Lorentz transform everything (or better yet, just use invariants!).

 

[STAii]

Umm ...
So suppose i was comparing what i see in two frames of reference.
Let's asuume that the first frame of reference is not moving.
The second frame of reference is moving at 0.8c (with the direction of the body in subject) comparing to the frist frame of reference.
Now our body is moving at 0.8c comparing to the first frame of reference.
An observer in the first frame of reference thinks that the object can only speed up for the amount of 0.2c (cause otherwise the object will reach the speed of light).
While the observer in the second frame of reference thinks that the object can still speed up with the amount of 1c.
Let's suppose that the object actually speeded up for 0.9c, the observer in the first frame of reference will see that the object is moving in the speed of 1.7c which is impossible, while the observer in the second frame of reference will see the object moving at 0.8c which is possible !

So which one of them is right ? (or where did i go wrong ?)

 

[Mulder]

Originally posted by STAii

where did i go wrong ?)
Let's suppose that the object actually speeded up for 0.9c,

Just there? .'c's the same in all inertial frames. Then you'd have to use the Lorentz transformations to work out it's new speed in a different reference frame.

 

[STAii]

Ah ...
Right, i got it now.
Thanks.