# Calculating Beta Factor: Frame of Reference?

• STAii
In summary, when calculating the beta factor in relativity, it is important to choose a consistent frame of reference. This can be the lab frame or the center-of-momentum frame. If switching between frames, Lorentz transformations must be used. A mistake can occur if the object's speed is not consistent in both frames, as the observer in one frame may see an impossible speed while the other may see a possible speed.
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 ?

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!).

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 ?)

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.

Last edited:
Ah ...
Right, i got it now.
Thanks.

## What is the beta factor in relation to calculating frame of reference?

The beta factor is a measure of how the movement of an object in a particular frame of reference is affected by the movement of the frame of reference itself.

## How do you calculate the beta factor?

The beta factor can be calculated by dividing the velocity of the object in the moving frame of reference by the velocity of the frame of reference itself.

## What is the significance of the beta factor in scientific research?

The beta factor is important in understanding the dynamics of moving objects and how they are affected by different frames of reference. It is especially relevant in fields such as physics and astronomy.

## What are some common applications of calculating beta factor?

Calculating beta factor is commonly used in fields such as mechanics, fluid dynamics, and astrophysics to understand the relative motion of objects in different reference frames.

## Is the beta factor always constant?

No, the beta factor can vary depending on the velocity and direction of the object and the frame of reference. It can also change over time as the velocities of the object and frame of reference change.

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