Relative Motion: Framing Object Velocity

[Edi]

So, for example, 2 objects are moving towards each other.
There is a frame where 2 object move with (for the sake of simplicity thy both move with the same velocity) the velocity V
Then there is a frame where one of the object stand still, but the other moves towards it with the velocity 2V.
That makes sense, it's what relativity is all about.

But the tricky part comes when the objects moving towards each other have the velocity, for example, 70% c
There is a frame where each one moves with 70% c (?)
There is a frame where one object stands still while other object moves with the velocity of 2*70% c = 140%c (??)

Clearly something is wrong with this, but I just can't put my finger on it...
Please teach me! ;)

 

[jtbell]

Velocities don't "add" the same way in relativistic physics as in non-relativistic physics.

http://hyperphysics.phy-astr.gsu.edu/HBASE/relativ/einvel.html

 

[Entropia]

In this scenario, the concept of relative motion becomes more complex due to the involvement of velocities close to the speed of light. The first thing to understand is that velocity is always relative to a chosen frame of reference. In simpler terms, it depends on the observer's perspective.

In the first scenario where both objects are moving towards each other with the same velocity V, it is important to note that this velocity is measured from a frame of reference where both objects are in motion. This means that if we were to measure the velocity of one object from a different frame of reference, it may appear to have a different velocity.

Now, in the second scenario where one object is standing still and the other is moving towards it with a velocity of 2V, the same principle applies. The velocity of the moving object is still measured from the frame of reference where both objects are in motion. However, from the frame of reference where one object is standing still, the velocity of the moving object would appear to be 2V.

But when we introduce velocities close to the speed of light, things start to get more complicated. According to Einstein's theory of relativity, as an object approaches the speed of light, its mass and length increase while its time slows down. This means that at 70% of the speed of light, the object's mass and length will already be significantly different from what they were at rest. This is why it is not possible for the same object to have a velocity of 140% of the speed of light in any frame of reference.

In conclusion, the key to understanding relative motion in scenarios involving high velocities is to always consider the chosen frame of reference and the effects of relativity on the objects' mass, length, and time. I hope this helps to clarify any confusion you had. Keep exploring and learning about relativity, it is a fascinating concept!