Special Relativity Velocity Addition
The principal model is from SR and manages the speed expansion in various inertial reference outlines. This is delineated in the figure beneath:
The reference outline S’ is moving with speed v rainbows reference outline S. A vessel is moving with speed v’ concerning S’ outline. What is u, the speed of that vessel as for casing S?
The “typical” approach to discover this speed is utilizing what is known as Galilean change. Here, since both v and v’ and in a similar course, the speed of the vessel regarding S casing is a straightforward expansion, for example
u = v + v’ (1)
Remember that outcome
Presently how about we take a gander at how we do this in SR, which is the more broad depiction of such kinematics. Here, we use what is known as the Lorentz change. Utilizing the figure from above as in the past, the speed u of the vessel in S edge is:
Where c is the speed of light in vacuum
Presently this appears to be unique than the Galilean change that we are utilized to in Eq. 1. This works for reference outline S’ at any speed v, regardless of whether it approaches c. At that esteem, Eq. 1 doesn’t work, and the speed expansion that we are utilized to bombs wretchedly.
Be that as it may, what happens when v«c, for example when reference outline S’ moves much more slow than the speed of light? This is the thing that we typically experience, for example somebody moving in a vehicle or a plane. For v«c, Eq. 2 disentangles a lot.
Without doing any sort of Taylor arrangement development on the denominator of Eq. 2, we would already be able to see that the proportion vv’/c^2 « 1, for example it is an exceptionally little portion short of what one (v’ can’t be more noteworthy than c).