**LORENTZ TRANSFORMATION, LORENTZ TRANSFORMATION EQUATION, WHAT IS LORENTZ TRANSFORMATION?**

Lorentz Transformation is a set of equations which correlates space-time
coordinate of an event occurring in space as observed by two observers in
different frame of reference moving with constant velocity relative to each
other.

To derive equation let us consider two inertial frame s and
s’. s’ is moving with velocity v, relative to s along the direction of x-axis.
Let us consider that at an instant the origin o and o’ of two frames. Suppose a
pulse of light is generated at t=0 at the origin. It will spread into the space
and consider the situation when pulse reaches at P. Observers at o and o’
measure coordinate of P as (x,y,z,t) and (x’,y’,z’,t’). When pulse is observed
by an observer at s then

As (z,z’) and (y,y’) axes are perpendicular to the direction
of motion coordinate will remain unaffected.

Now y = y’ and z = z’

So that from Eq. (1) and (2), we get

Where k is independent of x and t.

If we suppose that the system s is moving
relative to s’ with velocity v along +x direction. Then

Putting Eq. (4) into Eq. (5) we get

Putting x’ from Eq. (4) and t’ from Eq.
(6) in Eq. (3) we get

This is an identity and hence the
coefficient of various power of x and t must vanish separately. Equating the
coefficient of t*t to zero, we get

Putting this value in Eq. (5) we get

Also putting in Eq. (6), we get the
equation

Therefore Lorentz
Transformation Equations are:

Inverse Transformation
Equations are:

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