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Asked Feb 4, 2020

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Step 1

For the given problem, the invariance of the space-time interval has been considered for the transformations that take place between the inertial reference frames.

Let there be a stationary inertial reference frame defined by *S*, whose space coordinates are defined as

(*x, y, z*) and the time coordinate is defined as *t*.

Let there be another inertial reference frame defined by *S’*, whose space coordinates are defined as (*x’, y’, z’*) and the time coordinate is defined as *t’*.

Let the inertial frame *S’* be moving at a constant velocity *v* along the *x *direction with respect to the stationary reference frame *S*.

Let the interval in the *S *frame be denoted as Δ*s*.

This “interval” is mathematically expressed as,

Step 2

Consider an event that takes place in the *S* frame defined by the space time coordinates (*x, y, z, t*).

The corresponding event will transform in the moving *S’* frame as per the Lorentz transformations.

Step 3

Let the interval in the *S’ *frame be denoted as Δ*s’*

The correspondin...

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