If we do not consider the acceleration in a Minkowski space-time means we are avoiding the equation of motion of a charged particle in Minkowski space-time.If charge is zero then the equation of motion follows the law of inertia.If charge is not zero ,we may not construct a coordinates system in which the equation of motion follows the the law of inertia.

One way to justify the the existence of acceleration is to accept the non-inertial nature of Minkowski space-time for the electromagnetic force.It means the variation of mass ,the equivalence of mass -energy relation The existence of acceleration and force in Minkowski space-time are all due to the existence of the electromagnetic field in the Minkowski space-time.That is there exists two types of Minkowski space-time.One is inertial and the other is non-inretial.

The non-inertial Minkowski space -time as defined in the above paragraph may not be treated as an special case of Riemann geometry(The general relativity).

Futher,the role of the Lorent transformation will also,be revised for the non-inertial Minkowski space-time.

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