In this paper we treat the so called clock paradox in an analytical way. The rest clock is denoted as (1), the to-and-fro moving clock is (2), the inertial frame in which (1) is at rest in its origin and (2) moves is I and, finally, the accelerated frame in which (2) is at rest in its origin and (1) moves forward and backward is A. We will deal with the following questions: I) According to the point of view of I, when (2) and (1) reunite, they age differently, i.e. the proper time interval of (2) is shorter than that of (1). The usual special relativistic time dilation formula accounts for this effect when the acceleration of (2) is neglected. Does a finite value of the force F acting upon (2) preserve this situation, both qualitatively and quantitatively? We will use the hyperbolic motion of the Special Theory of Relativity in order to answer this question. II) Is this effect an absolute one, i.e. does the accelerated observer A comoving with (2) obtain the same results as that in I, both qualitatively and quantitatively? We will use the General Theory of Relativity and, again, a finite value of the force F felt by (2) in order to answer this question.
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