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## Revista de la Sociedad Científica del Paraguay

*Print version* ISSN 0379-9123*On-line version* ISSN 2617-4731

#### Abstract

SUAREZ-ANTOLA, Roberto. About the slowing down of accelerated clocks II: relativistic proper time and physical unus mundus.* Rev. Soc. cient. Parag.* [online]. 2018, vol.23, n.2, pp.199-226.
ISSN 2617-4731. https://doi.org/10.32480/rscp.2018-23-2.199-226.

The convergence of the integral that gives the proper time as a function of inertial time, when speed tends to the speed of light fast enough as inertial time tends to infinity, was studied in 1985. This problem is reconsidered here, in the framework of special relativity. Nothing special (besides the rate of growth towards infinity) seems to characterize the behavior of the tangent com- ponent of the fields of 3-force along the path of the accelerated clock, in relation with the conver- gence or divergence of the integral that gives proper time as function of inertial time. However, seen from the viewpoint of the proper acceleration of the clock, a physically meaningful difference appears between the tangential proper 3-acceleration histories that give a finite proper time for an infinite inertial time, and those tangential proper 3-acceleration histories that give an infinite proper time for an infinite inertial time: either a singularity in proper 3-acceleration for a finite value of proper time in one case, or its absence in the other case. The obtained results are compared, in the framework of general relativity theory, with the behavior of proper time relative to inertial time during the fall of a particle towards a black hole. The consequences of these results on the validity of a postulate that is at the base of the original formulation of the theory of relativity are empha- sized, according to which all observers in the universe, regardless of their state of movement, should be agree on the occurrence of certain events, such as explosions and implosions, births and deaths.

**Keywords
:
**restricted relativity theory; generalized relativity theory; proper time; inertial time; unus mundus; blackhole.