Can Time in Special Relativity Appear Frozen despite the Clock Hypothesis Says it Cannot

Abstract

According to general relativity, time in a gravitational field will appear slowed down, or close to a black hole even frozen to complete standstill. From an assumed equivalence between gravity and acceleration, one might thus expect that time in special relativity could similarly appear to be slowed down, or even frozen, when observing a system in strong acceleration even at moderate relativistic velocities. Specifically, this would seem to be the case for hyperbolic space time motion when accelerated motion takes place along a hyperbola corresponding to constant time in the Minkowski diagram. On the other hand, the original postulates in Einstein’s theory of special relativity are today normally supplemented with a new postulate, the clock hypothesis, stating that time is unaffected by accelerations. The present study concludes that there is however no inconsistency here: Without being in conflict with the clock hypothesis, time can still appear to be slowed down or even frozen in the special case of hyperbolic motion. This is then due to the special scaling properties of this type of motion, which happen to imitate a constant acceleration. Slowing-down of time can thus occur not only at extreme velocities close to light speed, but also at moderate relativistic velocities for sufficiently powerful accelerations.