Past exam of the short options paper shared by Prelims and Parts A and B of the physics course of the University of Oxford / 2015 / S27 / 3

Yes. Differential ageing between twins who separate and reunite can be calculated entirely within special relativity, provided gravity is negligible and ideal clock behaviour is specified. The theory is not confined to particles that remain inertial throughout their histories: accelerated timelike trajectories can be described in a single inertial coordinate system in flat Minkowski spacetime.

The invariant quantity recorded by an ideal clock is its proper time,Take one twin at rest in an inertial laboratory. Let the other travel out at speed $v$ for laboratory time $T/2$ and return at the same speed for $T/2$, idealizing the turnaround as very short. On reunion,Both times are compared at the same reunion event, so this is not a disagreement about observing a distant clock or choosing a convention for distant synchronization. Einstein's 1905 discussion already considers clock transport along a closed path; the proper-time integral supplies the general modern calculation.^[ref]

The apparent paradox applies reciprocal inertial time dilation as if both twins used one inertial frame from departure to reunion. They do not. The traveller changes inertial frames at the turn, and the associated assignment of simultaneity to distant events changes with it. Reciprocal time dilation for each separate inertial leg is compatible with unequal total proper times along the two worldlines.

Acceleration marks the asymmetry of this itinerary, but is not a universal extra term that locally slows a clock by an amount proportional to its acceleration. Smooth the turnaround and integrate along the resulting worldline: the answer depends on the full path. In the short-turnaround limit the extra proper time during the turn becomes small while the differential ageing of the long legs remains finite. One can even compare successive inertial travellers who relay clocks or records, avoiding the mistaken inference that general relativity is needed to describe the inertial legs.

The clock hypothesis adds the physical idealization that a suitable clock records metric proper time without additional acceleration-dependent damage or internal disturbance. A real biological twin or laboratory clock can of course suffer such disturbances; those are questions about the device's dynamics, not a logical contradiction in the relativistic prediction. General relativity is needed if significant spacetime curvature or gravity is part of the experiment, not merely because a worldline bends in a flat spacetime diagram.