Authors: Per Hokstad
Abstract. We investigate time dilation in the theory of special relativity, and discuss some basic questions and controversies. Starting out from the Lorentz transformation, we stress that the location of clocks used for time readings is essential for the magnitude of the observed time dilation. We focus on three observational principles: 1) A reference frame may apply a single clock (SC); 2) It may apply multiple clocks (MC); or 3) There is a completely symmetric situation between the two reference frames. We specify two types of simultaneity. First, there can be a direct comparison of clock readings at identical positions, (‘basic simultaneity’). Further, there is simultaneity ‘in the perspective’ of any reference frame. By also using an auxiliary reference frame – in combination with symmetry considerations – we also define ‘simultaneity at a distance’; becoming an essential concept in our investigations. Throughout there is a focus on symmetry. A main statement is to stress that the Lorentz transformation has a fully symmetric solution with respect to the two reference frames: We will always observe that a single clock on any reference frame goes slower than the passing clocks on the other frame. This is mutual for both frames. We use the obtained framework to give a thorough discussion of the travelling twin paradox, and arrive at a conclusion regarding the twins’ ages, which deviates from the prevalent view regarding this example.
Comments: 17 Pages.
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