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- Time dilation have opposite signs in hemispheres of recession and approach -
From Sci-Mate WikiMathematics > Classification by Discipline > Applied Mathematics > Mathematical Physics
Type: Research Report
Intention: For Publication
Read/Write Permissions: Open Access
15.01.2012 - Christopher Dyer - Sci-Mate
10.01.2012 - Mikael Franzén
Author information: 1. Manmohan Dash* 2. Mikael Franzén‡
In this paper we give a detailed analysis of the factual observation that time dilation or Doppler shift of frequency are oppositely signed relative to our line of sight in different regions of motion. We show that this depends on how these regions are connected to the actual path of motion and to the location of the observer/detector. For a static globe or circle/sphere of reference, we define two hemispheres; shifts will be red-shifted in the hemisphere of recession and blue-shifted, or violet shifted, in the hemisphere of approach, a fact which is not often mentioned. Indeed, it is a complete sphere where the motion can take place with respect to the line-of-sight, which we have studied in this paper, not just the direction of motion along a certain specific path. The transverse and longitudinal effects are special cases of this general effect. The transverse effect is always red-shifted consistent with the known effect of Relativity and it lies at the intersection of the hemispheres of approach and recession. By saying moving clocks run slower we conveniently forget this important effect. They also run faster, in the hemisphere of approach. We demonstrate this important result from the basic principles of the Special Theory of Relativity.
Download the article (pdf) from the Mathematical Physics Preprint Archive', mp_arc.
View the article online on Philica (Open Access Journal ISSN 1751-3030).
*Electronic address: mdash[at]vt[dot]edu †previously affiliated with VT, USA and KEK, Japan. ‡Electronic address: mikael.franzen[at]willgood[dot]org