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1 results

  • 2 - Global Non-Inertial Frames in Special Relativity

  • from Part I - Special Relativity: Minkowski Space-Time
  • Luca Lusanna
  • Book:
    Non-Inertial Frames and Dirac Observables in Relativity
    Published online:
    17 June 2019
    Print publication:
    04 July 2019, pp 12-26

  • Summary

    There is a description of the 3+1 approach allowing definition of global non-inertial frames in Minkowski space-time. One gives a time-like observer and a nice foliation with 3-spaces (namely a clock synchronization convention). Then one introduces Lorentz scalar radar 4-coordinates: the time is an increasing function of the proper time of the observer and the 3-coordinates live in the instantaneous 3-spaces. The connection of the radar coordinates with the standard ones defines the four embedding functions describing the foliation with 3-spaces. Then there is the definition of parametrized Minkowski theories for every kind of matter admitting a Lagrangian description. The new Lagrangian is a function of the matter and of the embedding, but is singular so that the embedding variables are gauge variables. As a consequence, the transition from a non-inertial frame to either an inertial or non-inertial frame is a gauge transformation not changing the physics but only the inertial forces.