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We have the lorentz transformation equations for relating inertial frame of references.

What will the transformation equations be if the frames are non inertial?

Is there any "pseudo-force like thing" in special relativity?

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  • $\begingroup$ Three distinct questions here with three distinct answers. $\endgroup$ – dmckee Jul 1 '18 at 20:10
  • $\begingroup$ Sorry,now I have edited the question. $\endgroup$ – Man_57 Jul 1 '18 at 20:18
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    $\begingroup$ Not to be snarky with you, but you have read through this: en.wikipedia.org/wiki/Non-inertial_reference_frame ? $\endgroup$ – user198207 Jul 1 '18 at 20:26
  • $\begingroup$ For a linear acceleration: en.m.wikipedia.org/wiki/Rindler_coordinates ; For non-zero y and z speeds, still Special Relativity (search for General Lorentz Transformation or Poincare Symmetry); for rotation you may need to use General Relativity. Fictitios forces are gravity in non inertial frames according to the equivalence principle. $\endgroup$ – safesphere Jul 1 '18 at 21:01
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SR (special relativity) theory describes inertial reference frames at constant relative velocity. Nevertheless a non inertial frame can be tracked in an inertial reference frame via a continuous set of inertial reference frames instantaneously at rest with the accelerated frame.

You choose as stationary frame an inertial frame (in which SR assumptions hold) and then you measure the non inertial frame with the Lorentz transformation, however with the relative velocity $v$ and the Lorentz factor $\gamma$ referring to the inertial reference frame at each instant in time at rest with the accelerated frame.

Note: By the way, this is also how to explain the twin paradox.

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  • $\begingroup$ Thank you so much!Can you tell me name of a book which has this theory explained in more details?perhaps mathematically too? $\endgroup$ – Man_57 Jul 2 '18 at 14:29
  • $\begingroup$ It is not a theory on top of SR. Simply you track the accelerated frame in that way. As for the mathematics, it is the Lorentz transformation. Of course, the velocity $v$ and the Lorentz factor $\gamma$ will vary at each instant in time. $\endgroup$ – Michele Grosso Jul 2 '18 at 17:03

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