What Equation Should Be Used for Accelerating Frames in Relativity?

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SUMMARY

The discussion focuses on determining the appropriate equation for transforming frames in a scenario involving uniform acceleration along the x-axis, where traditional Lorentz transformations do not apply. Participants conclude that tensor equations, particularly those related to Maxwell's equations in tensor notation, are essential due to their frame invariance. Additionally, it is established that the Lorentz transformation can be utilized by considering instantaneous speed with respect to the observer, ensuring proper transformation of four-acceleration and deriving four-velocity through integration over proper time.

PREREQUISITES
  • Understanding of Lorentz transformations in special relativity
  • Familiarity with tensor notation and tensor equations
  • Knowledge of four-acceleration and four-velocity concepts
  • Basic principles of uniform acceleration in relativistic contexts
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  • Research the derivation of four-acceleration and its implications in special relativity
  • Study the application of tensor equations in different inertial and non-inertial frames
  • Explore advanced topics in relativistic dynamics, including non-inertial reference frames
  • Learn about the integration of four-acceleration to derive four-velocity in accelerated frames
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Students and professionals in physics, particularly those studying relativity, as well as researchers interested in the mathematical frameworks of accelerating frames and tensor calculus.

astrozilla
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Homework Statement


A frame is accelerating uniformly along the x-axis relative to an inertial frame (x,y,z) with acceleration a.Find the transformation between the frames given that the origins concide at t=0.


Homework Equations


The lorentz transformations cannot apply here ,but what equation has to be used ?


The Attempt at a Solution


I think a tensor equation is what we need because tensor equations i.e maxwell equations in tensor notation are frame invariant.
 
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astrozilla said:

Homework Statement


A frame is accelerating uniformly along the x-axis relative to an inertial frame (x,y,z) with acceleration a.Find the transformation between the frames given that the origins concide at t=0.


Homework Equations


The lorentz transformations cannot apply here ,but what equation has to be used ?


The Attempt at a Solution


I think a tensor equation is what we need because tensor equations i.e maxwell equations in tensor notation are frame invariant.

Lorentz transformation applies just fine with instantaneous speed with respect to the observer. The boost from observer to the accelerating frame must be able to transform the four-acceleration properly, and the integration of four-acceleration over proper time gives you the four-velocity. Satisfying these two condition gives you the formula for the Lorentz transformation.
 

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