Acceleration in special theory of relativity

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Discussion Overview

The discussion revolves around the concept of acceleration in the context of the special theory of relativity, particularly focusing on the relationship between inertial frames of reference and constant acceleration. Participants explore whether an inertial frame can exist where a body undergoing constant acceleration in one frame appears to not accelerate in another frame.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions if there exists an inertial frame ##S'## moving with speed ##u## relative to an inertial frame ##S## in which a body undergoing constant acceleration ##a## does not accelerate.
  • Another participant argues that if the body does not accelerate in frame ##S'##, it must move with constant velocity in that frame, which contradicts the condition of acceleration in frame ##S##.
  • A participant inquires whether such a scenario could occur in Newtonian mechanics and what implications relativity introduces.
  • There is a repeated question about the existence of an inertial frame ##S'## where acceleration is not constant while it is constant in frame ##S##.
  • One participant suggests that if acceleration is constant in one system, it will not remain constant in a system moving with velocity ##u## relative to it, due to the changing velocity of the object in the acceleration formula.

Areas of Agreement / Disagreement

Participants express differing views on the existence of inertial frames where acceleration conditions change. No consensus is reached regarding the implications of relativity on these scenarios.

Contextual Notes

Participants reference the transformation of acceleration between frames, indicating that assumptions about the nature of acceleration and velocity are central to the discussion. The implications of these transformations remain unresolved.

LagrangeEuler
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In a inertial frame of reference ##S## body accelerate with constant acceleration ##a##. Can then exist inertial frame of reference ##S'## which moves with speed ##u## relative to ##S## in which body does not accelerate? And why?
 
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No. If it does not accelerate in S' then it moves with constant velocity with respect to that frame. Transforming that velocity to S yields another constant velocity. And that is in contradiction with body being accelerated.
That is true in both SR and non-relativistic mechanics.
 
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Can such a thing hgappen in Newtonian mechanics? If not, what does Relativity change?
 
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Thanks. And can exist inertial frame of reference ##S'## in which acceleration is not constant if in the system ##S## acceleration is constant?
 
LagrangeEuler said:
Thanks. And can exist inertial frame of reference ##S'## in which acceleration is not constant if in the system ##S## acceleration is constant?
Is that something you could work out for yourself? Using the transformation of acceleration from one frame to another, perhaps.
 
I think that if one system acceleration is constant in the system that moves with velocity ##u## relative to this one acceleration will not be constant, because in formula for acceleration is velocity of moving object that changes from point to point.
 
LagrangeEuler said:
I think that if one system acceleration is constant in the system that moves with velocity ##u## relative to this one acceleration will not be constant, because in formula for acceleration is velocity of moving object that changes from point to point.
Yes, exactly.
 
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