Accelerated obserevers in special (not general) theory of relativity

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Discussion Overview

The discussion centers on the treatment of accelerated observers within the framework of special relativity, questioning whether it is possible to address this topic without resorting to the mathematical language of general relativity. Participants explore the implications of acceleration on observations and measurements in special relativity.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant suggests that special relativity does not inherently accommodate accelerated observers and proposes an additional axiom stating that "acceleration is relativistic irrelevant."
  • Another participant argues that special relativity can indeed handle accelerations, emphasizing that acceleration affects the structure of spacetime and alters simultaneity, clock rates, and distances.
  • It is noted that when accelerating towards a distant star, the perceived distance and time experienced can lead to counterintuitive results, such as the star appearing closer due to length contraction.
  • A participant questions the correctness of their own calculations regarding proper time and seeks clarification on potential mistakes in their reasoning.
  • Some participants highlight the implications of acceleration on the twin paradox, noting that the effects of acceleration lead to differences in aging between twins depending on their respective frames of reference.

Areas of Agreement / Disagreement

Participants express differing views on the role of acceleration in special relativity. While some argue that acceleration can be addressed within special relativity, others maintain that it is a limitation of the theory. The discussion remains unresolved, with multiple competing perspectives present.

Contextual Notes

Participants reference various effects of acceleration, such as changes in simultaneity and the behavior of clocks, but the discussion does not reach a consensus on how these effects should be mathematically treated within special relativity.

  • #31
Nedeljko said:
Yes, I know that t_0 is the moment in the system S. But, what is wrong. I have think that it is correct formula for the proper time of bird i.e. time of the bird's clock from its pocket (the clock flying together with the bird). If this formula is incorrect what is correct.
I didn't say that it's wrong. It's not. I just explained what t0 is because you didn't.

Nedeljko said:
Yes, I know it, and I am expected this question. It is related to this remark:
Yes, JesseM explained it very well.

Nedeljko said:
I am interesting for following: If I use the same ideas for computing frame-invariant quantities in another examples, can I obtain incorrect results?
I'm not sure exactly what you mean by "the same ideas", but it clearly doesn't matter what frame you use to compute something coordinate independent like "proper time".
 
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  • #32
Fredrik said:
I'm not sure exactly what you mean by "the same ideas", but it clearly doesn't matter what frame you use to compute something coordinate independent like "proper time".

Let we assume that the observer's motion law is given in inertial system S. The ideas are:

1. Computing the time of inertial system as a function depending on the observer's proper time.
2. Computing values in inertial system S' co-moving with the observer in any fixed moment.
3. Considering these values as values measured by the observer in this fixed moment of the observer's time.
4. Expressing these values as functions depending on the observer's time.

That are brief description of the ideas. Consult the attached PDF for the example of computation. Can I use these ideas safely?
 

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