Relativity & Distance-Time: Is It True?

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Discussion Overview

The discussion revolves around the relationship between time, distance, and speed in the context of relativity, particularly focusing on whether a traveler can perceive their speed as exceeding the speed of light when measured by their own clock during acceleration. The scope includes theoretical considerations of relativity and its implications for understanding motion and speed.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant questions whether the time taken to travel a distance from the traveler's perspective is the same as in classical mechanics, suggesting that onboard measurements may imply exceeding the speed of light.
  • Another participant asserts that while the formulas for distance, speed, and time hold true for a single inertial observer, the concept of length contraction complicates the situation, preventing the traveler from measuring a speed greater than the speed of light.
  • A third participant references the concept of proper velocity, implying that it may provide insight into the discussion but does not elaborate on its implications.
  • A later reply expresses a personal opinion that relativity concepts should be taught in a different order, starting with proper velocity before introducing time dilation.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of speed from the traveler's perspective and the implications of relativity. There is no consensus on whether the concept of proper velocity should be prioritized in teaching relativity.

Contextual Notes

Participants highlight the importance of reference frames and the effects of acceleration on measurements, indicating that assumptions about distance and time may vary based on the observer's frame of reference. The discussion does not resolve these complexities.

Meanwhile
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Is it correct that the time it takes to travel a distance from the point of view of the traveler (measured by their clock) is the same as it is in classical mechanics?

I.e. if you start accelerating at a constant rate, at some point you will go "faster than light" if you define speed as distance divided by onboard time (despite you'll always stay sub c for an external observer)?
 
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Meanwhile said:
Is it correct that the time it takes to travel a distance from the point of view of the traveler (measured by their clock) is the same as it is in classical mechanics?
Yes. If the distance traveled is ##D##, the time taken on the journey is ##T##, and the speed is ##S## and all are measured by the same inertial observer, then ##D=ST##, ##T=D/S##, ##S=D/T##. But you have to remember that bit about "all are measured by the same inertial observer" - you cannot mix the values seen by different inertial observers or measured in different reference frames in these formulas.

Thus, it does not follow that:
I.e. if you start accelerating at a constant rate, at some point you will go "faster than light" if you define speed as distance divided by onboard time (despite you'll always stay sub c for an external observer)?
We know what your onboard time is, but what value do we use for the distance? As the ship accelerates, its speed increases so the distance between origin and destination as measured by the onboard observer is being reduced by length contraction. There is no moment in the journey, including at the end when the traveller zooms past the destination at very close to ##c##, that the distance as measured by the traveler divided by the travel time comes out greater than ##c##.
 
Meanwhile said:
I.e. if you start accelerating at a constant rate, at some point you will go "faster than light" if you define speed as distance divided by onboard time (despite you'll always stay sub c for an external observer)?
See:
http://en.wikipedia.org/wiki/Proper_velocity
 
Thank you. I was always wandering why such an obvious concept is hidden so deep in the theory. I think relativity should be taught "backwards": proper velocity first, THEN time dilation and so on.
 

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