Time Dilation: Moving Rocket 0.5c vs Accelerating Rocket 0.5c

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Discussion Overview

The discussion revolves around the concept of time dilation as experienced by two rockets moving at relativistic speeds, one at a constant velocity of 0.5c and the other accelerating from 0.3c to 0.7c. Participants explore the implications of acceleration on time dilation, particularly in the context of special relativity versus general relativity.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions which rocket's time the non-moving observer would perceive as running slower when both are at 0.5c.
  • Another participant inquires whether the time dilation formula accounts for acceleration.
  • A subsequent post reiterates the question about the necessity of considering general relativity due to the presence of acceleration.
  • In response, a participant asserts that special relativity can adequately address acceleration, emphasizing that studying accelerating reference frames contributed to the development of general relativity.
  • One participant provides links to transformation formulas for acceleration in special relativity and discusses the concept of proper acceleration, suggesting that calculations can be performed to compare the time experienced by both rockets.

Areas of Agreement / Disagreement

Participants express differing views on the role of acceleration in time dilation, with some asserting that special relativity suffices while others question the need for general relativity. The discussion remains unresolved regarding the implications of acceleration on time dilation.

Contextual Notes

The discussion includes references to complex mathematical concepts and transformation formulas, which may not be fully explored or agreed upon by all participants. There is also an implicit assumption that the observer is non-accelerating, which may affect the interpretation of time dilation.

pavelbure9
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A non-moving observer is looking at two different rockets in space. One rocket is moving at a steady velocity of 0.5c, and the other rocket is currently moving in 0.5c but has steadily accelerated from 0.3c and will continue accelerating until it gets to 0.7c.

Assuming that there is no gravity, currently (when both rockets are moving at a velocity of 0.5c), which rocket's time will the non-moving observer think is running slower?
 
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Does the time dilation formula include the acceleration anywhere?
 
Orodruin said:
Does the time dilation formula include the acceleration anywhere?
I was just wondering if I had to take General relativity into thought because there is an acceleration
 
No. Special relativity can handle acceleration just fine. And, as Orodruin implies, this question is straightforward.

Studying accelerating reference frames (not accelerating objects) was, I gather, one of the things that led Einstein to general relativity. Also, many special relativity courses avoid accelerating objects because you have to use fairly complicated calculus almost immediately. Taken together, this can lead to the impression that you can't do acceleration in special relativity. But that is wrong - as long as you're willing to do the maths, you can.
 
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pavelbure9 said:
A non-moving observer is looking at two different rockets in space. One rocket is moving at a steady velocity of 0.5c, and the other rocket is currently moving in 0.5c but has steadily accelerated from 0.3c and will continue accelerating until it gets to 0.7c.

Assuming that there is no gravity, currently (when both rockets are moving at a velocity of 0.5c), which rocket's time will the non-moving observer think is running slower?

The transformation formulas for acceleration in special relativity are well known:
https://en.wikipedia.org/wiki/Acceleration_(special_relativity)

From that, one obtains the formulas for proper acceleration (i.e. the acceleration that a comoving observer feels):
https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#Proper_acceleration

by which one finally obtains the formulas for constant proper acceleration, also known as hyperbolic motion, see
http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
https://en.wikipedia.org/wiki/Hyperbolic_motion_(relativity)
https://en.wikipedia.org/wiki/Acceleration_(special_relativity)#Curved_world_lines

Using those formulas, and plugging in some numbers, you should be able to compute the time of both rockets.
 

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