A question about stationary reference frame

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SUMMARY

The discussion centers on the implications of time dilation in special relativity, specifically involving two synchronized clocks on Earth and one clock on a spaceship traveling at 0.8c. According to the stationary observer on Earth, one year passes while only 0.6 years elapse on the spaceship's clock. Upon returning, the stationary clock shows two years have passed, while the spaceship clock shows 1.2 years. The conversation clarifies that the time dilation formula applies only in inertial frames, and the apparent paradox arises from misunderstanding the nature of reference frames and the effects of acceleration.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and reference frames.
  • Familiarity with Lorentz transformations and their application in inertial frames.
  • Knowledge of the implications of acceleration on time measurement in different frames.
  • Basic grasp of proper time versus coordinate time in the context of relativity.
NEXT STEPS
  • Study the Lorentz transformation equations in detail to understand their application in different inertial frames.
  • Explore the concept of proper time and coordinate time as discussed in Einstein's theory of relativity.
  • Investigate scenarios involving non-inertial frames and how they differ from inertial frames in terms of time measurement.
  • Review the Twin Paradox and its resolution to gain deeper insights into the implications of time dilation.
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Students of physics, educators teaching special relativity, and anyone interested in understanding the complexities of time dilation and reference frames in the context of Einstein's theories.

  • #31
Let's say I am the stationary observer and there is spaceship moving at .8c relative to me.

I see one year on my clock and I see .6 years on his clock. What time does he see on his own clock?

I want to say he sees 1 year on his clock and .6 on mine, but I'm not sure.
 
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  • #32
In either inertial frame, the spaceship twin or the Earth twin, it is valid for each to consider themselves at rest and the other as moving.

However, in order to compare the clocks, one, or the other, or both frameworks must undergo acceleration to bring them into a common frame. It is this acceleration which differentiates one inertial frame from the other.
 
  • #33
goodabouthood said:
Let's say I am the stationary observer and there is spaceship moving at .8c relative to me.

I see one year on my clock and I see .6 years on his clock. What time does he see on his own clock?

I want to say he sees 1 year on his clock and .6 on mine, but I'm not sure.
If you are changing your scenario so that the spaceship continues on in the same direction and doesn't turn around, then yes, in your FOR, when 1 year passes for you, .6 years passes for the ship and in the ship's FOR, when 1 year passes for it, .6 years passes for you.

But you should be aware that neither of you can actually see the others clock as you are asking about. When you see 1 year pass on your own clock, you will actually see 4 months (1/3 year) year pass on the ship's clock and in the same way when the ship see's 1 year pass on its own clock, it will see 4 months (1/3 year) pass on your clock. This is called the Relativistic Doppler effect and is a result of the time dilation of .6 years plus the time it takes for the image of the ship's clock to propagate across space to your clock and vice versa.
 
  • #34
so all moving bodies that are inertial are symmetrical to whatever inertial frame you choose, correct?
 
  • #35
No, they are symmetrical to each other but you can use any inertial frame you choose to define, analyze and demonstrate what is going on.
 

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