Frodo
Gold Member
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The key point to take away from the twin paradox is that the time difference is due to the moving twin's change of frame.
The acceleration is essentially irrelevant except for the fact that the moving twin must decelerate and accelerate so that they can change their frame.
You can easily set up a twin paradox without any accelerations. I use the values from above.
Set up a stationary observer on earth, another at the turning poiint and another at twice the distance of turning point. All three synchronise their clocks to read 0.
The moving twin_1 accelerates before the experiment starts in such a way that she is traveling at V when she passes earth, and she passes when the Earth clock reads 0. She looks at the Earth clock and sets her clock to 0.
A similarly moving twin_2 passes the point twice the turning point distance away, traveling at V towards earth.
The two moving travellers meet at the turning point. The stationary person's clock reads 5 but twin_1's clock reads only 4.5.
twin_2 sets her clock to be the same at twin_1, or 4.5. twin_2 continues to Earth and arrives at Earth when Earth says it is 10. However, twin_2's clock reads 9, made up of the 4.5 which she set, plus the 4.5 for her journey time, totalling 9.
So, whereas the Earth bound twin says 10 years have elapsed since twin_1 left, the total travel time measured by the two moving twins is only 9 years.
So, we have the same time difference but there have been no accelerations.
Acceleration has nothing to do with the twin paradox other than it is necessary for the moving twin to accelerate and decelerate to change her frame. The twin paradox is about changing frames.
The acceleration is essentially irrelevant except for the fact that the moving twin must decelerate and accelerate so that they can change their frame.
You can easily set up a twin paradox without any accelerations. I use the values from above.
Set up a stationary observer on earth, another at the turning poiint and another at twice the distance of turning point. All three synchronise their clocks to read 0.
The moving twin_1 accelerates before the experiment starts in such a way that she is traveling at V when she passes earth, and she passes when the Earth clock reads 0. She looks at the Earth clock and sets her clock to 0.
A similarly moving twin_2 passes the point twice the turning point distance away, traveling at V towards earth.
The two moving travellers meet at the turning point. The stationary person's clock reads 5 but twin_1's clock reads only 4.5.
twin_2 sets her clock to be the same at twin_1, or 4.5. twin_2 continues to Earth and arrives at Earth when Earth says it is 10. However, twin_2's clock reads 9, made up of the 4.5 which she set, plus the 4.5 for her journey time, totalling 9.
So, whereas the Earth bound twin says 10 years have elapsed since twin_1 left, the total travel time measured by the two moving twins is only 9 years.
So, we have the same time difference but there have been no accelerations.
Acceleration has nothing to do with the twin paradox other than it is necessary for the moving twin to accelerate and decelerate to change her frame. The twin paradox is about changing frames.
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