- #1
Gulli
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Hi, I'm an undergraduate physics student trying to comprehend why the twin paradox is not a paradox.
The standard reply usually amounts to this: the dude in the spaceship has to turn around at some point to come back to Earth. So he accelerated during his journey (by changing his direction midway) chopping his journey into two parts, each with its own frame of reference (apparently the acceleration required to get to relativistic speed and slow down again when back at Earth doesn't matter, (maybe because it's along the direction of movement) or maybe it does actually matter and it's exactly one of those subtleties I'm looking for here).
Anyway, the above "explanation" seems a bit like a cop out to me: while it's technically true the spaceman has to change to a new frame of reference when he turns around, this alone is a poor proof that the laws of nature will ensure the frame of reference of Earth is precisely right. The same way that saying the derivative of sin(x) is not 39 does not in itself proof the derivative of sin(x) is actually cos(x). I suspect (maybe wrongly) that there is a more thorough explanation.
To help myself gain more understanding I've prepared the following thought experiment:
In 600.000 AD a spaceman sets out in a spaceship from Earth to a star 20 lightyears away, he will travel at 0.5 c so the journey will take 40 years (to an oberver on Earth, 35 years to the spaceman) give or take (you tell me if the "give or take" part because of acceleration to 0.5c, near Earth, and deecceleration to a complete stop near the star, matters or not). Now, and I stress this, the spaceman DOES NOT return to Earth, he will stay near the star.
Now the spaceman tries to find out what year it is on Earth, he does this in 3 different ways:
1) He tunes into his radio dish, does he hear an Earth news broadcast from 600.020 AD, 600.015 AD or 600.025 AD?
2) Before he left Earth he asked someone to send a probe after him with a clock aboard. The probe travels at 30 km/s (c/10.000) which is safely non-relativistic. He waits until the probe arrives at his star. Does he have to wait 400.000 years, 399.995 years or 400.005 years?
3) A group of humans left Earth in the year 100.000 AD, they traveled to the star at 30km/s and established a colony on a planet orbiting the star. The spaceman decides to visit them and asks them what year it is according to their calendar (which is the same as Earth's). Will they answer 600.040 AD, 600.035 AD or 600.045 AD?
I designed this experiment to cut the U-turn from the original twin paradox. In theory (according to the standard explanation) this means the frames of reference of the spaceman and Earth (or the colony, which is pretty much stationary to Earth) are equally valid. So I hope the outcome of this experiment will help me understand the whole thing better.
I understand the math of SR, why Einstein's postulates lead to time dilation and Lorentz contraction and I even understand the solution to the barn and ladder paradox, but I'm having difficulty comprehending the twin paradox.
The standard reply usually amounts to this: the dude in the spaceship has to turn around at some point to come back to Earth. So he accelerated during his journey (by changing his direction midway) chopping his journey into two parts, each with its own frame of reference (apparently the acceleration required to get to relativistic speed and slow down again when back at Earth doesn't matter, (maybe because it's along the direction of movement) or maybe it does actually matter and it's exactly one of those subtleties I'm looking for here).
Anyway, the above "explanation" seems a bit like a cop out to me: while it's technically true the spaceman has to change to a new frame of reference when he turns around, this alone is a poor proof that the laws of nature will ensure the frame of reference of Earth is precisely right. The same way that saying the derivative of sin(x) is not 39 does not in itself proof the derivative of sin(x) is actually cos(x). I suspect (maybe wrongly) that there is a more thorough explanation.
To help myself gain more understanding I've prepared the following thought experiment:
In 600.000 AD a spaceman sets out in a spaceship from Earth to a star 20 lightyears away, he will travel at 0.5 c so the journey will take 40 years (to an oberver on Earth, 35 years to the spaceman) give or take (you tell me if the "give or take" part because of acceleration to 0.5c, near Earth, and deecceleration to a complete stop near the star, matters or not). Now, and I stress this, the spaceman DOES NOT return to Earth, he will stay near the star.
Now the spaceman tries to find out what year it is on Earth, he does this in 3 different ways:
1) He tunes into his radio dish, does he hear an Earth news broadcast from 600.020 AD, 600.015 AD or 600.025 AD?
2) Before he left Earth he asked someone to send a probe after him with a clock aboard. The probe travels at 30 km/s (c/10.000) which is safely non-relativistic. He waits until the probe arrives at his star. Does he have to wait 400.000 years, 399.995 years or 400.005 years?
3) A group of humans left Earth in the year 100.000 AD, they traveled to the star at 30km/s and established a colony on a planet orbiting the star. The spaceman decides to visit them and asks them what year it is according to their calendar (which is the same as Earth's). Will they answer 600.040 AD, 600.035 AD or 600.045 AD?
I designed this experiment to cut the U-turn from the original twin paradox. In theory (according to the standard explanation) this means the frames of reference of the spaceman and Earth (or the colony, which is pretty much stationary to Earth) are equally valid. So I hope the outcome of this experiment will help me understand the whole thing better.
I understand the math of SR, why Einstein's postulates lead to time dilation and Lorentz contraction and I even understand the solution to the barn and ladder paradox, but I'm having difficulty comprehending the twin paradox.
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