- #1
timpeac
- 14
- 0
Hi, I can see that this topic has been much discussed, but I haven't seen a thread on it with the particular spin I want to give it (just the journey out from Earth).
I understand the traditional view of the twin paradox (I think!): Two twins a and b are on Earth and each has a clock. The clocks are synchronised and one twin travels at, say, 60% the speed of light to a star exactly one light year away, stops and immediately returns. Due to time contraction, during the journey each twin judges that his brother’s clock is running slow – each only showing 0.8 seconds for each second of his own clock - each of which seems, to the holder, to be running normally. On return to Earth when the clocks are compared it is shown that it is the twin who has traveled away and come back whose clock shows less time than his brother’s.
This is the paradox – if you could equally view each twin as the one “at rest” while his brother travels away and back to him, and so both are correct in considering his brother’s clock to be running slow, then how can one of them be shown to really have the slow clock? The answer is that the twin traveling away from Earth has undergone four accelerations, albeit very quick, one when he set off from Earth, one when he arrived at the destination and stopped, one when he accelerated to start back to Earth and one when he decelerated to rest on arrival. This changed his frame of reference and thus changed which times can be considered as simultaneous in each twin’s frame of reference. So far so good – I have no problem with that.
However, my question involves a situation where only half the journey occurs. I can think of two situations (the first of which I can think of explanations for but the second I’d like some help to understand).
a) The first twin sets off as before. At the same time a signal of light is sent from the Earth to the star 1 light year away where someone is waiting to receive it. Since the Earth and the star are at rest with each other they share a frame of reference and can therefore agree on the simultaneity of the journey start. The twin then arrives at the star. Now, for him both the Earth and the star have been moving relative to him at 0.6c and so their clocks have been running slow at 0.8s. Similarly for both the twin on Earth and the person at the star the second twin has been traveling at 0.6c relative to them and they consider that his clock has been running slow (the person waiting at the star just has to remember to add 1 year on to the journey time to get simultaneity because of the time taken for the light signal to arrive).
Now, when the twin has performed this first half of his journey and compares times with the person at the star they can’t both then agree that each other’s clock is slow. On comparing they will see that it is again the twin’s clock which has been running slow. Now, I can understand that because the twin has still undergone two accelerations whereas the person waiting at the star has not. However – in scenario b) below there is no acceleration:
b) Say twin b is not on Earth but traveling from some earlier point at a constant 0.6c past the Earth. As he passes the Earth twin a who is on the Earth sends the light signal towards the star 1 light year away that twin b is also heading directly towards. When twin b approaches the star he doesn’t decelerate to stop but carries on past at the constant 0.6c. However, as he passes the star he and the person their show each other their clocks as they pass. In this situation there has been no acceleration, and again each party can consider the other moving and therefore to have the slow clock. Who will be correct? My suspicion is that again the twin in the spaceship will have the slower clock on comparison – but why? This time there has been no acceleration to change the frame of reference.
Any thoughts? Many thanks.
I understand the traditional view of the twin paradox (I think!): Two twins a and b are on Earth and each has a clock. The clocks are synchronised and one twin travels at, say, 60% the speed of light to a star exactly one light year away, stops and immediately returns. Due to time contraction, during the journey each twin judges that his brother’s clock is running slow – each only showing 0.8 seconds for each second of his own clock - each of which seems, to the holder, to be running normally. On return to Earth when the clocks are compared it is shown that it is the twin who has traveled away and come back whose clock shows less time than his brother’s.
This is the paradox – if you could equally view each twin as the one “at rest” while his brother travels away and back to him, and so both are correct in considering his brother’s clock to be running slow, then how can one of them be shown to really have the slow clock? The answer is that the twin traveling away from Earth has undergone four accelerations, albeit very quick, one when he set off from Earth, one when he arrived at the destination and stopped, one when he accelerated to start back to Earth and one when he decelerated to rest on arrival. This changed his frame of reference and thus changed which times can be considered as simultaneous in each twin’s frame of reference. So far so good – I have no problem with that.
However, my question involves a situation where only half the journey occurs. I can think of two situations (the first of which I can think of explanations for but the second I’d like some help to understand).
a) The first twin sets off as before. At the same time a signal of light is sent from the Earth to the star 1 light year away where someone is waiting to receive it. Since the Earth and the star are at rest with each other they share a frame of reference and can therefore agree on the simultaneity of the journey start. The twin then arrives at the star. Now, for him both the Earth and the star have been moving relative to him at 0.6c and so their clocks have been running slow at 0.8s. Similarly for both the twin on Earth and the person at the star the second twin has been traveling at 0.6c relative to them and they consider that his clock has been running slow (the person waiting at the star just has to remember to add 1 year on to the journey time to get simultaneity because of the time taken for the light signal to arrive).
Now, when the twin has performed this first half of his journey and compares times with the person at the star they can’t both then agree that each other’s clock is slow. On comparing they will see that it is again the twin’s clock which has been running slow. Now, I can understand that because the twin has still undergone two accelerations whereas the person waiting at the star has not. However – in scenario b) below there is no acceleration:
b) Say twin b is not on Earth but traveling from some earlier point at a constant 0.6c past the Earth. As he passes the Earth twin a who is on the Earth sends the light signal towards the star 1 light year away that twin b is also heading directly towards. When twin b approaches the star he doesn’t decelerate to stop but carries on past at the constant 0.6c. However, as he passes the star he and the person their show each other their clocks as they pass. In this situation there has been no acceleration, and again each party can consider the other moving and therefore to have the slow clock. Who will be correct? My suspicion is that again the twin in the spaceship will have the slower clock on comparison – but why? This time there has been no acceleration to change the frame of reference.
Any thoughts? Many thanks.
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