The Twin Paradox(again)
Recently I have been thinking about the twin paradox. For those of you who haven’t heard about it I got this from Wiki.
"In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. In fact, the result is not a paradox in the true sense, since it can be resolved within the standard framework of special relativity. The effect has been verified experimentally using measurements of precise clocks flown in airplanes and satellites.
Starting with Paul Langevin in 1911, there have been numerous explanations of this paradox, many based upon there being no contradiction because there is no symmetry—only one twin has undergone acceleration and deceleration, thus differentiating the two cases."
When I first learned about special relativity I considered the twin paradox. I couldn’t figure it out so I asked my teacher. My teacher told me that the paradox results from not taking General Relativity into account. One of the twins undergoes acceleration and to understand the effect of that acceleration requires General Relativity. I don’t understand General Relativity. The math is too complex for me. Still after talking to my teacher I felt satisfied that there was an answer, and that other people understood it. I didn’t think about it again for many years until this thread came up. Then I asked myself ‘why can’t they both accelerate’. This is a thought experiment you can do anything you want.
This is the revised twin paradox I can up with.
There are two identical spacecrafts, and two identical twins. The space crafts are controlled by computers which are both programmed the same way. The spacecraft will accelerate for a period of time. They will then do nothing for a period of time. They will then accelerate for a period of time. Then coast again. Then accelerate again until they both come back together into the same frame of reference. In this thought experiment you have perfect symmetry.
When observing each other I assume the Bob and Fred will see exactly the same thing. I assume this because there is perfect symmetry and so I can think up with no logical reason why they would see things any differently. Therefore I assume X=X’, and I will simple call this value X from now on. X can be any length, and according to special relativity the longer X is the more pronounced the effects of time dilation will be. In other words in this thought experiment the effects of time dilation can vary while the acceleration taking place stays the same. This leads me to wonder how the paradox can be solved with general relativity alone. I thought about this for a while, and came to the conclusion that the distance the two objects are away from each other must effect how they view each other. Based on this conclusion I came up with three possible solutions.
1) Time seems to go faster for things that are farther way. In the end I rejected this possibility because the two twins could stop their motion relative to each other and stay that way for any length of time. This creates a problem similar to the problem with X that I am trying to solve.
2) The General Relativity effects of acceleration are observed differently for things that are farther away. In this is the case the large X is the more pronounced the temporal effects the two twins will observe while the other ship is accelerating back towards them.
3) There is another force that pushes everything away from the observer based off of how far away it is. If this is the case it would be impossible to apply special relativity when large distances are involved. This one is the most bizarre because if it is true then every frame of reference will observe everything else accelerating away from it with the amount of acceleration increasing for things that are farther away.
I’ve reached the point were thinking about this on my own isn’t getting me anywhere. So I decided to post this here and see what other people think.