The Twins Paradox
This is the second most common example of the Time Travel Paradox.
The Twins Paradox is example where there appears to be a situation when two clocks are both ahead and behind each other at the same time.
Imagine a pair of twins who we will call George and Georgina. Each has a clock which are synchronised at the start of the experiment. They then move away from each other.
Einstein tells us that time is relative and that time of a moving object is slower relative to a stationary object.
So as far as George is concerned Georgina is moving and he sees her clock running slow. Therefore George's clock is ahead of Georgina's. However as far as Georgina is concerned George is moving and she sees his clock running slow. So Georgina's clock is ahead of George's. A clock cannot be both ahead and behind another. There must be a paradox.
If we imagine that the twins walk away from each other and take a circular route returning to meet again after an hour we must then ask will one be older than the other?
Well in actual fact they will both still be the same age. This is because the perspectives of George and Georgina are symmetric. They both move with uniform motion.
There is a further example however which appears to produce a paradox. This is where one twin flies off for a return trip in a rocket ship while the other remains behind on Earth.
So lets say George sets off with his clock in a rocket and travels as close as possible to the speed of light leaving Georgina with her clock behind on the Earth. As far as Georgina is concerned she sees George's clock running slow. Again this would put Georgina's clock ahead of George's. However as far as George is concerned he sees the Earth moving so he sees Georgina's clock moving slow. This puts George's clock ahead of Georgina's.
When they return to Earth it would appear that both twins are older and younger than each other which is clearly impossible! Hence a paradox.
In fact like before there is no paradox. George will have aged slower and will therefore be younger than Georgina. This is because this time the two perspectives are not symmetric. George uses a rocket that accelerates away from Earth, cruises, breaks, turns around, accelerates, cruises, breaks and lands back on Earth. Georgina remains stationary on Earth. So there is no paradox. It is simply an example of Einstein's theory of relativity. The same two events are experienced by two different observers experiencing two different intervals of time.
The following diagram shows a trip made by George which by his clock appears to take five years but which from Georgina's clock appears to take ten years. Both will experience each year as taking the same length of time which is shown by the same area of green to represent each year.
A practical example of this is a return trip made in an aeroplane from for example London to Tokyo. Because the aeroplane is moving the passengers must age slower than those people left behind on the ground at the airport. Even though the speed is only a fraction of the speed of light and the trip relatively short there still must be a difference between a clock in the aeroplane and a clock at the airport. With the passengers ageing slower than those people at the airport a clock in the aeroplane should be slower than a clock at the airport. In fact the clock in the aeroplane is faster. Although it has run slower due to the speed of the aeroplane this is compensated by a greater effect due to the weaker gravity of the aeroplane flying at altitude. Remember Einstein in his Theories of Relativity shows that gravity also effects time as much as speed. The weaker gravity at the altitude makes the aeroplane clock faster. For those interested in figures the difference is about 60 billionths of a second!
This effect was clearly shown by Dr Neil Johnson at The Royal Institution Children's Christmas Lectures 1999 with his lectures Arrows of Time. An excellent series of five hour long lectures backed up with an informative web site. The lectures covered time, Newton, Einstein, light, quantum and chaos theories and concluded with Time Travel.
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