The Twins Paradox

The Twins Paradox iin special relativity poses a situation where two clocks are both ahead and behind each other at the same time.

Imagine a pair of twins who we will call Adam and Zak. Each has a clock which are synchronised at timeThey 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 Adam is concerned Zak is moving and he sees her clock running slow, so his clock is ahead of Zak's. However as far as Zak is concerned Adam is moving and he sees Adam's clock running slow. So Zak's clock is ahead of Adam'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 Adam and Zak are symmetric. They both move with uniform motion.

There is a further example however which appears to produce a paradox. This is where one of them flies off for a return trip in a rocket ship while the other remains behind on Earth.

So lets say Zak sets off with his clock in a rocket and travels as close as possible to the speed of light leaving Adam with his clock behind on the Earth. As far as Adam is concerned he sees Zak's clock running slow. Again this would put Adam's clock ahead of Zak's. However as far as Zak is concerned he sees the Earth moving so he sees Adam's clock moving slow. This puts Zak's clock ahead of Adam'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. Zak will have aged slower and will therefore be younger than Adam. This is because this time the two perspectives are not symmetric. Zak uses a rocket that accelerates away from Earth, cruises, breaks, turns around, accelerates, cruises, breaks and lands back on Earth. Adam remains stationary on Earth. The symmetry is broken by Zak's acceleration.

Time dilation has real practical effects. |Short lived subatomic particles moving at speeds close to the speed of light appear to live longer than if they were stationary. This is a consequence of the time dilation predicted by special relativity.

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