Zeno of Elea was a Greek philosopher who was born around 490Bc and was famous for posing paradoxes which challenged mathematicians' view of the real world for many centuries.
Zeno's Paradox goes something like this:
'If you run a 100 metre race, in order to complete the distance you will have to pass a mid way point 50metres. In order to complete the last 50 metres you will have to pass a mid point of 25 metres. In order to complete the last 25 metres you must pass a mid point of 12.5 metres and so on with the distance getting smaller and smaller and since space is infinitely divisible you can never finish the race.
Zeno's paradox remained unsolved for over 2000 years and it can now be understood through Quantum Mechanics, a mathematical theory that can describe the behavior of objects that are roughly 10,000,000,000 times smaller than a human being.
As a result we must change assumptions and state that in the real world, unlike in the mathematical world, space cannot be divided into an infinite number of steps. Instead, we now acknowledge in Quantum Mechanics a Planck length otherwise known as a Zeno minimum, which is the smallest distance one can travel.
The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning and is roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton.
There also exists Planck Time which is the time it would take a photon travelling at the speed of light to cross a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning.
Within the framework of the laws of physics as we understand them today, we can say only that at the Big Bang the universe came into existence when it already had an age of 10-43 seconds.
This is not a paradox because Zeno taught us that neither time nor space, those two inseperable dimensions of being, can be divided beyond a certain point.
Monday, 7 January 2008
Where Zeno's Paradox meets Quantum Physics
Posted by
Moriarte
at
07:19
Labels: Science and Technology
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