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. One of 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 of 50 metres. 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.
On the one hand, Zeno’s paradox can be viewed as a maths problem, one in which the standard resolution is to say that whilst the runner would have to complete an infite number of ‘tasks’ in a finite amount of time to finish the race, in mathematics the sum of infinite, decreasing, quantities can have a finite result. Therefore, Zenox’s runner will be able to complete the race in a measurable amount of time .
However, Zeno’s paradoxes still challenge our understanding of space and time, and raises the question of whether time and space are continuous or discrete? In other words, can space and time be infinitely divided or is there some smallest interval of space/time that can’t be chopped into smaller chunks?
There’s a few solutions to this question, but my personal favorite is provided by Quantum Theory, which introduces the notion of the Planck Length, the smallest measureable length beyond which time and space cannot be divided. In the subatomic world, quantum physics states that if two particles were separated by the Planck length, or less, then it becomes impossible to tell their positions apart. Since you can never travel half a Planck length, there cannot be an infinite number of steps between any two points.
Planck Time And The Big Bang
The ideas of Planck length and Planck time impose a limit on the measurement of time and space, and maybe a limit on time and space, themselves. Its almost like saying that if the the universe was a simulation, a Planck length would represent the size of a single pixel.
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, as Quantum Physics tells us, neither time nor space, those two inseperable dimensions of being, can be divided beyond a certain point.
Planck Length, String Theory And Black Holes
The Planck length is a crucial component in Jacob Bekenstein and Stephen Hawking‘s equation to calculate the entropy of a black hole. In String Theory, theorists also believe that the Planck length is the size of the vibrating ‘strings’ that form all elementary particles. Whether or not string theory is actually true, one thing for certain is that understanding the Planck length will be an important element in physicists’ search for an ultimate ‘Theory of Everything’ (TOE).