Zeno’s Quantum Paradox

(ORDO NEWS) — Zeno of Elea (circa 490 BC – circa 430 BC) was an ancient Greek philosopher famous for his formulations of unusual paradoxes that challenged mathematicians’ views of the world for many centuries.

One of Zeno’s paradoxes goes something like this:

Let’s say you’re running a 100m race. To overcome the distance, you need to pass the middle point of 50 meters. To pass the remaining 50 meters, you need to pass the midpoint of 25 meters.

To complete the remaining 25 meters, you have to pass the middle point of 12.5 meters and so on, the distance will get shorter and shorter, and since the space can be divided indefinitely, you will never reach the finish line.

Zeno’s paradox

On the one hand, Zeno’s paradox can be viewed as a simple mathematical problem, the solution of which is that although a runner must perform an infinite number of actions in a finite time to finish the race, in mathematics, the sum of infinitely decreasing quantities can have a final result. In this way, Zeno’s runner will be able to complete the race in a measurable amount of time.

However, Zeno’s paradoxes still challenge our understanding of spacetime and raise the question of whether time and space are continuous or discrete? In other words, is it possible to divide space and time indefinitely, or is there some smallest interval of space-time that cannot be broken down into smaller components?

There are several solutions to this paradox, but the simplest answer comes from quantum theory, which introduces the concept of the Planck length, the smallest measurable length beyond which time and space cannot be separated.

According to quantum physics, if the distance between two subatomic particles corresponds to the Planck length (or less), then it becomes impossible to distinguish the position of these particles in space-time. Since you can never walk only half the Planck length, there cannot be an infinite number of steps between two points in space.

Zenos Quantum Paradox 2

Planck time and the Big Bang

Quantum mechanics is a mathematical theory that describes the behavior of subatomic particles. In quantum physics, the Planck length, named after the German physicist Max Planck (April 23, 1858 – October 4, 1947), is 1.6 10^−35 meters (ten to the minus thirty-fifth power), and the Planck time, the smallest measurable the time interval (the time during which the particle, moving at the speed of light, overcomes the Planck length) is approximately 5.391·10^−44 (ten to the minus forty-fourth degree) seconds.

The ideas of Planck length and Planck time impose a limitation on the measurement of time and space, and perhaps they themselves limit time and space. It’s funny, but if the universe were a simulation , then the Planck length would correspond to the size of one pixel.

Within the framework of the laws of modern physics, we can only say that our universe arose during the Big Bang, at a time when its age was approximately 5.391·10^−44 seconds. This suggests that Zeno’s paradox is not a paradox at all, since, according to quantum physics, neither time nor space can be “split” less than a certain length (Planck’s).

Planck length, string theory and black holes

The Planck length is a key component of Stephen Hawking and Jacob Bekenstein’s equation for calculating the entropy of a black hole . In string theory, physicists also believe that the Planck length is the size of the vibrating “strings” that make up all elementary particles.

Whether or not string theory is actually correct, one thing is for sure: understanding the Planck length will be an important if not key element in the quest for the ultimate “theory of everything.”


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