This video on Quantum Physics gives us a logical and scientific reason for irrational numbers.
Quantum Atom Theory is based on pre-established mathematics and can explain not just the paradoxes of quantum physics but also many of the other weird paradoxes of life.
Based on the simple idea that Heisenberg Uncertainty Principle is the same probability that the observer will have with any future event it can give us a reason why everything is always in permanent flux always changing. Why we have a future and past and also why light is a universal constant independent of the motion of the light source and independent of the observer of the light.
But there is one other strange paradox that Quantum Atom Theory can explain and that is irrational numbers like:
Pi 3.1415926535897932384626433832795028841971693993751058209749445923078164 062862089986280348253421170679……………… into infinity
In this theory Heisenberg Uncertainty Principle is formed by a quantum wave particle function that expands as an inverse light sphere of electromagnetic radiation
This is why we have pi in the equation for the quantum wave particle function representing the shape of the wave function in three dimensional spacetime. We also have pi in the equation for Heisenberg Uncertainty Principle. This is why pi is an irrational number and keeps on going forever just like time. Never forming a regular pattern with all the properties of a random number (probability) except that each of its digits are the same. There is always the same amount of even and odd numbers in the continuous sequence of pi. Just as if you continuously tossed a coin you would create a sequence of numbers with the same amount of odd and even numbers (heads and tails).
Light is always radiating out from its radius a square of probability This is the same square of probability you will have with any future event if you toss-up a coin you will mathematically create a square of probability. Because all objects even people radiate light or EMR continuously we are also creating our own future probability relative to our position and momentum just like the coin.
This is also the same square of probability that we have in quantum electrodynamics (QED).
It is easy to see that the infinite sequence of whole numbers can represent the infinity of three dimensional space because the numbers can be used to represent three dimensional shapes and because they go on into infinity. But the probability of the expanding curvature of spacetime can only be represented by the infinite irrational numbers sequence.
Therefore in Quantum Atom Theory it is the irrational numbers that drop out of the whole number sequence that represents the never-ending expansion of time. It is not just because they are infinite. It is their position within the whole number system that points towards their link with the forward momentum of time and the geometry of spacetime.
Link to Quantum Atom Theory on You Tube