Transcendental numbers such as pi and e appear very naturally in physical phenomena. This leads me to think that there is no special reason to think that fundamental constants should be rational. But, due to the number theoretical point that I made in your previous post, since any fundamental constant can only be known to a certain accuracy, surely there would be no way of testing such a statement?

Peter Breuer,

I mean if I allocate (not just anyhow but according to a unifying theory of physical constants of the quantum world and cosmology using quotients of two prime numbers) to the physical constants numerical values ​​in the form of quotients of prime numbers, for example 19 and 17, then the values ​​of these constants would be absolute and theoretical instead of experimental. But this work can only be done from experimental values. In other words, the irreducible ratios of two prime numbers will be for the FINE-TUNING of the physical constants of the two worlds. We can simply give the absolute value of the hydrogen atom only as a function, for example, of a fraction of a quotient of two prime numbers. The goal here is to search for an infinity of decimals, all EXACT. ALL MY PREPRINTS ON RG ARE MADE ON THIS BASIS.

BUT IN THIS CASE YOU HAVE NOT TO WORK WITH Pi BUT WITH ABSOLUTE LAMBDA BECAUSE AN ABSOLUTE LAMBDA IS A FUNCTION OF A QUOTIENT OF TWO PRIME NUMBERS?

Peter Breuer,

In mathematics, two twin primes are two prime numbers that differ by only 2. I work for example with : 19 and 17. etc.

For example my preprint* is made using quotients of twin prime numbers notably 19 and 17. One has only one way to obtain an absolute LAMBDA it is using prime numbers.

When one works with prime numbers one has all the time constants in close agreement with CODATA but the constant of CODATA can only have some exact decimals which are exactly the same when one works with prime numbers BUT prime numbers give ABSOLUTE constants with infinitely exact decimals.

One can have an absolute value of the speed of light simply using prime numbers.

One can absolutely link G, h, and c using the prime number 19.

All the physical constants are all in some way linked to the prime number 19.

All this will be detailed and explained in my future book of ABSOLUTE physics.

*Preprint; Absolute Frequencies of Strontium Atomic Clocks from Theoretical Dimensionless Ratios of Strontium frequencies to Quartz Frequency

When working with quotients of prime numbers in physics, one must eliminate Pi from the equations of physical constants and replace it in one way or another with an absolute LAMBDA. Absolute physics is not done via Pi. But to do absolute physics one must start from very precise constants that come from laboratory measurements, in other words from experiments. Absolute physics must confirm what comes out of the laboratory.

Peter Breuer,

I guarantee that there is nothing strange. In fact, it is enough to connect all the physical constants of the quantum world and cosmology via mainly four prime numbers including 17 and 19. Using prime numbers, especially twins, it is enough to create certain quotients and then it is necessary to fix the constants and physical parameters, for example LAMBDA or h on h reduced or the radius of the hydrogen atom to simple irreducible numerical quotients formed of two prime numbers, one in the numerator and the other in the denominator. What is extremely interesting is then when we make the right choice of the prime numbers that we are going to use, because we need an ultimate theory for that, we obtain, as I did for all the physical constants, values of the constants that agree at least with a few decimals of the constants provided by CODATA and by extremely serious work such as the Planck results of 2018 or even the results of muonic measurements on hydrogen, deuterium, and helium WITH an additional guarantee is that the new results that we obtain are absolute, that is to say they have an infinity of exact decimals. BUT THIS IS A REVISION OF CURRENT PHYSICS. To come to say that absolute physics is current physics whose constants are revised and refined until they become absolute and theoretical. BUT to achieve this we must add something else such as for example bringing some novelties to current physics such as for example as I have already done is to describe a new equation of the Lorentz factor which will be dedicated to cosmology and from there create a new constant for cosmology which will be the MOST IMPORTANT CONSTANT IN COSMOLOGY before LAMBDA and OMEGA. Then again we must find how to create a trick to attack quantum gravity via a constant that I call the rest mass of the Planck particle. AND THEN AGAIN WE MUST FIND AN EQUATION EQUIVALENT to the equation E=mcc via the mass of the quantum black hole that I call for example M depending totally on m. THEN we must eliminate Pi from the equations of physical constants and replace it with another ratio which depends on LAMBDA. Then we need to find another equation for the radius of the atom H and then another equation for the Rydberg constant, all of which must be related to LAMBDA and OMEGA. Then we need to find the value of the speed of the expansion of the universe that corresponds to H0. Etc. All of this will appear in my next book in detail. SOME OF MY PREPRINTS PRESENT ABSOLUTE VALUES FOR THE CONSTANTS BY FOLLOWING THIS TECHNIQUE.

Peter Breuer,

We can connect the constants h, G, and c via some prime numbers and prime number ratios. The ratio 2/3 also appears in the link model. In absolute physics, everything must converge towards unity. We must therefore connect the Planck units to each other via unity, that is, the number 1. And connect these Planck units with the cosmological parameters, notably LAMBDA, via another absolute value that is not unity but is very closely linked to LAMBDA. This would connect the infinitely small and the infinitely small.