It's important to note that physical constants, including those related to Pi, are only approximations and are subject to revision as more precise measurements and better theories become available. However, it's unlikely that Pi itself would prevent the unification of physical constants in a single theory of physics.
Pi appears in many physical constants, such as the circumference of a circle, but it is merely a mathematical representation of the relationship between a circle's diameter and its circumference. The physical constants related to Pi are often derived from other, more fundamental physical constants and laws.
In physics, the search for a unified theory that explains all the phenomena in the universe is ongoing. This search is motivated by the idea that there is a deep underlying simplicity to the physical world, and that all the different physical constants and laws can be derived from a single, fundamental set of principles.
It's important to keep in mind that the search for a unified theory of physics is an ongoing process, and that new discoveries and advances in our understanding of the universe may lead to the revision or even replacement of current physical constants and laws. However, Pi itself is unlikely to be a barrier to this process, as it is simply a mathematical representation of a physical relationship.
dear Salem Saleh, I invite you to read my answers to my technical questions and my answers to other technical questions asked by colleagues on RG you will find almost all the answers relate to this subject about constant Pi. In addition concerning my two articles mentioned on RG you will soon be able to consult their complete texts. These articles provide an absolute equation for the hydrogen radius which is not in link with constant Pi it emerges from a new theory I developped for hydrogen based in "new constants" which are the "muonic constants" beyond the standard model of particle physics. This theory relate not constants of hydrogen to Pi. I want to say that the constants of a unified physics do not need to be relate to Pi. People used Pi in the past because they have not another alternatives that time. I believe that in a physics as in mathematic Pi should only be a constants belonging to the geomety of a circle.
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