We think that the constants h and reduced h could have equations. Once discovered, the ratio (E/f)=h could be determined theoretically. And the effect on physics is a big change will be that set of constants can be calculated without going through laboratories!
According to our new theory for an ultimate physics the constants are determined theoretically without passing by labs. According to us it should exist a value which is about equal to Pi but it should be fonction of new cosmological parameters. We mean by ultimate physics the one which should be construct on exact constants which should be perform using cosmological paprameters and Pi is a constant of a circle not more. And the exact value of the ratio of h to the reduced Planck constant should slightly be inferior at Pi! But in these new conditions the formula of the Bohr radius should be replaced by one other more adequate. Means all the formulas of the constants of physics should be revised. The majority of them continue to exist but using the new value which should replace Pi. A few should be replaced as the formula of the Bohr radius. And the formula of the Rydberg constant should be replaced by another which should be in close link with the classical electron radius. New constants of physics should be developped to help to link all the constants of physics. But all this is a simple continuation of the existing physics.
The anthropic principle tells us that h did not change during at least the last 6 billion years.
A modification of h would modify the biochemical properties of molecules. This would disturb the molecular logistic of metabolic processes, which have been developed since billions of years. With a permanently modified Planck constant we would still be archaic life forms far from developing life capable cells.
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