Crossing the brachistochrone- Anthropic coincidences

We have already mentioned the numerical coincidence between Planck constant h and the graviton mass m_g,

or between the gravitational constant G and the (inverse of) the universe’s linear density ρ_U,

Such coincidences can be explored by using the energy equation of the brachistochrone,

so that, for example, if the value of the graviton’s wavelength λ_g coincides with 1ly, then

Another intriguing aspect, which we have also seen, is that by replacing the length L_Β of the brachistochrone with the radius R_U of the universe, and the mass M_Β of the brachistochrone with the mass M_U of the universe, then the wavelength λ of the reference photon will be equal to Planck length l_P,

where,

Inversely, equating in the energy equation of the brachistochrone the wavelength λ of the reference photon to Planck length l_P, we take

If the previous ratio gives us the speed of light (squared),

then the following product gives us the acceleration which we have called ℊ,

This acceleration, which is equal to 1ly/y², can be identified with the acceleration of gravity g_E on the Earth’s surface,

This way, in order to express the coincidences between the values of fundamental quantities, we can write down the following general identity,

where

Incidentally, the term ‘anthropic’ in the title refers to the anthropic principle. This is a definition of the principle:

“The cosmological principle that theories of the universe are constrained by the necessity to allow human existence.”
[https://www.google.gr/search?q=anthropic+principle+definition]

A consequence of this definition is not only that we can understand the universe, but also why we understand. Thus, apart from the apparent identity between numerical values, it is the ultimate relationship between physical phenomena and consciousness. But before we enter the field of consciousness in the universe, we will explore another coincidence, in the form of a principle which I call synchronicity.