Planck's constant has dimensions of angular momentum, or energy x time, i.e., M.L2.T-1 and the velocity of light has dimensions L.T-1 so their ratio can't be dimensionless.

Stam Nicolis

I believe that If someone arrives to write the equation of the Planck constant h he will find that it is dimensionless he will also find that it is in link with new cosmological constants and new cosmological parameeters. For me the dimensions of the Planck unities block people to perform a big progress in the researches using the Planck unities. Best regards.

What anyone believes doesn't matter-what matters is logic. The Planck constant, whatever its definition, has dimensions M.L2.T-1. These aren't the matter of convention that units are. The fact that the exponents aren't all zero means that Planck's constant isn't dimensionless. Its numerical value is a matter of convention.

Similarly, the fact that the speed of light is a speed, means that its dimensions are L.T-1. The fact that the exponents aren't all zero, means that it isn't dimensionless. Its numerical value is, similarly, a matter of convention. It's then a trivial exercise to show that no ratio of any power of Planck's constant to any power of the speed of light can be dimensionless.

The cosmological constant-just like Newton's constant-is another dimensionful quantity. It doesn't have greater significance for general relativity than Newton's constant. And neither is related to Planck's constant, because general relativity is a classical description.

The constants h and c might be indications of the "stiffness of space" from the viewpoints of quantum and relativity theories respectively. For instance, if space was "stiffer" gravitational waves would move faster and c would have a higher value. https://www.linkedin.com/pulse/plancks-constant-h-light-speed-c-two-sides-same-coin-warren-frisina/?trackingId=rl9A4x6WRGimf8VuMGzgNg%3D%3D . (2) How the speed of light might depend on Planck's constant (An explanation of causality) | LinkedIn

“…For me, this ratio [seems ћ/c] can be used in calculations which relate to the cosmological scale and in calculations concerning the quantum world. I'm based on the fact that I consider Planck's units derive from an ultimate theory of physics? In the same subject another question on my pages on RG "Why the Planck mass is involved in theories of the cosmological world and in theories of the quantum world?"…..”

- really the main Planck units, i.e. Planck length, lP, Planck time, tP, and the fundamental elementary physical action/angular momentum, ћ, as that is rigorously scientifically grounded in the in the Shevchenko-Tokarevsky’s informational physical model

https://www.researchgate.net/publication/354418793_The_Informational_Conception_and_the_Base_of_Physics,

- are parameters of the ultimate base of Matter – primary elementary logical structures – (at least) [4+4+1]4D binary reversible fundamental logical elements [FLE], which compose the (at least) [4+4+1]4D dense lattice, which is placed in the corresponding Matter’s fundamentally absolute, fundamentally flat, and fundamentally “Cartesian”, (at least) [4+4+1]4D spacetime with metrics (at least) (cτ,X,Y,Z, g,w,e,s,ct):

- lP is the FLE’s “size” in every space dimension above,

-tP is time interval at a change of FLE state – “binary flip” in every space dimension above,

- ћ is the angular momentum/ physical action that at least some “FLE flipping point” that cyclically moves along some 4D “helix” in the 4D space with metrics (cτ,X,Y,Z) – what is every particle – has so relating to the “axis of the helix”, when a particle that is at rest in the 3D space, and so moves along the helix in cτ-axis direction with the speed of light c=lP/tP having momentum P=m0c, while the radius of the helix is equal to the particle’s Compton length, λ=ћ/m0c.

So these ultimately fundamental 3 units fundamentally compose complete system at description and analysis of what exists and happens in Matter: 4D “space”, “time” [ct-dimension, though in mainstream physics and everyday practice time is cτ-dimension], inertia – i.e. “mass”, and so momentum and energy E=Pc,

- and so that relates to everything in Matter, while any/every material object/event/interaction can be characterized only by MLT units. Utmost natural so system of units is CGS system.

Newton gravitational constant G is a coefficient that links two fundamentally different parameters of particles [bodies, etc.] – the “inertial mass” and the charge of the fundamental Nature Gravity forces “gravitational mass”, and it exists because of at least at statics these masses are equivalent. That is, though fundamental, but rather specific constant, and, though in this case do is possible to construct corresponding “Planck unit” - “Planck mass”,

mP= (ћlP/tPG)1/2, however, again, that relates only to one of seems four fundamental Nature forces.

All that has no any relation to the cosmological Lambda constant, which is fundamentally nothing else than some purely artificial ad hoc parameter in the GR equations, which is purely ad hoc is introduced in cosmology.

More see the link above [and other the SS&VT model basic paper https://www.researchgate.net/publication/355361749_The_informational_physical_model_and_fundamental_problems_in_physics, though]

- and how, besides Gravity and the G constant, the other Forces’ constants describe the Forces strengths see

Shevchenko-Tokarevsky’s 2007 initial model of Gravity and Electric Forces in

https://www.researchgate.net/publication/366536729_The_informational_model_-Gravity_and_Electric_Forces_Version_2

- and of 2023 initial Nuclear Force model in

https://www.researchgate.net/publication/369357747_The_informational_model_-Nuclear_Force

Cheers

Stam Nicolis

Warren Frisina

Sergey Shevchenko

Many thanks for all your explanations and documentation.

Rana Hamza Shakil

Thank you for the explanations. Well, in new physics, the ratio of reduced Planck's constant to the speed of light will be used for calculation both in the quantum world and on the cosmological scale. This ratio will be very important in calculations in physics. Moreover for me there must be a way to calculate it theoretically via "new" constants and cosmological parameters without going through experimentation. Already the author "Espen Gaarder Haug" offers to use it. He describes the use of this ratio in his article "Simplifying Charge and Coulomb Force Without Affecting Predictions". Reference:

HAL ID: hal-03752631

https://hal.science/hal-03752631

Preprint submitted August 17, 2022.

Personally I find that this report is already used, without literally pointing it out. For me, its use is in some steps of the energy calculations in the 2010 muonic hydrogen experiments. To me, there must be many examples of its use.