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By constants, I'm talking about constants like a mass of electron or proton or gravitational constant $G$. If there are some examples, Please put it.

Thanks already.

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    $\begingroup$ When a constant is related by "theory" to other fundamental constants, it stops being "fundamental". Consider the Fermi constant, or , equivalently, the mass of the W boson. $\endgroup$ Oct 22, 2020 at 17:22
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    $\begingroup$ We predict that $G=1$ when we use geometrical units. $\endgroup$
    – G. Smith
    Oct 22, 2020 at 17:26
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    $\begingroup$ You are familiar with how Maxwell's equations postdict $c = 1/{\sqrt{\varepsilon_0\mu_0}}$, no? $\endgroup$ Oct 22, 2020 at 23:06
  • $\begingroup$ @CosmasZachos Yes ,I'm $\endgroup$ Oct 24, 2020 at 19:33
  • $\begingroup$ So, do you characterize this as theoretical correlation of fundamental constants? The SM of the weak interactions (above) did something analogous. $\endgroup$ Oct 24, 2020 at 19:37

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Physics, unlike mathematics, does not derive things from first principles. Instead models are created and then these are developed to the point where they can make predictions that can be measured experimentally. We have a lot of theories that either cannot be verified experimentally because we cannot produce a viable mathematical form that allows us to select one form of a model over others (like String Theory) or which can be developed to the point of making predictions, but those predictions do not match what is seen. We have yet more models that are "good enough" for a certain range of values (like Newtonian mechanics) but break down outside that range.

So physics theories are not really absolute statements of fundamental truth. They are just models of reality used for particular purposes. We look for better theories, more accurate theories, theories that cover a wider range of values.

So how does all that relate to fundamental constants ?

Fundamental constants can be thought of as the values we use to "tune" a particular model/theory to produce it's "best fit" to what we measure in experiments. None of these values are ones that can be derived from the model/theory itself. They are parameters.

The moment a theory derives a value for one of these constants they stop being fundamental.

A question we do not know is whether it is possible or impossible to develop a theory that allows us to move from a purely mathematical model to physical values without any parameters. Or put another way, is our universe one of a vast (or infinite) number of possible universes that could have been created depending on the values of a few random fundamental constants, or are those fundamental constants the only ones possible for some reason. We have no idea (as I write this) which of these is the case.

So even if we developed a theory that seemed to explain everything we see and measure, it would not necessarily be without the need for fundamental constants that "tune" the theory to our observed universe. It might not need any, but it might. We don't know.

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Theories cannot predict constants that have units, because the values of those constants are what they are purely because of our choice of a particular system of units.

Theories can predict unitless universal constants, but when we are able to predict (or retrodict) the value of such a constant, we tend to demote it from fundamental to non-fundamental. For example, we are able to predict fairly well using nuclear physics the ratio of the mass of the alpha particle to the mass of the proton. But the fact that we can do so makes us say, "Ah, that wasn't fundamental, that was derived."

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  • $\begingroup$ What about the speed of light? It has unit. $\endgroup$ Oct 24, 2020 at 19:34
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The Copernicus Constant K and Mass of Electron /*/

Applying the Copernicus Constant K to our expanding Universe we can get many interesting results , the Mach’s principle is embedded in our theory. Two problems of cosmological constant can be resolved naturally. The cosmological constant is determined by kinematics of de Sitter spacetime.

       Λ   =  3*c^2/R^2 = 3*c^2*K^2/lp^2  = 3*Ho*Ho    .  

It is wonderful that a connection between the Holographic Principle and our theory can be made through the Copernicus constant K . By that way we get the N bound number (number of bits, number of degrees of freedom) for our universe as follows .

1/K^2 = 10^124 / 137.03599914
= 7.2973525663 * 10^121 .

The question in the Solvay 23rd conference by prof. Joseph Polchinski has got an answer. Vacuum energy density = 9K^2 /32π * planck density . Exp(283) = 32π/(9K^2) .

It is wonderful that the mass of electron can be calculated as follows . Mass electron = (243/32π)^1/6 αmp*K^1/3 .

Where α is fine structure constant, mp is planck mass. K = Copernicus constant = mpHoG/c^3 . mp = planck mass . Ho = Hubble constant . G = Newton constant . C = light speed .

It means that some properties of elementary particles are related to global structure of observable universe.

Ref. /*/ . Lê sỹ Hội , December 2016, “The Copernicus Constant K and Mass of Electron” https://www.academia.edu/30454308/The_Constant_Copernicus_K_and_Mass_of_Electron

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    $\begingroup$ Please use Mathjax to enter mathematical expressions. It is the site standard. It is very like Latex if you are familiar with that. $\endgroup$ Oct 24, 2020 at 20:18

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