When it comes to deriving the various physical constants of nature, Planck units are indispensable. The speed of light, for example, is simply the ratio between the Planck units of length and time. In all, five units are defined; mass (\(Pm\)), length (\(Pl\)), time (\(Pt\)), temperature (\(Pk\)), and charge (\(Pc\)).

Question is, are they all

\(Pq = PmPl\)

In other words, the dimension of charge is simply the kilogram-meter! And by substituting that derivation into various physical equations we find a plethora of relationships revealed that would not be otherwise evident. For example, using dimensional analysis I was able to determine that the dimensions of resistance, current, and voltage are essentially just velocity, momentum, and energy.

Okay, so let's first see how it relates to the current definition in use, \(Pc\).

\(Pc = \sqrt{(Pq \times 10^7)}\)

What's with the odd constant term, you ask? Basically, it boils down to the fact that the coulomb was defined in terms of the force induced between two wires separated by a distance of one meter. That force is \(2 \times 10^{-7}\) newtons per meter. Half of that value obviously gives you the force upon each wire and the inverse of

On to the matter of a proof. Well unfortunately I have none! However, from a heuristic standpoint just consider the following observations. The SI unit of charge is of course the coulomb which is in turn defined in terms of Coulombs constant, \(Ke\). The value of \(Ke\) is

It should kept in mind that all of the above apply specifically to the realm of point-like physics. Extrapolation to higher domains will likely lead to even more interesting results. Still a very useful relation though. For example, using this revised formulation for the quanta of charge I've come to the conclusion that a generalized equation for

Question is, are they all

**truly**fundamental? Well \(Pk\) clearly isn't. It's value can be understood as a complex function of energy, Gaussian distributions, the degrees of freedom available to physical systems, etc. So strike that from the list. But what about \(Pc\)? Here's my theory: it is also a composite value (and somewhat ad-hoc in it's present form at that). It's true formulation, I believe, (which I'll denote as \(Pq\)) should have been\(Pq = PmPl\)

In other words, the dimension of charge is simply the kilogram-meter! And by substituting that derivation into various physical equations we find a plethora of relationships revealed that would not be otherwise evident. For example, using dimensional analysis I was able to determine that the dimensions of resistance, current, and voltage are essentially just velocity, momentum, and energy.

Okay, so let's first see how it relates to the current definition in use, \(Pc\).

\(Pc = \sqrt{(Pq \times 10^7)}\)

What's with the odd constant term, you ask? Basically, it boils down to the fact that the coulomb was defined in terms of the force induced between two wires separated by a distance of one meter. That force is \(2 \times 10^{-7}\) newtons per meter. Half of that value obviously gives you the force upon each wire and the inverse of

*that*is precisely the term which appears in the above expression. Insofar as why taking the root of the right hand term is necessary, observe that quantities of charge in physics equations are typically squared (that is to say if we had used \(Pq\) in the first place, no square term needed).On to the matter of a proof. Well unfortunately I have none! However, from a heuristic standpoint just consider the following observations. The SI unit of charge is of course the coulomb which is in turn defined in terms of Coulombs constant, \(Ke\). The value of \(Ke\) is

**precisely**equal to \(c^2 \times 10^{-7} H m^{-1}\) (where \(c\) is the speed of light, \(H\) is Henries, and \(m\) is meters). Since the Henry is dimensionally orthogonal to the other electrical units it thus follows that the speed of light is ostensibly the only term which is not. And indeed by substituting \(Pq\) in the expression for \(Ke = PmPl^3Pc^{-2}Pt^{-2}\) we obtain the remarkable result that \(Ke = Pl^2Pt^{-2} = c^2\)!It should kept in mind that all of the above apply specifically to the realm of point-like physics. Extrapolation to higher domains will likely lead to even more interesting results. Still a very useful relation though. For example, using this revised formulation for the quanta of charge I've come to the conclusion that a generalized equation for

*all of the natural forces*may be quite possible. More on that later though...
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