The Planck charge is not a fundamental constant!

Thread Starter

xox

Joined Sep 8, 2017
382
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 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... :)
 
Last edited:

Glenn Holland

Joined Dec 26, 2014
686
My humble opinion is that the charge on an electron should be the standard unit instead of the Coulomb.

The unit of charge would then be 1.000 (one) "electron unit" (EU) and larger charges would be simple multiple of the EU. In fact, Miliken found that the charge on a large group of electrons was a multiple of the fundamental charge measured in the oil drop experiment.

However, experiments with electricity (and defining the unit of charge as the Coulomb) were performed before the electron was formally discovered.
 

Thread Starter

xox

Joined Sep 8, 2017
382
My humble opinion is that the charge on an electron should be the standard unit instead of the Coulomb.

The unit of charge would then be 1.000 (one) "electron unit" (EU) and larger charges would be simple multiple of the EU. In fact, Miliken found that the charge on a large group of electrons was a multiple of the fundamental charge measured in the oil drop experiment.

However, experiments with electricity (and defining the unit of charge as the Coulomb) were performed before the electron was formally discovered.
I agree, much cleaner.

That still wouldn't effect the Planck charge, of course; Planck units are essentially system-agnostic (you can express \(Pl\) for example in terms of meters, feet, rods, cubits, or whatever).

That said, there is one peculiar anomaly concerning the Planck charge that makes me wonder. A lot of physics equations dealing with charges rely on this magic number of sorts, the dimensionless fine structure constant (\(\alpha\)). Perhaps \(\alpha\) is in reality just a component of the true value of the Planck charge? Lo and behold, if you divide the square of the electron charge (again, charges are almost always squared to begin with) by the proposed redefinition \(Pq\), you simply get back \(\alpha\)! Pretty cool eh?

So let's just pretend for a moment that the actual Planck charge (call it \(Pa\)) is in fact equal to the charge of an electron squared (that is to say \(Pa = \alpha \times Pq\). The implication there would be that the other fundamental Planck units would necessarily have to be wrong (which would almost be a relief, considering that the Planck mass for one thing is even more massive than the elements found on the periodic table!). o_O
 
Last edited:

nsaspook

Joined Aug 27, 2009
6,610
My humble opinion is that the charge on an electron should be the standard unit instead of the Coulomb.

The unit of charge would then be 1.000 (one) "electron unit" (EU) and larger charges would be simple multiple of the EU. In fact, Miliken found that the charge on a large group of electrons was a multiple of the fundamental charge measured in the oil drop experiment.

However, experiments with electricity (and defining the unit of charge as the Coulomb) were performed before the electron was formally discovered.
That's being fixed.
https://www.nist.gov/news-events/news/2016/08/counting-down-new-ampere
In 2018, however, the ampere is slated to be re-defined in terms of a fundamental invariant of nature: the elementary electrical charge (e).*** Direct ampere metrology will thus become a matter of counting the transit of individual electrons over time.
https://forum.allaboutcircuits.com/threads/what-exactly-is-an-amp.124970/page-2#post-1009673
 
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