Excerpts from the "Maxwell, Metavariables, Radiels, etc" Thread

This was originally a series of posts from DozensOnline, in a thread titled “Maxwell, Metavariables, Radiels, etc.”.

Post #114 on Jan 8, 2017:

There are a number of innovations I'd like to introduce into the nomenclature surrounding electromagnetism and Maxwell's equations, as well as “force fields” in general, that would be reflected in the quantitels used to name their units:

(1) “ELECTRICITY” and “ELECTRELS”. I think we should favor the term quantity of electricity () over “electric charge”, on the grounds that we now know of several quantum properties that are all some sort of “charge”, so this term would not be unique to electric charge. (Even “mass” is seen as a kind of “charge”.) The important thing about electric charge is that it is the fundamental property that underlies all the phenomena of electricity. So instead of calling the unit of this a “chargel”, I want to switch to calling it an electrel (εtℓ). (If anyone wants to continue with the “charge” nomenclature, then electrochargel could remain as a synonym, but electrel is more succinct.) The electrel for SI is the coulomb (C). The electrel in TGM is the Quel (Ql) -- in fact, this name is a contraction of “quantity of electricity”. In the current formulation of Primel, the primel·electrel (⚀εtℓ) is 58.35471425_d microcoulombs (tiny in comparison to the coulomb, but on the other hand the coulomb is quite a large amount of static electricity).

(2) “MAGNETISM” and “MAGNETELS”. I want to introduce the term quantity of magnetism to refer to the essential property that underlies all  the phenomena of magnetism. What is that property? Well, the definitive condition for “magnetism” is simply electricity in motion. The term we are looking for is the product of electricity and velocity, i.e. . Wendy has mentioned this quantity, but she groped about with awkward terms like “charge momentum”, or erroneous concepts like “magnetic charge”. But “magnetism” is not some kind of “charge” that we can imbue on a particle and create a “magnetic monopole”. The proper physical interpretation is simply that, if we take some quantity of static electricity, and give it a velocity, then we have “magnetism”.

Special relativity tells us that the velocity we see in any object is a function of the reference frame we pick. In another reference frame moving alongside the object, the object is considered stationary. If that object has some electric charge, then in any frame where it is moving it has some “magnetism” too. But in the frame where it is stationary it has no “magnetism” (just as it has no “momentum”).

We should distinguish both “electricity” and “magnetism” from the forces they produce, or the shape of the fields in which those forces occur. Just as the presence of “mass” within two objects causes a gravitational force between them, and just as the presence of static “electricity” within two objects causes an electric force between them, so too the presence of “magnetism” (electricity in motion) within two objects causes a magnetic force between them. But those forces are not the same thing as the “mass” or “electricity” or “magnetism” within those objects; the forces are the effect of those properties.

In particular we need to emphasize that this definition of “magnetism” is a vector quantity () analogous to momentum (). Generating its associated fields involves a cross product with a displacement vector (or its unit vector ), so that the direction of the resulting field vector follows the right-hand rule.  Then when this field vector interacts with another object, there is another cross product with the “magnetism” vector of that object, again following the right-hand rule, to yield the actual force vector acting on that object.

All of this might seem odd at first, but it turns out that this notion can have a nice affect on how the concepts and terminology for electromagnetism can be organized. (See the following.)  

The quantitel for “magnetism” would be the magnetel (μtℓ). In SI units, this would be the coulomb·meter/second (C·m/s) or the ampere·meter (A·m). In TGM units, this would be the Quel·Vlos (QlVl), or the Kur·Grafut (KrGf) -- although we might imagine Pendlebury contracting the phrase “quantity of magnetism” to Quam (Qm); this is equivalent to about 0.146576545_d A·m. In Primel, the primel·magnetel (⚀μtℓ) would be 16.54146_d μA·m; the primel·quadqua·magnetel (⚀q↑μtℓ), equivalent to 0.343003729_d A·m, might be more convenient.

(3) “CURRENT” AS AN EMERGENT PROPERTY. Note that, under the above defintion, “magnetism” is not current. Rather, current (), is an emergent phenomenon due to magnetism, i.e., .  Current can be described as the timic (temporal) density of electric charge, or the lineic density of magnetism.  A way to think about it is: if a certain quantity of electricity is moving at an average velocity of , producing a “magnetism” of , and this is occurring down a wire of length , then the rate of flow of electric charge (current) all along this length will be .

This concept of “magnetism” also helps make sense of “magneto-motive force”. It's really not the amount of current we have, nor the number of “coils” that we have, that determines the strength of the resulting magnetic field. It's the amount of “magnetism” present that determines this. If the “magnetism” is due to electric charge moving down a conducting wire, then every time the same wire intersects normal to  a given cross-sectional area, it is equivalent to having an entire extra circuit contributing another instance of the same .  It doesn't matter whether each of these loops is an actual extra circuit, or just the same circuit with the same current, looped around.  It's a simple multiplication of effect, and doesn't have anything to do with whether the charges are moving in a circle or moving in straight lines. Of course, the actual geometry of a particular system does have an aggregate effect on the overall shape of the resulting magnetic field, but this can be determined by means of integral calculus: adding up an effectively infinite number of effectively infinitesimal instances of “magnetism” vectors cross-multiplied with their displacement vectors .

The quantitel for current would be the currentel (ctℓ). In SI units, this would be the ampere (A). In TGM units, this would be the Kur (Krf); this is equivalent to about 0.495722_d A. The primel·currentel (⚀ctℓ) would be about 2.0167389_d mA.

(4) AVOID “FIELD” and “FIELDELS”. A “field” is a general concept in physics; it simply means some kind of quantity that has a value at every point in space.  A “vector field” is a “field” that has a vector value (with a magnitude and a direction) at every point in space. There are too many things associated with electricity and magnetism that are called some kind of “field”. So don't name any of these as the “electric field” or “magnetic field”, and don't use fieldel (or even electrofieldel or magnetofieldel) as the quantitel for any of these quantities. Instead, come up with more specific terms for each quantity.

(5) “ELECTRIZATIONELS” and “MAGNETIZATIONELS” for AREIC DENSITIES:  I want to use the terms electrization and magnetization for the areic density of “electricity” and “magnetism”, respectively.  ”Electrization” subsumes both the idea of electric displacement field (think of it as “electrizing” a surface with the free electric charge enclosed within it) as well as the idea of polarization field in a dielectric material (think of it as “electrizing” the bound charges within the material).  (In fact, Silsbee mentions that “electrization” was actually proposed as a term for this purpose during his era, but it didn't catch on.) “Magnetization” subsumes both the idea of the magnetizing field as well as magnetic polarization in a magnetic material.

The quantitel for electrization would be the electrizationel = areanelic·electrel = electrel/areanel (εtzℓ = arℓ\εtℓ = εtℓ / arℓ). The SI unit for this would be the coulomb/meter² (C/m²).  The TGM unit for this is the Quenz = Quel/Surf (Qz =Ql/Sf) (contraction of “quantity-of-electricity density”). The primel·electrizationel (⚀εtzℓ) would be equivalent to 0.867416326_d C/m².

The quantitel for magnetization would be the magnetizationel = areanelic·magnetel = magnetel / areanel (μtzℓ = arℓ\μtℓ = μtℓ / arℓ). The SI unit for this would be the ampere/meter (A/m). The TGM unit for this is the Magra = Kur/Grafut (Kr/Gf) (contraction of “magnetic gradient”). The primel·magnetizationel (⚀μtzℓ) would be equivalent to 0.245881301_d A/m.

Since the electrizing field and the magnetizing field are already areic densities, their surface integrals and would simply cancel out the division by area, and recover the enclosed (scalar) quantities of electricity and magnetism . So would simply be measured in electrels. And would simply be measured in magnetels.

(6) “ELECTRODENSITELS” and “MAGNETODENSITELS” for VOLUMIC DENSITIES:  The quantities and represent volumic density of electricity. The quantitel for this would be the electrodensitel = volumelic·electrel = electrel / volumel (εdsℓ = vmℓ\εtℓ = εtℓ / vmℓ).  The SI unit for this would be the coulomb/meter³ (C/m³).  The TGM unit for this is the Quel/Volm (Ql/Vm).  The primel·electrodensitel (⚀εdsℓ) would be equivalent to 105.75561_d C/m³.

The quantities and represent  volumic density of magnetism (or areic density of current). The quantitel for this would be the magnetodensitel = volumelic·magnetel = magnetel/volumel (μdsℓ = vmℓ\μtℓ = μtℓ / vmℓ). The SI unit for this would be the ampere/meter² (A/m²). The TGM unit for this would be the Kur/Surf (Kr/Sf). The primel·magnetodensitel (⚀μdsℓ ) would be equivalent to 29.97790823_d A/m².

(7) “ELECTRELIC·” and “MAGNETELIC·” as RECIPROCAL PREFIXES.  I want to use electrelic· and magnetelic· as ISO-31 style prefix forms for the reciprocals of electrel and magnetel, i.e., when these quantities appear in a denominator. Note that in other cases above, where electrel and magnetel appear in the numerator instead, I make use of prefixes electr(o)· and magnet(o)· to create combination forms.

(8) “ELECTRELIC·FORCELS”, “MAGNETELIC·FORCELS”, and “MASSELIC·FORCELS”.  The field is a vector field expressing force per quantity of electricity . In other words . So I would like to call this quantity the “electric force” field, and use the quantitel electrelic·forcel = forcel / electrel (εfcℓ = εtℓ\fcℓ= fcℓ /εtℓ) to measure it. The SI unit for this would be the newton/coulomb (N/C) or the volt/meter (V/m). The TGM unit for this is the Elgra = Pel/Grafut (Egr = Pl/Gf) (a contraction of “electric gradient”). The primel·electrelic·forcel (⚀εfcℓ) is equivalent to 92.63094_d N/C.

The field is a vector field expressing force per quantity of magnetism . In other words . (Actually, since “magnetism” is a vector quantity, we have to state this more carefully as .) So I would like to call the “magnetic force” field, and use the quantitel magnetelic·forcel = forcel / magnetel (μfcℓ = μtℓ\fcℓ= fcℓ / μtℓ) )). The SI unit for this would be the tesla = newton / ampere·meter = weber / meter² (T = N/A·m = Wb/m²).  The TGM unit for this would be the Flenz = Mag/Quam = Flum/Surf (Fz = Mg/Qm = Fm/Sf). The primel·magnetelic·forcel (⚀μfcℓ) is equivalent to 326.7820_d T.

In a gravitational force field, the property generating the force, and affected by the force, is “mass”. So the “massic force” (aka “specific force”) field would be the vector field for gravity analogous to the “electric force” field , and the “magnetic force” field associated with electricity and magnetism. But “massic force” is simply acceleration, i.e. , and the quantitel for this would of course be the accelerel (accℓ).  The TGM unit for this, the Gee (G), approximates Earth's gravity. The primel·accelerel (⚀accℓ) also approximates Earth's gravity (but slightly differently). The SI unit of acceleration, the meter/second² (m/s²), does not approximate Earth's gravity; it is simply the acceleration unit coherent with the rest of SI.

(9) “INFLUENCE”. I want to introduce the term influence to refer to the surface-integral of force: .  This would be a purely mechanical quantity related to force fields specifically. The quantitel for this would be the influencel = forcel·areanel = energiel·lengthel (nfℓ = fcℓ·arℓ = ngℓ·lgℓ). The SI unit for this would be the newton·meter² (N·m²) or the joule·meter (J·m). The TGM unit for this would be the Mag·Surf (MgSf) or the Werg·Grafut (WgGf). The primel·influencel (⚀nfℓ) would be equivalent to 3.63647×10^-7_d N·m²).  The primel·hand·influence = primel·hand·force × primel·hand·area (⚀hd·nf = ⚀hd·fc × ⚀hd·ar), equivalent to 0.0904871_d N·m², might be a more convenient size.

When a point source has some property that generates a force field that follows an inverse-square law, an interesting feature is that the “influence” of that point source is constant and not dependent on distance. Even though the force diminishes as the square of the distance, the surface area of the sphere is increases as the square of distance too, so this exactly balances out. So the total “influence” of the point source is only dependent on the property generating the force; so long as that is not changing, the “influence” also remains constant.

The areic density of influence would simply be force. So there is no need for “influence density” as a term.

Note that using “influence”, rather than “flux”, for the surface integral of force avoids confusion with “flux” as a rate of flow of something.  There is nothing that is “flowing” in a force field; it just exerts its “influence” over the space around it. “Radiant flux” and “luminous flux” don't refer to [i]force[/i] fields, they refer to fields where energy or visible energy is being radiated, i.e. “flowing”, at a certain rate; that is why “radiant power” and “luminous power” are also apt terms for these. “Mass flux” would refer to the rate of flow of mass in a fluid dynamic system. And so forth.

(ᘔ) “ELECTRELIC·INFLUENCELS”, “MAGNETELIC·INFLUENCELS”, and “MASSELIC·INFLUENCELS”.  Given this new terminology, the surface integral of the “electric force” field would be electric influence . This expresses mechanical influence per quantity of electricity affected. The quantitel for this would be the electrelic·influencel = influencel / electrel (εnfℓ = εtℓ\nfℓ = nfℓ / εtℓ). The SI unit for this is the newton·meter²/coulomb (N·m²/C) or the volt·meter (V·m). The TGM unit for this is the Mag·Surf/Quel (MgSf/Ql), or the Pel·Grafut (PlGf). The primel·electrelic·influencel (⚀εnfℓ) is equivalent to 6.231670_d mV·m.

The surface integral of the “magnetic force” field would be magnetic influence . This expresses mechanical influence per quantity of magnetism affected. The quantitel for this would be the magnetelic·influencel = influencel / magnetel (μnfℓ = μtℓ\nfℓ = nfℓ / μtℓ). The SI unit for this is the weber = volt·second = joule/ampere (Wb = V·s = J/A). The TGM unit for this is the Flum = Pel·Tim = Werg/Kur (Fm = PlTm = Wg/Kr). The primel·magnetelic·influencel (⚀μnfℓ) is equivalent to 21.98399_d mWb.

The analogy for gravity would be massic influence , the surface integral for the “massic force” (”acceleration”) field : . The quantitel for this would be the masselic·influencel = influencel / massel (msℓ\nfℓ = nfℓ / msℓ).  The SI unit for this would be the meter³/second² (m³/s²). The TGM unit would be the Gee·Surf (GSf). The primel·masselic·influencel (⚀msℓ\nfℓ) would be equivalent to 6.59052×10^-4_d m³/s².

This is the unit for the standard gravitational parameter (or the “rationalized” gravitational parameter , where is the “sphere constant”). We would then be talking about this as the “massic influence” of planets and other astronomical bodies, rather than use the clunky term “standard gravitational parameter”.

(Ɛ) “BIELECTRELIC·INFLUENCELS”, “BIMAGNETELIC·INFLUENCELS”, and “BIMASSELIC·INFLUENCELS”. The quantities in (ᘔ) are all the result of dividing the influence of a force field by the relevant property of the object to be influenced. What happens if we divide this again by the relevant property of the object exerting the influence? Answer: we wind up with a force constant.  Each of these constants expresses the ability of their relevant properties (electricity, magnetism, or mass) to generate the associated force between two objects bearing those properties, per the amounts of those properties in both objects.

The bielectrelic·influencel (εtℓ²\nfℓ) would be the generic quantitel for the units of the force constant in Coulomb's law (and elsewhere). The SI version of this is of course N·m²/C². The TGM unit for this is 1/Mitt.  The primel·bielectrelic·influencel (⚀εtℓ²\nfℓ) would be equivalent to 106.789482_d N·m²/C².

The bimagnetelic·influencel (μtℓ²\nfℓ) would be the generic quantitel for the units of the force constant in the Biot Savart law (and elsewhere). The SI version of this is of course N/A². The TGM unit for this is the Meab. The primel·bimagnetelic·influencel (⚀μtℓ²\nfℓ) would be equivalent to 1329.02349_d N/A².

The bimasselic·influencel (msℓ²\nfℓ) would be the generic quantitel for Newton's gravitational constant (or the “rationalized” gravitational constant . The SI unit would be the meter³_/second²/kilogram (m³/s²/kg). The TGM unit would be the Gee·Surf/Maz (GSf/Mz). The primel·bimasselic·influencel (⚀msℓ²\nfℓ) would be equivalent to 1.194427044_d m³/s²/kg.

While the magnetic quantity would be synonymous with “permeability” (), the electric quantity would not be synonymous with “permittivity” (), because, curiously enough, appears in the denominator of Coulomb's law, so it is actually the reciprocal of the what we're looking for here.  In fact, the Wikipedia article on permittivity notes that this quantity, being the reciprocal, actually expresses resistance to generating force from electricity.  It should have been called something like “forbiddance” rather than “permittivity”.

It might actually be useful to have symbols for not only and , but also their reciprocals.  I would like to propose the following:

The position of the bars indicate whether the constant belongs in the numerator or the denominator of a force law. and are what we are used to, and what appears in:

but would be more appropriate in Coulomb's law:

I am trying to come up with replacement terminology for all four of these quantities, but I'm not satisfied with what I've come up with so far: electrofluency for , magnetofluency for , electrohibition for , magnetohibition for . [EDIT: Later, these got replaced with elastivity for , capacitivity for , inductivity for , and reluctivity for .]

(10_z) TO BE DONE: The above is enough for now, but I am also working on the following possible quantitels:

potentialel or potel repurposed as a synonym for energiel or workel or heatel, because “potential”, or “potential energy”, is just a kind of “energy”.

electrelic·potentialel or electrelic·potel for “electric potential”, because that actually is energiel/electrel.

magnetelic·potentialel or magnetelic·potel for “magnetic potential”, because that actually is energiel/magnetel. (This is the unit for the so-called “vector magnetic potential” ).

tensionel for lineic·forcel = forcel / lengthel, which is a linear analog for pressure.

electrelic·tensionel for and .

magnetelic·tensionel for and .

Explanation of why the statelectrel and the abmagnetel would both be and why that's a foolish idea.

Post #120 on Jan 10, 2017:

(11_z) "TENSIONELS", "ELECTRELIC·TENSIONELS", and "MAGNETELIC·TENSIONELS".

Linear density of force is a quantity known as tension. It's primarily useful for measuring surface tension in liquids. The generic quantitel for this would be the tensionel = lengthelic·forcel = forcel lengthel (tsℓ = lgℓ\fcℓ0 = fcℓ / lgℓ). The SI unit for this is the newton/meter (N/m). The TGM unit for this is the Tenz = Mag/Grafut (Tz = Mg/Gf).  The primel·tensionel (⚀tsℓ) is equivalent to 0.659034_d N/m.

I would like to use the term electric tension to refer to linear density of electric force .  This would be the quantity expressed in terms such as and . The generic quantitel for this quantity would be the electrelic·tensionel = tensionel/electrel) (εtsℓ = εtℓ\tsℓ = tsℓ / εtℓ).  The electrelic·tensionel in SI would be the newton/meter/coulomb (N/m/C) or the volt/meter² (V/m²).  The electrelic·tensionel in TGM would be the Tenz/Quel (Tz/Ql) or the Pel/Surf (Pl/Sf). The primel·electrelic·tensionel (⚀εtsℓ = ⚀εtℓ\tsℓ) is equivalent to 11293.587_d N/m/C.

I would like to use the term magnetic tension to refer to linear density of magnetic force .  This would be the quantity expressed in terms such as and . The generic quantitel for this quantity would be the magnetelic·tensionel = tensionel/magnetel (μtsℓ = μtℓ\tsℓ = tsℓ / μtℓ).  The magnetelic·tensionel in SI would be the tesla/meter (T/m).  The magnetelic·tensionel in TGM would be the Flenz/Grafut (Fz/Gf). The primel·magnetelic·tensionel (⚀μtsℓ = ⚀μtℓ\tsℓ) is equivalent to 39841.344_d T/m.

(12_z) "ELECTRELIC·PRESSURELS" and "MAGNETELIC·PRESSURELS".

I would like to use the term electric pressure to refer to areic density of electric force .  This would be the quantity expressed in terms such as and . The generic quantitel for this quantity would be the electrelic·pressurel = pressurel/electrel (εpsℓ = εtℓ\psℓ = psℓ / tsℓ).  The electrelic·pressurel in SI would be the pascal/coulomb (Pa/C) or the volt/meter³ (V/m³).  The electrelic·pressurel in TGM would be the Prem/Quel (Pm/Ql) or the Pel/Volm (Pl/Vm). The primel·electrelic·pressurel (⚀εpsℓ = ⚀εtℓ\psℓ) is equivalent to 1376916.9_d Pa/C.

I would like to use the term magnetic pressure to refer to areic density of magnetic force .  This would be the quantity expressed in terms such as and .  The generic quantitel for this quantity would be the magnetelic·pressurel = pressurel/magnetel (μpsℓ = μtℓ\psℓ = psℓ / μtℓ).  The magnetelic·pressurel in SI would be the tesla/meter (T/m²).  The magnetelic·pressurel in TGM would be the Flenz/Surf (Fz/Sf). The primel·magnetelic·pressurel (⚀μpsℓ = ⚀μtℓ\psℓ) is equivalent to 4857466.4_d T/m².

Post #122 on Jan 10, 2017

(13_z) "POTENTIALELS" = "ENERGIELS"; "ELECTRELIC·POTENTIALELS" and "MAGNETELIC·POTENTIALELS".

I would like to repudiate the use of "potential", unadorned, to refer to electric potential. Instead, I'd like to repurpose the term potential to be a synonym for "energy" or "work" or "heat". "Potential energy" is a form of energy, after all. Work or potential is, among the other things, the result of integrating force by length: . The generic quantitel for this would be the potentialel or potel (ptℓ), but this would be synonymous with the energiel = workel = heatel.  The unit for this in SI is the joule (J). The unit for this in TGM is the Werg (Wg).  The primel·potentialel (⚀ptℓ) is equivalent to 44.336_d μJ.

I would like to use the term electric potential to refer to ... well, electric potential!  This would be the quantity expressed by a term like , i.e., the result of integrating electric force by length. The generic quantitel for this would be the electrelic·potentialel = potentialel/electrel = powerel/currentel (εptℓ = εtℓ\ptℓ = ptℓ / εtℓ = ptℓ / εtℓ = pwℓ / ctℓ).  The SI version of this would be the volt = joule/coulomb = watt/ampere (V = J/C = W/A). The TGM version of this would be the Pel = Werg/Quel = Pov/Kur (Pl = Wg/Ql = Pv/Kr).  The primel·electrelic·potentialel (⚀εptℓ) is equivalent to 0.75976660_d V.

I would like to use the term magnetic potential to refer to magnetic vector potential.  This would be the quantity expressed by a term like , i.e., the result of integrating magnetic force by length. (Actually, since this is a vector quantity, a more careful definition is that the curl of the magnetic potential is the magnetic force: .) The generic quantitel for this would be the magnetelic·potentialel = potentialel / magnetel (μptℓ = μtℓ\ptℓ = ptℓ / μtℓ).  The SI version of this would be the weber/meter = newton/ampere (Wb/m = N/A). The TGM version of this would be the Flum/Grafut (Fm/Gf) or Mag/Kur (Mg/Kr).  The primel·magnetelic·potentialel (⚀μptℓ ) is equivalent to 2.680293_d Wb/m.

Post #140 on Jan 9, 2018

This post introduced a slightly different take on ISO-31 style reciprocal quantitels: "quantitelic" units. The trouble with just replacing the -el suffix with -ic is that it creates an adjective that is too generically broad in its meaning. "Electric" and "magnetic" in particular just mean "pertaining to" electricity and magnetism, and don't specifically signify "dividing by the quantitel for" those quantities. On the other hand "electrelic" and "magnetelic", formed by directly appending "-ic" to the original quantitels, would be unique and unambiguous forms. The nice thing is that this rule could be applied to any quantitel to derive a reciprocal.

Previous posts in this thread were modified to make use of this naming scheme. The post also included a table summarizing the electromagnetic quantities explored in the thread: