Talk:Centimetre–gram–second system of units

Values of parameters in different systems of units

The table of parameters in the section "Various extensions of the CGS system to electromagnetism" has incorrect entries in the columns for ε₀, μ₀, λ, and λ′ that contradict the text of the article and other articles. According to the text ESU and Gaussian are not rationalized, and so, according to the text, λ = λ′ = 4π in these systems. Whence it follows from the formula for λ in the table that ε₀ = 1 in these systems.

The table assumes that ε₀μ₀ = 1/c² in all systems, but this is incorrect, the correct formula being ε₀μ₀ = 1/α_L²/c². Hence, μ₀ = 1/c² in ESU, and μ₀ = 1 in Gaussian and Lorentz–Heaviside.

The same conclusions can be reached in another way. According to the text, D = ε₀E and B = μ₀H in free space in all systems. But according to the articles Gaussian units and Lorentz–Heaviside units D = E and B = H in free space in Gaussian and Lorentz–Heaviside. Therefore, ε₀ = μ₀ = 1 in these systems. The formulas for D and B in these articles also plainly show that λ and λ′ are 4π in Gaussian and 1 in Lorentz–Heaviside.

Accordingly, the quadruple (ε₀, μ₀, λ, λ′) should be changed to (1, 1/c², 4π, 4π) for ESU, to (1, 1, 4π, 4π) for Gaussian, and to (1, 1, 1, 1) for Lorentz–Heaviside. 72.251.58.64 (talk) 02:05, 14 November 2017 (UTC)

This is quite a long series of posts, so I'll start by noting that the values for ε₀ and μ₀ are in complete agreement with Table 2 of the Appendix on Units and Dimensions in the Jackson reference, while (with the conversions given below the table) the various k constants agree with Table 1. In Wikipedia, the references are paramount. Contrary to the statement by the IP editor, the column for λ does agree with those for k_C and ε₀ through the formula λ = 4 π k_Cε₀. RockMagnetist(talk) 16:42, 15 December 2017 (UTC)

I have belatedly realized that the table is correct because the IP editor changed it. Thank you! RockMagnetist(talk) 17:44, 15 December 2017 (UTC)

The following pertains to the section "Alternate derivations of CGS units in electromagnetism."

Theorem. λ = 4πε₀k_C and λ′ = 4πα_B/(μ₀α_L).

Corollary. If λ = λ′, then c² = 1/(ε₀μ₀α_L²).

Proof. Begin with the equations in SI. Let λ, λ′, σ, τ be independent variables. Define β = λστ and β′ = λ′στ. Perform the following multiplications:

B by σ/β′ and D by τ/β

E by σ and H by τ

M by β′/σ and Q, ρ, I, J, P by λτ/β

μ by λ′σ²/β′² and ε by λτ²/β²

Notice that the cross products P × E and M × B are invariant under this transformation since they represent torque densities. After eliminating σ and τ from the resulting equations, we obtain the most general system subject to the usual constraints. It may be seen that λ and λ′ have the meanings given them in the text. That the formulas in the theorem are valid in the general system can be verified directly. For λ this is obvious by inspection; for λ′ use the fact that λ/β = λ′/β′.

The corollary follows from the theorem and the formulas k_C/k_A = c² and k_A = α_Lα_B given in the text. 72.251.58.81 (talk) 02:28, 12 December 2017 (UTC)

The general system has six parameters, λ, λ′, β, β′, ε₀, μ₀, subject to two constraints, λ/β = λ′/β′ and c² = ββ′/(ε₀μ₀). It therefore has four degrees of freedom in the choice of units. It may be thought of as having seven base units, including the three mechanical units. The units of P and M, however, are directly derived from those of E and B, respectively.

In terms of these parameters the constants defined in the text have the following values:

α_L = 1/β′

k_C = λ/(4πε₀)

α_B = λμ₀/(4πβ)

k_A = λμ₀/(4πββ′)

72.251.58.233 (talk) 04:22, 13 December 2017 (UTC)

The text states that 4πε₀k_C is a dimensionless quantity, but since ε₀ is arbitrary, including its unit, this is not necessarily so. In general both ε₀ and μ₀ may be selected at will, but if it is required that λ = λ′, then the only limitation is that indicated in the corollary. It would be very convenient to assign a unit to λ and λ′ (if they are equal) in order to facilitate conversion from one system to another. The unit that seems most appropriate is that of a solid angle. The difference between unrationalized and rationalized systems would be that the former use the steradian as the unit of solid angle whereas the latter use the sphere. 72.251.62.29 (talk) 03:02, 14 December 2017 (UTC)

The proof of the theorem refers to the "usual constraints." These are conditions and equations that are invariant under the transformation in the proof. They include the equation of continuity, the formulas D = εE and B = μH, and the definitions of electric and magnetic moments as torques per units of E and B, respectively. There are, however, systems that violate the constraints. The most notorious offenders are variants of the Gaussian system. One such measures charge in ESU and current in EMU; this system violates the equation of continuity. The standard Gaussian system was carefully constructed to satisfy the constraints. For example, the magnetic moment of a small current loop is defined as m = IA/c. The c is inserted here to ensure that M is measured in EMU, as are B and H. If it is omitted, then M is measured in ESU and λ′ = 4π/c. If electric and magnetic dipole moments are defined by p = 4πQd and m = 4πIA/c, respectively, then λ = λ′ = 1. This in no way, however, makes the system rationalized. The way to rationalize the standard Gaussian system (without changing the units of E, B, P, M) is to choose ε₀ = 1/(4π) and μ₀ = 4π.

Rationalization, as the word is ordinarily understood, requires that ε₀ and μ₀ be so chosen that k_C = 1/(4πε₀) and α_B = μ₀α_L/(4π). 72.251.59.120 (talk) 03:39, 15 December 2017 (UTC)

Can anyone summarize the issue? Also, it would help if you make a wiki user. MaoGo (talk) 13:32, 15 December 2017 (UTC)

The IP editor was correct about the table, and I would encourage them to add the other material to the article. However, they should be aware of the core Wikipedia policy of verifiability and provide citations of a reliable source for anything they add. RockMagnetist(talk) 17:55, 15 December 2017 (UTC)

This all seems reasonable and I would encourage 72.251 (who was also very helpful at Talk:Gaussian units last month) to feel welcome and encouraged to edit the text yourself.

My only gripe about the table is that I wish the ε0 and μ0 columns were named something else, ideally meaningless symbols with no prior associations, like "k_2" and "k_3" for example. For example, the statement "ε0=1 in Gaussian units" is I think prone to being misunderstood ... for example I worry that a reader will see that and then feel entitled to replace ε0 with 1 in translating random formulas (like Coulomb's law) from SI to Gaussian. That statement is really supposed to be "ε0=1 in Gaussian units, where ε0 is by definition the ratio D/E in free space". That statement is correct, but it would still be equally correct if we used a different symbol besides ε0. Just my opinion, and I don't think it's a huge deal. --Steve (talk) 20:24, 15 December 2017 (UTC)

I am the IP editor. There are three problems with the text as currently written. (1) It implies that λ and λ′ may be chosen independently of ε₀ and μ₀; I hold that this is only possible if P and M have unusual units. (2) It states that 4πε₀k_C is a dimensionless quantity; I hold that this is not necessarily so. (3) It states that rationalization depends upon the values of λ and λ′; I hold that, if the formulas of the theorem do not hold, then it depends, rather, on the values of ε₀ and μ₀.

I cannot cite any sources, since I do not have access to any books that discuss these issues in sufficient detail. But the statements of the text ought themselves to be verifiable if they are to stand. The only reference in the text that seems to be relevant is to Jackson, whose discussion of the subject is wholly inadequate. The text seems to draw unwarranted inferences from what he does say (or doesn't say). (1) Jackson says nothing about the relationships between λ and λ′, on the one hand, and ε₀ and μ₀, on the other; the text infers that there are no necessary relationships. (2) Jackson says, "λ and λ′ are chosen as pure numbers"; the text infers that they must be so chosen. (3) Jackson says, "λ = λ′ = 1 in rationalized systems"; the text infers that this is the definition of "rationalization," and it calls λ and λ′ "rationalization constants."

I propose that the text "The factors … be 'rationalized'" be replaced with the following:

The units of P and M are usually so chosen that the factors λ and λ′ are equal to the "rationalization constants" $4\pi k_{\rm {C}}\epsilon _{0}$ and $4\pi \alpha _{\rm {B}}/(\mu _{0}\alpha _{\rm {L}})$, respectively. If the rationalization constants are equal, then $c^{2}=1/(\epsilon _{0}\mu _{0}\alpha _{\rm {L}}^{2})$. If they are equal to one, then the system is said to be "rationalized"

Zophar (talk) 04:44, 17 December 2017 (UTC)

Here is a direct proof that rationalization means that what I call the rationalization constants are equal to one. Rationalization means that Maxwell's equations in material media for static fields have the form

∇·D = ρ and ∇×E = 0

∇·B = 0 and ∇×H = α_LJ

In free space these become

∇·E = ρ/ε₀ and ∇×E = 0

∇·B = 0 and ∇×B = μ₀α_LJ

From these we may derive Coulomb's law and the Biot-Savart law using the usual mathematical arguments. The results are

k_C = 1/(4πε₀) and α_B = μ₀α_L/(4π)

whence it follows that the rationalization constants are equal to one. Zophar (talk) 04:58, 18 December 2017 (UTC)

emfd

Gavo atoms (talk) 07:08, 28 February 2020 (UTC)can you help me to have question and answers of EMFD unit

As others have noted, the talk page is for discussing the article, or improvements to the article. If there is an EMFD unit that should be included, then we can discuss that. (As far as I know, there is no such unit, at least in the CGS contexts.) I try to be a little flexible, and give people the benefit of the doubt, that the question might have some use for improving the article. But deleting this posts doesn't even allow discussion of the relevance to the article. (Though I agree, that I suspect that there isn't any.) Gah4 (talk) 01:44, 29 February 2020 (UTC)

What is an EMFD unit? Dondervogel 2 (talk) 09:29, 29 February 2020 (UTC)

Method of reconciling systems

I am uncomfortable with Centimetre–gram–second system of units § Various extensions of the CGS system to electromagnetism. I know it is referenced, but there are other completely different ways to reconcile metrological systems (I can't access the two references, but the one is just a response to the other). This approach seems to be to insert various constants into equations so that the equations end up constructed as for each of the systems when the constants are chosen for the system, but removes the understanding that the quantities (e.g. "charge") are different in each of the systems and does not help intuition. This leads to misunderstandings such as the idea that 10⁴ G = 1 T. They correspond, but equality is mathematical nonsense, and quickly produces confusion and contradictions. I have seen too much OR on WP that is based on this misunderstanding. I suggest simply deleting this section. —Quondum 16:56, 7 June 2020 (UTC)

I agree it is strange, but it is also useful and important. It looks to me that the distinction is well explained, but maybe it can be explained better. Yes one has to be careful with units but if, for example, I buy a magnet that says 1T, I can replace that value with 10000gauss, and if I have a gaussmeter, I know what it should say. But yes, one has to be careful with equations when doing that. Deleting the section does not reduce confusion, people will just find it somewhere else. The only way people will know about the possible misunderstanding is to explain it. Gah4 (talk) 19:38, 7 June 2020 (UTC)

The current explanation does not distinguish the definition of charge in the different systems (these are different quantities, like the radius and circumference of a circle being different quantities, but both giving the same information); it just emphasizes that the units are different. Expressing things in different units is familiar, e.g. the circumference of a circle being expressed in feet and metres. This is not what is happening in the difference between CGS and SI. Yes, explanation is necessary, and it seems I might need to write one, but what we have at the moment is worse than an explanation: it is effectively incorrect, hence my suggestion to delete it. —Quondum 20:31, 7 June 2020 (UTC)

prefactor

In some places, or maybe in edit summaries, there is mention of no prefactor. I think this isn't quite right. In some cases, a prefactor is defined for convenience, and not for units. For example, it might be a power of 10, or might have a 4pi in it. The important point is that it is dimensionless. Gah4 (talk) 19:41, 7 June 2020 (UTC)

I don't see how you see that. It is not dimensionless as used in this article. In any event, where it is used it seem to be tied in with the thread above, and needs rewriting. —Quondum 20:36, 7 June 2020 (UTC)

So what would you call a dimensionless power of 10 that was in an equation? Gah4 (talk) 03:42, 8 June 2020 (UTC)

Maybe I misunderstood our comment. As far as I see it, the term "prefactor" has been used to mean any multiplier that is not dimensionless 1. I see only one instance where it is dimensionless: "Ampère's force law simply contains 2 as an explicit prefactor", which seems to result from the ratio of a 4π (from the spherically symmetric Coulomb force law) with a 2π (from a cylindrically symmetric Ampère's force law). I am still in the dark about what point you are trying to make, but this may be moot since all these references to the nonstandard term "prefactor" should be rewritten. —Quondum 10:54, 8 June 2020 (UTC)

I was taking it as any term in front of the appropriate physical variables, which would include the 2 you mention. Partly this comes from recent (last few days) interest in the definition of the volt, convenient sized for common electrochemistry, and otherwise for common usage. It took getting powers of 10 in the right place to make that work. Note also the significance of using units scaled by powers of 10, such as the centimeter in CGS, and the kilogram in SI. Gah4 (talk) 13:12, 8 June 2020 (UTC)