Talk:Heaviside–Lorentz units

fundamental units set to one
The article states, that we set $$\mu_0$$ and $$\epsilon_0$$ equal to $$1$$, yet we use the speed of light $$c$$. However the speed of light is defined as $$c:=\frac{1}{\sqrt{\mu_0 \epsilon_0}}$$, so how come it is not equal to $$1$$? What is the numerical value of $$c$$ in this system, and in what units? The article Natural units says that Lorentz-Heaviside units sets permittivity and permeability to one as well as (evidently optionally) the speed of light and planks constant. but it also says that it sets Z to one. Nowhere can I find a definition of Z. Every webpage that I find on Lorentz-Heaviside units just refers me to cgs units. I hope that someone will someday expand this article because I am very much interested in knowing more about it. Lemmiwinks2 (talk) 19:18, 30 August 2009 (UTC)


 * Z is the impedence of a vacuum, or $$\mu c$$. CODATA gives its value in si is 376.730313462 ohms.  In mksa, it's 29.9792458 ohms.  Wendy.krieger (talk) 08:44, 12 January 2012 (UTC)

Our "Electrodynamics" course didn't mention anything about it and I wasn't able to find an explanation on wikipedia. Lurco (talk) 18:57, 7 February 2012 (UTC)


 * Setting $$\mu_0$$ and $$\epsilon_0$$ equal to $$1$$ is perhaps a little confusing when you start from the equations in SI units. The equations actually get rearranged so that the identity $$\mu_0 \epsilon_0 c^2 = 1$$ no longer holds.  So the units of $$c$$ are cm⋅s−1.  This should be clear from the article.
 * The article on natural units appears to be misleading. The choice to set additional constants to 1 is not part of the Lorentz–Heaviside units.  The part of the Lorentz–Heaviside units used in that article is essentially the choice of rationalized units – which is a choice of how the equations are written. — Quondum☏✎ 20:09, 7 February 2012 (UTC)


 * SI is not terribly coherent with the school that sets $$\mu_0$$ and $$\epsilon_0$$ to unity, even when c is set to unity. You can do it, but not a lot of people do it correctly, because SI, unlike CGS, is a mixed system. Wendy.krieger (talk) 09:26, 8 February 2012 (UTC)

Identify people
Which Heaviside? Which Lorentz? The article should say. 121a0012 (talk) 04:40, 16 October 2010 (UTC)


 * Done. Dicklyon (talk) 07:01, 16 October 2010 (UTC)

Heaviside-Lorentz is a system for forming units.
Of names, see: german wikipedia: Es ist nach Oliver Heaviside und Hendrik Antoon Lorentz benannt. (it is named after OH and HAL)

The system roughly follows the gaussian scale, in that epsilon and mu (electric and magnetic constants), are unity, but change the size of the derived measure of charge, so that the force between two unit charges by coulomb's law gives 1/4p dynes, not 1 dyne. This means that the relevant charge is 1/(2.sqrt pi) of the cgse.

However, since hlu is a set of formulae based on three base units, (length, mass, time), it is possible to set these three independently, so one might have fps hlu or various atomic hlu.

The hlu are not simple multiples of the practical units, and never came into practical use.

Note also that there is a reference in Stephen Dresner ('Units of Measurement, An Encyclopaedic Dictionary') that refers to HLU, but actually constructs a mix of cm.g.s.Fr and cm.g.s.Bi, the units being out by various powers of 2sqrt(pi). --Wendy.krieger (talk) 11:09, 7 January 2011 (UTC)

Paragraph wrong
"This demonstrates the simplicity that rationalizing the Lorentz–Heaviside units provide over equivalent unrationalized units. Note that there is no D flux density vector nor H magnetic field vector. With rationalized, natural LH units (with c=1) in free space, flux density is precisely the same quantity as electric field, D=E, and likewise, H=B describe the same magnetic field, thus unifying the concepts. There is no fundamental physical difference between the two. Additionally, if the magnetic interaction is understood as the electrostatic interaction with consideration of the effect of special relativity, it becomes clear that all electromagnetic interactions derive solely from electrostatic interaction."


 * This is plain wrong. Rationalisation is about $$4\pi$$, not c.  The HLU already have $$4\pi$$ in the rationalised form.  Because it is like the gaussian, it also has D=E=H=B.  (eg the value of E and H in the em wave are the same size and unit).


 * Magnetics have nothing to do with electrostatics. You need motion, which in nature, comes from electrons in their orbits and magnetic dipoles lining up in domains, flowing currents and something.  Wendy.krieger (talk) 08:58, 12 January 2012 (UTC)


 * Not exactly. The magnetic field is the unique extension of the electrostatic field (with the assumption of charge conservation across all frames of reference) that is consistent with special relativity. Thus, it is reasonable to say that magnetism derives from electrostatics. — Quondum☏✎ 14:15, 21 January 2012 (UTC)


 * It's reasonable to say that magnetism arises from electricity, but not from a static arrangement of charge. Magnetism acts on moving electrical charges, and is caused by moving electrical charges.  Changing the frame of reference also causes the charge to move, and thus is no longer electrostatics.


 * It's also not unique, since a similar process has been proposed for gravity. Wendy.krieger (talk) 08:39, 25 January 2012 (UTC)


 * You seem to think that the word "electrostatics" implies some unnecessarily strict constraints. Even if one assumes that it implies time invariance of the field and a "static arrangement of charge" relative to some inertial observer, special relativity allows us to deduce the magnetic field observed by another observer moving relative to the first (with, as I said before, an assumption about the conservation of charge).
 * Yes, a similar process applies with gravity, and (assuming flat Minkowski space) one ends up with similar results: gravitoelectromagnetism. There are subtle differences because the charge conservation premise changes.  I fail to see the relevance, though.
 * It would be more constructive if we focused on suggested changes to the article. As per your comment about rationalized units, Gaussian units do not distinguish between E and D either.  The benefit of rationalization is that the $4π$ disappears from Maxwell's equations. This is not made clear in the article other than in the lead, but should be. There are further shortcomings, for example, it seems to imply that $c=1$ is a choice that is independent of the choices $ε_{0}=1$ and $μ_{0}=1$, which is not the case.
 * I've made a minor copyedit to the parapgraph, but probably have not yet addressed either your or my concerns. — Quondum☏✎ 09:52, 25 January 2012 (UTC)


 * The paragraph attrits to rationalisation things that do not come from rationalisation. Gaussian already has E=H=D=B, but provides different units for H (oersted) vs B (gauss).  I really can't see the benefit of eliminating any of E, H, D or B, even when they chance to be equal.  Depending on who you read, it's E and H, or E and B or H and D.  This is something that Heaviside railed against.


 * In all the six-dimensional glory, the maxwell equations are div D = ρ/β, div B = 0, κ curl E = -τB, and κ curl H = τD + J/β, along with D = εE and B = μH.  τ = d/dt, a time derivitive, written as a replacement for 'dot-over'.  β and κ are constants which in SI are set to unity, but might be freely set.  From this, you can easily show that εμc² = κ², which allows ε=μ=1, κ=c.


 * Gaussian has β=1/4π, κ=c. HLU puts β=1, κ=c.  SI puts β=1, κ=1.  I've recorded a system where β=1/4π, κ=10.  It's nothing to get worried about.


 * What rationalisation does is to replace the radiance constant γ=(intensity at radius² / source) with the gaussian divergence constant (β=flux through a surface / enclosed sources). One can easily show that γ=4πβ, by considering the case of a sphere around a point, and intensity as density of flux.  The older models sets γ=1, while the rationalised systems have β=1.


 * The relation between electricity and magnetism, is probably just an effect of a moving field, since Heaviside showed that the same equations exist between a electrostatic as newtonian gravity, and electromagnetic as co-gravitation. Jeffimenko develops the idea.  It's not unique.  Wendy.krieger (talk) 08:53, 26 January 2012 (UTC)


 * I rather like the explanation of rationalization that you have given here. It is essentially that given in the CGS article.  I have taken the liberty of including it in the article along with a bit of additional structure.  The result is still a bit rough though, but IMO considerably better already.  — Quondum☏✎ 14:21, 26 January 2012 (UTC)

Some History
Oliver Heaviside's "Electromagnetic Theory" appears to be the first text written in rationalised theory. This is done by slight of hand, in that, for example, the flux D is equal to the displacement of charge, whereas the regular factor of 4pi is called for. It also is one of the earliest references for using bold ('claredons') text for vectors, rather than fraktur font

Heaviside actually proposed a different set of rationalised units in "Electromagnetic Theory, Vol II" of 1899. The discussion is page 275 et seq, basically suggests that the V, A, Ohm etc ought be replaced by new units, like a.V, A/a, a^2.Ohm etc. Since these were still regarded as CGS extensions, further rationalisations were possible, such as eliminating different powers, and having variously 10^8 or 10^9 of the HLU. The value of the magnetic constant is then 1e-9 H/cm.

There is correspondence between Heaviside and Giorgi http://www.iec.ch/about/history/documents/documents_giovanni.htm here. This shows that Heaviside was rather dismayed that G was going to have mu=4pi E-7 H/m, particularly the 4pi factor.

The HLU in pretty much its modern form appears in Lorentz's work "The theory of Electrons" 1916 Teubner, Leipzig. He credits Heaviside and Hertz with banishing the 4pi's by resizing the units. (p2 op cit). In any case, the book is certianly more readable to a modern reader than say Heaviside.

Wendy.krieger (talk) 10:15, 27 September 2013 (UTC)

Errors in Conversion Table
The quantities "current" $$I$$ and "current density" $$\mathbf{J}$$ are listed in the wrong entry in the table. These quantities are in the "EMU" rather than the "ESU" category, so properly speaking the conversions should be:

$$I_{\mathrm{LH}} = \sqrt{4\pi} I_{\mathrm{G}} = \sqrt{\mu_0} I_{\mathrm{SI}}$$

$$\mathbf{J}_{\mathrm{LH}} = \sqrt{4\pi} \mathbf{J}_{\mathrm{G}} = \sqrt{\mu_0} \mathbf{J}_{\mathrm{SI}}$$

This should place them in the same category as "magnetization" $$\mathbf{M}$$ and "magnetic dipole moment" $$\mathbf{m}$$. This is necessary for the following conversion to be true:

$$q_{\mathrm{SI}} = I_{\mathrm{SI}} t$$ $$q_{\mathrm{LH}} \sqrt{\epsilon_0} = I_{\mathrm{LH}}\frac{1}{\sqrt{\mu_0}}\ t$$ $$q_{\mathrm{LH}} = I_{\mathrm{LH}}\frac{1}{\sqrt{\mu_0\epsilon_0}}\ t$$ $$q_{\mathrm{LH}} = I_{\mathrm{LH}} c_0 t$$

This highlights the intrusion of $$c_0$$ into the relationship between current and charge, under LHU (and Gaussian). Kodegadulo (talk) 22:11, 5 January 2017 (UTC)

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Consolidating Maxwell's equations
A number of articles exist that contain descriptions of Maxwell's equations (and thus have a table similar to the one containing the differential form of the equations here), but they all appeared slightly differently. I've begun collecting these tables in template pages that can be transcluded across all of these articles in an effort to homogenize things a little bit and make finding relevant information a little bit easier. Glosser.ca (talk) 17:58, 14 August 2017 (UTC)

Question regarding the value of $β$ in CGS units
The page says that $∇⋅D = ρ / β$ while simultaneously saying $D = ε_{0}E$.

Rather than saying that LH units set $ε_{0} = 1$ while also setting $β = 1$, wouldn't it be more accurate to say that $β$ is set to $1 / ε_{0}$, and similarly with Gaussian units setting $β = 1 / 4πε_{0}$?

Ericvilas (talk) 09:09, 6 December 2019 (UTC)


 * No, setting β = 1 / 4πε0 is wrong. The flux from a charge is $$Q/\beta = \Phi$$ there is no $$\varepsilon$$ in the formula. The $$4\pi = \gamma / \beta$$ arises from the surface of the sphere vs the radius squared.  Wendy.krieger (talk) 10:16, 7 October 2022 (UTC)

"Heaviside-Lorentz units are also a type of Planck units"
, your claim that would need a reliable source to warrant its inclusion here. A simple falsification of your claim: Heaviside–Lorentz units are a form of metric system that does not rely for its definition of units on the size of any fundamental constant (with the arguable exception of the implicit use of the electric constant, whose only role is to eliminate the electromagnetic dimension). The system of Planck units, and its variants, are all entirely premised on defining the unit sizes as products of powers of fundamental constants (in contrast, in the original Planck units system, the electromagnetic dimension is entirely ignored). Since they have no commonality at the level of units whatsoever, the one cannot be a subtype of the other. The only real commonality seems to be Heaviside's idea of "rationalization".

With your, it would seem to suggest that there might be a modified (rationalized) system of Planck units that is given the name "Lorentz–Heaviside Planck units", but notwithstanding the sharing of portions of the name, this does not make one an example of the other type, and particular, Heaviside–Lorentz units are most emphatically not "a type of Planck units". I think you might have meant that "Heaviside–Lorentz Planck units are a variant of Planck units", which is not the same thing at all. If you have a reliable source for "Lorentz–Heaviside Planck units" as currently described after your edits, this section would belong at Planck units, but in any event, it does not belong in this article.

If Lorentz–Heaviside Planck units are indeed notable (and as described, a more appropriate name would be "rationalized Planck units", which shows the weakness of the connection to this article), surely you should be able to source this? I notice the complete lack of references for this section, and as such, it presents the appearance of original research being published in Wikipedia, which is not permitted. If you can add reliable sources, I would encourage you to move this section to Planck units. In any event, it is my considered opinion that this section has no place in this article. —Quondum 11:33, 17 July 2020 (UTC)


 * "Heaviside-Lorentz" doesn't just refer to CGS, but can describe any system with rationalized units, e.g. in Srednicki p.345, p.566, in professional physicists' vernacular. Being "natural" doesn't exclude a system from being "Heaviside-Lorentz," and such usage bears mention here. — wing  gundam  00:25, 13 September 2020 (UTC)