Talk:Vacuum permittivity

Serious problem in this article
ERASED sentences explaining why the editor put less decimals on furmlas. unneeded and DISTRACTING — Preceding unsigned comment added by 77.210.125.31 (talk) 17:32, 15 May 2012 (UTC)

How can a measured value be defined? Electric permittivity is measured using a capacitor circuit. It then so happens that the inverse of the product εμ is close to the square of the speed of light. But you cannot apply the defined speed of light in SI units order to determine the measured value of ε.

This all goes back to Weber and Kohlrausch in 1856. They did an experiment using a Leyden jar and obtained an electromagnetic/electrostatic ratio that was closely linked to the measured speed of light. The physical importance of it all lies in the convergence of two measured results. We cannot replace these experiments with definitions of c and μ.

The lead in this article is totally confused as it is attempting to explain what cannot be explained. It needs to be drastically re-written. David Tombe (talk) 12:24, 13 August 2009 (UTC)


 * You cannot measure the permittivity of vacuum, because the meter is defined in terms of the speed of light which comes from the permittivity. (e.g. how do you measure the distance between the plates of your capacitor in a way that is independent of the permittivity of vacuum?  You can't.)  You can only try to measure the relative permittivity of different materials/conditions.  — Steven G. Johnson (talk) 00:07, 14 August 2009 (UTC)


 * (Please provide a reputable source stating that it is possible to measure the permittivity of vacuum in the SI unit system if you have any intention of debating this. — Steven G. Johnson (talk) 00:15, 14 August 2009 (UTC))


 * Tombe's misunderstandings show why it is better to move the article to Electrical constant. /Pieter Kuiper (talk) 14:18, 14 August 2009 (UTC)


 * Pieter, You would need to elaborate on that statement so that I can see exactly what your misunderstandings are. David Tombe (talk) 19:24, 14 August 2009 (UTC)

Steven, There was an experiment with an electric circuit involving a capacitor which was used to measure the electric permittivity of the vacuum, prior to the 1983 SI definition of the metre. The value obtained could be subsituted into the equation c^2 = 1/(εμ) to obtain a value that is very close to the speed of light.

We have got no automatic right to reverse the situation using the directly measured speed of light in order to obtain the value of ε through this equation. We have two independent measurements of two different quantities which appear to be linked through the equation c^2 = 1/(εμ). We cannot deny the significance of this important result in physics simply by invoking a new SI definition of the metre.

It is a total tautology, based on the benefit of hindsight, to suggest that we can obtain the value of ε by using the equation c^2 = 1/(εμ) and the post-1983 defined speed of light. David Tombe (talk) 11:50, 14 August 2009 (UTC)


 * Since you haven't given any reputable source, discussion is futile. — Steven G. Johnson (talk) 14:35, 14 August 2009 (UTC)

The defined exact value of the electric constant is discussed here. It is not seen as a problem. Like the other defined constants, it could be taken to be 1 in the proper set of units, but that's not the units we chose. Dicklyon (talk) 15:14, 14 August 2009 (UTC)

Here's a 1993 book by a guy who seems to have not got the 1983 memo. Dicklyon (talk) 15:22, 14 August 2009 (UTC)

Here is a sensible discussion by Halliday. As you see, the problem is not with this article. It's just the way it is; the electric constant is now a constant, not a measured value. Dicklyon (talk) 15:22, 14 August 2009 (UTC)


 * The key point is that it is no longer even possible to measure the permittivity of vacuum (or at least, its linear part), any more than it is possible to measure the speed of light in vacuum, since its value is bound up in our system of units that defines the measurement. (If it were possible, there would be an extensive literature from experimental physics, NIST, and others, trying to measure the permittivity of vacuum with greater and greater precision, just like for every other physical property that it is possible to measure).  This is extensively discussed in an appendix of Jackson (Classical Electrodynamics); he gives an interesting example from a century ago of when Congress tried to define dependent physical units in terms of different measurements: "Soon afterward, because of systematic errors in the experiments outside the claimed accuracy, Ohm's law was no longer valid, by an act of Congress!" — Steven G. Johnson (talk) 16:10, 14 August 2009 (UTC)

Steven, You asked me for a source. Nelkon & Parker "Advanced Level Physics" (1979) describes the experiment that is used to determine the value of electric permittivity. It uses an electric circuit with a capacitor in it. Are you seriously trying to tell me that that experiment became null and void when the metre was re-defined in 1983?

The equation c^2 = 1/(εμ) came about in the first place as a consequence of the experimental determination of the electric permittivity (ε). That equation yields a number that is very close to the speed of light, and that fact is a matter of great interest to physicists. You cannot then work backwards using a defined speed of light in order to obtain a defined electric permittivity (ε). That is known as cooking the books with the benefit of hindsight.

You cannot wipe out history with a mere definition. The 1856 experiment with the Leyden jar was one of the most important experiments in the history of electromagnetism. David Tombe (talk) 19:17, 14 August 2009 (UTC)


 * The interpretion of the experimental results changes as the definition of the units change. Early experiments to measure the speed of light would, in the modern definition, not be measuring the speed of light itself but quantities such as (for example) the speed of the earth around the sun relative to the speed of light.  That doesn't make them invalid experiments, but if since we are now defining the meter in terms of the speed of light you can no longer measure the speed of light (in vacuum).   In the old days, when a meter was defined as the length of a certain platinum rod in Paris, you could not meaningfully measure the length of that rod to see if it differed from a "meter" in length; now you can, not because the experiments have changed, but because the definition of the quantities you are measuring has changed.


 * Anyway, since you still haven't provided a reputable source explaining how, in the current definition of units, it is possible to measure the permittivity of vacuum, this discussion is still pointless. I'm not going to explain SI units to you. — Steven G. Johnson (talk) 03:38, 15 August 2009 (UTC)

Steven, I'm fully aware of the current definitions in SI units. And I fully understand your point of view. Your point of view is that since both c and μ are defined, then ε automatically becomes defined through the equation c^2 = 1/(εμ). That is all pretty straightforward.

However, the point that everybody seems to be missing is that the equation c^2 = 1/(εμ) arises in the first place because of experimental measurements of ε. Hence it is a tautology to define ε using an equation which only exists because of experimental determinations of ε. And this tautology pulls the mat from underneath the famous work of Wilhelm Eduard Weber and Rudolf Kohlrausch in 1856 with the Leyden jar. It reduces the equation c^2 = 1/(εμ) to a meaningless conversion factor. This is a classic case of maths having gone off the rails and lost all connection with the physics that it was supposed to be describing. David Tombe (talk) 11:49, 15 August 2009 (UTC)


 * I see you still have no reputable sources explaining how, in the current definition of units, it is possible to measure the permittivity of vacuum. Hence this discussion is still pointless.  (And no, you don't understand SI units.) — Steven G. Johnson (talk) 23:50, 15 August 2009 (UTC)

Steven, I have a reputable source. I have an advanced level physics textbook which describes the experiment for measuring the electric permittivity. The experiment involves an electric capacitor circuit with a vibrating reed switch. It utilizes the equations Q = CV and C = εA/d. It doesn't make any difference what system of units is used to define the metre. The only thing of importance in the experiment is that we can actually measure A, V, d, and the time derivative of Q.

Surely you are not seriously trying to tell me that this experiment became defunct in 1983 following the re-definition of the metre in SI units? The reputable source is "Nelkon & Parker" 'Advanced Level Physics. It is the 1979 version. I will be interested to find out if this experiment has been dropped from the most up to date version. If it has been dropped, I will accept that your reversion has merit under wikipedia's rules. But I will never accept that this experiment has been nullified by a mere re-definition of the metre. David Tombe (talk) 01:00, 16 August 2009 (UTC)


 * I'm not saying the experiment became defunct, but rather that the interpretation of what is being measured changed because the definitions of the measured quantities changed.


 * I see you still have no reputable sources explaining how, in the current definition of SI units, it is possible to measure the permittivity of vacuum. Hence this discussion is still pointless. — Steven G. Johnson (talk) 05:58, 16 August 2009 (UTC)

Steven, A 1993 reference was supplied above. It uses SI units and it points out that electric permittivity is an experimentally measured quantity.

Also, you are now contradicting yourself. One moment you are saying that it is impossible to measure the permittivity of the vacuum within the current definition of SI units, and the next moment you are saying that we can still measure it, but that the interpretation of the measured quantity has changed from what it used to be.

We are measuring the quantity ε as per the equation C = εA/d. There hasn't been a physical interpretation of this quantity since the time of Maxwell, so I can't see how any interpretation could have changed as a consequence of the re-definition of the metre in 1983. In the experiment in question, d will be substantially the same whether based on the pre-1983 definition of the metre, or the post-1983 definition of the metre. So I can't see that there is any argument at all to say that ε is not a measured quantity. It can only become a defined quantity if we work backwards through an equation that only came about in the first place because of the measured value. David Tombe (talk) 14:39, 16 August 2009 (UTC)


 * You can measure the permittivity of another material relative to the permittivity of vacuum, just as you can measure velocities of various bodies relative to the speed of light in vacuum. I don't see any place where that book says that you can measure the absolute permittivity of vacuum itself. You're just confused about what is being measured: what you're doing is equivalent to pointing to a modern mechanics textbook saying that speed is distance/time and describing measurements of speed for various bodies, and saying "aha, you can measure speed, therefore you can measure the speed of light in vacuum".


 * (The modern definition of "permittivity" is bound up in the understanding of electromagnetism provided by Maxwell's equations. If there were so great an upheaval in physics as to imply that the speed of light were no longer $$1/\sqrt{\epsilon \mu}$$, the whole concept of permittivity and our system of electromagnetic units would need to be revisited; it is not simply a matter of measuring a different value for the permittivity of vacuum.  In the same way, if relativity were disproved and the speed of light in vacuum were somehow not a frame-independent constant, that would be such a huge upheaval that it would require rethinking of the whole concept of velocity and the whole system of SI units; one can perform experiments to test the validity of relativity, but it's not simply a matter of measuring the speed of light per se.)


 * Again, if it were possible to measure the absolute (linear) permittivity of vacuum, there would have been many, many experiments published trying to do so to as high a precision as possible. Point out one since the units were redefined, or even a reputable proposal for one, or this discussion is pointless. — Steven G. Johnson (talk) 15:47, 16 August 2009 (UTC)

Steven, The source is quite clear that it is talking about the absolute permittivity of free space, and it gives the measured value. The formula in question is C = εA/d, and the vibrating reed switch/capacitor experiment can be used in conjunction with that formula to measure the permittivity of any material, including the vacuum. Nothing can possibly have changed in relation to this experiment as result of the 1983 re-definition of the metre. If the space between the capacitor plates, d, was 1cm before 1983, it will likely have remained at 1cm after 1983. It's a simple matter of knowing the values of A, d, Q/t and V and we will obtain an experimental value for ε.

The precision of this experiment is irrelevant. It was never very precise. But nevertheless, you keep overlooking the fact that the equation c^2 =1/(εμ) came about because of experimental measurements. We should not therefore be using that equation in reverse to determine ε, even though that has been common practice, even before the 1983 re-definition of the metre, due to the fact that the experimental method was difficult. David Tombe (talk) 17:13, 16 August 2009 (UTC)


 * David, we understand that Maxwell noticed that the square of the speed of light was about equal to 1/(εμ); that led to the theory that now implies c^2 =1/(εμ). If you want to do the experiment you're talking about, you can check the theory by seeing if it agrees with your experimental result (within your probable error).  So what's the problem?  The 1983 definitions tie the theory to a particular value based on the way the system of units is defined; so what?  Dicklyon (talk) 17:22, 16 August 2009 (UTC)

Dick, The problem is that the equation in question comes from the experimental determination of ε. Steven has been trying to tell me that since 1983, the experiment no longer means what it meant before, and that we can only determine ε theoretically from the equation that was first based on the experiment.

This is an extended tautology of the already existing tautology that lies in the poost-1983 speed of light. David Tombe (talk) 17:47, 16 August 2009 (UTC)


 * I'm trying to argue that your statement "the equation in question comes from the experimental determination of ε" is not very true, and not very relevant. The equation comes from EM theory; even when Maxwell first noticed that his theory predicted EM propagation at the speed sqrt(1/(εμ)) and noticed that it agreed with estimates for the speed of light, the equation c^2 =1/(εμ) was based on theory, even if c and ε and μ had been measured experimentally.  Dicklyon (talk) 18:02, 16 August 2009 (UTC)

Dick, The linkage of the equation c^2 = 1/(εμ) to the speed of light has always been purely experimental. The theoretical equation itself was Newton's equation for the speed of sound [equation (132) in Maxwell's 1861 paper] but the numbers, and hence the linkage with the speed of light, began with Wilhelm Eduard Weber and Rudolf Kohlrausch in 1856. If we do away with the experiments that produced that linkage to the speed of light, then we do away with the equation altogether in relation to the speed of light. We cannot retain the equation with its connection to the speed of light and use it in reverse to define ε. That truly is cooking the books. The introduction to this article is sheer propaganda, and it is a new physics which was unknown even in recent times. It doesn't appear in my textbooks. I'm not going to discuss the matter anymore on this page. I'm going to take the matter to a wider arena because this article is the nonsensical conclusion of what was only the tip of the iceberg at the speed of light page. David Tombe (talk) 21:47, 16 August 2009 (UTC)
 * No, David. The statement that "The linkage of the equation c^2 = 1/(εμ) to the speed of light has always been purely experimental." Is simply not true. Maxwell's theory of electromagnetism has (from the very beginning) predicted that EM waves propagate with a speed sqrt(1/(εμ)). The historical relevance of the Weber/Kohlrausch experiments is that they noticed that this speed closely approximated the speed of light, giving strength to the hypothesis that light is an EM wave. Once you expcept that light is an EM wave (I think that there is no dispute about that) it is a simply consequence of Maxwell's theory that c^2 = 1/(εμ).
 * I also fail to understand your surprise at the fact that ε_0 is fixed in the modern definition of the SI. You seem to hold no such surprise for the SI definition for the Ampere fixing the value of μ_0, and seem to be blissfully unaware of the plethorea of alternative units used before the SI in which ε_0 was a dimensionless constant of value 1. (e.g. Gaussian units, ESU, etc.)(TimothyRias (talk) 08:29, 17 August 2009 (UTC))

Timothy, I've looked into magnetic permeability already and I know that it is a defined unit. I know the story. It was Gregorio de Giorgi of Rome's idea, and he promoted it at the sixth international electrical congress in St. Louis, Missouri in 1904. I don't have a problem with it because it doesn't lead to any tautologies. So long as permittivity remains a measurable quantity then nothing is destroyed as regards the 1856 experiment of Weber and Kohlrausch, which is of course about a numerical ratio.

Getting back to the main point, yes, Maxwell used the theoretical form of the equation c^2 = 1/(εμ). In fact in his 1861 paper, it appears at equation (132). It is in fact Newton's equation for the speed of sound. But the linkage to the number that closely relates to the speed of light is exclusively a consequence of the 1856 experiment. Maxwell never produced that number from his theory. He travelled down from Galloway to London in order to look up the results of Weber and Kohlrausch's experiment. That equation, when it involves the speed of light, is not a product of Maxwell's work alone. It is a combined product of Maxwell's theoretical work and the experimental work of Weber and Kohlrausch.

This matter is now being discussed at the wiki-physics project page. I no longer wish to discuss it on this page because the matter has a wider significance for physics in general beyond this particular article. David Tombe (talk) 11:12, 17 August 2009 (UTC)

Explaining the physical significance in the lede
Would it be possible (without opening up a whole can of worms...) to put a sentence or two in the lede to explain how epsilon_0 is related to the physical quantities such as force and charge. Something along the lines of:


 * $$\epsilon_0$$ relates the electrostatic force between two separated electric charges to the magnitude of those charges and the distance between them (Coulomb's law):
 * $$\ F = \frac{q_1 q_2} {4 \pi \epsilon_0 r^2}. $$

(with appropriate footnotes to make it clear that this relationship defines q, rather than provides a basis to measure $$\epsilon_0$$, is only exact in free space, etc.)

As it stands, the article (and especially the intro) covers the metrology aspects, but doesn't explain why we bother defining it at all! Djr32 (talk) 13:18, 10 October 2009 (UTC)


 * Physically there is no reason to define $$\epsilon_0$$ at all. Its existence is mostly an historical accident. It's value is not determined by any property of nature but by the units we decide to use for charge, time, length and energy. It carries no more physically information then for example Boltzman's constant.
 * That being said, the lead can and should be much more clear about the role it traditionally plays in physics. (TimothyRias (talk) 20:49, 10 October 2009 (UTC))

Name (yet again)
This was discussed at some length above, but that was back in 2007. I'll open the question again: can we move the article to electric constant, the name preferred by CODATA, the BIPM and NIST?

Let's take a look at the normal definition of permittivity:
 * $$\mathbf{D}=\varepsilon \mathbf{E}$$

where D is the electric displacement field and E is the electric field. You cannot use that definition to define a "vacuum permittivity" because there cannot be an electric displacement field in a vacuum (at least, not in classical terms). I guess that's why the name became "electric constant" in the first place, although I haven't got any reference to back up that hunch. The change is relatively recent – the 1986 CODATA set of values was still using "permittivity of vacuum" while the 1998 set uses "electric constant". Physchim62 (talk) 01:13, 1 April 2010 (UTC)

I agree. I've had 3 emags textbooks over the past 4 semesters, and all of them said "Electric constant". And while I know Google is not an oracle, "electric constant" is recognized by Google Calculator while "Vacuum Permittivity" and "Permittivity of free space" are not. Dmesg (talk) 15:01, 1 April 2010 (UTC)


 * I support the move, but I see that User:Stevenj is still active, and I do not wish to get in another fight with him over this. /Pieter Kuiper (talk) 23:31, 22 July 2010 (UTC)


 * I support considering the move as well, since NIST, CODATA, and BIPM use "electric constant" according to User:Physchim62. If this is pursued further, I suggest we look at WP:COMMONNAME and make sure "vacuum permittivity" is not much more commonly used in the literature than "electric constant". 71.113.43.168 (talk) 07:31, 26 December 2010 (UTC)


 * Comment: the statement "there cannot be an electric displacement field in a vacuum" is incorrect. It is nonzero in vacuum whenever there is an electric field.  —Quondum 22:32, 17 January 2017 (UTC)

Displacement in a vacuum?
From the article: In the vacuum of classical electromagnetism, the polarization P = 0, so εr = 1 and ε = ε0.

Therefore D = ε0. E. But what can be displaced in a vacuum??? — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 15:08, 20 February 2020 (UTC)

Proposed merge Coulomb constant → Vacuum permittivity
The Coulomb constant is already discussed fully at Vacuum permittivity; it does not warrant own page as this is just duplication of content. —Quondum 17:40, 8 March 2023 (UTC)


 * Support – as proposed and as nom. —Quondum 13:47, 25 March 2023 (UTC)
 * Oppose: The vacuum permittivity of free space is just a rationalization of the Coulomb constant; the fact that we find the former convenient is mostly due to the fact that we usually calculate forces between plates (e.g. capacitors) and not point charges – but this is very anthropocentric. It would be a bit like having a page for the gravitoelectric constant $$~\varepsilon_g = \frac{1}{4\pi G }$$ without having a page for the gravitational constant. --Grufo (talk) 17:37, 10 March 2023 (UTC)
 * Support merge. In both cases, to discuss two closely related constants, you only need one page. In case of gravitation, it is by convention gravitational constant. In case of electromagnetism, the SI equations are usually written in terms of vacuum permittivity. Due to importance of the SI, the natural choice for the merge direction is Coulomb constant —> vacuum permittivity. Jähmefyysikko (talk) 16:51, 12 March 2023 (UTC)
 * Due to importance of the SI The SI's main goals are exactness, reproducibility and what is easy to measure, to the point of arriving to define the ampere instead of the coulomb as base unit (which would be a total idiocy if it weren't for the fact that an ampere is easier to build in a laboratory than a coulomb); this is simply how metrology works. But physics is something else, and having as main page a derived (rationalized) constant just because we deal with capacitors is for electricians, not physicists (and would have little encyclopedic value). At the moment the SI considers the Coulomb constant as derived from the vacuum permittivity, but (1) a stronger argument would be necessary to bring physics under the SI' exclusive jurisdiction (2) the SI changes position every 10-15 years and currently there is a lot of debate about the opportunity of choosing as base what is clearly derived (3) the Coulomb constant has quite a big historical significance. And even if all these three points are addressed, the Coulomb constant might still deserve its own page. --Grufo (talk) 17:29, 12 March 2023 (UTC)
 * Note that different systems have different ways of defining the two constants (k_e is 1 in Gaussian units.) Ultimately then, the difference only exists in semantics, which should not necessitate multiple articles. It may be advantageous to combine both articles to these differences can be acknowledged and for easier bookkeeping, without cross referencing two pages. Axxerty (talk) 03:52, 24 March 2023 (UTC)
 * By playing with natural units you can easily define both the Coulomb constant and the vacuum permittivity as composite constants (e.g. a “fundamental force” divided by the square of a “fundamental charge” multiplied by the square of a “fundamental distance” in the case of the Coulomb constant, or the inverse multiplied by $1⁄4π$ in the case of the vacuum permittivity). This passage might be needed because both the Coulomb constant and the vacuum permittivity don't express meaningful stand-alone dimensions (i.e. the Planck constant expresses an angular momentum, c expresses a speed, the Boltzmann constant expresses a heat capacity, but what meaningful dimensions do the Coulomb constant and the vacum permittivity express? They just look like proportionality constants!). So, if not pure semantics, as you said, we are very close to that. The choice is then whether Wikipedia should prefer a constant used for what occurs naturally (point charges) or instead a constant used for what occurs artificially (e.g. capacitors). Or, as my opinion goes, whether it should not favour any of the two but preserve instead both pages as they currently are. --Grufo (talk) 12:20, 27 March 2023 (UTC)
 * Support merge. The vacuum permittivity is the more fundamental of the two, as it appears in the fundamental Gauss's law. In fact, past point charges, the physics student will seldom use the coulomb constant again. The only possible downside of merging is for new physics students searching for answers, but leaving the correct redirect to an appropriate section would easily fix the issue. Axxerty (talk) 03:42, 24 March 2023 (UTC)
 * “Past point charges”? There is literally nothing else in nature other than point charges. --Grufo (talk) 11:57, 27 March 2023 (UTC)
 * Support merge. We have too many tiny physics articles scattered all over the place, and we should be organizing concepts by what they are, not by what they're called. Having both Coulomb constant and Vacuum permittivity is redundant and makes for harder maintenance. XOR&#39;easter (talk) 17:17, 16 March 2023 (UTC)
 * Support merge. The Coulomb constant is basically defined by vacuum permittivity, and there is no reason to have both pages up. As Axxerty said, just leave the redirect up and it should be fine.
 * Captain Chicky (talk) 14:39, 7 May 2023 (UTC)

Merged per consensus here. —Quondum 23:16, 9 May 2023 (UTC)

A question on notation
What is the "(14)" in 8.8541878188(14)×10−12 ? Times 14? Reference 14? 14 sig figs? Bystrc (talk) 15:07, 10 June 2024 (UTC)


 * It is the uncertainty in "concise form"
 * https://physics.nist.gov/cgi-bin/cuu/Value?ep0 Bystrc (talk) 15:10, 10 June 2024 (UTC)