# Talk:Vacuum permittivity

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## What is this article meant to be about ? (and "name" again)

Hi ! I have some expertise in this area, and have been doing some tidy-ups on this article. In doing so, I have removed some material that appears to be irrelevant to the topic under discussion, and also I have removed a couple of statements that in my view are not technically well formulated. [For example, in the same way that you cannot "put π=1", you cannot "put ε0 = 1".] You can certainly manipulate the form of Coulomb's law, but (post 1970) this is not a technically correct way of describing how to do it. I have also added a section on why ε0 has the value it does, which does cover the issue of other unit systems.

I have done the tidy-ups because (quite apart from the name issue) there appears to be some confusion about what this article ought to be about. In my view, it should be about the parameter ε0 - which basically is a mathematical parameter associated with the design of the current international system of measurement, and about this alone. This article should probably not include material about the properties of the vacuum.

On the name issue, the problem with the name "vacuum permittivity" is that the Standards Organizations apparently regard names of this type as confusing or potentially confusing, because they contain the hidden message that ε0 represents some physical property of free space and/or the vacuum. This is my view too. It may be the most popular name - but what is the point - in an encyclopedia - of using a name that the technical experts regard as confusing ? Does this expedite or slow down the progress of science ?

I appreciate that opinions are strongly held on both sides, so can I suggest a compromise - namely that this article is called: "The scientific parameter ε0" (or something like that), and that re-direct links are put in from all the accepted alternative names. If no-one has objection to this, then I will do this in due course, and also deal with the question of disambiguation from the mathematical quantity ε0. (RGForbes (talk) 01:02, 27 March 2009 (UTC))

I think that "The scientific parameter ε0 is not a very good article name; and it's unclear whether subscripts can work in a name. The present name is still what this parameter is most widely known as, so I'd leave it. Dicklyon (talk) 02:13, 27 March 2009 (UTC)
I am not inclined to attempt to press this point if it is not thought helpful. "Vacuum permittivity" is ok as a title as long as the article itself is clear about the nature of ε0 and does not contain confusing material. .(RGForbes (talk) 15:05, 27 March 2009 (UTC)).
I'd agree with Dick that naming the article "The scientific parameter ε0" is not going to help. First, it will make the article impossible to find directly unless a host of redirects are invented. That solution simply puts the plan back to square one: it's no better than leaving things as they are. At least one can google "electric constant" or "permittivity of free space" or "vacuum permittivity" and find actual printed works where this terminology is used.
As pointed out at various places above, the article must make clear to the new reader some confusion about several closely related but different things:
1. The role of ε0 as a property of free space
2. The role of ε0 as a property of an ideal model of vacuum
3. The relation between "free space" and a model of "ideal vacuum"
4. The ambiguity in usage of "vacuum" to refer variously to the reference state free space and also to realizable vacuum like outer space; ultra-high vacuum; quantum vacuum; QCD vacuum; etc., leaving it to the reader to infer from context what is meant
My take is that one can, of course, define a model of vacuum (call it ideal vacuum) where ε =ε0 and μ = μ0. Having done that one can inquire whether (for example) outer space ultra-high vacuum etc are well approximated by this model. This is an experimental issue. One can also inquire whether QCD vacuum or quantum vacuum agree with this ideal model. That is ultimately an experimental issue also, but lacking the technique, it is more a theoretical issue right now.
One can also ask how this ideal model relates to the reference state referred to as "vacuum" by BIPM and NIST. This is a metrology issue, not an issue of accuracy of the model, but an issue of utility to the community of a particular point of reference. (Like the length of the king's arm for a yard, the choice of reference is arbitrary, but some choices are more convenient than others.)
Rewriting the article is fine, but these issues should be dealt with to avoid continually re-rewriting the article because of confusions that arise in every new reader of the article. Brews ohare (talk) 02:42, 27 March 2009 (UTC)
As I see it, the only way that "physics" rather than measurement system decisions might enter into the allocation of a numerical value to ε0 is via the parameter c0, commonly called the "velocity of light in free space" or the "velocity of light in vacuum". My take on this is that, if c0 were to be considered as a measured quantity (which it was some years ago, but now is not), then it would be better to call it (or think of it as) "the velocity of light in real vacuum" (which may have all the features and problems that you describe of it). I leave aside the issue of the relative permittivity and permeability of air, which have to be corrected for. If real polarisable vacuum is different from free space and different from old-style non-interactive vacuum, then these latter two ideas are presumably hypothetical ideas that have no role (or only a limited role) to play in physics. The measurements of the velocity of light that took place some years ago (when c0 was not a defined constant) took place in real polarisable vacuum (possibly with some gas in it). Therefore, the existing defined value of c0 takes into account that light actually travels in a real vacuum (whatever we think that is). Therefore, discussion of hypothetical ideas of "free space" and "ideal vacuum" are simply not relevant in an article that discusses ε0. The discussion of ε0 is already set in the context of the real world in which light travels in a polarisable vacuum. [Alternatively, you might want to take the view that, nowadays, the term "free space" is synonymous with "real polarisable vacuum".]
This is my current view. If, however, you were able to show that, in real polarisable vacuum, Maxwell's equations are not correct, and/or that it is not true that ε0μ0=1/(c0)2, then the Standards Organizations would presumably take this into account (and you might get a Nobel prize !) At present they have not considered it necessary to do so, as far as I know.
I have no problem with the basic idea that the speed of a photon might be affected by its interaction with virtual electron-positron pairs. So I do not dispute the reasonableness of your views about considering the nature of a vacuum: I dispute their relevance to this article, which is about ε0 (whatever we individually prefer to call it). I do not see how the matters you raise could affect the value allocated to ε0. Why not add your views to an existing article on free space or vacuum or the speed of light, or put them in a separate article on the electromagnetic properties of vacuum ? There is also the question of whether, in the context of an article on ε0, your views constitute "original research" of a kind that should not be included.
Aside from all this, I do think that you have established a case for making the point briefly in the article that (c0), called the "velocity of light in free space", really means the "velocity of light in a real vacuum".(RGForbes (talk) 15:05, 27 March 2009 (UTC))

Hi RG: I disagree with your summary that "velocity of light in free space", really means the "velocity of light in a real vacuum". The point is that free space is not a real (realizable) vacuum, but is a reference state, unobtainable in practice. However, the defined values of speed of light, ε0, etc. do apply to free space. Maybe they apply to real vacuum with some error bars attached, but certainly not with defined values. Brews ohare (talk) 15:47, 27 March 2009 (UTC)

Hi ! First, I think that my use of the term "in free space" may be confusing discussion, so I'll stick to "vacuum". Main point is: No - I think that logically it has to be the other way round - I agree with you that we have to make a distinction between "real vacuum" and what I'd like to call "ideal vacuum" - but the original experiments on measuring the velocity of light took place in "real vacuum" (possibly with some gas molecules in, of course, but let's assume that this can be corrected for), so the defined velocity that we now have must be the velocity that applies to real vacuum. I think that the issue is what do the words "in vacuum" mean in the definition of c0 as the velocity of light "in vacuum". I think that - in this context - they have to be interpreted to mean "in real vacuum". Maybe in other contexts they should be interpreted to mean "in ideal (unrealizable) vacuum". Where your arguments possibly go is to suggest that Standards Organizations need to be more precise in defining what is meant by "vacuum". However, I think that, if you raise this matter, then you might get the reply that it is thought to be obvious that "vacuum" means "real vacuum", because it is is impossible to perform experimental measurements in hypothetical unrealizable vacuum (so why would Standards Organizations be interested in specifying quantities applying to this). (RGForbes (talk) 23:32, 27 March 2009 (UTC)) (Richard)

Hi Richard: I hope you will have some patience with the following summary of events. It might be helpful if we have some common background for the present discussion:

No doubt the speed of light was measured originally using a "standard meter". That led to the number for c_0 eventually settled upon. These measurements came from various sources, but I gather the definitive values came from microwave cavity resonators, which used the relation c = λf, with λ based on measured cavity dimensions using the standard meter.
Later came the decision to define c instead of the meter, and use λ = c/f = cT to determine the meter instead of measuring c using the standard meter. That decision is based upon where the errors come from, and the decision that for now the errors come from establishing frequency. To avoid massive retooling expense they stuck with a number for c close to the measured value, instead of rounding it off at some nice value.
The definition of the meter refers to "vacuum", but description of what "vacuum" means is oblique, shall we say. The closest we come is some remarks about "corrections to account for imperfection of the vacuum", and about using lengths short enough that spacetime curvature is not a factor and so forth. When push comes to shove, they will sell you a list of standard corrections they have accumulated so far.
The problem is recognized: Mohr et al., after pages of math about vacuum polarization etc. say things like "The improvements that led to the reduction in uncertainty include a more stable external reference cavity for locking the 486nm cw dye laser, thereby reducing its linewidth; an upgraded vacuum system that lowered the background gas pressure in the interaction region, thereby reducing the background gas pressure shift and its associated uncertainty;… and: "The most notable change in the experiment is that in the new apparatus the entire balance mechanism and moving coil are in vacuum, which eliminates the uncertainties of the corrections in the previous experiment for the index of refraction of air in the laser position measurements… ". However, I have yet to find any detailed discussion of how the errors contributed by imperfect vacuum compare to those in determining frequency.
So what are we doing when we correct for imperfections?
I'd suggest that what is going on is that there are theoretical expressions for the parameters of any particular medium, for example, air, in terms of measurable "imperfections" such as partial pressures of contaminants. So one measures the partial pressures, or estimates them indirectly from other considerations, and then cheerfully subtracts these "corrections" to refer the results to "vacuum".
I'd say that the brief way to say all this is that extrapolation is being used to take real measurements back to a baseline that is some "ideal vacuum" that never can be realized, a nirvana where c=c_0 μ = μ_0 by definition. For example, interference fringes are counted as a chamber is pumped down, and a theoretical fit is extrapolated to zero pressure. Should it evolve that this procedure is pure fantasy, and that no such "ideal vacuum" exists even in principle, it really doesn't matter as long as the convention is to follow the procedure with the established corrections so that everything is measured from the same reference point, be that a fiction or not. I'd say that in fact, it is abundantly clear from theory so far that, in fact, there absolutely is no such medium as one with c=c_0 μ = μ_0; it certainly will be impossible to prove existence by experiment, because experiment always has error bars. It will, however, eventually become possible to show experimentally that there exists absolutely no known medium in which the speed of light is unreservedly field-independent, polarization-independent, isotropic and dispersionless.
Is this your view of the situation? Brews ohare (talk) 01:13, 28 March 2009 (UTC)
Hi Brews! I concur that we should attempt to reach consensus on the physics, before discussing what to do about it in the context of Wikipedia. I agree with the first part of what you say, but want to analyze the second part more carefully. Let me use some temporary terminology.
Ideal classical vacuum is defined to be hypothetical classical "definitely empty" space. In particular, ideal classical vacuum has in it no gas atoms or molecules, or anything else that could be classically polarized by an electric field.
On the other hand, "ideal quantum-mechanical vacuum" is defined to be space that is free of "classical polarizable objects" (such as atoms and molecules), but may contain phenomena or entities associated with electromagnetic zero-point energy and/or virtual electron-positron pairs, and/or anything else of this general kind that theoreticians tell us is always there (I am not an expert on what's currently considered to be there).
Now, I assume that 100 years ago, when Maxwell's equations were formulated, an assumption was around that "real ideal vacuum" was what I have just called "ideal classical vacuum". However, nowadays we assume that "real ideal vacuum" is "ideal quantum-mechanical vacuum".
The 1700s and 1800s experiments that underlie Maxwell's equations were conducted in air, which we now understand to be "ideal quantum-mechanical vacuum with polarizable atoms and molecules in it".
Therefore, in my view, when corrections for the presence of polarizable atoms and molecules were made in metrology before c0 became a defined quantity, what was done was to correct the value of the speed of light back to a reference state that is the "ideal quantum-mechanical vacuum". Obviously, at some time in the past, metrologists may have thought that they were correcting the value of light back to a reference state that was "ideal classical vacuum", but it seems to me that the "classical" method of making corrections takes us back to ideal quantum-mechanical vacuum, not to ideal classical vacuum.
Certainly, in the Mohr article, when considering energy levels, they are working in the context of "quantum-mechanical vacuum".
There might be a question of whether additional corrections should be made to take the velocity of light back to the hypothetical reference state of "ideal classical vacuum", but in my view there is no reason why this should be done (certainly not as part of normal metrological activity). This is because there is no way that experiments can be done in ideal classical vacuum (so why should a Standards Organization bother to make a correction to this hypothetical state).
Obviously, in principle, there are a number of questions that could be asked both about ideal classical vacuum and about ideal quantum-mechanical vacuum. These include: Do Maxwell's equations take exactly the same form in both cases ? Is the speed of light isotropic in both cases ? Is the speed of light the same in both cases ? What form should the constitutive relationships take ? Whether it is really sensible or useful to ask such questions, I am not quite sure, because I am not an expert on these things. But they do not appear to me to be obviously stupid questions – even if accepted answers already exist to some possible questions.
I assume that, if the velocity of light were not isotropic and uniform in "real ideal vacuum" (i.e., in "ideal quantum-mechanical vacuum"), then: either (1) we would know about it (for example, as a consequence of experiments done to test the special and general theories of relativity); or (2) any anisotropy or speed non-uniformity is so small that it is masked by other (more significant) errors and/or uncertainties. If (2), then at this point of time we do not need to concern ourselves about these things in the context of an article on ε0.
This is my view of the physics. If there is a difference between our views, I think it would relate to the issues of: (1) what reference state actually is used by Standards Organizations when defining the velocity of light; and, possibly (2) what reference state should be used by Standards Organizations. However, I think that it is more likely that we would agree that the reference state is what I have called "ideal quantum-mechanical vacuum".
Where I think these arguments might take you is to the conclusion that the constitutive relation (relating the D-field to the E-field) needs amendment. Perhaps there could be a need to write this in the form:
D=ε0E + Pclass = ε0E + PtotalPquantum
where Pclass is the classical polarization of a medium, Pquantum represents effects due to "quantum mechnical polarization of the vacuum", and Ptotal is the "total polarization of the medium". I abstain on whether this is sensible physics or not.
There are then issues relating to Wikipedia. The first is – if these are original research discussions then maybe these issues should not be included in Wikipdeia at all – I abstain on this, as I have not looked for references to discussions of this kind in the literature. The second is – should these issues be discussed in the context of an article on ε0? My view is that they are primarily issues that relate to the speed of light and/or to the nature of the concept of vacuum, or the concept of free space. Therefore, in my view, the primary discussion should be in one or more of these places, with a link or links to it from this article on ε0.
In particular, I would personally prefer to see the section on "Realizable vacuum and free space" moved to a more relevant article, with links to it from this article. This is because (in my view) you do not have to go into these complicated issues when trying to tell an undergraduate physicist or electronic/electrical engineer what ε0 is. (RGForbes (talk) 19:08, 29 March 2009 (UTC)) (Richard)

## Last paragraph of intro

Presently reads:

A common mistake is to think that ε0 is a physical constant that describes some physical property of the vacuum or of free space. This is not true: ε0 is a measurement-system constant introduced and defined as a result of international agreement. In physics there may be issues relating to the physical properties of the vacuum or of free space, but they are separate from issues relating to the meaning and value of ε0.

This paragraph tries to do too much in too few words. Here is a proposed replacement:

A common mistake is to think that ε0 is a physical constant that describes some physical property of a realizable "vacuum". This thought is not true: ε0 is a measurement-system constant introduced and defined as a result of international agreement. It refers to a property of what sometimes is called free space, which is not a realizable vacuum, but is a reference state or benchmark simply used as a baseline for comparison of measurements made in all types of real media. In physics there may be issues relating to the physical properties of realizable vacuums such as outer space, ultra-high vacuum, QCD vacuum or quantum vacuum, but they are separate from issues relating to the meaning and value of ε0, all of which are metrology issues. Brews ohare (talk) 03:00, 27 March 2009 (UTC)

I've inserted a modified version of the above proposal intended to separate the notion of free space from realizable vacuum. Brews ohare (talk) 17:24, 27 March 2009 (UTC)

Not totally happy with the revised statement, but I'll think about it. (RGForbes (talk) 23:36, 27 March 2009 (UTC)) (Richard)

Have concluded that the only further change needed is to make it clearer that the issue is the velocity of light in the reference state/situation, and have implemented this change (RGForbes (talk) 23:53, 29 March 2009 (UTC)) (Richard)

## 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 [1]. 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 ${\displaystyle 1/{\sqrt {\epsilon \mu }}}$, 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:

${\displaystyle \epsilon _{0}}$ relates the electrostatic force between two separated electric charges to the magnitude of those charges and the distance between them (Coulomb's law):
${\displaystyle \ F={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}.}$

(with appropriate footnotes to make it clear that this relationship defines q, rather than provides a basis to measure ${\displaystyle \epsilon _{0}}$, 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 ${\displaystyle \epsilon _{0}}$ 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:

${\displaystyle \mathbf {D} =\varepsilon \mathbf {E} }$

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)