# Electrical Permittivity of Classical Vacuum - Physical?

Gold Member
The Vacuum Permittivity of the classical vacuum seems to be for just conversion of units in Coulomb's Law, like Coulomb's Constant in disguise.

Does the Electrical Permittivity of the Vacuum in classical electromagnetism have any real physical significance other than in the above context?

Staff Emeritus
This sounds like philosophy. I can measure it. Isn't that enough to make it "real" and "physical"?

Gold Member
True, you can measure it. But consider Coulomb's Law. The "variables" are force, electric charge, the distance between the charges and ε0 (permittivity of the vacuum). My question is ε0 something fundamentally distinct from the other 3 variables, or, with a little algebra, just a function of those 3 variables?

Staff Emeritus
I still don't think you have asked a clear question. What does it mean to be "fundamentally distinct" as opposed to a "just a function"?

Summary:: Vacuum Permittivity

The Vacuum Permittivity of the classical vacuum seems to be for just conversion of units in Coulomb's Law, like Coulomb's Constant in disguise.

Does the Electrical Permittivity of the Vacuum in classical electromagnetism have any real physical significance other than in the above context?

Interesting question- I argue that the permittivity and permeability do have real, physical significance- they relate to the speed of light being finite, for one thing- but the specific numerical value of ε_0 is now considered a consequence of the defined value of speed of light c_0 and measured vacuum permeability μ_0.

c_0 has its specific value defined to ensure 'backwards compatibility' with prior (measured) definitions of the meter and second, leaving the value of ε_0 dependent on both c_0 and μ_0.

But yes, just as c_0 is a way to convert meters into seconds (and vice-versa), ε_0 can be used to convert between (for example) Farads and length.

• LarryS
Gold Member
Interesting question- I argue that the permittivity and permeability do have real, physical significance- they relate to the speed of light being finite, for one thing- but the specific numerical value of ε_0 is now considered a consequence of the defined value of speed of light c_0 and measured vacuum permeability μ_0.

c_0 has its specific value defined to ensure 'backwards compatibility' with prior (measured) definitions of the meter and second, leaving the value of ε_0 dependent on both c_0 and μ_0.

But yes, just as c_0 is a way to convert meters into seconds (and vice-versa), ε_0 can be used to convert between (for example) Farads and length.

Yes, it's as if ε0 is only half of the story. As if it only has physical meaning when it's taken together with either μ0 or c.

Homework Helper
2022 Award
In the end it is only the value of the dimensionless quantities that have any effect upon reality as we know it. The complicating factors include how to measure flux (entire sphere or steradian ) and whether c is primary. One just has to persevere...it is annoying. Dimensionless quantities.

• LarryS
Gold Member
The charge of an electron is fixed in Nature, so the Coulomb force exerted between two of these at a certain distance should give a phyical meaning to εo,

Yes, it's as if ε0 is only half of the story. As if it only has physical meaning when it's taken together with either μ0 or c.

Yes- and that's because the electric field is only half the story :)

Gold Member
2022 Award
This sounds like philosophy. I can measure it. Isn't that enough to make it "real" and "physical"?
The question is, how you can measure it? The answer depends on the system of units used, and I can only guess that the OP is referring to the permittivity of the vacuum ##\epsilon_0## in the SI. So we have to discuss the SI.

Since 2019 the needed "network" of unit definitions to answer this question concerns only the four base units for time (second), length (metre), mass (kg), electric current (A).

The 2nd is defined by the frequency of the a hyperfine transition of the Cs atom. That's the only "material dependent" definition of a base unit left in the SI since 2019. All other units are defined by choosing values of fundamental constants.

Thus length is defined by defining the speed of light.

The kg is defined very implicitly by defining the value of Planck's quantum of action.

The unit of charge is defined by defining the value of the elementary charge (with the electron having -1 elementary charge). In this sense rather electric charge is a base unit (C). However, officially it's still the unit Ampere for electric currents that's a base unit, and of course this directly follows from the definition of the electric charge and time units.

That said makes it clear that ##\epsilon_0## and ##\mu_0## are measurable indeed measurable constants within the SI. They are no fundamental natural constants but just conversion factors due to the choice of the SI units.

• • PeroK and hutchphd
Staff Emeritus
I still think this question is ill-defined.

In some units of measurement (mostly earlier ones), c (to pick a better example) is a measured quantity. In others (mostly later ones), it is defined. Does that mean it was "real and physical" before 1983 and not afterward?

• Motore and tech99
Gold Member
2022 Award
Well, the speed of light is a fundamental physical constant within our current understanding of fundamental physics. It's the "limiting speed" of relativistic space times. That's why it can be used to establish the conversion between the units of time and length as in the SI.

In earlier times, when relativity was unknown, it was of course just a constant of the dimension of speed occurring in Maxwell's equations using quite different units than used today. A classic experiment by Kohlrausch and Weber determined this constant from measuring charges in electrostatic and magnetostatic units respectively, and famously they found this constant to be the same as the then also measured speed of light, leading Maxwell to the conjecture that light is an electromagnetic wave, predicted by his theory.

Mentor
Note that in Gaussian units, neither ##\varepsilon_0## nor ##\mu_0## appear in electromagnetic equations in vacuum: Maxwell's equations, Coulomb's Law, etc.

In a medium, ##\varepsilon## and ##\mu## do appear in these equations, and depend on the properties of the medium.

• PeroK and vanhees71
Staff Emeritus
So ε0 is this a "real physical quantity" in SI and not in CGS?

This is why I say it is ill-posed.

• vanhees71
Gold Member
2022 Award
Of course, if you wish you can express physics entirely without such "artificial" conversion factors, setting all the "fundamental constants" (##G##, ##c##, ##\hbar##, and ##k_{\text{B}}##) equal to one (Planck units). Then you have no more "human arbitrariness" in the fundamental equations of physics.

Gold Member
I still don't think you have asked a clear question. What does it mean to be "fundamentally distinct" as opposed to a "just a function"?
Again, take Coulomb's Law. I don't believe it is confusing to say that Charge (Coulombs or Ampere-Seconds) is real and physical. Likewise, distance squared (space) and Force are also clearly real and physical. Nature "knows" about those things. I don't think it is confusing to ask if the Electrical Permittivity of the Vacuum is equally real and physical or is it just number that relates those fundamental parameters?

Staff Emeritus
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