# Permittivity of free space [closed]

Free space is a region in which there is no matter and no electromagnetic or gravitational field. Which means that the resistance in free space is zero, because there is no resisting force and as far as I know, free space is a synonym for "vacuum" and there is no resistive force in a vacuum. So, how is the permittivity of free space, not zero? Permittivity is a property that measures the opposition against an electric field, but there is no resistance in free space, no opposition?

• Who says that the scale for permittivity needs to start at 0? In vacuum the susceptibility vanishes (and thus the polarization is zero), which corresponds to a (relative) permittivity of 1. I don't see the problem... Aug 6 at 15:07
• "Free space" means a region with no charge or current, not a region with no fields. It's also unclear what you mean by "resisting force," since that is not standard terminology.
– Buzz
Aug 7 at 1:27
• what i mean by "resisting force" is air friction. Aug 30 at 15:06

$$\epsilon_0 \rightarrow 0$$ would cause the Coulomb force:

$$F = \frac 1 {4\pi\epsilon_0} \frac{q_1q_2}{R^2}$$

to diverge because:

$$\nabla\cdot\vec E = \rho/\epsilon_0$$

would lead to an infinite electric field.

Of course, in Gaussian units, there is no permittivity nor permeability, they are absorbed in $$c$$.

But back to SI units: the impedance of free-space is:

$$Z = \sqrt{\frac{\mu_0}{\epsilon_0}}\approx 377\,{\Omega}$$

I think the essential point here is the difference between a multiplicative constant and an additive constant. The permittivity is a proportionality constant appearing in a formula such as $$F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{ r^2}$$ This might be compared to the gravitational formula $$F = G \frac{m_1 m_2}{r^2}.$$ We would not expect $$G$$ here to be equal to zero, nor infinity. In a similar way we should not expect $$\epsilon_0$$ to be either zero or infinity. The reason why you might have thought zero is because of the name, "permittivity of free space". So perhaps that name is offering a slight misdirection.

Permittivity is a property that measures the opposition against an electric field

In my opinion that is not a good way of thinking about permittivity. I prefer to think about it as a dielectric property.

In a dielectric consisting of matter there are for instance polarized molecules present. The permittivity correlates with how much energy it takes to reorient the polarized molecules, bringing them into alignment with an external electric field. That reorientation of molecules sets up a stress in the material. There is a correlation between the energy required for that reorientation to happen, and the tendency of the material to revert to neutral state when the external electric field goes away.

The permittivity of free space is an essential factor in the propagation of electromagnetic waves. That is, if free space would not have any permittivity then propagation of electromagnetic waves would not exist.

Comparison:
In free space there is no matter present, and consequently: in free space there is no propagation of sound.

The speed of propagation of electromagnetic waves correlates with the tendency to revert to neutral state. The stronger that tendency, the faster the propagation of the wave.

On the physics of propagation of electromagnetic waves:

Maxwell, in his work towards a theory of electromagnetism, proposed that there is a background state of something omnipresent, that background state is thought of as uniform, neutral. Maxwell proposed that the mediator of the electrostatic force is a stressed state of that entity. When the source of the electrostatic potential is neutralized the thing that goes away is the state of stress of the background entity, the background entity itself does not go away, it reverts to uniform, neutral state.

As we know: in Maxwell's time physicists referred to that background entity as: 'the luminiferous Aether'.

As we know: upon the introduction of Special Relativity, in 1905, many concepts changed profoundly.

But there were also things that carried over to relativistic physics. As we know: it was not necessary to create a replacement for Maxwell's theory of the electromagnetic field. In retrospect we see that Maxwell's electromagnetism anticipated relativistic physics.

In retrospect: before the introduction of relativistic physics Maxwell's theory of the electromagnetic field was already a theory that exhibited Lorentz invariance.

The permittivity is a constant of proportionality between charge and the electric field the charge generates. Specifically Maxwell's equations tell us:

$$\nabla\cdot\mathbf E = \frac{\rho}{\varepsilon}$$

Here $$\rho$$ is the charge density and roughly speaking $$\nabla\cdot\mathbf E$$ is how much electric field the charge density creates. If the permittivity of the vacuum was zero, as you suggest, then even the tiniest charge would create an infinite electric field.

The numerical value of $$\varepsilon_0$$ depends on the units we choose for the electric field and the charge. Choosing volts and coulombs gives us the well known value:

$$\varepsilon_0 \approx 8.854 \times 10^{-12} C~V^{-1}m^{-1}$$

The vacuum may not be completely devoid of anything? It may not be a complete vacuum.

The permittivity of free space, $$\epsilon_0 = 8.8541878128 \times 10^{-12} F⋅m^{-1}$$ (Farads per meter).

So, there could be a resisting force, as permittivity has the SI units of Farads per meter $$F/m$$, or in basic units $$F/m \equiv kg^{-1}⋅m^{-2}⋅s^4⋅A^2⋅m^{-1}$$. Force is from $$F = ma \equiv$$ $$kg \ m s^{-2}$$ (units). So, the units of force are located in permittivity of free space (i.e. kilogrammes, $$kg$$, meters, $$m$$ and seconds, $$s$$). It's just the vacuum is a difficult concept to understand!

"A vacuum is a space devoid of matter. The word is derived from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space..." (1)

"...The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around $$20$$%. But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth ($$10^{-12}$$) of atmospheric pressure ($$100$$ nPa), and can reach around $$100$$ particles/$$cm^3$$. Outer space is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space..." (1)

"...Later, in 1930, Paul Dirac proposed a model of the vacuum as an infinite sea of particles possessing negative energy, called the Dirac sea. This theory helped refine the predictions of his earlier formulated Dirac equation, and successfully predicted the existence of the positron, confirmed two years later. Werner Heisenberg's uncertainty principle, formulated in 1927, predicted a fundamental limit within which instantaneous position and momentum, or energy and time can be measured. This has far reaching consequences on the "emptiness" of space between particles. In the late 20th century, so-called virtual particles that arise spontaneously from empty space were confirmed." (1)

References

• Isn't spacetime a component of "empty space"? Aug 7 at 0:00