# What causes the permittivity and permeability of vacuum?

When light travels through a material, it gets "slowed down" (at least its net speed decreases). The atoms in the material "disturb" the light in some way which causes it to make stops on its path. This is expressed in the material's permittivity and permeability: Its ability to transmit electromagnetic waves.

But then what causes the limited permittivity and permeability of vacuum? There are no atoms there to disturb the light, so what is keeping it from travelling at infinite speed? Is there a special property of space itself which determines the speed of light? Or is it the virtual particles in vacuum which interact with the light?

• Excellent question. Short answer: nobody knows. A much simpler (but closely related) question is why is c equal to 3 x 10^8 m/s? Saying that this is the speed achieved by an EM wave moving through a material with the same permittivity and permeability of a vacuum at best takes you nowhere and at worst is circular. There are lots of constants like these in physics for which we have no explanation (eg Planck's constant, the force of gravity), maybe one day we will know why they are what they are ... – Peter Webb Mar 1 '15 at 13:45
• Not a single answer........which fully satisfy the question querry – dr. honey Mar 27 '17 at 13:23
• Since the speed of light is not infinite, vacuum permittivity has to be nonzero as well. In a loose sense, with a bit of handwaving, nonzero vacuum permittivity is the result of information about changes in an electric field (for example due to the movement of some charge) having to take some time to travel across some distance. You see, a vacuum doesn't necessarily "obstruct" or "interact with" electrical flux, but will have at least some kind of nonzero "permittivity measurement associated with it" due to electrical flux information not traversing a nonzero distance infinitely fast. – ManRow Sep 13 at 10:20

I think that the fact that Electro-Magnetic Waves (EMW) have a finite speed in vacuum can be explained by two things in the classical theory of electromagnetism:

• There is no action at a distance

• EMW are excitations of an EM field

The fact that the EM field in itself does not need any material substance has been debated a lot at the end of 19th century but that's an actual fact that has been proven true in the beginning of the 20th century.

The question is then how does an EM field propagate?

• First an oscillating current induces an oscillating electric field
• electric field that in turn induces a rotating magnetic field
• that itself induces another electric field
• and so on and so forth

as depicted in the figure The field, even in vacuum has an intrinsic resistance to "curvature" where the resistance for an electric curvature would be different from that of a magnetic. These perimitivity and permeability are responsible for the time scale needed for all these fields to induce one another (without dissipation). At the end of the day, we just measure experimentally that this intrinsic speed of propagation is $c$ and appears to be invariant upon change of frame of reference.

• This doesn't constitute an explanation of the cause of the values of $\epsilon_0$ and $\mu_0$. If it did, then it would also be an explanation of the cause of the value of $c$, which is related to them. But there can't be any fundamental explanation of the value of $c$, for the reasons explained in my answer and in more detail in the paper by Duff that I referenced there. – Ben Crowell May 16 '13 at 21:57
• This explain how light does not have an infinite speed in vacuum. I did not want to enter the discussion on the actual values of the permitivities as they depend on the units used. – gatsu May 16 '13 at 22:12
• This is actually a very nice visual explanation for why the wave has a finite propagation speed, even in vacuum. The fields simply cannot "bend back" any faster, so they cannot cause the wave to go faster either. How physically accurate this explanation is, is not clear to me yet. But thanks for the image and the clear relation between the wave and the oscillating field that causes it. – Koen Van Damme May 18 '13 at 15:50
• Just to reassure you, this is a physically accurate description that gives a rational on how light can have a finite speed. Even in quantum field theory, that is the best description we have on the world so far, light is still described with a field. One could still wonder however, if there could exist a magic medium in which light could travel even faster than in vacuum (up to infinity) and the answer seems to be no as it has be shown in Einstein's special and general relativity theories (mentioned by xaxa who does not deserve 2 downvotes btw) – gatsu May 18 '13 at 19:24
• OK Thanks for the explanation. This is actually the answer I was looking for. – Koen Van Damme May 21 '13 at 7:35

What causes these constants to have the values they do is simply our choice of a system of units.

When you have a unitless constant, it makes sense to ask why it has the value it does. For example, two of the lines in the visible spectrum of hydrogen have wavelengths in the exact integer proportion of 28/25. When this was first discovered, it made sense to ask why it had this exact value, and the answer was unknown. Later the answer was discovered. Similar considerations apply to other unitless constants of physics such as the ratio of the masses of the proton and electron, or the fine structure constant. There is at least in principle some hope of finding some future theory of physics that can explain their values.

There can never be any such explanation for the value of a constant that has units. That's because the units themselves are arbitrary. Here is a nice discussion of that in relation to the speed of light: Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093

• OK, but I wasn't asking about the reason for the exact values, only for the reason why they're finite. If the vacuum is really empty, nothing would prevent it from permitting an infinite amount of electricity or magnetism to pass through. The limited speed of light in a material is caused by atoms that "block" the waves, at least temporarily. So what causes the waves to be "blocked" in empty space? – Koen Van Damme May 18 '13 at 15:55
• @KoenVanDamme: I don't think the interpretation given in your comment is correct. Materials don't slow down electromagnetic waves by partially blocking them. When an EM wave encounters a material, the charges in the material oscillate and produce a secondary wave. The superposition of the two waves is a wave that moves at less than $c$. – Ben Crowell May 18 '13 at 18:36
• This answer confuses the reader more, please explain in more detail.. – mcodesmart Apr 13 '14 at 1:24

In the cgs system {E,D} and {B,H} have the same units. (This alone is reason enough to use cgs.) In the absence of any medium the response functions must therefore be $\epsilon=1$ and $\mu=1$ and these are dimensionless. Clean and logical.

Yes, it's the structure of space-time itself. Special theory of relativity deals with it.

• No, SR does not explain the value of these constants. – Ben Crowell May 16 '13 at 21:55
• Well, OP actually asks why $c$ is not infinite... – xaxa May 17 '13 at 9:06

I will try relating my answer to quantum degeneracy pressure in electron-gas model of solids. In that case , the pressure is a complete consequence of the symmetrization requirement of the fermions , and it is not any physical "pressure" as such. Similarly , free space has Quantum field fluctuations and the electromagnetic field in free space is quantized (from quantum electrodynamics). And so, this quantization requirement (analogous to symmetrization requirement) results in the physical "opposition" (analogous to pressure) like effect in this electromagnetic wave propagation (Electron-gas solid model) at classical level . So, permittivity and permeability of free space are an indirect consequence of QFT which needs to be traced further .

Permeability is Constant of negative energy. Its counterpart-permittivity- is Constant of positive energy. Interaction between both of them create a physical entity called SPACE-TIME geometry. It is this space-time geometry which makes the speed of light finite. Negative energy attracts inward and acts as glue to make the universe finite and positive energy pulls the universe outward with equal force. In this seeming tug of war, the universe fluctuates between sometime static state and sometime expanding state, depending on where and when an observer perceives the universe.

• Do you have any evidence for any of this? – Kyle Kanos Jul 1 '14 at 19:52