If we look at the formula for the inverse square law for force between two charges Q1 and Q2, a permittivity term is in the denominator. If the permittivity was hypothetically zero, the force between the two charges would be infinite.
Thus the finite permittivity of the vacuum seems like some sort of "sponginess" that prevents this force being infinite and prevents the speed of light being infinite.
The question is what is the origin of this sponginess? Is it explained via virtual particles, zero-point fluctuations, and the quantum foam? Is the explanation quantitative or only a vague picture?
Permittivity and Permeability of vacuum are not just proportionality constants. They are dimensional parameters of great significance in characterizing the physical properties of the entity called 'vacuum'. Fundamental properties of this vacuum or empty space are given by these two parameters and c, the speed of light in vacuum.
In order to really appreciate this let us consider the overall consequence of assumed zero value of the Permittivity (e0) & Permeability (m0) of vacuum on the observable universe. The following are the consequences:
1-c will become infinite as seen from the relation, Sqrt(e0.m0) = 1/c = 0
2-1/c=0 results in the complete collapse of special theory of relativity.
3- A direct result of zero permeability of vacuum is that no magnetic field will be produced by charges in motion- Biot-Savart law.
4-The fourth major consequence that follows from 1/c = 0 & m0 = 0 is that electromagnetic waves will not exist in the vacuum. Even the photons will not be able to exist, since for any finite energy and corresponding finite frequency, their wavelength will approach infinity.
5-The fifth major consequence that follows from 1/c = 0 and the mass-energy relation m = E/c2 = 0 is that the inertial mass m of all elementary particles with energy content E, will be zero.
6-The sixth consequence that follows from e0 = 0 & m0 = 0 is that the force of attraction between opposite charge particles will be infinitely large while their inertial mass and momentum will be zero. As a major consequence of this situation, all opposite charges will mutually annihilate themselves and no atomic structure will be able to exist.
7- The seventh consequence that follows from 1/c=0, and the definition of interval 'd(s)' in four dimensional space-time continuum, is that the time elapsed 'd(t)' between any two events occurring in the space-time continuum will be zero. Hence as a major consequence of this situation, the very concept of time will cease to exist.
From the foregoing we conclude that the overall consequence of assumed zero value of the Permittivity (e0) & Permeability (m0) of 'vacuum' will be the virtual collapse of the observable Universe with no atoms, no electromagnetic waves, no photons and even no time existing any more.
The origin of the non-zero value of these two parameters has recently been investigated by Marcel Urban et al. They show that the vacuum permeability and permittivity may originate from the magnetization and the polarization of continuously appearing and disappearing fermion pairs.
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The quantum vacuum as the origin of the speed of light, The European Physical Journal, March 2013, 67:58
The permittivity of vacuum doesn't have any physical meaning. It is just a constant reflecting the relation between historically introduced electrical units, such as Coulomb, Volt, etc. For physics it is more convenient to use the CGS (or Gaussian) system of units, in which Amperes, Ohms, Watts etc are expressed through Gram, Centimeter, and Second. Then the force between two charges is simply expressed as q1q2/r², with no permittivity of vacuum appearing anywhere.
It is a pity that students all over the world are obliged to memorize numbers like permittivity of vacuum, impedance of vacuum and others, and most professors do not explain where these bizarre things come from. However the advantage is that one obtains results directly in units used by electrical engineers.
Vacuum has non-zero permittivity due to quantum mechanical effects. Virtual particles are continuously created and annihilated. I think the following link will try to answer your question: http://en.wikipedia.org/wiki/QED_vacuum
You should think of the permitivity as a part of the charge. Consider the fine structure constant:
alpha = (e^2/4pi*epsilon_0) / (h_bar*c) = 1/137
where e = elementary charge and h_bar = reduced planck constant. The fine structure constant represents the coupling of charge to the electromagnetic field, and is the same value in all measurement systems (since it's unitless).
Also the quantity
e^2 / 4*pi*epsilon_0 = 1.44 MeV * nm
is in units of energy*length. This is where CGS units come from. The elementary charge is defined to be the square root of this quantity, and so charge is now measured in terms of energy^1/2*length^1/2, and the 1/4pi*epsilon disappears from Coulomb's force law: F = e^2 / r^2
Permittivity and Permeability of vacuum are not just proportionality constants. They are dimensional parameters of great significance in characterizing the physical properties of the entity called 'vacuum'. Fundamental properties of this vacuum or empty space are given by these two parameters and c, the speed of light in vacuum.
In order to really appreciate this let us consider the overall consequence of assumed zero value of the Permittivity (e0) & Permeability (m0) of vacuum on the observable universe. The following are the consequences:
1-c will become infinite as seen from the relation, Sqrt(e0.m0) = 1/c = 0
2-1/c=0 results in the complete collapse of special theory of relativity.
3- A direct result of zero permeability of vacuum is that no magnetic field will be produced by charges in motion- Biot-Savart law.
4-The fourth major consequence that follows from 1/c = 0 & m0 = 0 is that electromagnetic waves will not exist in the vacuum. Even the photons will not be able to exist, since for any finite energy and corresponding finite frequency, their wavelength will approach infinity.
5-The fifth major consequence that follows from 1/c = 0 and the mass-energy relation m = E/c2 = 0 is that the inertial mass m of all elementary particles with energy content E, will be zero.
6-The sixth consequence that follows from e0 = 0 & m0 = 0 is that the force of attraction between opposite charge particles will be infinitely large while their inertial mass and momentum will be zero. As a major consequence of this situation, all opposite charges will mutually annihilate themselves and no atomic structure will be able to exist.
7- The seventh consequence that follows from 1/c=0, and the definition of interval 'd(s)' in four dimensional space-time continuum, is that the time elapsed 'd(t)' between any two events occurring in the space-time continuum will be zero. Hence as a major consequence of this situation, the very concept of time will cease to exist.
From the foregoing we conclude that the overall consequence of assumed zero value of the Permittivity (e0) & Permeability (m0) of 'vacuum' will be the virtual collapse of the observable Universe with no atoms, no electromagnetic waves, no photons and even no time existing any more.
The origin of the non-zero value of these two parameters has recently been investigated by Marcel Urban et al. They show that the vacuum permeability and permittivity may originate from the magnetization and the polarization of continuously appearing and disappearing fermion pairs.
---------------------------------------------------------------------------------
The quantum vacuum as the origin of the speed of light, The European Physical Journal, March 2013, 67:58
Thank you for your detailed explanation, Issam. In my cosmological model, the speed of light in vacuum along with the permeability of vacuum are functions of the gravitational potential.
The great physicist, Sir Eddington speculated a lot on the value of the fine structure constant and tried to calculate it from first principles. Another interesting discussuion of the natural constants I found in the book BBarrow-Tipler: The Anthropologcal Cosmic Principle.
Hi Derek,
I started asking myself similar questions...
Two points in addition to what has been said:
1. your assumption that interaction forces will go infinite are still based on the assumption that vacuum will enable electrostatic field lines to connect the two electrons/ enable interaction via electromagnetic field . What I would question is WHY vacuum allows this to happen ? The obvious consequence is that w/o this property our universe will be forever dark, there will be no chemistry to enable formation of molecules and no life etc.
2. If you look at magnetic properties, there is indeed a material that experiences zero magnetic permeability...the superconductors...it makes no sense talking about speed of light in a metal, but assume a transparent superconductor is ever discovered...would that mean the speed of light through a superconductor would be infinite?
Let me try to help with this interesting question:
1. We could think that the value of the permeability or the permittivity of the vacuum are just phenomenolgical values to accept as the value of the electric charge, Planck constant, fine structure constant, etc...Why not?
2. Some people said that if the permeability or the permability of vacuum were zero then Coulomb law would give an infinite force among the electric charges placed in vacuum. This is obviously out of our experience or physical reality.
3. But curiously the people who notice this difficulty in Coulomb law they don't mention another more inmediate: if the distance between the electric charges is reduced then it happens even worse because this variable enters as one square in this formula. And if you consider the electric field we can say that its value tends to infinite.
4. Notice that the consequences of these values can be quite catastrophic. For instance, if the electric field is so enormeus this means the electromagnetic mass would be also huge and no motion of charges allowed at all!
5. Obviously this means that our limits are wrong the same as our conclusions. The lower limit of classical electrodynamics is quantum electrodynamics and this problems were solved with the name of renormalization of the charge or the mass for the electromagnetic field.
6. The limit at which the classical electric field (or potential) let to be no longer valid is at the Compton wavelength. At such scale the Coulombic potential needs to introduce a new value of the vacuum permeability.
Epsilon zero must be multiplied by the factor
[1-(2a/3ᴫ) ln(r/rc)]-1 when rc >> r
[1+(a/4ᴫ1/2) (r/rc)-3/2 e-2r/rc]-1 when rc
Gentlemen
Don't try to expertise about vacuum's electric permittivity /magnetic permeability when you have no-idea about the nature of electrostatic charge.Both the above are related to it.When after centuries of the study of electrostatic interaction using MKS or CGS units (Coulomb force) or E/M field (Maxwell 's laws) ,still you call as unit of electrostatic charge (cb) , electric current (amp) etc............and you are not bothered about the chaos in front of you that is created by these arbitrarily given names to observable phenomena, spare the rest of us about these useless discussions.Go and do some research at last and present to rest of us some realities like mass ,length , time and the derivatives of them.Please........
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