How permittivity arises in vacuum?

[aditya23456]

I've read that permittivity is resistance offered to flow of field lines,But vacuum does not have anything in it to resist or alternatively to get polarized.but we've seen that vacuum has permittivity constant..How's this possible??

 

[Bill_K]

aditya23456, The so-called permittivity and permeability constants ε₀ and μ₀ have no fundamental significance. They are artifacts of the SI system of units and are not present in other systems. The only fundamental quantity is the speed of light c, derived from their product, c = (ε₀μ₀)^-1/2

 

[Bob S]

aditya23456, The so-called permittivity and permeability constants ε₀ and μ₀ have no fundamental significance. They are artifacts of the SI system of units and are not present in other systems. The only fundamental quantity is the speed of light c, derived from their product, c = (ε₀μ₀)^-1/2

The permeability of free space μ_o and the permittivity of free space ε_o represent the fabric of the vacuum, and have fundamental significance. As you point out, the speed of light depends on them. Also the ratio of the magnitude of E to H in an EM wave is
$$Z_{o}=\left\lceil \frac{\mu_{o}}{\epsilon_{o}} \right\rceil^{1/2} \text{ = 377 ohms}$$ which determines the impedance of radio antennas.

 

[Bill_K]

The permeability of free space μ_o and the permittivity of free space ε_o represent the fabric of the vacuum, and have fundamental significance.

Absolutely false - I'm shocked. Bob S, you need to learn about the Gaussian system of units, in which E and B have the same dimension, and the ratio of E to B in a plane wave is 1.

 

[Bob S]

Absolutely false - I'm shocked. Bob S, you need to learn about the Gaussian system of units, in which E and B have the same dimension, and the ratio of E to B in a plane wave is 1.

I tried for a while to conform, but the World seems to insist on using SI units. No one sells voltmeters that read statvolts. By the way, what is the value of a resistor with "brown" "black" and "red" stripes in Gaussian units?

 

[K^2]

Absolutely false - I'm shocked. Bob S, you need to learn about the Gaussian system of units, in which E and B have the same dimension, and the ratio of E to B in a plane wave is 1.

Oh, and GR units, speed of light is 1. So it must be an irrelevant quantity as well!

 

[PhilDSP]

But the separate physical effects of permittivity versus permeability are observable in the phenomenon of polarization, dispersion and refraction, aren't they? So one issue is the numeric juggling of their respective measurements (seemingly trivial) and another is whether they have independent existence as generators of physical effects.

 

[Bob S]

But the separate physical effects of permittivity versus permeability are observable in the phenomenon of polarization, dispersion and refraction, aren't they? So one issue is the numeric juggling of their respective measurements (seemingly trivial) and another is whether they have independent existence as generators of physical effects.

The best way of directly separately measuring the permeability μ_o and permittivity ε_o of free space is to measure the low frequency capacitance of a parallel plate capacitor and the magnetic field (or inductance) of an air-core coil (torioidal geometry is best). At visible light wavelengths, measuring the index of refraction essentially measures changes in the product (εμ)^1/2.

 

[Bill_K]

The value of μ₀ is simply defined to be 4π x 10^-7. Nothing of "fundamental significance" about that, and nothing you can "measure", it's just a conversion factor from one unit to another.

 

[Bob S]

The value of μ₀ is simply defined to be 4π x 10^-7. Nothing of "fundamental significance" about that, and nothing you can "measure", it's just a conversion factor from one unit to another.

Absolutely correct. In fact, there are four parameters of free space; the permeability μ_o, permittivity ε_o, the speed of light c, and the impedance of free space Z_o. Because there are two equations constraining their values, only two can be defined (c and μ_o), and the other two (ε_o and Z_o) are dependent. Unfortunately, all four have units, and therefore depend on the system of units selected.

 

[Meir Achuz]

Bill K: I gave up on PF a few months ago because of threads like this one.
I'm going to quit again. Maybe you should give up too.
Best wishes, Clem

 

[aditya23456]

Well..Is it concluded that εo has no physical meaning? I meant u can't define it as speed of light is defined ( distance travelled/time taken)
And What physical meaning does μo have??

 

[kmarinas86]

Ok, folks! The dimensions (or lack thereof) and precise number used to define permittivity is not relevant or fundamental at all! The question is why is permittivity, fundamentally NOT ZERO, in a vacuum, and NOT about justifying some special "fundamental" number which is used to describe it.

But vacuum does not have anything in it to resist or alternatively to get polarized.

Sure it does.
But that's outside the domain of "classical physics".

http://en.wikipedia.org/wiki/Vacuum_state#Electrical_permittivity_of_vacuum_state

In principle, quantum corrections to Maxwell's equations can cause the experimental electrical permittivity ε of the vacuum state to deviate from the defined scalar value ε0 of the electric constant.[10] These theoretical developments are described, for example, in Dittrich and Gies.[5] In particular, the theory of quantum electrodynamics predicts that the QED vacuum should exhibit nonlinear effects that will make it behave like a birefringent material with ε slightly greater than ε0 for extremely strong electric fields.[11][12] Explanations for dichroism from particle physics, outside quantum electrodynamics, also have been proposed.[13] Active attempts to measure such effects have been unsuccessful so far.[14]

5. ^ a b Walter Dittrich & Gies H (2000). Probing the quantum vacuum: perturbative effective action approach. Berlin: Springer. ISBN 3540674284.
10. ^ David Delphenich (2006). "Nonlinear Electrodynamics and QED". arXiv:hep-th/0610088 [hep-th].
11. ^ Klein, James J. and B. P. Nigam, Birefringence of the vacuum, Physical Review vol. 135, p. B1279-B1280 (1964).
12. ^ Mourou, G. A., T. Tajima, and S. V. Bulanov, Optics in the relativistic regime; § XI Nonlinear QED, Reviews of Modern Physics vol. 78 (no. 2), 309-371 (2006) pdf file.
13. ^ Holger Gies; Joerg Jaeckel; Andreas Ringwald (2006). "Polarized Light Propagating in a Magnetic Field as a Probe of Millicharged Fermions". Physical Review Letters 97 (14). arXiv:hep-ph/0607118. Bibcode 2006PhRvL..97n0402G. doi:10.1103/PhysRevLett.97.140402.
14. ^ Davis; Joseph Harris; Gammon; Smolyaninov; Kyuman Cho (2007). "Experimental Challenges Involved in Searches for Axion-Like Particles and Nonlinear Quantum Electrodynamic Effects by Sensitive Optical Techniques". arXiv:0704.0748 [hep-th].

http://en.wikipedia.org/wiki/QED_vacuum

Fluctuations
Main article: Vacuum fluctuations

The QED vacuum is subject to fluctuations about a dormant zero average-field condition:[4] Here is a description of the quantum vacuum:[5]

“The quantum theory asserts that a vacuum, even the most perfect vacuum devoid of any matter, is not really empty. Rather the quantum vacuum can be depicted as a sea of continuously appearing and disappearing [pairs of] particles that manifest themselves in the apparent jostling of particles that is quite distinct from their thermal motions. These particles are ‘virtual’, as opposed to real, particles. ...At any given instant, the vacuum is full of such virtual pairs, which leave their signature behind, by affecting the energy levels of atoms.”

    -Joseph Silk On the shores of the unknown, p. 62

Electromagnetic properties
See also: Lamb shift, Casimir effect, and Spontaneous emission

As a result of quantization, the quantum electrodynamic vacuum can be considered as a material medium.[19] It is capable of vacuum polarization.[20][21] In particular, the force law between charged particles is affected.[22][23] The electrical permittivity of quantum electrodynamic vacuum can be calculated, and it differs slightly from the simple ε0 of the classical vacuum. Likewise, its permeability can be calculated and differs slightly from μ0. This medium is a dielectric with relative dielectric constant > 1, and is diamagnetic, with relative magnetic permeability < 1.[24][25] Under some extreme circumstances (for example, in the very high fields found in the exterior regions of pulsars[26]), the quantum electrodynamic vacuum is thought to exhibit nonlinearity in the fields.[27] Calculations also indicate birefringence and dichroism at high fields.[28] Many of electromagnetic effects of the vacuum are small, and only recently have experiments been designed to enable the observation of nonlinear effects.[29]

4. ^ Ramamurti Shankar (1994). Principles of quantum mechanics (2nd ed. ed.). Springer. pp. 507. ISBN 0-306-44790-8.
5. ^ Joseph Silk (2005). On the shores of the unknown: a short history of the universe. Cambridge University Press. pp. 62. ISBN 0-521-83627-1.
19. ^ M Bregant et al. (2003). "Particle laser production at PVLAS: Recent developments". In Neil John Curwen Spooner, Vitaly Kudryavtsev. Proceedings of the Fourth International Workshop on the Identification of Dark Matter: York, UK, 2-6 September 2002. World Scientific. PVLAS = Polarizzazione del Vuoto con LAser.
20. ^ Kurt Gottfried, Victor Frederick Weisskopf (1986). Concepts of particle physics, Volume 2. Oxford University Press. pp. 259 ff. ISBN 0195033930.
21. ^ Eberhard Zeidler (2011). "§19.1.9 Vacuum polarization in quantum electrodynamics". Quantum Field Theory, Volume III: Gauge Theory: A Bridge Between Mathematicians and Physicists. Springer. p. 952. ISBN 3-642-22420-2.
22. ^ Michael Edward Peskin, Daniel V. Schroeder (1995). "§7.5 Renormalization of the electric charge". An introduction to quantum field theory. Westview Press. pp. 244 ff. ISBN 0-201-50397-2.
23. ^ Silvan S Schweber (2003). "Elementary particles". In J. L. Heilbron, ed. The Oxford companion to the history of modern science. Oxford University Press. pp. 246–247. ISBN 0-19-511229-6. "Thus in QED the presence of an electric charge eo polarizes the "vacuum" and the charge that is observed at a large distance differs from eo and is given by e=eo/ε with ε the dielectric constant of the vacuum."
24. ^ John F. Donoghue, Eugene Golowich, Barry R. Holstein (1994). Dynamics of the standard model. pp. 47. ISBN 0-521-47652-6.
25. ^ QCD vacuum is paramagnetic, while QED vacuum is diamagnetic. See Carlos A. Bertulani (2007). Nuclear physics in a nutshell. Princeton University Press. p. 26. ISBN 0-691-12505-8.
26. ^ Peter Mészáros (1992). "§2.6 Quantum electrodynamics in strong fields". High-energy radiation from magnetized neutron stars. University of Chicago Press. p. 56. ISBN 0-226-52094-3.
27. ^ Frederic V. Hartemann (2002). High-field electrodynamics. CRC Press. pp. 428. ISBN 0-8493-2378-9.
28. ^ Jeremy S. Heyl, Lars Hernquist (1997). "Birefringence and Dichroism of the QED Vacuum". J Phys A30: 6485–6492. doi:10.1088/0305-4470/30/18/022.
29. ^ José Tito Mendonça, Shalom Eliezer (2008). "Nuclear and particle physics with ultraintense lasers". In Shalom Eliezer, Kunioki Mima. Applications of laser-plasma interactions. CRC Press. p. 145. ISBN 0-8493-7604-1.

As for the above discussions in this thread which squabble about which values are "real" and which ones are "defined" (as if that was mutually exclusive!) - it's not relevant at all. Forget about all that nonsense.

 

[aditya23456]

whew..really thanks for info..so permittivity is due to quantum fluctuations.! But since these fluctuations are random and not necessary to be same through out the medium..since virtual particles may appear at higher density at certain places compared to others(due to randomness)..now how can vacuum be treated with a constant value of peemitivity..?

 

[Bob S]

whew..really thanks for info..so permittivity is due to quantum fluctuations.! But since these fluctuations are random and not necessary to be same through out the medium..since virtual particles may appear at higher density at certain places compared to others(due to randomness)..now how can vacuum be treated with a constant value of permitivity..?

Absolutely not. Permittivity ε₀ and permeability μ_o are unit-dependent constants that appear in Maxwell's equations to relate E and H fields in vacuum. They have nothing to do with quantum fluctuations and virtual particles.

 

[phyzguy]

Bill_K, let me ask you this. If I have two current carrying wires separated by a fixed distance in a vacuum, there will be a certain force between them. In fact, this was the basis of the original definition of the ampere. If I now double the value of μ0 in the space between the conductors, the force between them will double. If μ0 has no significance and is just an arbitrary parameter, then how can it impact the force between two wires?

 

[PhilDSP]

Absolutely not. Permittivity ε₀ and permeability μ_o are unit-dependent constants that appear in Maxwell's equations to relate E and H fields in vacuum. They have nothing to do with quantum fluctuations and virtual particles.

Then again, one can regard quantum virtual photons and vacuum fluctuations as as an alternate model of the physics behind the Maxwell equations - one based on discrete primitives which sum in the microscopic or macroscopic realm to the Maxwell equations of continuous fields. Alternatively, the continuous fields of the Maxwell equations can be quantized by assuming boundary conditions that give the equivalent to the quantum mechanics discrete primitives for a local point in time and space.

 

[jtbell]

If I now double the value of μ0 in the space between the conductors

How do you do that without redefining the ampere?

 

[Bob S]

Bill_K, let me ask you this. If I have two current carrying wires separated by a fixed distance in a vacuum, there will be a certain force between them. In fact, this was the basis of the original definition of the ampere. If I now double the value of μ0 in the space between the conductors, the force between them will double. If μ0 has no significance and is just an arbitrary parameter, then how can it impact the force between two wires?

How do you do that without redefining the ampere?

lAlso, because the speed of light is given by $c=\frac{1}{\sqrt{\epsilon_o\mu_o}}$ in solvihg Maxwell's equations, the value of ε_o will have to be changed.

 

[PhilDSP]

The best way of directly separately measuring the permeability μ_o and permittivity ε_o of free space is to measure the low frequency capacitance of a parallel plate capacitor and the magnetic field (or inductance) of an air-core coil (torioidal geometry is best). At visible light wavelengths, measuring the index of refraction essentially measures changes in the product (εμ)^1/2.

That's a good observation. But one particular problem is that historically the dimension of permittivity has a root dimension of capacitance, the Farad, right?

But in the last half century (apparently in conjunction with the redefinition of the speed of light) the Farad has evaporated as a dimension into the apparently more primitive dimensions of energy, time and length. Effectively the establishment of Special Relativity, as a basis for dimensionality, has destroyed the possible decomposition or recombination possibilities of the classical electromagnetic primitives regarding μ and ε. Or is there some other critical point to be considered?

 

[Bob S]

That's a good observation. But one particular problem is that historically the dimension of permittivity has a root dimension of capacitance, the Farad, right?

Actually ε_o has dimensions Farads per meter

But in the last half century (apparently in conjunction with the redefinition of the speed of light) the Farad has evaporated as a dimension into the apparently more primitive dimensions of energy, time and length. Effectively the establishment of Special Relativity, as a basis for dimensionality, has destroyed the possible decomposition or recombination possibilities of the classical electromagnetic primitives regarding μ and ε. Or is there some other critical point to be considered?

Capacitance C = Q/V Coulombs per volt, and C = ε_oA/d for a parallel plate capacitor, so the permittivity can be defined as Coulombs per meter-volt. Coulombs are defined by amps and time. The volt is defined by the amp and the watt.

We have the speed of light c =(1/μ_oε_o)^1/2 as a fundamental invariant constant in any inertial system. But we also need one more. It can be either the permeability μ_o, the permittivity ε_o, or the impedance Z_o=(μ_o/ε_o)^1/2 of free space.

 

[phyzguy]

lAlso, because the speed of light is given by $c=\frac{1}{\sqrt{\epsilon_o\mu_o}}$ in solvihg Maxwell's equations, the value of ε_o will have to be changed.

Of course, if μ0 changes, lots of things will change. I'm not suggesting that this is possible, because it is a fundamental property of space beyond our control. I was taking issue with Bill_K's contention that these quantities have no physical significance, and are merely arbitrary consequences of our system of units. This is clearly not the case, as I was trying to illustrate by using the fact that the force between two current carrying wires depends on the value of μ0, regardless of what system of units you use.

 

[PhilDSP]

Capacitance C = Q/V Coulombs per volt, and C = ε_oA/d for a parallel plate capacitor, so the permittivity can be defined as Coulombs per meter-volt. Coulombs are defined by amps and time. The volt is defined by the amp and the watt.

Okay, that's nearly what I was hinting at. But there are other breakdowns such as the following where the basic dimensions are Q charge, M mass, L length and T time.

$\epsilon_0 = \frac{F}{m} = \frac{C^2}{Nm^2} = (\frac{Q^2}{L^2})(\frac{T^2}{ML}) = \frac{Q^2T^2}{ML^3}$ $\ \ \ \ \ \ \ \mu_0 = \frac{H}{m} = \frac{N}{A^2} = (\frac{ML}{T^2})(\frac{T^2}{Q^2}) = \frac{ML}{Q^2}$

Where F is Farads, H is Henrys, C is Coulombs, N is Newtons, A is Amperes and m is meters

Then $\epsilon_0 \mu_0 = (\frac{Q^2T^2}{ML^3})(\frac{ML}{Q^2}) = \frac{T^2}{L^2}$