# How permittivity arises in vacuum?

1. Mar 27, 2012

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??

2. Mar 27, 2012

### 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

3. Mar 27, 2012

### Bob S

The permeability of free space μo and the permittivity of free space εo 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.

4. Mar 27, 2012

### Bill_K

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.

5. Mar 27, 2012

### Bob S

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?

6. Mar 27, 2012

### K^2

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

7. Mar 28, 2012

### 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.

8. Mar 28, 2012

### Bob S

The best way of directly separately measuring the permeability μo and permittivity εo 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.

9. Mar 30, 2012

### 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.

10. Mar 30, 2012

### Bob S

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

11. Mar 30, 2012

### clem

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

12. Apr 27, 2012

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??

13. Apr 27, 2012

### 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.

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

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

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

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.

Last edited: Apr 27, 2012
14. Apr 28, 2012

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..?

15. Apr 28, 2012

### Bob S

Absolutely not. Permittivity ε0 and permeability μo 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.

16. Apr 28, 2012

### 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?

17. Apr 28, 2012

### PhilDSP

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.

Last edited: Apr 28, 2012
18. Apr 28, 2012

### Staff: Mentor

How do you do that without redefining the ampere?

19. Apr 28, 2012

### Bob S

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 εo will have to be changed.

20. Apr 28, 2012

### PhilDSP

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?

Last edited: Apr 28, 2012