# Measuring the magnetic and electric constants

## Main Question or Discussion Point

Has the permeability and permittivity of vacuum ever been measured in a vacuum or space?

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The permeability of free space is defined as u0 = 4 pi x 10-7 Henrys per meter in the mks system of units. Because the speed of light is a defined quantity, and 1/sqrt(u0 e0) = c = speed of light, e0 is then derived as 8.85 x 10-12 Farads per meter. So the measurement of the permittiviy depends on the the speed of light, which is now an exact defined quantity, because the meter is based on the speed of light: The meter is the distance light travels in 1/299792458 seconds.

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So it isn't measurable? You can't go into outer space, and measure the permeability and permitivitty of vacuum..

The permeability and permittivity of free space are now defined by other quantities, such as the length of a meter and the speed of light. Suppose you measured the capacitance of two one-square-meter plates separated by 1 millimeter in vacuum. Because the meter is defined by c, and c = 1/sqrt(u0e0), the measurement is not an independent measurement. the value of all the fundamental constants are based on a variety of interdependent quantities, every value is over determined, and least square fits are used to get the most probable values. In the 2002 table of the fundamental constants (which I am now looking at), both the permeability and permittivity of free space are "exact" defined quantities, meaning no uncertainty in value.

So you cannot go out into intergallactic space and measure them, because of their dependence on other quantities. On the other hand, dimensionless quantities, like alpha, are dimensionless and measurable.

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Added detail- Look at the Particle Data Group page
http://pdg.lbl.gov/2008/reviews/contents_sports.html
Click ion the first catergory (constants), then look at about lines 13 and 14 for permeability and permittivity of free space. They are shown as EXACT quantities, because they are based on a) definition of the permeability of free space and b) the speed of light.

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Why do you need to go into outer space to measure a quantity in a vacuum? Got a bell jar?

So is all the above correct? Vacuum constants can't be measured? I know they're derived from the speed of light... But wouldn't saying "the vacuum constants can't be measured" be similar to saying "the speed of light can't be measured"? And if the constants have no physical significance, why are they used in so many useful equations? I'm lost

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f95toli