Permittivity of free space?

[Martin]

Maybe we could use a thread to collect people's various ideas about the "permittivity of free space"

 

Is it a real physical quantity or just an artifact of the way MKS units are defined? In some units systems---like some version of the CGS---there isnt any "permittivity of free space", or so we are told:

 

http://www.newton.dep.anl.gov/newton/askasci/1993/physics/PHY48.HTM

 

this is a link from the Wikipedia article on the subject, they say "for further discussion see..." and give this.

 

So maybe it is controversial, or maybe permittivity of free space has only a semantic existence---and is an artifact of whatever (possibly arbitrary) convention is used to define the unit of electric charge.

 

If it is controversial, than this thread can serve to air different opinions.

 

Also what about "magnetic permeability of free space"? is it an actual physical property of something in nature? or is it just an arbitrary constant employed in the definition of a particular system of units?

 

Any thoughts?

 

I did a quick search of Usenet's "sci.physics.research" and found a post by J.J. Lodder

http://www.lns.cornell.edu/spr/2000-01/msg0020633.html

Re: Permittivity and Permeability Constants of Vacuum

 

sample quote:

"Physics is about those aspects of Nature

that -do not depend- on our human conventions.

Hence eps_o is not a physical quantity."

 

for a considerable block of opinion among scientists "epsilon-naught" (vacuum permittivity) is not real thing in nature. For other scientists, it apparently seems real. Maybe this cannot be settled.

[Martin]

http://www.lns.cornell.edu/spr/2002-02/msg0038977.html

 

---here's a quote---

> In article <1f6rofw.1ta4nlk1hqqu9vN@de-ster.demon.nl> ,

> nospam@de-ster.demon.nl (J. J. Lodder) wrote:

> ....

> > PS For real physisists the problem doesn't exist:

> > they always use units in which eps_0 and c are equal to one ;-)

> > You may learn howto next year.

>

> hey Jan,

>

> can you tell me what the real physicists use for units (for time, length,

> energy) so that eps_0 and c are equal to one?

 

If you consult the units section of any advanced electromagnetism

textbook (Jackson for example) you will find that ME units

with eps_0 = 1 were the rule (Gaussian units, Heaviside-Lorentz units)

until so-called practical people spoiled the unit system.

And quite needlessly to: the (very practical Ampere differs from the

(of course quite unpractical abampere by merely a factor 10.

 

Having c also 1 would be possible even in the SI-like systems by

measuring all distances in seconds.

(as general relativists do all the time.)

The only reason for not doing it in everyday life

is backwards compatibility.

 

More practical physisists use natural units.

These are defined by taking c = 1 hbar =1 , and using any suitable

energy unit, for example the MeV.

Length and time are then measured in MeV^{-1}

---end quote---

 

in essence the view is, i guess, that "epsilon-naught" and "mu-naught" are phony, from a theoretical physics standpoint

 

they got into things when so-called "practical" people spoiled the units system.

 

apparently they are not fundamental---grounded in basic theory like quantum electrodynamics---but are reserved for macroscopic behavior as in classical (pre quantum) electrodynamics

but in the main textbook on that subject, Jackson's "Classical Electrodynamics", one sees that there used not to be these things

until people fiddled with the units. Adjusting them to be the right sizes for engineers? Anyway some "practical" reason required some shimming or some FUDGE and so "epsilon-naught" and "mu-naught" were inserted

 

I believe the official value of mu-naught in the rationalized MKS system is

4 pi x 10^-7

 

that is, 4 multiplied by 0.000000314159265...

 

OK so mu-naught is supposed to be a real property of nature (??) and its value in metric units is 0.000001256637...

 

and the official value of epsilon-naught is something you cook up from that together with the officially adopted number 299792458

it is ONE OVER (mu-naught x c-squared)

 

 

epsilon-naught = 1/(0.000001256637... x 299792458²)

 

I think the idea is that these are in no sense experimentally determined numbers

they are just two numbers arbitrarily fixed up so that WHEN YOU MULTIPLY THEM TOGETHER SOME STUFF CANCELS AND YOU GET ONE OVER THE SQUARE OF 299792458

 

just pick any two numbers that do this

 

epsilon x mu = 1/299792458²

 

and anything will be fine, it just affect comparative sizes of magnetic and electric units.

you can even make one of them something crazy like 4 times pi time

one over tenmillion, and it's cool, those two numbers can be epsilon-naught and mu-naught.

 

=====================

now that is one view, and there is an opposing view that we really should try to get expressed here, that is that the vacuum permit'y and permeab'ty are actual properties of nature. epsilon-naught and mu-naught actually mean something and actually even EXPLAIN something!

their sizes are not just arbitrary but their sizes actually EXPLAIN THE SPEED OF LIGHT!

 

this is a sharp difference of opinion, obviously, and we need to hear both sides

 

remember that the speed of light is not just the speed of light!

it is a speed that is important for a lot of other things'

like it is an unattained upper limit on the speed of neutral massive particles like neutrinos! the whizzing of neutrinos has nothing to do with light.

light is electromagnetism. they, on the other hand, are neutral

electromagnetic non-entities

and the have a top speed that they come arbitrarily close to but never quite achieve, and it is c

 

so if you are going to explain c you have to explain other things that have nothing to do with classical electrodynamics and Maxwell's equations.

 

and if you explain c you have to explain the relations between various observers and why E = Mc² and so on, a lot of which does not have to do with electricity and magnetism (or issues of "permittivity" and "permeability") but has to do with the symmetries of spacetime---Lorentz group or Poincare group, whatever.

 

so some would say that these two cooked-up numbers that "practical" people relatively recently stuck into Maxwell equations when they ruined the units do NOT explain c

and others would say that the two numbers epsi and mu DO explain c

and apparently it gets to be quite a debate

 

there is a bunch of threads on sci.physics.research about it, but hard to know what to pick

[swansont]

remember that the speed of light is not just the speed of light!

it is a speed that is important for a lot of other things'

like it is an unattained upper limit on the speed of neutral massive particles like neutrinos! the whizzing of neutrinos has nothing to do with light.

light is electromagnetism. they' date=' on the other hand, are neutral

electromagnetic non-entities

and the have a top speed that they come arbitrarily close to but never quite achieve, and it is c

 

so if you are going to explain c you have to explain other things that have nothing to do with classical electrodynamics and Maxwell's equations.

[/quote']

 

But that was all part of Einstein's motivation for doing relativity - Maxwell's equations give you a wave equation with speed c, and c has to be invariant in order to still have a wave equation when there is relative motion. Einstein just made it invariant for mechanical systems, too.

[Martin]

But that was all part of Einstein's motivation for doing relativity - Maxwell's equations give you a wave equation with speed c, and c has to be invariant in order to still have a wave equation when there is relative motion. Einstein just made it invariant for mechanical systems, too.

 

You are absolutely right, the motivation for 1905 Special Rel came straight from electrodynamics. maxwell's equations invariant under Lorentz transf.

beautiful stuff

 

and still a bit mysterious dont you think, that mechanical systems obey even if no electromagnetism involved

[Martin]

have to confess personally I'm still awed by the fact that there should be a speed that looks the same to all observers

and cant imagine why or how space could be constructed so that this is true

(if there is spacetime that has some independent existence on its own and is not merely a web of relationships manifesting the gravitational field whatever that is (geometry itself?))

its one of these truly fundamental things I feel totally clueless about

[Martin]

we live in an exciting time

there are people seriously proposing that not only is there this speed that looks the same to all observers (recognized in 1905)

but there could also be a length that is invariant

that is, looks the same to all observers

(thru an extension of Lorentz symmetry)

needless to say very hard to conceive of