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peteshimmon
2011-Oct-08, 07:47 PM
For some time now I have been puzzled
that the permeability of the vacuum is
defined at some exact value. I thought
it had to be measured. Now looking at a
table of constants I have twigged. They
are taking it as read that permittivity
and permeability give the speed of light
so they use the well measured c with
permeability to derive permeability and
make it 4.pi.

But I would still like to know the best
measured value these days. It keeps in
touch with the great insight Clerk Maxwell
had in seeing the analogy with mechanical
matters and finding the speed of light as
an electromagnetic wave. A breakthrough in
physics I still think as the greatest.

peteshimmon
2011-Oct-08, 07:50 PM
Doh!...well measured c with permittivity..

grapes
2011-Oct-08, 09:26 PM
What criteria do you use to measure it? The modern criteria gives you the modern value, no?

peteshimmon
2011-Oct-09, 01:30 PM
Well I presume Clerk Maxwell had to use
a measured value from work before him.
Unless it was just a well judged guess
such as Newton did with the gravitational
constant. Actually Franklin was the
Inductance man I believe. Or Henry!

I'm just curious how closely modern
techniques get to the derived value
of permeability.

grapes
2011-Oct-09, 05:26 PM
No, it's definitely an interesting question, I've pondered it myself. The speed of light is c, which didn't use to be a constant, the permittivity is \epsilon_0, which didn't use to be a constant, whereas permeability \mu_0 is 4\pi \times 10^{-7}, which value always was a constant. Clearly, what must have happened, was the length of the meter was determined two hundred years ago (and the second long before that), and then they found an approximation to the speed of light, measured in meters per second. After establishing what amounted to a coulomb, they could determine the permittivity, measured in coulombs-squared per kilogram-meter-cubed. O yeah, the kilogram had been established. That leaves permeability, which, although usually expressed in henrys per meter, is also, let's see, newtons per amperes-squared, or wow kilogram-meters per coulombs-squared. Basically, once you define what a coulomb is, and the kilogram and meter, you're stuck with the answer. Probably, all this was discussed at the time they decided to define the meter in terms of the speed of light.

It's not an isolated coincidence. I've always wished that they'd stuck with one of the original definitions of the meter, the length of the seconds pendulum--had they done that, the acceleration of gravity, g, would be exactly \pi^2, instead of only approximately. :)

peteshimmon
2011-Oct-09, 06:42 PM
I have just clarified it for myself looking
it up on Wiki. It seems Ampere is the man,
he specfied the Amp as the current producing
an attractive force of something between two
wires a metre apart. Permeability comes from
this artificial construct. Not really a constant
of nature at all I read.

Clever of me to do the research after
posing the question here I know but
it has been a puzzle for a while:)

grapes
2011-Oct-10, 01:02 AM
It seems Ampere is the man,
he specfied the Amp as the current producing
an attractive force of something between two
wires a metre apart. Permeability comes from
this artificial construct. Not really a constant
of nature at all I read. I wouldn't say it wasn't a constant of nature, per se. Just because it works out so neatly--after all, in some systems, the speed of light is exactly 1. Still a constant of nature, so to speak, but cleaner because of the way we've chosen our units.

grapes
2011-Oct-10, 01:13 AM
It's not an isolated coincidence. I've always wished that they'd stuck with one of the original definitions of the meter, the length of the seconds pendulum--had they done that, the acceleration of gravity, g, would be exactly \pi^2, instead of only approximately. JOOC, I wondered what the speed of light would've been. Since g is defined to be 9.80665 m/s/s, and pi squared is 9.86960, a pi meter would have to be 9.80665/9.86960 smaller, which means the speed of light would be 9.86960/9.80665 larger, or 301716994 and 3/8 m/s. I guess I don't see any real advantage there, that's even farther from 300000000.

Gsquare
2011-Oct-10, 02:57 AM
JOOC, I wondered what the speed of light would've been. Since g is defined to be 9.80665 m/s/s, and pi squared is 9.86960, a pi meter would have to be 9.80665/9.86960 smaller, which means the speed of light would be 9.86960/9.80665 larger, or 301716994 and 3/8 m/s. I guess I don't see any real advantage there, that's even farther from 300000000.

Yes, but doesn't gravitational field shrink the meter and lengthen the second....so measurements on earth are skewed, compared to that of a distant observer, no?
.

G^2

grapes
2011-Oct-10, 10:20 AM
I think we could discuss that, under the general topic of "original" measurement. :)

The time dilation on earth (http://en.wikipedia.org/wiki/Gravitational_time_dilation) is not that great, is it? Does it even affect the numbers that I quoted in that post (sixth decimal place)? That wiki mentions nanoseconds, but for a distant observer, the effect could add up. Time to calculate...

undidly
2011-Oct-10, 11:33 AM
The time dilation on earth is one part in 10^9.

HenrikOlsen
2011-Oct-10, 11:36 AM
Or, for another round-number definition, which is really just as arbitrary and won't make sense any other place, defined the second so the tropical year is exactly pi*1010 seconds. :)

Anyway, that permeability expressed in SI units comes out a nice number is a consequence of having one of those units defined in terms of the physics governed by permeability. That doesn't make it less of a constant(as far as we know).

grapes
2011-Oct-10, 01:14 PM
Or, for another round-number definition, which is really just as arbitrary and won't make sense any other place, defined the second so the tropical year is exactly pi*1010 seconds.Square root of a quadrillion works for me.

ETA: Wait a minute! That's not pi*1010

Gsquare
2011-Oct-10, 05:48 PM
I think we could discuss that, under the general topic of "original" measurement. :)

The time dilation on earth (http://en.wikipedia.org/wiki/Gravitational_time_dilation) is not that great, is it? Does it even affect the numbers that I quoted in that post (sixth decimal place)? That wiki mentions nanoseconds, but for a distant observer, the effect could add up. Time to calculate...

So.... ignoring the magnitude of the effect for a second (er, for a time dilated second), what changes for the distant observer ? .... his measurement of the permittivity, the permeability, or BOTH ?


G^2

grapes
2011-Oct-10, 06:16 PM
So.... ignoring the magnitude of the effect for a second (er, for a time dilated second), what changes for the distant observer ? .... his measurement of the permittivity, the permeability, or BOTH ?
Why would it have to change? Does the speed of light change? In what fashion?

Once you have the speed of light fixed, and the permeability as 4 pi x 10-7, that pretty much sets it, no?

Gsquare
2011-Oct-10, 07:52 PM
Why would it have to change? Does the speed of light change?

Of course; the value of c is different as measured by a distant observer outside of the g field.... for the distant observer the electromagnetic radiation is delayed through a gravitational field; isn't that what Shapiro time delay is all about ?

A distant observer bounces a EM beam off the earth and measures a (coordinate) change in the vaue of c.
Do Maxwell's equations change, ? (the value of c is still the inverse square root of the product of permittivty and permeabilty)....I ask again; Does he measure a permittivity change or permeability change, or both.

The answer would seem to be related to a dimensional analysis, which you addressed pretty well, so I asked you....

G^2