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a resistance that's the same all over the universe

March 14 2003 at 3:07 PM
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Leonard 

 
This site gets an unexplained abundance of readers (the March log says) despite only a handful of people ever posting. If you read here then you should and probably do know about the resistance which would be discovered by any civilization at any time in any galaxy----a ratio of voltage to current which, in 1990 metric terms, is 25,812.807 ohms.

Find it at the us.gov fundamental constants site.
It is in the "internationally adopted values" section.

In Old Metric, pre-1990, which is still official due to institutional inertia, the figure has more digits an uncertainty of 3.7 ppb. The 1990 electric standards are based on the adopted exact value given here. But it doesn't matter what it is in metric terms, of whatever flavor. The fact is there is this quantum Hall resistance that is built into nature---what number you attach to it just reflects what units you happen to be using.

There is a cold solid state device exhibiting this exact ratio of voltage to current, every time.
You put a current down the main axis of the chip and a proportional transverse voltage appears which always equals the current multiplied by this exact resistance.

In terms of other constants, as you can see at the us.gov site, this R equals 2pi hbar/e^2. So you can calculate it from whatever values you have for hbar and the electron charge e.

In cp-oz units the values of hbar and e are E-30 and E-15. And squaring e gives E-30. So the value of this
universal ratio of voltage to current in OUR units is simply 2pi. Have a nice day metric, with your 25,812.807 and (official only) uncertainty of 3.7 ppb.

So since there is a fixed ratio of current to voltage you can anchor to (and this is what all country's national labs do) all you need is a VOLTAGE STANDARD, and then you automatically get a current standard and a (currentxvoltage) power standard---and on that if you care to you can base the energy unit and so on.
All the units can be grounded on a minimal basis of frequency and voltage standards. This is what the work going on around the "watt balance", an electric force-measuring tool of extremely high accuracy, is all about---extending the electrical and atomic clock frequency standards to every other type of quantity.
There are some urls about this which I might post later though many readers here have probably already seen the articles I'm talking about.

 
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pintdrinker

2 pi vs. 25 812.807 Ohms

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March 15 2003, 4:34 AM 

How wonderful to have something we can sink our teeth into and rip apart! Maybe we share souls with dogs; or (as many would be wont to say in my own particular case) "son-of-bitches"! This is but another point about Leonardian Planckery which is so compelling. As you have mentioned on numerous other prior occasions, "it is not going to go away". The 2 pi figure for the U Ohm is incredible, Leonard. In fact i find it so UTTERLY incredible that i would like to ask you HOW you arrive at the figure of of 2 pi "Ohms" as the U resistance. How does it relate thus to 25 812.807 (metric) ohms? By mere "coincidence"? Is this yet another serendipitously bestowed event (from ?God? knows where)? Or did you DEFINE it as 2 pi?

 
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pint drinker

26 000 ohms exactly vs 25 812.807 ohms

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March 15 2003, 4:46 AM 

Now let us suppose that instead of 25 812.807 ohms that the U resistance is equal to 26 000 ohms exactly. And now let us derive the "trimmed metric" joule and/or coulomb therefrom. Ditto e-. I would now guess that we would no longer have sufficient degree of freedom to define e- as we wish. What would we come up with then? Maintaining our course toward the trimmed metre of 3E-08 c, do we now have a nice relatively neat set of coefs or will we have to pick select and choose WHICH coef to sweep under the metric rug (so to speak).

 
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Leonard

the resistance (voltage/current ratio) in the "quantum Hall effect"

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March 15 2003, 6:51 AM 

Hello pint drinker,
this resistance was discovered by a German named
(this always makes me involuntarily pause) von Klitzing.

he was born some time in the forties in someplace that is now part of Poland and now has a different name, as I recall.

he got the Nobel for finding this resistance,
which is h/e^2, or if you write it with hbar instead of h, is 2pi hbar/e^2.

Von Klitzing's resistance is superficially similar to a (*non-constant*!!!) resistance that a Mr Hall noticed a long time ago---but fundamentally different because a von Klitzing device is at a low temperature where quantum effects take over and the resistance is a universal constant. But all the same there is this superficial similarity to an old old chestnut known as the "Hall effect", where an external magnetic field causes a transverse voltage to appear in a conductor that is proportional to the current going thru the conductor.

For a long time (seventies and eighties) people just said "quantum Hall effect" and "quantum Hall resistance" because either they didn't know von Klitzing's name or didn't feel dignified saying something that sounded like Clits. They used the symbol R sub H, pretending that it was "Hall resistance", but now they are gradually getting around to calling the resistance R sub K.

 
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Leonard

trying numbers, also a caltech physics animation goodie

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March 15 2003, 7:31 AM 

You are so stubborn (as I am myself in similar matters) that I wonder if you will end up making something pretty out of the metric system. It seems impossible but one never knows. :-)

You were considering at one time having hbar be E-34 joule second.

This was a hair over 5 percent change in the joule, like 5.4 percent, and it caused a change in the kilogram of about the same size. I don't know what you eventually decided to do about that.

If you made the coulomb charge unit E19 e, then e would be E-19 coulomb and e^2 would be E-38.
So then hbar/e^2 would be E-34/E-38 or exactly ten thousand.

So in that case your "quantum Hall resistance" would be exactly 2piE4, or 2pi times ten thousand.

On the other hand the coulomb charge unit is presently closer to 6E18 e. (6.2415....)
If you were conservative and averse to changing the sizes of units you might decide to make it exactly 6E18 and then e would be (1/6)E-18 and e^2 would be (1/36)E-36 and then what about
hbar/e^2 ?

Assuming you are tolerating that 5.4 percent and making hbar equal E-34 then it would be 36E-34/E-36
and that is 3600.

Putting the 2 pi in gives 2pi x 3600 ohms.

22,619 ohms.

Or you could be really insistent on keeping close to present sizes and say hbar is 1.05E-34 and the coulomb is 6.2E18 e and then the resistance would come out even closer to the present value.

Did you ever see the electric field caused by a single point-charge? Here is a neat physics goodie.

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html

Go to the menu where it says "linear motion" and pull it down to "circular motion"

also with "user control" you have a little "helm" that lets you "steer" the electron around in space and watch how its field changes.

if the electron is standing still or moving straight and steady then the field is sort of like an asterisk. not very interesting. but circular or spiral motion is more interesting.

only takes a minute and you might like it.

 
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pint drinker

Just a quick note...

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March 15 2003, 8:08 AM 

Just a quick note. I am dogsitting today and this yellow lab is VERY DETERMINED to go out for a romp.

I realize we are not going to have 100% beautiful coefs in this system. Nevertheless i would like all of them 'beautified' as much as possible, but with the least amount of possible change. Basically i am committed to coefs of no more than 2 sigfigs at present-- this being the constructive substrate from which we have been able to mine the 5% variance limit.

 
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