How many digits can a meter have?

[photon]

Yep, it IS a matter of definition, in the "new" S.I.

The new definition will  fix e (electron / elementary charge ) to an exact value , instead of an approximation by measuring it, and the same goes for h (Planck constant).
Both constants of nature will afterwards have zero uncertainty, by definition.
Frank

What is the advantage of fixing the elementary charge to an exact value with infinite precision? Is this value going to change, say 20 years from now, when we have a better estimate from a device more precise than a Josephson Junction?

[T3sl4co1l]

If it's defined as exact, there's no such thing as "more exact"!

The sausage effect pushes the uncertainty onto other free variables.  Those that are fixed by theoretical relations (like the characteristic of a Josephson junction) also have no uncertainty.  Others (like G or k_B) limit the precision of related measurements.

How about a color analogy?  Suppose the primary and secondary colors are simply what people call them as; there's no theoretical or absolute definition of "red" or "cyan", they're just what people take them as.

In this state, you know that, if you take about half and half proportions of the color called red, and mix it with the color called green (additive light here), you get what's called yellow.

This is a simple, informal relation: R + G = Y.  None of them are really quantitative, it's more like a Boolean statement.

Suppose a Theory of Color is discovered, which fixes the values of R, G and B.  And secondary colors are indeed proven to consist of primary colors.  It is found that the color that's called "yellow" contains 57% R, 43% G.  This proportion is now a measured quantity, in the same way that resistance is a measured ratio between voltage and current.

Suppose the Theory of Color was later refined: it is discovered that, although the above is still true for additive lights, the exact opposite is true of subtractive pigments -- Y + C = G!  And because of this, earlier standards which defined colors in terms of primaries only, but which had some bad tolerances (suppose, we can't get a good precise blue from incandescent lamps, so we've always had trouble building precise colors that contain blue), can now be defined in terms of pigments (which are now fixed fundamentals of chemistry instead).

Incorporating some of these new definitions, suppose it is found that "common yellow" is 97.3% theoretical yellow, with a little bit of red thrown in.  It's like redefining the inch in terms of the meter (1 in == 0.0254 m): it's slightly different from the accepted value, but close enough not to matter in many cases.  With an exact correspondence, it no longer matters which format one uses to express their colors; it's just a matter of preference which color system they use.

Now the state of things is such that, colors and mixtures are defined partly by lights and pigments; and that combinations of both can be used to get even more precise standards.

Suppose the Theory of Color is proven complete.  Now R, G, B and Y, C, F are fixed theoretical constants: the primary (light) colors are emissions at certain wavelengths, and the secondary (pigment) colors are absorptions at the same wavelengths.  There is no longer any uncertainty whatsoever in the pure colors; and any color in the rainbow (or more importantly, that we can sense visually) can be expressed in any desired amount of precision.

This is the future that physical standards aim for; whether it's theoretically possible (provable completeness) is still up for grabs.  It is known that a certain limited set of physical constants (as measured parameters rather than fixed definitions) is necessary.  Whether those are "top level" (spooky quantum parameters like h and c) or derived parameters (like the meter), doesn't matter to the theory, as long as the degrees of freedom are conserved.

For more reading, check out alternative dimensional systems, like Planck units -- defining the fundamentals as unity (1.0 exact), and making customary units (like time and length) derived through proportions.

Tim

[Dr. Frank]

What is the advantage of fixing the elementary charge to an exact value with infinite precision?

There are more changes to come: e, h, k and N(A) will get fixed values with zero uncertainty, and the units of mass, electrical current and the temperature will be defined differently.
Especially, the IPK International Prototype Kilogram (an artefact body) will no longer be defining the mass.

The advantage will be, that the physical units will be more based on constants of nature, and that the important units kilogram, Volt, Ohm, Ampère will have much lower uncertainty, in definition and also in realization.

Is this value going to change, say 20 years from now, when we have a better estimate from a device more precise than a Josephson Junction?

These then fixed values will very probably not change any more.

First, the numerical values for e and h will simply be arbitrary definitions (to the best measured uncertainty as of today), like  the speed of light and the length of the meter.
Second, the definition of volt and ohm will be based on an elementary physical effect, independent  from the material used to a very high degree of uncertainty.

That is subtly different to the definition of  the time [second], as this depends explicitely on the element Cesium, and today, there already exist more stable optical clocks (times 100), based on other elements.
If you would change the definition of the second, you would also need a new fixed value for the new transition frequency.


The uncertainty of today of Volt, Ohm (on the order of 2e-7) will be transferred into the definition and/or realization of other units or constants of nature, like epsilon(0) and µ(0).

If these cross link measurements will be improved in the future, then the value and uncertainty for these other units will change, but not the volt or ohm themselves.

There's a quite descriptive explanation of the change and its implications, especially see table 3:

http://www.physics.usu.edu/dennison/3870-3880/Class_Notes/Lectures/Newell%202014%20PhysToday-SI%20Units.pdf


and here similar FAQs on the BIPM site:

http://www.bipm.org/en/measurement-units/new-si/faqs.html

Frank

 

[george graves]

I'd guess that in order to measure a voltage, you have to draw a small amount of current, no?  However small that might be.  (if there is not current flowing at all, then the potential across the measuring terminals would be zero, no?  Say you want to measure a tiny, tiny voltage.  Lets assume it ssooooooooo tiny it's only 1 electron per second entering the meter.

And since you can't have 1/2 and electron flowing, it has to be discrete and whole electrons flowing into the meter.  So that's a whole number. 1, 2, 3 or 4 electrons.

So at some point you would run into the limit of how few electrons were flowing through the meter at a given voltage.  The lower the voltage, the less electrons.

So I guess you could wait for X amount of time to count the flow of electrons....But voltage doesn't have anything to do with time? Or does it? Ok, now I confused myself.

[Dr. Frank]

I'd guess that in order to measure a voltage, you have to draw a small amount of current, no?  However small that might be.  (if there is not current flowing at all, then the potential across the measuring terminals would be zero, no?  Say you want to measure a tiny, tiny voltage.  Lets assume it ssooooooooo tiny it's only 1 electron per second entering the meter.

And since you can't have 1/2 and electron flowing, it has to be discrete and whole electrons flowing into the meter.  So that's a whole number. 1, 2, 3 or 4 electrons.

So at some point you would run into the limit of how few electrons were flowing through the meter at a given voltage.  The lower the voltage, the less electrons.

So I guess you could wait for X amount of time to count the flow of electrons....But voltage doesn't have anything to do with time? Or does it? Ok, now I confused myself.

You obviously confused that with the electrical current (Ampère), which is related to electrical charge.

According to Maxwells equation, the "Volt", or to be precise, the electrical field does not need electrical charge!

Also, Volt, Ampère and Ohm are three independent physical units, which are coupled by Ohms law.
This indeed describes that the voltage over a resistor is linearily proporational to the charge rate flowing through it.

In contrast, what you are describing, resembles the more intuitive Ampère definition by counting electrons per time.

These devices already exist and are called SET, Single Electron Tunneling.
If they were improved further, to give reasonable uncertainties, then an independent current standard will be available, based on the second.
And then, the Metrological Triangle can be closed, that means it would be possible to check the validity of Ohms law with a high degree of precision:
http://rsta.royalsocietypublishing.org/content/363/1834/2221.full
 
Frank

[FrankBuss]

Right, number of electrons is current, voltage is speed of electrons. So I guess all you need would be one electron?

[wiss]

No, voltage is potential energy of an electron.

[FrankBuss]

A question to the physics experts here: is there a voltage quantization? This would define the maximum possible number of digits for a meter, which would even depend on the voltage range (if you measure a voltage near the quantization level, it would be just a few digits).

[FrankBuss]

No, voltage is potential energy of an electron.

Ok, what I meant was if you manage to let one electron flow from the voltage you want to measure with a sufficient high resistor, you could measure the speed of it and then calculate the voltage

[george graves]

Very interesting topic!

Isn't voltage the potential to do work, and not work itself?

But to measure voltage, you have to let it do some work - how ever small that could be.  I'm reminded of my college courses where we would measure a static charge with a jar and two gold leafs attached to an electrode to the top of the jar.  The fact the two gold leafs moved, means that work was done.  So *some* current must have flowed. (pic below is only one gold leaf - but same idea)



I understand you don't need current flow to have the existence of a difference in a potential, but to measure it, you must make it do *some* work. No? (or are we arguing the "observer effect" http://en.wikipedia.org/wiki/Observer_effect_%28physics%29

Maybe I need to crack open my old text books.  I think there is an analogy of the classic kinematic equations and electricity that might make more sense.  In a derivative/integral sort of way.

[HKJ]

But to measure voltage, you have to let it do some work - how ever small that could be.  I'm reminded of my college courses where we would measure a static charge with a jar and two gold leafs attached to an electrode to the top of the jar.  The fact the two gold leafs moved, means that work was done.  So *some* current must have flowed.

No.
You use a adjustable voltage source and then measure the difference between the two voltage. When the difference is zero and no current is flowing, you can measure the adjustable voltage source and get the correct voltage without loading the original voltage.

[Dr. Frank]

A question to the physics experts here: is there a voltage quantization? This would define the maximum possible number of digits for a meter, which would even depend on the voltage range (if you measure a voltage near the quantization level, it would be just a few digits).

The electrical charge is quantized, i.e. the electron.

Voltage is a potential difference, i.e. a field, and is not quantized.

Electrical charge CAN create electrical fields and also magnetic fields, but both fields also exist without the presence of electrical charge, in the vacuum. That is called electro-magnetic radiation.

Frank

[george graves]

You use a adjustable voltage source and then measure the difference between the two voltage. When the difference is zero and no current is flowing, you can measure the adjustable voltage source and get the correct voltage without loading the original voltage.

Isn't that using a ruler to measure a ruler?

[dom0]

You use a adjustable voltage source and then measure the difference between the two voltage. When the difference is zero and no current is flowing, you can measure the adjustable voltage source and get the correct voltage without loading the original voltage.

Isn't that using a ruler to measure a ruler?

No, it's how in the old times high impedance sources were measured. It's called a null-volt-meter and the main characteristic is that the input impedance is extremely high if the meter is zero.

(You could call a precision supply and a null volt meter a voltage measurement bridge, if you want)

(And the specific procedure he mentions is called a transfer-measurement. Note that this is one of the reasons there were precision supplies with decimal dials for voltage setting)

[T3sl4co1l]

I'd guess that in order to measure a voltage, you have to draw a small amount of current, no?  However small that might be.  (if there is not current flowing at all, then the potential across the measuring terminals would be zero, no?  Say you want to measure a tiny, tiny voltage.  Lets assume it ssooooooooo tiny it's only 1 electron per second entering the meter.

And since you can't have 1/2 and electron flowing, it has to be discrete and whole electrons flowing into the meter.  So that's a whole number. 1, 2, 3 or 4 electrons.

So at some point you would run into the limit of how few electrons were flowing through the meter at a given voltage.  The lower the voltage, the less electrons.

So I guess you could wait for X amount of time to count the flow of electrons....But voltage doesn't have anything to do with time? Or does it? Ok, now I confused myself.

So you're saying currents are magically quantized in units per second?  What a magical constant this "second" must be.

Current flow is not at all required to measure voltage; even the earliest galvanometers and bridges worked on this principle.  When current is zero through a resistor, the voltages are equal on either side; therefore you have matched your test voltage to the reference.

Even for a potential difference, current flow is not necessary; MOSFETs work just fine with a voltage difference and very little current flow.  They are charge controlled rather than current controlled devices.

Current flow need not be quantized in any magic "unit per time period" either; current can be perfectly continuous.  Water doesn't magically pop through a hose, one end to the other, a molecule at a time; the position varies continuously with time, proportional to velocity.

It's noteworthy that, on occasions where that DOES happen, electrons popping past a partition, through an energy barrier -- that tends to cause noise, specifically, shot noise.  Partition noise in tetrodes and pentodes (old technology), for instance.

There is, however, an electric current quantum.  At least... I think there is?  Maybe not... there is a magnetic flux quantum, which implies a nonzero ground state current.  However, the amount of current depends on the inductance (and consequently, the dimensions and geometry) of the structure holding that flux quantum, so I think there need not be a fundamental current quantum at all.  Which makes sense, as current is a continuous property.

So, voltage is just a pressure or potential; you don't need any current to sense it, and it need not be quantized.  Though you most likely need charge to perform the measurement (since the voltage sensor is made of material, which therefore has some capacitance), but that needs only a small transient current, not DC.  And again, charge need not be quantized, because charge is carried by electron position, not just the absolute presence or absence of particles.

A Josephson junction measures voltage proportional to time/frequency, so that the value can be counted in a quantized manner (discrete states of a frequency counter), but the parameter (voltage - frequency) is continuous.

Tim

[dom0]

Oh and just btw. the reason null volt meters are obsolete today is that any modern multimeter has >10 M? input impedance, which is good enough. Good meters will have an input impedance near their isolation impedance (G?) on the lower ranges.

[FrankBuss]

Voltage is a potential difference, i.e. a field, and is not quantized.

Electrical charge CAN create electrical fields and also magnetic fields, but both fields also exist without the presence of electrical charge, in the vacuum. That is called electro-magnetic radiation.

Ok, but the electromagnetic field is quantized, says Wikipedia, doesn't this mean that voltage is quantized, too? The Planck constant is very small, maybe it would allow 20 digits meters in theory for the 1V range.

[AndyC_772]

Interesting philosophical discussion...

If our voltmeter is implemented as a bridge at balance, it's certainly true that no current flows, so the externally applied potential (ie. the potential being measured) should be unaffected by the presence of the meter.

But then the question becomes, how do we tell when the bridge is balanced?

The bridge is balanced when no current flows into or out of the meter. Current is charge per unit time, and charge is quantised.

So, then it becomes a question of, how small a current is "no current"?

If we wait for 1 second and count 0 electrons, is that "no current"? I'd argue that yes, for that 1 second period, there is indeed no current... but does that mean we can call the voltage measurement "exact"?

What if we'd sampled the current for 10 seconds, and counted 4 electrons during that time? That's a current, so now we know our bridge is slightly out of balance. Perhaps we can adjust it slightly, and get a closer measurement. Ultimately, the precision we can achieve is limited by how long we're prepared to wait to see how close our bridge is to perfect balance.

Remember also the definition for electric potential at a point in space, being the work done in moving a unit charge from infinity to that point. The charge may be quantised, but < flame suit > distance isn't </ flame suit >.

[wiss]

Photons are quantized, there can be one or two or several.
The wavelength of a photon is not quantized, it can be anything.

[T3sl4co1l]

If we wait for 1 second and count 0 electrons, is that "no current"? I'd argue that yes, for that 1 second period, there is indeed no current... but does that mean we can call the voltage measurement "exact"?

...

Remember also the definition for electric potential at a point in space, being the work done in moving a unit charge from infinity to that point. The charge may be quantised, but < flame suit > distance isn't </ flame suit >.

So you've answered your own question.   Suppose we could observe electrons as they move through a wire (assuming absolute zero temperature, so no random thermal motion here).  The drift of an electron, in an unbound state, need not be quantized (stepwise).  Therefore, with suitable apparatus, we can detect currents arbitrarily close to zero, in arbitrarily small periods of time, limited only by the uncertainty principle (since the fields themselves fluctuate due to probability).

Another way to think of it: the electric or magnetic field intensity might be quantized, but its position need not be.

Some types of conductors do exhibit quantized (bucket brigade style) flow, such as solid ionic conductors (e.g., hot ZrO2 in fuel cells).  These exhibit excess noise, corresponding to the mechanism, whereas simple metallic conductors exhibit very little excess noise (i.e., almost entirely Johnson noise).

Tim

[FrankBuss]

Photons are quantized, there can be one or two or several.
The wavelength of a photon is not quantized, it can be anything.

But nobody knows if space itself is quantized, as loop quantum gravity predicts. Then the wavelength would be quantized, too.

[Fungus]

Remember also the definition for electric potential at a point in space, being the work done in moving a unit charge from infinity to that point. The charge may be quantised, but < flame suit > distance isn't </ flame suit >.

Yep.

What we call voltage is all about electron "pressure" - the desire of individual electrons to move to an area of lower electron density when there's electron overcrowding.

This is related only to the distances between electrons. This makes voltage is a continuously varying value, it doesn't matter if the charge on the electrons is quantized or not.

(nb. many languages actually call it "pressure", or "tension")

[Dr. Frank]

Ok, but the electromagnetic field is quantized, says Wikipedia, doesn't this mean that voltage is quantized, too? The Planck constant is very small, maybe it would allow 20 digits meters in theory for the 1V range.

Nope. The Electrical field alone is not quantized!

Photons are the quantized particles of the electromagnetic field, but these are a combination of electrical and magnetic field only.
Additionally, these quantized photons can anyhow have any random value, simply change its wavelength or energy continuously..
Whereas  electrical charge - as far as we know today - is always an integral multiple of the Elementary Charge, i.e. the electron... there does not exist a fraction of e.

Current is also not quantized, as time is not quantized, and Current is (the quantized) Charge divided by (continuous) Time, giving a continuous variable also.

Frank

[T3sl4co1l]

Ok, but the electromagnetic field is quantized, says Wikipedia, doesn't this mean that voltage is quantized, too? The Planck constant is very small, maybe it would allow 20 digits meters in theory for the 1V range.

Nope. The Electrical field alone is not quantized!

Photons are the quantized particles of the electromagnetic field, but these are a combination of electrical and magnetic field only.
Additionally, these quantized photons can anyhow have any random value, simply change its wavelength or energy continuously..
Whereas  electrical charge - as far as we know today - is always an integral multiple of the Elementary Charge, i.e. the electron... there does not exist a fraction of e.

Current is also not quantized, as time is not quantized, and Current is (the quantized) Charge divided by (continuous) Time, giving a continuous variable also.

Frank

Charge need not be quantized, because net localized charge results from electron displacement -- which as you note, is a continuous variable.  Likewise, the electric field (which is customarily in units of V/m, but the displacement field D = e_0 E is in units of coulombs -- analogous to the magnetic flux density field B = mu_0 H, if you aren't familiar with D) is not quantized, so it follows from both directions that charge need not be quantized either.

The sources of charges -- the particles -- are necessarily, however.  (Note that, strictly speaking, the most elementary charge is 1/3 its customary value, because electrically charged quarks are considered to have such fractional charges.  This would make the electron charge 3e' (e' = e/3), but such a distinction is hardly worthwhile, so it hasn't been implemented.)

Tim

[Fungus]

Current is charge per unit time, and charge is quantised.

Yes, but it's perfectly possible for the average number of electrons passing through a wire per second to be 3.14159 ... or any other number you can imagine.

The fact that electron charge is quantized doesn't tell you anything about volts or amps.