# Thread: Definitions of volt using SI's fundamental magnitude

1. I need help with the definition of volts. We know that the ampere is the unique electric fundamental magnitude in SI system. And It's define like:

the constant current that will produce an attractive force of 2 × 10–7 newton per metre of length between two straight, parallel conductors of infinite length and negligible circular cross section placed one metre apart in a vacuum
So, how can we define volts? Becuase we can't says that a volts it's

Because resistor is not defined yet and we are looking for a formal definition. So the only way is that a volt is the dissipated energy of 1 joule in 1 second by a current of 1 ampere.

Those that correct? this is how the volt is defined formally?

2. Basically yes. 1 V is the potential difference between two points of a conductor when a current of 1 A flowing between those points dissipates 1 W of power.

3. Thanks. And other question. Why is define like fundamental the current and not the carge? I think that is practical way. It's really dificult measure charge?

4. Originally Posted by julian403
I need help with the definition of volts. We know that the ampere is the unique electric fundamental magnitude in SI system. And It's define like:

So, how can we define volts? Becuase we can't says that a volts it's

Because resistor is not defined yet and we are looking for a formal definition. So the only way is that a volt is the dissipated energy of 1 joule in 1 second by a current of 1 ampere.

Those that correct? this is how the volt is defined formally?
If by "formally" you mean "officially" you should know that the volt is now defined as traceable to frequency.

5. whay do you mean with it's now defined as traceable to frequency.

6. Originally Posted by julian403
whay do you mean with it's now defined as traceable to frequency.
The energy of a photon is related to frequency through Planck's constant: E = hf

Next, you find something that evinces a similarly solid relationship between frequency and voltage. A Josephson junction turns out to be a handy element that has what you need: Josephson effect - Wikipedia, the free encyclopedia

So you illuminate a JJ with a microwave source of precisely known frequency (like that of the hyperfine transition of caesium), and out comes a standard voltage. No messy ohms or amperes involved at all.

7. It's been a while since I've looked at such things, but it that now the definition adopted by S.I.?

8. The new definition has been in place since 1990.

9. Bolding added:
Originally Posted by btr
It's been a while since I've looked at such things, but it that now the definition adopted by S.I.?
Originally Posted by x0x
The new definition has been in place since 1990.
As interesting as that is, my question was specifically whether that is now the definition adopted in the S.I. To be sure, I checked with BIPM and NIST, and according to both the 2008 edition of NIST Special Publication 330 and the 8th edition of the S.I. brochure (essentially the same document), the S.I. volt is still defined as I said above:

Volt (unit of potential difference and of electromotive force). — The volt is the potential difference between two points of a conducting wire carrying a constant current of 1 ampere, when the power dissipated between these points is equal to 1 watt.
The BIPM emphasise that the practical realisation in terms of the Josephson junction (via a defined value KJ-90 for the Josephson constant KJ) does not consitute a new definition. In their words (bolding added):

Originally Posted by BIPM
Recommendations 1 (CI-1988) and 2 (CI-1988) do not constitute a redefinition of SI units. The conventional values KJ-90 and RK-90 cannot be used as bases for defining the volt and the ohm (meaning the present units of electromotive force and electrical resistance in the SI). To do so would change the status of from that of a constant having an exactly defined value (and would therefore abrogate the definition of the ampere) and would also produce electrical units which would be incompatible with the definition of the kilogram and units derived from it.
(RK-90 is a conventional value for another constant, one arising in the quantum Hall effect, and used in a practical realisation of the Ohm.)

In fact, based on current empirical data, the volt realisation in terms of the Josephson junction (denoted V90) differs from the S.I. definition of the volt by the following amount:

10. So, the definition of volt is still the derivate of amperio. But, Why using a new patron like Josephson junction will changes some value of SI, like

11. It a bit like how the definition of the metre changed ever so slightly from being the circumference of the earth/40,000,000. It is now the radius of the earth/40,075,000 ish for convenience.

12. Originally Posted by btr
As interesting as that is, my question was specifically whether that is now the definition adopted in the S.I. To be sure, I checked with BIPM and NIST, and according to both the 2008 edition of NIST Special Publication 330 and the 8th edition of the S.I. brochure (essentially the same document), the S.I. volt is still defined as I said above:
Thanks very much for the clarification, btr. I had been confused by various other NIST publications that presented language like this:

"By the mid-1980s, the national standards laboratories of most major industrialized countries
used the Josephson effect to define their unit of voltage and maintain it constant in time." [see pg. 17 of http://www.nist.gov/director/plannin...eport01-1.pdf]

I guess they were being a little sloppy with their language. Quite a few of their other documents say pretty much the same thing, so they've conflated "here's how we define it practice" and "here's how it is defined."

13. Originally Posted by julian403
So, the definition of volt is still the derivate of amperio. But, Why using a new patron like Josephson junction will changes some value of SI, like
First, we fix the unit of time (the second) in terms of certain atomic transitions. Then the metre is defined in terms of the second and the speed of light, and the kilogram is defined in terms of a lump of platinum alloy kept just outside Paris. Now we can measure length, time, mass, velocity, acceleration, momentum, force, energy, power and so on.

To define the ampere, we consider the attractive force between two parallel, idealised wires a distance 1 metre apart, carrying equal constant currents. By Ampere's law the force depends on the current flowing, so we can define our unit of current, the ampere, as that current which produces a force per unit length of newtons per metre. If we now define the volt to be exactly 1 watt per ampere, as the present standard does, we find that the vacuum permeability has to be exactly volt-seconds per ampere-metre.

If someone then comes along and says that from now on, the volt is defined in terms of the physics of Josephson junctions in the way mentioned previously, we will find that 1 volt is equal to about watts per ampere, and that no longer has quite the same value as before.

14. Originally Posted by tk421
Thanks very much for the clarification, btr. I had been confused by various other NIST publications that presented language like this:

"By the mid-1980s, the national standards laboratories of most major industrialized countries
used the Josephson effect to define their unit of voltage and maintain it constant in time." [see pg. 17 of http://www.nist.gov/director/plannin...eport01-1.pdf]

I guess they were being a little sloppy with their language. Quite a few of their other documents say pretty much the same thing, so they've conflated "here's how we define it practice" and "here's how it is defined."
No problem. As I said, it has been a while since I've looked at this stuff myself, as on the whole I find standards documents make for pretty tedious reading.

I agree the wording of several publications is confusing on this matter. It took a little while to get to the bottom of it, but this page was a real help.

15. Sorry if this if off-thread julian403, but the units we use are fascinating. I always meant to put these down in one place in a manner that each is derived from the previous ones. Some of you will know all of these, some may be a surprise, some have changed very slightly due to convenience, but here goes:

Metre = circumference of earth/40,000,000
Second = length of day/ 24/ 60/60
Degree C = temperature of boiling point-temperature of freezing point of water/100
Joule = energy required to raise the temperature of 1 cubic cm of water by one degree
Newton= force required to create one joule of energy per metre the force moves though
Ampere= current flowing though 2 parallel infinite wires one metre apart that creates a force of one Newton between them
Coloumb = charge passing per second when a current of one ampere flows.
Volt = potential difference required to create power of one joule per second if one ampere is flowing.
Henry =If the rate of change of current in a circuit is one ampere per second and the resulting electromotive force is one volt, then the inductance of the circuit is one henry.
Magnetic permeability= Henry's per metre.
Farad= One farad is defined as the capacitance of a capacitor across which, when charged with one coulomb of electricity, there is a potential difference of one volt
Electric permittivity= farads per metre

It is striking how all our units are related to the properties of water and the earth.

16. Originally Posted by Jilan
Sorry if this if off-thread julian403, but the units we use are fascinating. I always meant to put these down in one place in a manner that each is derived from the previous ones. Some of you will know all of these, some will be a surprise, some have changed very slightly due to convenience, but here goes:

Metre = circumference of earth/40,000,000
Second = length of day/ 24/ 60/60
Degree C = temperature of boiling point-temperature of freezing point of water/100
Joule = energy required to raise the temperature of 1 cubic cm of water by one degree
Newton= force required to create one joule of energy per metre the force moves though
Ampere= current flowing though 2 parallel infinite wires one metre apart that creates a force of one Newton between them
Coloumb = charge passing per second when a current of one ampere flows.
Volt = potential difference required to create power of one joule per second if one ampere is flowing.
Henry =If the rate of change of current in a circuit is one ampere per second and the resulting electromotive force is one volt, then the inductance of the circuit is one henry.
Magnetic permeability= Henry's per metre.
Farad= One farad is defined as the capacitance of a capacitor across which, when charged with one coulomb of electricity, there is a potential difference of one volt
Electric permittivity= farads per metre

It is striking how all our units are related to the properties of water and the earth.
One more for your list: the kilogram was originally the mass of 1 litre of water at 4 °C.

17. Originally Posted by btr
One more for your list: the kilogram was originally the mass of 1 litre of water at 4 °C.
How did I even get that far without the kilogram? Scratches head!

18. Originally Posted by Jilan
How did I even get that far without the kilogram? Scratches head!
Oh, We need that too for force = mass times acceleration.
So the kilogram = the force required in Newtons /acceleration in metres per second,
Lol it been a long week, many thanks !

19. Originally Posted by Jilan
It is now the radius of the earth/40,075,000 ish for convenience.
No, it is not, the meter is defined as the distance covered by light , in vacuum, in 1/299,792,458 of a second.

Second = length of day/ 24/ 60/60
Not the correct definition either. It is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest at

20. Yes the definitions get changed for good reasons. You wouldn't want the second to be defined by the rotation of the earth in case it changed.

21. Originally Posted by Jilan
How did I even get that far without the kilogram? Scratches head!
I've thought a bit more about this and I think that maybe the reason I didn't need it is that perhaps it is a duplication. If the Newton can be derived from the joule then you don't need mass as well.

22. Originally Posted by Jilan
I've thought a bit more about this and I think that maybe the reason I didn't need it is that perhaps it is a duplication. If the Newton can be derived from the joule then you don't need mass as well.
This is how it goes currently (as you probably already know): the kilogram is defined in terms of the International Prototype (or, in the good old days, by a litre of water at 4 °C), then the newton is defined as the force required to produce an acceleration of 1 m s-2 when applied to a mass of 1 kg, then the joule is defined as the work done by a constant force of 1 N applied over a displacement of 1 m.

By the way, a small correction for your list which I've just noticed:

Originally Posted by Jilan
Joule = energy required to raise the temperature of 1 cubic cm of water by one degree
That's a calorie, rather than a joule. A joule is about one-quarter as large.

23. Originally Posted by btr
This is how it goes currently (as you probably already know): the kilogram is defined in terms of the International Prototype (or, in the good old days, by a litre of water at 4 °C), then the newton is defined as the force required to produce an acceleration of 1 m s-2 when applied to a mass of 1 kg, then the joule is defined as the work done by a constant force of 1 N applied over a displacement of 1 m.

By the way, a small correction for your list which I've just noticed:

That's a calorie, rather than a joule. A joule is about one-quarter as large.
Oh heavens I have had that wrong in my head since I was a teenager. Thanks for solving my issue, it all makes more sense now.

24. Glad to have been of help.

25. Originally Posted by btr
First, we fix the unit of time (the second) in terms of certain atomic transitions...
Cough. It's actually the duration of 9,192,631,770 periods of the radiation. The hyperfine transition emits light. Microwaves. People say they're of a particular frequency, but you can't talk of frequency when you're defining the second, because Hertz is cycles per second. So we effectively sit there counting in 9,192,631,770 microwaves one by one, and then jumping up an saying a second has elapsed! So we define the second and the metre using the motion of light. Then we use them to measure the motion of light. Tautology!

The Watt balance section of the Wikipedia kilogram article is worth a read:

"With the watt balance, while the kilogram would be delineated in electrical and gravity terms, all of which are traceable to invariants of nature; it would be defined in a manner that is directly traceable to just three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the meter. By fixing the Planck constant, the definition of the kilogram would depend only on the definitions of the second and the meter. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs. The meter depends on the second and on an additional defined physical constant: the speed of light c. If the kilogram is redefined in this manner, mass artifacts—physical objects calibrated in a watt balance, including the IPK—would no longer be part of the definition, but would instead become transfer standards."

26. Originally Posted by Farsight
Cough. It's actually the duration of 9,192,631,770 periods of the radiation. The hyperfine transition emits light. Microwaves.
I know. I didn't go into details on the definition of the second, as it wasn't the focus of my post.

Originally Posted by Farsight
People say they're of a particular frequency, but you can't talk of frequency when you're defining the second, because Hertz is cycles per second. So we effectively sit there counting in 9,192,631,770 microwaves one by one, and then jumping up an saying a second has elapsed! So we define the second and the metre using the motion of light. Then we use them to measure the motion of light. Tautology!
The definition of the metre is based on the physical assumption that the locally-measured speed of photons in vacuo truly is a universal constant, an assumption which was very well tested (against the pre-existing standards) before the definition was adopted. It does not mean that we could not measure physically important phenomena due to non-local variations in their speed (e.g. the Shapiro time delay), or that we could not detect frequency-dependent speed variations (dispersion) if they existed. The length unit definition is OK unless it turns out that the physical assumption about the locally-measured speed is wrong; for example, if, against most people's expectations, it turned out that photons have a very tiny mass (it would have to be very tiny), the speed of photons would no longer be a universal constant and the definition of the metre would have to be revised.

The definition of the second does not really depend on assumptions about the speed of light; it only depends on the physical assumption that the frequency of light emitted in the hyperfine transition is a good constant (again, this assumption was well-tested against the pre-existing standards before the definition was adopted). If the caesium-133 atom were embedded in some strange material with a refractive index that varied wildly from place to place, and we were embedded in some other part of the material, we could still use exactly the same definition and end up with exactly the same unit of time. Even though the speed of the radiation would be varying all over the place, the frequency would not.

Originally Posted by Farsight
The Watt balance section of the Wikipedia kilogram article is worth a read:

"With the watt balance, while the kilogram would be delineated in electrical and gravity terms, all of which are traceable to invariants of nature; it would be defined in a manner that is directly traceable to just three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the meter. By fixing the Planck constant, the definition of the kilogram would depend only on the definitions of the second and the meter. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs. The meter depends on the second and on an additional defined physical constant: the speed of light c. If the kilogram is redefined in this manner, mass artifacts—physical objects calibrated in a watt balance, including the IPK—would no longer be part of the definition, but would instead become transfer standards."
I'm all for getting rid of the IPK. It seems like a rather anachronistic and impractical way to define the SI unit of mass.

27. Originally Posted by btr
I know. I didn't go into details on the definition of the second, as it wasn't the focus of my post.
OK noted.

Originally Posted by btr
The definition of the metre is based on the physical assumption that the locally-measured speed of photons in vacuo truly is a universal constant, an assumption which was very well tested (against the pre-existing standards) before the definition was adopted.
The point I wanted to make is that it's constant by definition. Like Magueijo and Moffat said, it's a tautology. Or was that Ellis? It isn't "truly a universal constant". It's something like a man in a movie defining the second to be the duration of 25 frames, and then declaring that the movie always runs at 25 frames a second, even though I've just pressed the slo-mo button. Or pause.

Originally Posted by btr
It does not mean that we could not measure physically important phenomena due to non-local variations in their speed (e.g. the Shapiro time delay), or that we could not detect frequency-dependent speed variations (dispersion) if they existed. The length unit definition is OK
It's OK anyway. Think about it. The metre is the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second. If I snap my magic fingers and make the light go half the speed, the second is the time it takes for 9,192,631,770 microwaves to comes past you, so the second is twice as big. Then you use this second that's twice as big with the speed of light that half as fast, and you get the same old metre.

Originally Posted by btr
unless it turns out that the physical assumption about the locally-measured speed is wrong; for example, if, against most people's expectations, it turned out that photons have a very tiny mass (it would have to be very tiny), the speed of photons would no longer be a universal constant and the definition of the metre would have to be revised.
They can't have any mass because of the principle of equivalance. But that's one for another day.

Originally Posted by btr
The definition of the second does not really depend on assumptions about the speed of light; it only depends on the physical assumption that the frequency of light emitted in the hyperfine transition is a good constant (again, this assumption was well-tested against the pre-existing standards before the definition was adopted). If the caesium-133 atom were embedded in some strange material with a refractive index that varied wildly from place to place, and we were embedded in some other part of the material, we could still use exactly the same definition and end up with exactly the same unit of time. Even though the speed of the radiation would be varying all over the place, the frequency would not.
With respect, btr, this is incorrect. Like I said, you cannot speak of frequency when defining the second. And if the caesium-133 atom was below sea level, the second defined as 9,192,631,770 periods of radiation would be bigger. It isn't exactly the same. Gravitational potential can be likened to refractive index, as per Inhomogeneous Vacuum: An Alternative Interpretation of Curved Spacetime

Originally Posted by btr
I'm all for getting rid of the IPK. It seems like a rather anachronistic and impractical way to define the SI unit of mass.
It certainly is. But look closely at the Watt balance definition. There's a reference to h, but not to anything else you might be interested in. Remember what I was saying about the photon field? Perhaps we need a new thread on mass.

28. Originally Posted by Farsight
The point I wanted to make is that it's constant by definition. A tautology. It isn't "truly a universal constant". It's something like a man in a movie defining the duration of the second to be 25 frames, and then claiming that the movie always runs at 25 frames a second, even though I've just pressed the slo-mo button.
I see this as two questions: (1) does the local speed of light actually vary (from what I think you might call a "God's eye view"), and (2) could we objectively improve our present physical theories by incorporating a variable local speed of light? I think (1) is ill-defined operationally speaking, while (2) lacks any real experimental support.

Originally Posted by Farsight
With respect, btr, this is incorrect. Like I said, you cannot speak of frequency when defining the second.
Bear in mind that we're not defining frequency or time themselves, which is a whole different kettle of fish; we're just talking about the official standard for the S.I. second, which is merely one among many time unit standards (nearly all of which pre-date the present S.I. second). Had we not already the notions of "time" and "frequency", there is no way we'd have been motivated (or able) to make such a definition at all.

I sense, though, that we are straying rather into the territory of your other threads, so perhaps we should continue elsewhere on these topics.

29. Originally Posted by btr
I see this as two questions: (1) does the local speed of light actually vary (from what I think you might call a "God's eye view"), and (2) could we objectively improve our present physical theories by incorporating a variable local speed of light? I think (1) is ill-defined operationally speaking, while (2) lacks any real experimental support.
Whilst I think (1) is blindingly obvious, and (2) is essential for improving the Standard Model!

Originally Posted by btr
Bear in mind that we're not defining frequency or time themselves, which is a whole different kettle of fish; we're just talking about the official standard for the S.I. second, which is merely one among many time unit standards (nearly all of which pre-date the present S.I. second). Had we not already the notions of "time" and "frequency", there is no way we'd have been motivated (or able) to make such a definition at all.
I'm not sure I agree, but nevermind.

Originally Posted by btr
I sense, though, that we are straying rather into the territory of your other threads, so perhaps we should continue elsewhere on these topics.
Yes OK, sorry about that.

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