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Counting Down to the New Ampere (2016)

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Re: Counting Down to the New Ampere (2016)

#21

Post by bonzini »

Thorondor wrote: post #7
perlgeek wrote: post #6

A mostly unrelated question, in case any metrology geeks are around: why is the Kelvin an SI unit? Naively, there seem to be multiple approaches to derive temperature from other, more fundamental units. Like using the thermodynamic definition, 1/T = dS/dE, or using Boltzmann's law to approach temperature from the mean kinetic energy of gas particles. Are none of them suitable for precise measurement?

It's not really possible to derive temperature from other more fundamental units. For example, you can't define entropy as an absolute number; it needs to be assigned a unit, and the standard way of doing this is to multiply it by the Boltzmann constant, which depends on a unit of temperature. The mean kinetic energy of gas particles (3/2 kT) also depends on the Boltzmann constant.

Currently the SI is making the triple point of water fixed. I think his point is to make the Boltzmann constant fixed, like the SI is doing for the speed of light, and derive the Kelvin from there. For example 1K could be the temperature at which an atom of (insert some gas here) has a mean kinetic energy of 1.3806488 * 3/2 * 10^-23 J.

However, you have to make sure the definition can be made into an experiment, unlike the old Ampere definition from the article. A definition that mentions perfect gases wouldn't work, if no actual gas exists that can provide a better precision than the triple-point experiment.

Edit: the Kelvin is changing too: https://www.eurekalert.org/pub_releases/2017-04/pb-rft040517...

Re: Counting Down to the New Ampere (2016)

#23

Post by amluto »

Thorondor wrote: post #7
perlgeek wrote: post #6

A mostly unrelated question, in case any metrology geeks are around: why is the Kelvin an SI unit? Naively, there seem to be multiple approaches to derive temperature from other, more fundamental units. Like using the thermodynamic definition, 1/T = dS/dE, or using Boltzmann's law to approach temperature from the mean kinetic energy of gas particles. Are none of them suitable for precise measurement?

It's not really possible to derive temperature from other more fundamental units. For example, you can't define entropy as an absolute number; it needs to be assigned a unit, and the standard way of doing this is to multiply it by the Boltzmann constant, which depends on a unit of temperature. The mean kinetic energy of gas particles (3/2 kT) also depends on the Boltzmann constant.

> For example, you can't define entropy as an absolute number; it needs to be assigned a unit,

You can define entropy directly without reference to other units, although it's a bit awkward. Entropy is the log of the number of microstates that correspond to a system's macrostate. Concretely, if you put n mols of ideal gas molecules in a box of volume V at a pressure P and temperature T, there is some large number of microstates corresponding to all those parameters. Entropy is the log of this number.

In classical mechanics, there's a normalization problem if you try to get an actual number out of this type of problem -- the microstates and all the macroscopic parameters are continuous. In quantum mechanics, though, this issue is solvable, although it's still awkward.

I can imaging a different type of system in which entropy really can be calculated, though. Imagine a particle that can be in exactly one of two states that are macroscopically identical. Now try to cool the system so that the particle is in one of those states of your choice. To do so, you will need to dump exactly 1 bit of entropy.

1 bit of entropy is tiny, but adiabatic demagnetization refrigerators work kind of like this, albeit in reverse, and I could imagine an experiment that would use a device like an adiabatic demagnetization fridge to remove a calibrated number of bits of entropy from some object. From this, you could, in principle, define entropy directly.

Re: Counting Down to the New Ampere (2016)

#25

Post by URSpider94 »

arjo129 wrote: post #22

Why is an ampere a fundamental unit but,not a coulomb?

If you go back in history to when the SI units were defined, there would have been no way to measure a Coulomb of electrons, since in nature you'd somehow have to distinguish the electrons you are counting from all the other electrons sitting around. With the invention of single electron counting, we could do it now, but we aren't going to change the SI system a century in. And, the idea was that the seven primary units are both independent (you can not derive one from any of the others) and sufficient to derive all of the other units of measure. Once you have the Ampere, you can define a Coulomb as a relative quantity.

Re: Counting Down to the New Ampere (2016)

#26

Post by URSpider94 »

amluto wrote: post #23
Thorondor wrote: post #7

Earlier quoted context omitted.

It's not really possible to derive temperature from other more fundamental units. For example, you can't define entropy as an absolute number; it needs to be assigned a unit, and the standard way of doing this is to multiply it by the Boltzmann constant, which depends on a unit of temperature. The mean kinetic energy of gas particles (3/2 kT) also depends on the Boltzmann constant.

> For example, you can't define entropy as an absolute number; it needs to be assigned a unit, You can define entropy directly without reference to other units, although it's a bit awkward. Entropy is the log of the number of microstates that correspond to a system's macrostate. Concretely, if you put n mols of ideal gas molecules in a box of volume V at a pressure P and temperature T, there is some large number of m…

While you are right that this is the statistical definition of entropy, there are two issues: first, entropy is a unitless quantity, so defining it exactly doesn't actually move the ball forward in terms of defining units of measure. Second, outside of its theoretical underpinnings, physicists and chemists hardly ever talk about absolute values of entropy, they almost always use differences in entropy -- which factors out the need to define the exact number of microstates present before and after.

Re: Counting Down to the New Ampere (2016)

#27

Post by Filligree »

pdonis wrote: post #9
pavpanchekha wrote: post #5

Earlier quoted context omitted.

Meter is already specified by fixing the speed of light. Seconds are defined in terms of Cesium atom vibrations.

> Seconds are defined in terms of Cesium atom vibrations. Not vibrations of the atoms themselves. The second is defined in terms of the period of the radiation corresponding to a particular hyperfine transition of the Cesium atom.

What does "hyperfine" actually mean, in this context?

Re: Counting Down to the New Ampere (2016)

#28

Post by pdonis »

Filligree wrote: post #27
pdonis wrote: post #9

Earlier quoted context omitted.

> Seconds are defined in terms of Cesium atom vibrations. Not vibrations of the atoms themselves. The second is defined in terms of the period of the radiation corresponding to a particular hyperfine transition of the Cesium atom.

What does "hyperfine" actually mean, in this context?

It's a reference to a particular kind of splitting of the energy levels of electrons in atoms, due to interactions between the electrons and the nucleus.

Basically, as more and more precise measurements of the energy levels of electrons in atoms were made in the 1920s, 30s, and 40s, physicists kept finding that energy levels that were thought to be degenerate (i.e., multiple states with the same energy) were actually split into multiple, closely spaced levels. The original quantum model was the non-relativistic Schrodinger equation as applied to the atom. Then it was found that electron energy levels that were degenerate in that model were actually split into multiple levels because of the effects of electron spin and certain relativistic corrections; this splitting was called "fine structure". Then it was found that there was even further splitting, of energy levels that were degenerate in the fine structure model, due to interactions between the electron and the nucleus; this further splitting was called "hyperfine structure".

More here:

https://en.wikipedia.org/wiki/Hyperfine_structure

Re: Counting Down to the New Ampere (2016)

#29

Post by averagewall »

More exciting is that the mol and Avogadro's constant will be pushed off to the side on their own. Hopefully an even more future update will remove them entirely. They're really quite redundant and pretty much only exist to facilitate the needless presence of the non-SI mass unit, the unified atomic mass unit, which thankfully will now be defined in terms of the kg instead of having two independent mass units like we have now.
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