# Strictly about the new system of SI units

Recently, an article entitled Revision of the SI unit system has been published : new definitions of ampere, kilogram, Kelvin and mole from alizar user. In the comments there was a discussion. I realized that this article is alizar 'and poor-quality, and also noticed that many commentators are mistaken in certain things. Therefore, I am writing this article.

The article will be devoted to explaining the basic things. As sources I used the knowledge in physics and chemistry obtained at school, Wikipedia articles, the current SI (8th edition) and the draft of the new SI (9th edition), which they are going to accept. I will try to be objective, I will simply explain what physicists already know.

Do not use the mentioned article from alizar as a source of information. The first sentence is incorrect (more precisely, the caption to the first picture: “Silicon-28 sphere with a purity of 99.9998% can be taken as a standard for the unit of measurement of the amount of a substance”), we will return to it ( UPD from 2017-11 05 19:30: corrected). As good sources of information, I propose an article in the English Wikipedia about the new SI , the original article Nature , the old SI , a draft of the new SI , the FAQ about the new SI .

"Definition". To begin with, the word “define” (as well as the words “set” and “definition”) in the context of our discussion has two meanings at once: 1) put, set, enter definition, define , 2) find out, calculate, find out, determine . So, I will use the word "define" ("set", "definition") in the first sense, if not otherwise stated (however, in the comments I can forget and use not in that sense). That is, if I say that the second is defined in terms of cesium-133, then this means that the definition (that is, a formal explanation of what the second is recorded in the documents) refers to cesium-133. Why I am paying attention here to this terminology will become clear further.

Let me explain what a constant is, known with absolute precision, using the example of the speed of light. A meter is defined as the distance that light travels in 1/299792458 seconds. As a consequence, the speed of light with absolute accuracy is 299792458 m / s. This follows from the definition of the meter. That is, the meter is tied to a certain numerical value of the speed of light and to the second. Physical constants are divided into two types: ordinary (such a majority), which are found out from the results of experiments, are known only with some error and are constantly refined, and those that have exact numerical values, since they are used to determine the units of measurement. The speed of light refers to the second.

Kilogram and its definition in the new SI. Now a kilogram is defined as the mass of a special object, the standard of a kilogram (I emphasize: a specific object, and not any object from the same material of the same size). The standard weight of a kilogram with absolute accuracy is equal to a kilogram. By definition. The standard has copies scattered around the world. So, the masses of the standard and its copies change relative to each other. At the same time, it is impossible to understand which of these items is lighter and which is heavier, since there is nothing to compare with. There is no even more precise reference against which to compare. From this it follows that the mass of the standard of the kilogram changes (simply because it would be very strange to suppose that the mass of copies of the standard changes, but the standard itself does not). But despite this, his weight is still always equal to a kilogram. By definition. Just the kilogram itself is changing with the standard.

As a result, the current definition of kilogram is unsatisfactory. And so the new SI decided to change it. Namely, to bind a kilogram to a certain numerical value of Planck's constant, as well as to a meter and a second. That is, to act with a kilogram in the same way as you have long since acted with a meter: bind to a certain value by some constant. Then Planck's constant will go over to the category of constants, which, by definition, have absolute accuracy (the speed of light also applies there). But in order to do so, you must first decide what kind of numerical value of Planck’s constant we will fix in the definition of a kilogram. And for this you first need to measure the Planck constant as accurately as possible. For this you need to conduct an experiment. And in the experiment should participate in the current standard kilogram. Why? Because we need the most accurate value of the Planck constant, obtained on the basis of the current kilogram. On the basis of which (the obtained value of the Planck constant) we define a new kilogram. To the new kilogram was as close as possible to the old. And this experiment was conducted. Namely, they measured the current standard of kilogram on the so-called watt weights (watt balance, Kibble balance). This allowed us to obtain the most accurate value of the Planck constant, expressed in kg · m 2 · s -1 , where by "kg" we mean the old kilogram, i.e. the current standard of the kilogram. And then the resulting number will be declared, by definition, the absolutely exact value of Planck's constant, expressed in kg · m 2 · s -1 , where the new kg will be understood as a new kilogram.

Is the new kilo equal to the old? To be very strict, no. Because they are defined differently. They cannot be equal with absolute precision. However, when figuring out the value of Planck’s constant, which should be included in the definition of a kilogram, scientists tried to calculate it as accurately as possible. As much as possible at the current level of technology development. As a result, at the current level of technological development it is impossible to experimentally identify the difference between the new and the old kilogram. I mean, it's impossible to say which one is more. As a result, from a practical point of view, they (at the current level of technological development!) Are equal. This means that all existing scales of the world will not have to change.

At the moment, the standard weight of the kilogram is exactly 1 kg. And the Planck constant is known with an error. After the adoption of the new SI, Planck's constant will be known exactly. But the mass of the standard kilogram will be known only with an error (even if we assume that the standard will not be lighter or heavier, as he is doing now). And even if we forget that the standard of the kilogram changes its mass, it is possible that when we learn to measure the mass more precisely than now, we find out that the mass of the standard of the kilogram differs from the (new) kilogram.

And now attention. Using watt weights, we determined ( in the second sense , i.e., we calculated) the most accurate numerical value of Planck’s constant, with the help of which they would determine ( in the first sense , i.e., they would define) kilograms. Do you understand?

All the same applies to all other units that change their definition in the new SI. New definitions are tied to certain numerical values ​​of the constants that will be known with absolute precision. To do this, you first need to calculate these constants as accurately as possible using the old definitions of these units. And for this you need to conduct experiments, which often include those phenomena and standards that were used in the old definitions of these units. After that, the corresponding physical constant will be known with absolute accuracy, but the old definition of a unit will be true only with an error (and before that it was the other way around).

The new definition of a mole. In the new SI, the mole will be determined by fixing the Avogadro number. For this, his (Avogadro number) was measured. To do this, they did the following: they made a sphere of silicon-28, the amount of matter of which (from the point of view of the old definition of a mole) is known, and counted the number of atoms in it. Just like with a kilogram, I will not repeat. Just do not think that supposedly a sphere of silicon-28, and even more so a specific sphere of silicon-28 will become the standard of a mole. The sphere was only used in the experiment to find out the Avogadro number, and the definition of a mole will simply refer to the specific numerical value of the Avogadro number and will not mention the sphere. This is the question of why the first sentence in the article from alizar is incorrect ( UPD from 2017-11-05 19:30: corrected).

Also, as I understand it, the experiment with watt weights is not the only experiment to find out Planck's constant, which will be conducted in preparation for the adoption of the new SI. And the experiment with the sphere of silicon is not the only one to find out the Avogadro constant.

Mole and atomic mass unit (a. E. M.). In the old SI, the mole was defined as the amount of a substance in 12 grams of carbon-12. And a. that is, m. was defined as the mass of carbon-12 divided by 12 (quotation from the current SI: "The dalton (Da) and the unified atomic mass unit (u) are 1/12 of a carbon atom atom at 12 This led to the fact that the molar mass of any substance, expressed in grams per mole, was exactly numerically equal to the mass of the molecule of this substance, expressed in a. E. m. Avogadro's number was defined as the number of particles in a mole, that is, in fact, it was also determined through carbon-12.

In the new SI, the Avogadro number will be fixed, that is, it will simply be given a number, and the mole will be determined through it. And a. E. m. (judging by the latest draft of the SI) will continue to be determined through carbon-12. As a consequence, the aforementioned equality will only be true approximately.

However, from this comment I learned that the SI does not install a at all. e. m., but simply gives a definition that is introduced in other sources. Well, believe this comment. So everything is not so bad, I will hope that after the adoption of the new SI, the sources that establish a. e. m., correct their definitions.

Also recall that the masses of atoms expressed in a. E. m., are not exactly equal to the number of protons and neutrons in the nucleus. That is, for example, the mass of the silicon atom-28 is not equal to exactly 28 a. e. m., it is approximately equal to 27.9769265325 and. e. m. Since the masses of the proton and neutron differ, and there is also the concept of mass defect. The only atom whose exact mass is in a. E. m. we know - this is carbon-12, its mass is 12 a. e. m. by definition.

UPD from 2017-10-27 0:25. Before asking questions, read the FAQ on the new SI and these are my comments:

UPD from 2017-11-01 19:41. See also this my comment (about the mole) . And once again I remind you that the situation with the new definition of kilogram is no different from the situation with the new definition of a mole and from other definitions that have changed in the new SI. And also from any other situations where the definition of a unit has changed in the past (say, the situation with the transition to the current definition of a meter: through the speed of light). In all cases, the new definition is considered absolutely correct and the numerical values ​​of the constants fixed in it can no longer be refined in the future. So in my article you can replace the “kilogram” everywhere with any other unit that has ever changed its definition. And in the comments about the speed of light, again, you can replace the "meter" for other units.