Talk:Atomic units/Archives/ 1

The meaning of 'e'?

I wonder if the symbol "e" as used in the context of SI differs from its use in the context of atomic units?

In

• Karplus, Martin, and Richard Needham Porter. "Atoms and molecules; an introduction for students of physical chemistry." Atoms and molecules; an introduction for students of physical chemistry (1970).

Coulomb's law is written:

$F={\frac {q_{1}q_{2}}{4\pi \epsilon _{0}r^{2}}}$

and the $e$ is called the electron charge.

In Tomilin,

• Tomilin, K. "Natural systems of units. To the centenary anniversary of the Planck system." Proceedings Of The XXII Workshop On High Energy Physics And Field Theory. Vol. 287. 1999.

the factor $k_{e}$ is set to the constant in Coulomb's law, so Karplus and Porter have $k_{e}=1/(4\pi \epsilon _{0})$, while Tomilin claims that Hartree chose $k_{e}=1$.

Uzan,

• Uzan, JP. Varying Constants, Gravitation and Cosmology. Living Rev. Relativ. 14, 2 (2011).

does not speak directly to this issue but Uzan writes out Stoney's units and then remarks: "where the 𝜀0 factor has been included because we are using the SI definition of the electric charge." (the formulae directly above this quote include the factor $k_{e}=1/(4\pi \epsilon _{0})$. Johnjbarton (talk) 17:14, 29 December 2023 (UTC)

The contexts to be distinguished are systems of quantities (in this case Gaussian quantities vs. the system of the SI). Hartree atomic units translate into either context.

By "e", Hartree was referring to the quantity e′ = e / √4πε₀, which is the quantity in the Gaussian system that corresponds to e, the SI concept of the elementary charge. When e′ and e are kept distinct, everything is consistent. Note that when Tomilin says "Hartree chose k_e = 1", he is referring to the corresponding Gaussian quantity k_e′ = k_e · 4πε₀.

My suggestion would be to put the new material in a History section, and give the relationship to the modern symbols. —Quondum 20:05, 30 December 2023 (UTC)

Thank you. Now I think I understand your point of view and I can try to explain mine.

Let's ask: why do none of the three famous texts cited in the article as sources for atomic units mention the issue you raise?

I think the reason is that atomic units are "application-specific units", designed for use in atomic physics which relies on Hamiltonian mechanics. The entire science relies on energy calculations, never force. These sources don't mention $4\pi \epsilon _{0}$ because this it not a notable fact. It will "never" be used in atomic physics calculations.

Similarly, Jackson's Classical Electrodynamics (or any EM book) spends pages on this topic: electromagnetic force is critical to the subject matter and the corresponding conversion factors play a critical role in the calculations.

Tomilin needs it to compare across systems of units, an "artificial" use of the atomic units concept. These units exist within their area of application. The conversions needed for atomic units are called out by the references, primarily energy and distance.

That is why the Natural units page seems off target to me. It is almost entirely focused on numerical conversions rather than on comparison of arenas of application.

Does that make sense? Johnjbarton (talk) 23:11, 30 December 2023 (UTC)

I can see where you are coming from, but it only makes sense to me in the specific context where you have already thrown out electric charge as a separate dimension (i.e., you are already working within the Gaussian framework, which arbitrarily eliminates the coefficient in Coulomb's law, in so doing already building force into the definition of charge).

Given only the SI value of e, but neither e′ nor ε₀, you cannot derive the atomic units (or, for that matter, the energy of the Hamiltonian) from the given constants. Force is derivable from the energy in this configuration (the hydrogen atom), so your observation about "never force" is entirely moot. The books you mention presumably work in the Gaussian system of quantities, as is very common in particle physics. They use the quantity e′, not e. The other way around works too: given the SI values of e, ħ, c and any one of m_e, a₀, E_h, you can determine ε₀, so it is unavoidable when charge is as defined in the SI. You cannot insist that scientists abandon the SI in the field of atomic physics.

So really, you are saying that, in the tradition of particle physics, charge is not given its SI value; instead, the Gaussian definition of charge is what is used. I say this too: it is a traditional choice by the practitioners in the field, who possibly have a bit of difficulty admitting that it is not the only feasible choice of quantities or units for their field. It would not be sensible to insist that SI units cannot (or even should not) be used to describe atomic physics. —Quondum 00:33, 31 December 2023 (UTC)

Yes, exactly: "in the specific context" is the point. In the context where atomic units are used, SI units are by design not critical.

"Given only the SI value of e" is not a starting point for atomic units; I don't "insist that scientists abandon the SI in the field of atomic physics", I'm saying that in the context of atomic units SI concerns are not the top issue. An article on "atomic units" should be about these units and their use first and foremost, with SI only to the extent that it is relevant for the application. We should have a specific section on "Relationship to SI units" because they are important to science but the article should not be organized around SI.

To say this another way, your suggestion that "Gaussian system of quantities, as is very common in particle physics" would recommend that point of view in the article. I guess you would not want this; fine by me because I think the focus should be on the nature and use of atomic units, not on EM.

Now we do need to be clear and not confusing older and newer notation. But we shouldn't force atomic units into a form other than what the sources use just to make them line up with SI.

The usefulness of SI or not in atomic physics may be discussed if we had a reference, but to me this is secondary information: the article is about the usefulness of atomic units, not SI.

Perhaps we can discuss about some specific changes based on some common understanding if not complete agreement. Johnjbarton (talk) 01:51, 31 December 2023 (UTC)

You really seem to be in a place where you are not thinking about the reader's ease of interpretation, and I'd suggest that you have not taken the trouble to seek more modern sources. Why would NIST give the CODATA values of the atomic units exclusively in SI units if they were not appropriate for the context? I should step out of this; I'm not enjoying the interaction. You could ping others for input. —Quondum 02:42, 31 December 2023 (UTC)

I don't have access to any more modern sources. Maybe next weekend I can drive to a bookstore. Johnjbarton (talk) 03:07, 31 December 2023 (UTC)

A modern reference that should be sufficient for your purposes here: International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 125, ISBN 92-822-2213-6, archived (PDF) from the original on 2021-06-04, retrieved 2021-12-16

This is the only edition of the SI brochure that contains this information. —Quondum 20:28, 31 December 2023 (UTC)

ok thanks, I added this and two other references, esp. McWeeny's Nature article which bridges the older work into SI time frame. Ironically the meaning of $\epsilon _{0}$ changed since the 8th ed. but I see no reason to go into that here. Johnjbarton (talk) 00:48, 1 January 2024 (UTC)

The SI meaning of ε₀ changed, even since I was a kid (aside from the usual SI-redef/CODATA-value tweaks)? That seems unthinkable: there must be something amiss. Incidentally, the existing McQuarrie reference seem to cover atomic units through the SI lens as well – accessible through Google Books. —Quondum 01:16, 1 January 2024 (UTC)

On review, the article now gives a much improved sense of context and timeline, with a perfectly coherent description of the unit systems. The 1973 switch by one author to SI quantities is actually not so strange: it was not long after the SI was formalized in 1960. I tend to forget how recent the SI is. —Quondum 16:57, 1 January 2024 (UTC)

Nondimesionalization reference.

The section "Non-relativistic quantum mechanics in atomic units" says:

• Nondimesionalization involves a substitution of variables that results in equations in which these constants (, , and ) "have been set to 1".

with a citation to McQuarrie. However, according searching on Google Books, his book never uses the word "Nondimesionalization". Johnjbarton (talk) 17:50, 31 December 2023 (UTC)

I think that employing the concept of nondimensionalization here is undue: it really adds nothing. As you point out, there is not much to reference this to, either. I would be happy with the entire section being removed. —Quondum 16:47, 1 January 2024 (UTC)

Thanks. I think the section actually contains important information that should be near the top of the article: it supplies the motivating example for having atomic units. But the intro bit obscures that aspect. I will rework it. Johnjbarton (talk) 16:51, 1 January 2024 (UTC)

The benefits of using atomic units can be made without bringing in the concept of nondimensionalization: just by employing the specific constants used in atomic units makes many equations involving the dynamics of electrons (or of their wavefunctions) take an appealing form. The argument that we can make a substitution of variables so that the constants are absorbed and disappear from view is additional, but is hardly specific to this topic. We could reword it to remove the nondimensionalization/substitution of variables part. —Quondum 17:18, 1 January 2024 (UTC)

Yes, exactly. Johnjbarton (talk) 17:27, 1 January 2024 (UTC)

Would it make sense to change "using the the Hartree atomic units" to "rescaling variables using the Hartree atomic units"? Just saying "using the the Hartree atomic units" implies understanding that what is meant is rescaling, requires a whole undiscussed process in which the variables with the same name actually are different (rescaled) variables. Saying "rescaled" at least makes clear that this process is meant. —Quondum 17:45, 1 January 2024 (UTC)

I'll find a way of emphasizing the convention that you have been using a little more. I don't have access to Mcweeny, but we definitely should have clear referencing for the convention that results in removing constants from equations. —Quondum 19:04, 1 January 2024 (UTC)

I'm fine with all this, it's clear that the concept isn't critical to the concept article or anything, but wanted to mention that fyi that although the word "nondimensionalization" does not appear in McQuarrie, the concept is implicit in Problem 9.5, p. 489. "This conversion can be achieved in all of our equations by letting m_e=e=$\hbar$ = $4\pi \epsilon$₀=1. Show that this procedure is consistent with the definition of atomic units used in this chapter" (referring to pp. 435-437). To me this is a minor point, and need not be covered in the article. Qflib, aka KeeYou Flib (talk) 17:13, 2 January 2024 (UTC)

@Qflib if you have any references on this subject, please add them to Nondimensionalization or at least mention them in the Talk:Nondimensionalization. Johnjbarton (talk) 17:35, 2 January 2024 (UTC)

Defining constant form

In retrospect, I am unconvinced that my change of the form of the defining constant for permittivity makes sense, and I do not have access to the Mcweeny reference. The way I left it has an element of circularity in the definition by virtue of the name of the quantity that is in the reference for the value. If you have any opinion about it, please feel free to undo my edit. —Quondum 23:46, 2 January 2024 (UTC)

I found McWeeny's 1973 article via "The Wikipedia Library", under the Nature collection, searching for the title "Natural Units in Atomic and Molecular Physics".

McWeeny does not seem to mention anything special about the $4\pi$ factor. He calls his $4\pi \epsilon _{0}$ "permittivity", but he also says "...where $epsilon_{0}$ is the permittivity of free space. In his tables of base units and derived units, in the "SI equivalent" column, he writes it as $4\pi \times {}$8.8541878128(13)×10⁻¹² F⋅m⁻¹.

The version with $4\pi \times {}$8.8541878128(13)×10⁻¹² F⋅m⁻¹ is more consistent with the McWeeny source but the CODATA value is referenced in the table. I think it is fine to leave it as is. Johnjbarton (talk) 00:06, 3 January 2024 (UTC)

Oh, wow! It took me some time to get to this, but I have managed to get this ref at last. WP:LIB will be very useful for hunting out specific refs. Thank you! —Quondum 16:45, 5 January 2024 (UTC)

Here is another tip to avoid frustration with WP:LIB: avoid using the search in the top Library level ("Search the library"). For me it almost never gives the right resource. Instead, figure out which of the "collections" (ie publisher) has the research and use the search inside of the collection. Johnjbarton (talk) 17:01, 5 January 2024 (UTC)

Yep, I ran into that immediately. Your inclusion of "under the Nature collection" quickly put me on the right path :)

Incidentally, I am leaning towards quoting Hartley more faithfully, e.g. using "H-atom". —Quondum 18:54, 5 January 2024 (UTC)

Great; I'm good either way. Johnjbarton (talk) 19:09, 5 January 2024 (UTC)

Article title

Given the greater historical context, the more appropriate title for this article might be "Atomic units". There may have been an element of disambiguation involved in prefixing the "Hartree" (there are presumably other types of of atomic units), but the term "atomic units" presumably predominates massively. —Quondum 17:32, 1 January 2024 (UTC)

If you read the Talk page above here, you'll see several people asking questions who confuse (Hartree) atomic units with Planck_units. One the one hand, putting "Hartree" in the name of the article may be helping a little with that. On the other hand, I can't say I've ever seen them referred to as "Hartree atomic units" in the literature, which I think supports your point. Qflib, aka KeeYou Flib (talk) 17:32, 2 January 2024 (UTC)

I think maybe one ref from 1959 calls them Hartree atomic units. Every other reference is "atomic units". Johnjbarton (talk) 17:56, 2 January 2024 (UTC)

Qflib, I see no such confusion above – have I missed something? In general, atomic units could be grouped together with Planck units under natural units, but it would be rare to confuse them. —Quondum 19:14, 2 January 2024 (UTC)

See the 2019 name change. Qflib, aka KeeYou Flib (talk) 18:20, 8 January 2024 (UTC)

The 2019 name change edit comment says: "As said in the lead, "this article deals with Hartree atomic units". I see that as simply aligning title with content. The introduction of "Hartree atomic units" into the article seems to date back to this revision, which suggests an uncertainty ("which one might name ...") about veracity. Anyhow I think we've sort of chased this one down a rabbit hole —Quondum 19:07, 8 January 2024 (UTC)

I'm revising my first choice of the title to "System of atomic units" (alternatively "Atomic units system"). My reason is that if weight is given to the convention where equations are written without the constants c, ħ, m_e, etc. as suggested by Hartree, then it is not only a set of units, but also covers a system of quantities that may be used, like the International System of Units. I am well aware that people use the phrase "Gaussian units" to mean "the Gaussian system of units and quantities", and similarly for "atomic units", but it helps to be a bit more explicit in this area where the majority of editors and readers seem to have difficulty with separation of two concepts when the same phrase is used for both (which can be very frustrating when you're trying to communicate with editors). With atomic units, the problem is more acute, since there are at least two conventions: one in which the quantities are written without units (e.g. q = 10, which is where the constants do not occur in the equations as just mentioned), and a second in which the quantities are written with units (e.g. q = 10 e, which is where the constants still occur in the equations); the article already deals with both conventions. —Quondum 21:13, 6 January 2024 (UTC)

I think these two views may be very clear in your mind but not all to at least this editor. I think a better strategy would leave the article at "Atomic units" and have an early section "As a system of units" to set out these differences. Then using the "system of atomic units" in the appropriate way in the article.

To be honest, I don't understand "q=10e" as anything other than a unit conversion equation. It can't be and equation in atomic units, as e=1 in atomic units. Johnjbarton (talk) 22:25, 6 January 2024 (UTC)

Ask yourself the question: what are the units of atomic units? If you are using the term consistently with you statement here, the answer is "1", period. The conflation of terms makes it difficult to communicate distinctions, or to be mathematically correct in technical writing. Our article will be an exercise in defining atomic units by analogy with the SI system, with nary an equation connecting them. You need to be able to produce a framework that contains both SI and atomic units without contradiction to be able to mathematically relate them. The sheer amount of lost productivity on WP alone resulting from this fuzzy thinking (confused and arguing editors) that I have seen is staggering. I have seen worse than here: for example an editor who insisted that 1 Hz = 2π rad. I see that the sources do not even treat this issue consistently. Some do not mention the "shortcut" that the units can be treated as 1 or that the constants be dropped from formulae (Shull&Hall, Jerrard&al). Some call it a "shortcut" (McWeeny). Others just implicitly use the shortcut (Hartree). We can't just cite different viewpoints; they lack context when mixed and introduce inconsistency. Somehow we need to be able to present a consistent context in which we integrate all the sources, which is possible when formalizing it in terms of transformations between "systems". —Quondum 01:24, 7 January 2024 (UTC)

To be clear, I'm sure your point of view is correct as in "Operators Manual for Atom Units" correct. Given that we are not writing that manual and that the audience here include us confused editors, how that that point of view be best expressed? My feeling is that "System of atomic units" sets the editor and reader in the "operator manual" frame of mind. I think the "oh, what's atomic units?" frame of mind is a better place to start, then "As a system of units" comes in as "hmm, I see one needs to be clear and careful".

As I understand it, atomic units have two advantages: "scale" and "abbreviation". Velocity is $v=\Delta r/\Delta t$ and you can use any units you like. If you are interested in the Hydrogen atom electron velocity, atomic units will give a numerical answer close-ish to 1.0. That's scale. Abbreviation does not come into a simple defn with no fundamental constants.

In the He atom quantum formula, the abbreviation comes in because we "set constants to one". Then we can manipulate simpler formula with a side table: the side table says "these formula are in atomic units". At the end we pay the piper. We face two costs. One related to scale: we need to convert to SI. One is related to abbreviation: we killed any hope of checking our manipulations with dimensional analysis because 1.0 has lots of different dimensions. I think what I called "abbreviation" is what you called "short cut". The most amazing expression of this issue is in Page 36 of Gravitation Part 3 By Charles W. Misner, Kip S. Thorne, John Archibald Wheeler · 1973 They produce the mass of the Sun in gms, cms, and ergs.

As I understand your two points of view, it is the difference between using "abbreviation" or not. In the "no abbreviation " case we have say "q=3e" where e is one atomic unit of charge or 1.6 some odd ten to minus 19 C. The 'e' is not abbreviated, just using a unit that will mean "3" is close to the answer, no 1.6 and many tens to think about. The "q=3" approach means we need to figure out what "3" means first. Oh "3e"! Then we continue with the conversion.

Does this make any sense? I'm hoping that by describing my point of view we can come to a common understand on how to present the concepts. Johnjbarton (talk) 02:41, 7 January 2024 (UTC)

I think you have a point (or two): an appropriate title, and the strategy that you suggest.

Firstly, the article title, where you point out that a more "proper" title might actually trigger the wrong expectation by the reader, contrary to my perspective. In this case, a move to "Atomic units" would still be appropriate. (There are minority competing uses for that title, such as the atomic units of Rydberg and such, but disambiguators might be appropriate if any such article is ever written and not included as a section in this article).

Secondly, the strategy, where you suggest a section in this article to deal with the different systems of quantities (to speak formally of what is happening, but even that is a but of a mouthful to the average reader). Let's try this. And yes, we need to figure out hoe to present this for the target reader. Unfortunately, I always head off to the "formal"/"obscure" end of the spectrum. I have replaced a section as a rough attempt at doing this at Hartree atomic units § Systems used. —Quondum 03:29, 7 January 2024 (UTC)

I like the new section. Let's do page rename to "atomic units". Johnjbarton (talk) 19:09, 7 January 2024 (UTC)

Move requested here. —Quondum 19:19, 7 January 2024 (UTC)

I like the new section as well. Qflib, aka KeeYou Flib (talk) 18:20, 8 January 2024 (UTC)