Talk:Natural units

In particle physics/Gaußian units: 4πε₀=1, μ₀=1, c=1

Well, that is impossible. ;) --Chricho ∀ (talk) 22:49, 12 February 2012 (UTC)

Because c² = 1/(ε₀μ₀)

Just granpa (talk) 23:10, 12 February 2012 (UTC)

It's grossly inaccurate to say that "In Gaussian units, 4πε₀=μ₀=c=1". See Gaussian units. The differences between Gaussian and SI units cannot be summarized by saying what the values are of ε₀ and μ₀ and c. It's far more complicated than that, and much better to just link to the other article (Gaussian units) than to try to explain it here. I just cleared out this and many other misleading oversimplifications of electromagnetism quantities. --Steve (talk) 02:21, 13 February 2012 (UTC)

That edit was a major improvement. What may still be a little understated relates to this confusion, especially the assumption (from SI) that c²ε₀μ₀ = 1. Along with the normalization choices in a system of units, there are some complications, such as choices in the form of equations. I guess this could also be treated as a normalization, in the sense that SI clearly makes the normalisation/assumption expressed in this equation that some of the other systems do not make. I would think that mention of this is appropriate in this article, as it serves to confuse many. — Quondum^☏✎ 11:02, 13 February 2012 (UTC)

I added a little note about that. I think it's better to describe this as a specific complication of electromagnetic units, rather than try to fit everything into a grand framework, which this article does far too much already :-/ --Steve (talk) 14:02, 13 February 2012 (UTC)

I agree with the special treatment only in the EM case. I've extended it, since I feel the specific case mentioned is confusing to anyone first trying to figure it all out, and an early pointer on this aspect may save such a person a lot of trouble (even though it is possibly misplaced in this specific article: revert it if you feel so). — Quondum^☏✎ 15:36, 13 February 2012 (UTC)

Thank you, it is much better that way. Indeed, I was confused by $\varepsilon _{0}\mu _{0}c^{2}=1$, which was even used in the table. --Chricho ∀ (talk) 10:04, 28 May 2012 (UTC)

You know, Steve, I don't think this edit is so good. It plops in some interpretation of the differences between rationalized and non-rationalized units that is from a particular POV. Someone else may very well say the opposite, that non-rationalized units are more complicated than rationalized. Putting the 4π in the denominator with the r² in an inverse-square law is more natural (and simpler) because it connects the denominator of the inverse-square law directly to the surface area of a sphere in 3-space and to the concept of flux density which gets integrated with Gauss's law to yield the contained charge. It's pretty flimsy to claim that that

$F=G{\frac {Mm}{r^{2}}}$

is less complicated than

$F=G'{\frac {Mm}{4\pi r^{2}}}$ where $G'=4\pi G$

just because the latter has this extra 4π in the denominator. Rationalized units are conceptually less complicated than non-rationalized units. 70.109.178.237 (talk) 03:53, 28 May 2012 (UTC)

You misread what I wrote. The "complication" is the fact that the symbolic law of physics is different depending on the system of units. The "complication" is not the factor of 4pi. I will add a few words to make it clearer. --Steve (talk) 13:18, 28 May 2012 (UTC)

Doesn't look any better. And I don't think I am misreading you. The main difference between rationalized and unrationalized units is that one puts a 4π in the denominator with the r² in an inverse-square law (where it belongs in my opinion) and the other doesn't. (There may remain a scaling constant in the law if the units are not "natural" in some sense.) The complication that electrostatic cgs units have is that charge (or current) is not considered to be a fundamental quantity like it is in SI. So they do to charge like what nearly every unit system does with force, they infer the dimension of something new (force or electric charge) out of what exists (time, length, mass). In cgs electric charge becomes dimensionally force^1/2 × length. And it isn't true, except for convention that "Newton's law is F = ma in every system of units." We could define our unit of force to be whatever force is needed to compress some prototype spring (stored in Sèvres) by 1 cm, and then Newton's 2^nd law would be F = kma where k would be a constant that would be experimentally determined and listed at the NIST site. And k would be dimensionally (force × time²)/(mass × length). It would not be dimensionless and force would not be the same thing as (mass × length/time²). That is what the complication is about regarding cgs electrostatic units. It is not about "rationalized" vs. "unrationalized". The complication regarding electrostatic units is that some people have defined the Coulomb constant to be the dimensionless 1 and others have defined charge as a unique dimension of physical quantity (so with them, generally the Coulomb constant is not dimensionless). But natural units usually whack the Coulomb constant anyway. 70.109.178.237 (talk) 00:56, 29 May 2012 (UTC)

Again, I am saying that the complication is not the 4pi, which I personally like in Coulomb's law just as much as you do. The complication is that 4pi might or might not be there depending on the system of units.

Can you make mechanical units as complicated and inconsistent as electromagnetic units are? Yes, if you are sadistic! You can torture students of physics by inventing a new system of units where force is a fundamental quantity, etc. etc. Thank heavens, no one has ever done that to my knowledge! Therefore, in the world we live in, with the unit systems that are actually in use in the world, mechanical units are "simple". There is no unit system I've ever heard of where F=ma is not the correct equation to use.

Many readers looking at this article will have already had the experience of using the same formula, like "F=ma" or "distance = velocity * time", in various different units like meters and centimeters (and inches in USA). They will naturally draw on this experience when thinking about how unit conversions work in general. Therefore it is helpful to point out that the simplicity they might have expected from experience with mechanical equations will not be present in the more complicated world of electromagnetism equations. You seem concerned that readers will get the impression that electromagnetism units are more complicated because there is something fundamentally different about electromagnetism units. I'm happy to add some text clarifying that EM units are complicated because of human reasons (history and sociology) not physics reasons.

Out of the multitude of differences between Gaussian and SI units, I agree with you that rationalized versus nonrationalized is not a particularly important difference. Charge-units being fundamental in SI but not Gaussian would be a more important difference. BUT, this is not a section comparing Gaussian and SI units! It is comparing Gaussian and Lorentz-Heaviside units! In BOTH of those systems, charge is not considered to be a fundamental quantity. In fact, I believe the only difference between them is rationalized versus nonrationalized. That's why it's used as an example! --Steve (talk) 18:18, 30 May 2012 (UTC)

Okay, if we agree (and other interested editors) that the complication regarding rationalized units is not because the 4π in the denominator with the r², and that the complication regarding electrostatic cgs units is because the Coulomb constant, 1/4πε₀=1 which forces electric charge to take on a derived dimension of force^1/2 × length rather than being some unique dimension of physical quantity, then we should state it as so in the article. If you disagree with this essential assessment of what complicates EM units, then we are not in agreement here about what the facts are. If we are in agreement about the facts, then we should write it differently in article. Since Gaussian units#"Rationalized" unit systems seems to be the only Wikipedia discussion of what is meant by "rationalized", I tried to spell this out there. But the issue of a derived dimension for charge (because 4πε₀=1) is not the same issue as rationalized units vs. unrationalized. And I cannot tell that from what is in this article now. 70.109.176.173 (talk) 20:11, 30 May 2012 (UTC)

I tried to rewrite again. I guess I had structured the section a bit strangely, with the last paragraph being redundant with the others. Maybe that helped cause confusion.

The fact that electric charge has a derived dimension is true in both Gaussian and Lorentz-Heaviside. So again, if we're contrasting these two systems, the fact that charge has a derived dimension is not one of the differences. But...when I think about it, it is a relevant fact for the article anyway so I put it in at the top before introducing the two variations.

I don't understand why you think it is unclear or misleading to say that the two EM unit systems are very inconsistent because there are two natural-units versions of Coulomb's law but only one version of Newton's laws. But whatever. I deleted that and tried a different approach: I described how to get either Gaussian or L-H units starting from SI. I think that is an equally good way to convey the information. --Steve (talk) 14:19, 31 May 2012 (UTC)

Dimensional consistency and natural units.

In this edit [1], another IP added

"... but it creates more confusion (see below Greater ambiguity paragraph) because the equality is dimensionally inconsistent as mass and momentum have different dimensions or qualities and therefore cannot be summed to give the dimension of energy."

These quantities that are represented in whatever system of natural units are dimensionless. E.g. in Planck units, the mass term is really the mass divided by Planck mass and the momentum and energy are also scaled by the reciprocals of their respective Planck units. I guess my reversion of the edit needed more explanation. 70.109.178.237 (talk) 01:14, 28 May 2012 (UTC)

I understand the phrase "whatever system of natural units are dimensionless" to assert that Dimensional analysis is simply a pseudo algebra created by our choice of measurement. I believe the situation is different and related to the edit by User:86.125.179.179.
If we are measuring mass in Planck units of mass, energy in Planck units of energy and speed in Planck units of speed, I believe mass, energy, and velocity are still distinct concepts and measurements. Surely we don't really mean that mass, energy, and velocity are identical and indistinguishable. (There would however be a certain beauty in saying that all equations reduce to 1 = 1.)
I believe we still mean that a unit of (Planck) mass is related to (can be transformed to) a unit of (Planck) energy by a function of (Planck) velocity. I understand User:86.125.179.179 to be asserting that the Planck normalization of equations produces an appearance of simplicity which ignores selected unitary functions. I believe we still must recognize that dimensional analysis reflects valid concepts that can help validate our equations of existence.
SBaker43 (talk) 04:16, 28 May 2012 (UTC)

Okay, I am saying that neither

$E^{2}=(pc)^{2}+(mc^{2})^{2}\,$

nor

$\left({\frac {E}{E_{P}}}\right)^{2}=\left({\frac {p}{m_{P}c}}\right)^{2}+\left({\frac {m}{m_{P}}}\right)^{2}\,$

are dimensionally inconsistent.

Physical law that says

$E=mc^{2}\,$

or

${\frac {E}{E_{P}}}={\frac {m}{m_{P}}}\,$

isn't saying "this much mass is that much energy" or that "this mass is that energy", is it? Maybe it is. Maybe not. What is the correct interpretation?

Or does

$E=k_{B}T\,$

or

${\frac {E}{E_{P}}}={\frac {T}{T_{P}}}\,$

say that this much energy (per particle) is that much temperature? Is temperature simply another way of saying what the per particle energy content is?

Is Newton's law of motion relating two different kinds of physical quantity or are they the same?

$F={\frac {dp}{dt}}$

Is force the very same thing as the time derivative of momentum or is force only proportional to the rate of change of momentum and the two physical quantities are different "stuff"?

Physical law relates different quantities of different kinds of physical quantity together. 70.109.178.237 (talk) 05:14, 28 May 2012 (UTC)

Normalization of α

The section "Choosing constants to normalize" contains the sentence "In a less trivial example, the fine-structure constant, α≈1/137, cannot be set to 1, because it is a dimensionless number." First thing, I agree with the section as a whole. In particular, I agree that it is "not possible to simultaneously normalize all four of the constants...". I'm not arguing about that. Taken in context perhaps the sentence is okay, but it seems to assert a particular idea on its own that is not correct.

There is no reason that α cannot be redefined to be 1 any more than the other constants, and certainly not because it is dimensionless. For example, define $\alpha '=\alpha /137={\frac {k_{\mathrm {e} }e^{2}}{\hbar c137}}$ and likewise $e^{\prime }=e/{\sqrt {137}}$. This entails scaling the primary electric charge. This is always allowable in defining a new system and the value of e could be scaled in any of the unit systems. There may be some confusion between basic numerical scaling and redefining an entity with different dimensionality (by absorption/multiplication of various constants) as what happens when defining natural unit systems. Both may produce different numerical values for certain entities; however, they are not the same operation, neither are they mutually exclusive.

Next, it's not clear what "less trivial" is supposed to mean. I understand the importance the fine-structure constant in modern physics, but when it comes to the game of normalizing constants and redefining various symbols, I think there is nothing significantly different about the value of alpha. If it is indeed "less trivial" or in any way different than the constants on the other side of the equation or the mass of elementary particles, it needs to be qualified. Also as a matter of pedagogy, "trivial" is overused and should be avoided. There is nothing "trivial" about this subject or even a single example--especially to a student learning these ideas--in choosing and using a well-defined, correct system of units and converting between them. A suggested phrase is "In a more overarching example, ...". --cperk (talk) 17:45, 8 October 2013 (UTC)

I agree. The section is reformulated as to not make any explicit claims. YohanN7 (talk) 14:09, 7 June 2015 (UTC)

Don't share your perspective. It's not just a claim. It's a fact. $\alpha ={\frac {e^{2}}{(4\pi \epsilon _{0})\hbar c}}$ cannot be normalized to a predetermined dimensionless number. You can, with choice of units, normalize three of the four dimensionful constants that define α, but not all four. Neither can you, simply with the choice of units, normalize the Proton-to-electron mass ratio, which will always be around 1836 and dimensionless. 71.36.148.25 (talk) 17:20, 9 June 2015 (UTC)

Where does that attitude come from? My perspective is both as an educated physicist, but also as a student continuing to learn. My perspective as the student sees the "sacredness" of alpha as rather arbitrary. I added this section so that there could be an insightful discussion about the "why" of the claims, prompting further edits or discussion to improve the article. But now I'm just supposed to bow to an anonymous contributor that essentially tells me to shut up and just take Wikipedia as "fact"? I showed that it is perfectly possible to mathematically set $\alpha$ to 1 without destroying any physics. I did not contradict the statement about normalizing more than three constants since I showed that to do this, another of the constants must be scaled (e.g. electric charge). Other than some historical and practical reasons, there is also no universal sacredness to the numerical value of the electric charge. User 71.36.148.25 essentially just repeated what is said in the article, adding no additional insight or explanation. I said nothing of the proton-to-electron mass ratio, so that isn't relevant unless 71.36.148.25 meant it to explain the reasons for claims about $\alpha$. Besides, masses are of the same dimension, so scaling one value scales the other and the ratio remains unchanged. $\alpha$ is not a simple ratio of only two values, but multiple values of different dimensions of which the scaling can be shifted from one to another without destroying the physical relationships between the constants. Please don't just restate what is in the article and demand that it is fact. Please share insightful details rather than being the article's dictator. cperk (talk) 00:01, 20 July 2015 (UTC)

Sure, you can, I suppose, redefine 2 to be 1 by redefining it to be ${\frac {2}{2}}$. Why not?

Actually, if I were dictator of the world, instead of the current definition of $\alpha$, I would define the primary dimensionless value to be ${\sqrt {4\pi \alpha }}={\frac {e}{\sqrt {\epsilon _{0}\hbar c}}}=0.30282212$ (and derive the ${\frac {1}{137.036}}$ number from that). And that is " a simple ratio of only two values": the ratio of the elementary charge to the natural unit of charge in rationalized Planck units. And it's not 1. (But it's in the ball park.)

And $e$ and ${\sqrt {\epsilon _{0}\hbar c}}$ are every bit the same dimensions as are $m_{p}$ and $m_{e}$ the same dimension of stuff. Then, again, we could just redefine $\mu ={\frac {m_{p}}{m_{e}}}$ to be ${\frac {m_{p}}{1836.15267245\cdot m_{e}}}$ and then that value is 1 too, and we didn't destroy physics. Dunno why we can't do that. 70.109.187.202 (talk) 01:47, 20 July 2015 (UTC)

Normalizing $G$ and not $4\pi G$

Seriously, by removing $4\pi$ in the denominator we neglect the connection between inverse square laws and how the surface area of a sphere relates to its radius.--195.194.89.243 (talk) 12:52, 25 February 2015 (UTC)

Totally agree. Take a look at the Planck units article. The problem, 195, is historical and some understandable inertia in the discipline. Whether it's $G$ or $4\pi G$ that is normalized to 1 (by the judicious choice of units) or if it's $4\pi \epsilon _{0}$ or $\epsilon _{0}$ that is normalized, the Planck scale is still about the same order of magnitude. So a lot of physicists think "why bother" regarding changing the meaning of something, even if the change is more optimal and more natural. 65.183.156.110 (talk) 04:46, 26 February 2015 (UTC)

Silliness about Planck units

revert (Several issues. k_e is not as well known as epsilon_0. In this article, Planck units do not necessarily normalize k_e.) seems a little POV, so I summarily re-reverted it. Look a little closer:

k_e is not as well known as epsilon_0

This seems to be a difficult claim to justify. Looking at the Google Ngram viewer, it is known pretty well.

In this article, Planck units do not necessarily normalize k_e

Whyever not? One could argue that ε₀ could be normalized in Planck units, I guess, but the choice of normalization would have to be stated. Consistency with the article Planck units would require normalization of the Coulomb constant, and no justification is given in this article for any other normalization. The text explicitly says: "Planck units are a system of natural units that is not defined in terms of properties of any prototype, physical object, or even elementary particle. They only refer to the basic structure of the laws of physics ...", so to introduce a rather arbitrary choice of the elementary charge and the fine structure constant (and then to normalize a complicated expression of these) goes directly against that.

Technically speaking, Planck did not introduce an electromagnetic unit at all. Perhaps we should simply omit the Planck charge from this entry (as well as in Plank units)? A system of units should not be artificially extended by Wikipedia. —Quondum 06:27, 2 March 2015 (UTC)

There apparently are sources for the unit Planck charge. Whether it was created by Planck or named for him later, it seems appropriate to include here. Bcharles (talk) 21:47, 21 March 2015 (UTC)

Gravitation (Misner, Thorne, Wheeler), for example, mentions Planck units for time, length and mass, but makes no mention of charge or temperature. I managed to find an explicit naming in a "reputable" reference (Roger Penrose, The Road to reality), but even here it is rather unsatisfactory, as he gives the normalization choices leading to Planck units, but these choices (G = c = ℏ = k_B = 1) do not determine a Planck charge, yet he then concludes what the value of the Planck charge is (about 11.7 proton charges). Several sources say something like "one could define a Planck charge as...". I have no in-principle objection to the idea that charge and temperature could have been considered to be part of the system post-dating Planck, as long as we get this from a reputable source. At least all the sources that do give a value that I looked at were consistent in their choice, not giving the alternate CGS-Gaussian version of Planck units that I reverted. Whatever the origin, Planck charge and temperature seem to have some momentum. —Quondum 03:41, 22 March 2015 (UTC)

Greater ambiguity?

I am deleting this bullet point under "advantages and disadvantages". There is no reason to presume that m_P and l_P would be omitted when stating values in Planck units. Bcharles (talk) 22:41, 21 March 2015 (UTC)

This does not really hold: it is reasonable that when using Planck units, many people would omit their explicit mention, and examples are not difficult to find. For example, Penrose says "... in terms of Planck units, gram = 4.7×10⁴", where he omits m_P. Nevertheless, the point was made rather fuzzily in the article, and I'm not going to argue that it should be retained. —Quondum 04:08, 22 March 2015 (UTC)

Same dimension of space and time

In natural units space and time have the same dimension due to c=1. This statement deserves further details.--5.2.200.163 (talk) 13:52, 1 February 2016 (UTC)

Bohr atom in Heaviside Lorentz Units

The bulk of the NIST CODATA tables can be explained in terms of Bohr's atom, since this provides the units for further calculations, and this is what the CODATA values do. Since the bohr atom throws up a dimensionless constant (fine-structure constant), setting the base to this allows many more units to become simple values. Everything relating to the electron are simple values of π or the reciprocals of 137/π.

One then uses K=137.036 etc, as an exponent-marker like E=10, so as E5 = 10^5 then K^5 means 137.036^5. The tables are set so that the speed of light, the electron mass and the electron charge are set to K-units (eg K4 'm/s'). The unnamed K-units occupy the same space as the given SI unit.

There is a thread on Dozensonline->Applications->New Systems of Measure->Other measurement systems->Ku And Ko

KU follows much of modern metric theory, CGS lightly rationalised to SI. If the same light rationalisation is applied to give a HLU theory, then the charge is reduced by a factor of \sqrt{4\pi}. We see that the electron mass is K-2 (so the unit is about the size of a boron atom, and N_a is a number bigger than 1), and the speed of light is K3. The unit of charge is K-1.

KO shows the results of calculating Bohr's atom in HLU theory, from first principles. We still have the electron charge at K0, and the electron mass at K-2, but the speed of light is set to K4. One will notice that lengths and times are increased by a factor of 4π, which represents a change from radius to circumference or surface of a sphere, and from radian-times (\lambdaba and \hbar) to cycle-times (\lambda and h). The value of h changes from 2pi to 1/2.

The tables represent the 'exact values' of the CODATA variables, since the errors have been moved into conversion from this system.

--Wendy.krieger (talk) 11:13, 1 April 2016 (UTC)

length units

under the flag of "natural units" often dimensionless length units are in use like M~rG=rs/2. These are usually built using Planckunits, or G c° kB ke and h°, I denominate them with a sub-"r":

• m_r=lP*m/mP
• Q_r=lP*Q/QP
• L_r=lP*L/h°
• T_r=lP*T/TP

I think these should be mentioned in the article too. Ra-raisch (talk) 19:26, 8 December 2016 (UTC)

codata

codata2014 lists (table VI) natural units and atomic units:

• v_nu=c, v_au=α·c
• L_nu=L_au=h/2π
• m_nu=m_au=me
• E_nu=c²me, E_au=E_h=α²c²me
• p_nu¹=c*me, p_au¹=L_au/a_0
• l_nu=L_nu/(me·c), l_au=a_0
• t_nu=L_nu/c²me, t_au=L_au/E_au

further several electric au, based upon Q_au=e and ε_au=e²/(a_0·E_au). Ra-raisch (talk) 12:27, 3 August 2017 (UTC)

Before you change anything, we might appreciate it if you express exactly what you are proposing to change, with both text and with equations and expressions written with the use of ${\text{LaTeX}}$. It will be easier to understand exactly what you are saying. Now I am just guessing. 96.237.136.210 (talk) 04:23, 5 August 2017 (UTC)

a.u. units With CODATA 2014 the following "a.u." (atomic units) as well as 15 other derived units were defined:

• charge e
• mass m_e
• action ℏ
• length a₀ (Bohr radius)
• velocity α·c ≈ c/137 (maximum speed of an electron in Bohr's model with fine structure constant α)
• energy E_h (Hartree energy)
• time ℏ/E_h
• permittivity e²/a₀E_h

n.u. units with CODATA 2014 the following "n.u." (natural units) were defined:

• velocity c (vacuum speed of light)
• action ℏ
• mass m_e
• energy c²m_e
• momentum c·m_e
• length ℏ/(c·m_e) (reduced Compton wavelength of the electron)
• time ℏ/(c²m_e)

something like that? Following the articel not mentioning these CODATA natural units should be considered exotic? Ra-raisch (talk) 21:32, 20 August 2017 (UTC)

or may-be rather like this Ra-raisch (talk) 10:27, 22 August 2017 (UTC)

Unit	Metric value	Derivation
1 n.u. of length	386.1×10−15 m	ℏ/mec
1 n.u. of mass	9.109×10−31 kg	me
1 n.u. of time	1.288×10−21 s	ℏ/c²me
1 n.u. of temperature		not listed
1 n.u. of electric charge		not listed

Unit	Metric value	Derivation
1 a.u. of length	0.529×10−10 m	a0
1 a.u. of mass	9.109×10−31 kg	me
1 a.u. of time	2.418×10−17 s	ℏ/Eh
1 a.u. of temperature		not listed
1 a.u. of electric charge	1.602×10−19 C	e

7 natural units ("n.u.") and 18 atomic units ("a.u.") were published in CODATA 2014 Table VII.

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Clarification of lead section

There is a contradiction between the lead section, which limits "natural units" to physical constants. And the Introduction, where it is written: "Natural units are "natural" because the origin of their definition comes only from properties of nature and not from any human construct" (For example, the mass of a cm³ of water, could be a "natural unit" -- but this does not seem to fit with the way the lead section writes about the "natural units". Perhaps the lead section could add an indication that a "narrow" definition is being used. Or maybe it could be expanded to indicated different meanings? Sdc870 (talk) 15:27, 16 April 2018 (UTC)

Why no article on "absolute units"?

Some few articles in Wikipedia refer to "absolute units" such as watt, ohm, International System of Electrical and Magnetic Units, Centimetre–gram–second system of units, History of the metric system, History of the metre. There are about 30 articles altogether right now -- where some of these pages are referring to units in webpage design. It seems appropriate/useful to have such a page (so I can read more about it!) Sdc870 (talk) 15:27, 16 April 2018 (UTC)

How to represent the reduced Planck constant?

After modifying the section "System of natural units" to make the proper symbol U+210F ℏ PLANCK CONSTANT OVER TWO PI appear wherever I saw a plain italic h, I called up page history and noticed that it already was some kind of barred h with italics, probably U+0127 LATIN SMALL LETTER H WITH STROKE + italics. All I can say is that for some reason the original character looked like a plain italic h (with no stroke) in the CologneBlue skin I'm using. I suppose that in this case U+210F is the proper character to use anyway. — Tonymec (talk) 08:55, 17 April 2020 (UTC)

I think that on different systems (browser default font selection, installed fonts, etc.) either if these may occasionally present a problem. U+210F often renders as though it is not from a matching font and is generally pre-italicized, making it non-ideal. I had assumed that the Latin Extended-A character set, having been present from a very early version of Unicode, would have wider support than the Letterlike Symbols set, but this could have been wrong, and your experience might suggest otherwise. Some Unicode characters are present for legacy reasons and are essentially deprecated (an example being U+00B5 micro sign). My guess is that either way will present problems in some systems – the question probably being which works best on most. —Quondum 12:33, 17 April 2020 (UTC)

"natural units" on NIST

The NIST website lists several "natural unit of ..." units ([2]). These are clearly based on c, ħ and m_e and together form a mechanical system (no dimension of electric charge). There are several historical unit systems mentioned by Tomilin ("NATURAL SYSTEMS OF UNITS. To the Centenary Anniversary of the Planck System") that fit this, except that these all include an electrical dimension. This is not reflected in any of the systems listed in this article. Does anyone know or have a reference that might illuminate what NIST is basing this on? —Quondum 00:20, 15 May 2020 (UTC)

I see that the 8th SI Brochure defines natural units of speed, action, mass and time based on these constants, and describes them as "used only in their own special fields of particle and atomic physics". It seems very probable that this is the basis of NIST's natural units that I described above. I suspect that these fields also so routinely take ε₀ and μ₀ as being dimensionless 1 that it is rarely mentioned (as I can show, for example, that Wilczek does). It seems that this would be a separate system of natural units, possibly worth adding, since it can readily be sourced. —Quondum 01:35, 31 May 2020 (UTC)

Boltzman Constant

${2~\pi ~\hbar \over c~Q_{e}}$ is the boltzman constant in whatever unit system you are in though those units c, \hbar, q_e might be different values in different systems want multiple people to confirm this math is correct before I push the edit up

Summary table

Quantity / Symbol	Planck	Stoney	Hartree	Rydberg
Defining constants	$c$, $G$, $\hbar$, $k_{\text{B}}$	$c$, $G$, $e$, $k_{\text{e}}$	$e$, $m_{\text{e}}$, $\hbar$, $k_{\text{e}}$	$e^{2}/2$, $2m_{\text{e}}$, $\hbar$, $k_{\text{e}}$
Speed of light $c$	$1$	$1$	${\frac {1}{\alpha }}$	${\frac {2}{\alpha }}$
Reduced Planck constant $\hbar ={\frac {h}{2\pi }}$	$1$	${\frac {1}{\alpha }}$	$1$	$1$
Elementary charge $e$	$-$	$1$	$1$	${\sqrt {2}}$
Gravitational constant $G$	$1$	$1$	$G$	$G$
Boltzmann constant $k_{\text{B}}$	$1$	$-$	$-$	$-$
Electron rest mass $m_{\text{e}}$	$m_{\text{e}}$	$m_{\text{e}}$	$1$	${\frac {1}{2}}$

where:

• α is the fine-structure constant, α = ⁠e²/4πε₀ħc⁠ ≈ 0.007297,
• A dash (–) indicates where the system is not sufficient to express the quantity.
• Q_e is the electron charge

The newest Current Stoney Hartree Rydberg values are ${2~\pi \over \alpha }$, ${2~\pi ~\alpha }$, and ${\pi ~\alpha \over {\sqrt {2}}}$ respectively. Provided my math is correct waiting for a few people to get the same answers

also may need to include something about avogadro constants in each system for instance avogadro for the planck mass is:

$P_{A}=1.310679E19mol^{-1}={N_{A} \over m_{p}}={6.02214076\times 10^{26} \over 2.176434\times 10^{-8}}$

Glas(talk)Nice User skin 18:37, 26 January 2022 (UTC)

Proposal to change this into a summary of natural units.

This article accumulated a lot of detail. The tables are huge and why?

To me this article ought to introduce the concept of natural units and summarize the full articles. No tables are needed. The formulae are all in the main full articles. @Quondum ? Johnjbarton (talk) 04:02, 26 December 2023 (UTC)

This article has suddenly acquired a huge amount of detail, turning it into a monster. It has become reminiscent of what someone expanded it to before, before it was trimmed back; it even looks a lot like parts of the article previously introduced by now-banned editors has been re-inserted (a bad omen?).

Yes, the article should introduce the concept of natural units without expanding on much detail for individual systems, deferring detail to the individual articles. I quite like the idea of removing the tables altogether. These have, in any event, acted to attract addition of excessive detail that does not belong here, and as is happening now. Even in the specific articles, this level of detail makes it look like some undergrad's doodle pad. —Quondum 20:28, 26 December 2023 (UTC)

All conversions should be to SI units.

The current text has some cryptic notation, "LH" and "G" with an unspecified purpose. If all of the comparisons to units were in SI, the article would be much clearer. Johnjbarton (talk) 04:17, 26 December 2023 (UTC)

@‎61.224.130.40 I would appreciate you input since it looks like you added these notations. Johnjbarton (talk) 17:57, 26 December 2023 (UTC)

The 'original', 'G' and 'LH' are all apparently synthesis. The "original" case is pure nonsense for Planck units: Planck did not reference charge in his system of units, and in thinking he used (which was inherently Gaussian, given the role of G in the F = mM/r² formulation of Planck units), would inherently have led to the 'G' form only. The 'LH' form seems to be the rationalized Planck units, so why invent a name ("LH") in WP without reference that is used exactly to mean "rationalized", and then link to Heaviside–Lorentz units (which makes the intended meaning obscure, since these are not natural units)?

The latest "Summary table" in the current version is strikingly similar to in this version (but for an added column). —Quondum 21:47, 26 December 2023 (UTC)

If that's the "summary" table, I'd hate to see the full one. XOR'easter (talk) 18:18, 28 December 2023 (UTC)

yeah, well, I guess the heading referred to summarizing of the article contents, but the table (and the article) then became a compendium of possible variants of these systems. But in line with the thread above, perhaps the table should be removed altogether. —Quondum 19:04, 28 December 2023 (UTC)

nondimensionalization?

We have whole article on nondimensionalization with no references and here in the intro it takes up one of the two paragraphs. Anyone know anything about it? Johnjbarton (talk) 19:58, 28 December 2023 (UTC)

I may be guilty of introducing the wording here. The problem is that there is a tendency to conflate nondimensionalization (which is achieved by defining a dimensionless scaled version of a quantity, and substituting, e.g. define v_n = v/c, then substitute v → cv_n) with defining the units in a way that certain constants that often appear in fundamental physics formulas have numeric value 1 but are not dimensionless (e.g. c = light-second/s). These are absolutely nonequivalent. This tendency is common in sources (they often do not make clear or are confused about which they are doing), but perpetuating this in WP seems unencyclopaedic.

The article Nondimensionalization is likely primarily an essay by editors, but since it is not nonsense, it is handy for clarifying the distinction elsewhere, whether sourced or not. Ideally, we should just be able to find a suitable source that discusses the topic more fully, and add it to Nondimensionalization. —Quondum 20:53, 28 December 2023 (UTC)

That's helpful, thanks. But also confusing ;-)

If I apply the v → cv_n procedure to E=mc² I end up with E_n = m just as if I had set c=1 as my units. I have a hard time distinguishing the procedure from a change of units. In nondimensionalization, in setting constants to one, and in changing units, the procedure looks the same to me and the end result is the same? Johnjbarton (talk) 00:12, 29 December 2023 (UTC)

Removed time unit

Johnjbarton, I don't follow this edit at all. Can you explain your rationale? —Quondum 22:12, 28 December 2023 (UTC)

Because the table had not caption nor explanation in the text, I chose to interpret it as a tabular form of the defining constants with their values in SI. In that case the time value is no correct. Perhaps you have some other caption where the value makes sense? Johnjbarton (talk) 23:07, 28 December 2023 (UTC)

This edit also removes critical information. You need to take into account the convention that an author is using. When using the Gaussian system of quantities (i.e., where the equation F = qQ/r² is used), "electric charge" is the name given to a quantity that differs from electric charge in the SI by a dimensional constant, and 4πε₀ is already inherently a defining constant. Everything falls apart if you do not have this. —Quondum 23:03, 28 December 2023 (UTC)

I am only going by the sources and up through Shull and Hall (see Hartree atomic units) that is what they say. However I have another ref that will change the Hartree page and add back the charge. Johnjbarton (talk) 23:11, 28 December 2023 (UTC)

See the first part of

• Wilczek, Frank. "Fundamental constants." Visions of discovery (2020): 75-104.

As far as I understand it, the atomic units place the conversion factor $4\pi \epsilon _{0}$ in the formula, eg $F=qQ/(4\pi \epsilon _{0}r^{2})$ rather than the units.

• "The first procedure, which regards quantity of charge as a separate concept, independent of its mechanical effects, appears natural if the concept quantity of charge has some other independent physical meaning. In atomic physics, of course, we learn that it does. There is an operationally defined, reproducible unit of electric charge, the charge of an electron. We can express other charges as numerical multiples of that unit. Then ǫ0 becomes a measurable “fundamental constant”, parameterizing the Coulomb force between electrons."

To me, this is the kind of material we should discuss in the article. Johnjbarton (talk) 23:50, 28 December 2023 (UTC)

On details like this (use of a factors of 4π, ε₀, 4πε₀), Wilczek seems to be rather inconsistent, even within the same paper. He is switching conventions without properly signalling when he does so. And for the principle of what he is trying to communicate, this is not central. Which make him an unreliable reference for details. He uses phrases such as "in this system", without being clear that the only way to collectively analyze different "systems" is to avoid treating quantities of different systems as the same thing any more than you would not treat the radius and diameter of a circle as the same quantity in different systems, even though they each parameterize the size of a circle just as well and use the same name for them. Using expressions like ħ = c = 1 in such a discussion is guaranteed to create confusion where it should be avoided. For example, when discussing natural unit systems, he says "... since the fine structure constant {{math|1=α = ⁠e²/4πħc²⁠ is a pure number ...", it should be clear that locaqlly in the discussion of the three natural systems, he is using quantities for which the equations are all written like the SI equations, except that ε₀ has been replaced by 1 (inconsistently with the paragraphs just preceding your quoted passage). In other papers he replaces 4ε₀ with 1.

There are references such as Tomilin,that list the underlying constants more explicitly. For the Hartree system, on p. 291 Tomilin explicitly includes k_e, unlike Wilczek.

In short, the only way I find to successfully navigate sources on this topic is to infer the underlying system of quantities being used, ensure that this is consistent (with corresponding quantity translation) with the standard SI equations, and then to present the source translated to the corresponding to SI quantities. Where the quantities to be presented are not the SI quantities (or more correctly, quantities of the ISQ), for clarity I annotate them distinctly, despite having a shared name. —Quondum 01:35, 29 December 2023 (UTC)

In the Tomilin source the discussion of the EM units is conspicuously positioned after the citation of the primary source, as if the original authors were silent on the subject (as I claim).

I suppose what we do depends on what we think our goal should be. The current page (or maybe the page before I mucked with it ;-) seems to focus on treating the multiple system on equal footing. In that case the EM units issue needs to be sorted. I'm more interested in what the sources said and less in making them all line up; in that case the EM only comes up to the extent the authors discuss them.

As long as we are clear in referencing Tomilin (or whatever) for the source of EM choices, I'm fine with add this info. I just don't think that Planck/Stoney/Hartree should be spoken for.

More broadly I'm interested in trying to get across "what and why natural units". and "Why natural units vs SI"? These are very different use cases. Johnjbarton (talk) 03:33, 29 December 2023 (UTC)

Context matters, especially in WP. I see that Hartree atomic units has been partially translated into one or more unstated anachonistic systems of quantities, and may now use a mix of equations from Gaussian, Heaviside–Lorentz and SI systems. It then goes on to say that "The atomic units can related to the International System of Units" and provides the SI value of e, which produces garbage in the formulae already given. This is mixing presentations from different eras, which produces internal inconsistencies.

It is the responsibility of any editor who is deviating from the system of quantities (and units) used in the SI to make this clear to the reader. It makes much more sense, as almost any author does, to translate the concepts into the modern framework rather than expect the reader to learn an anachronistic framework just to properly understand what is being said (very few people, even trained physicists, are properly capable of this). Presenting a mishmash of statements from sources from disparate frameworks is just ... irresponsible. —Quondum 14:51, 29 December 2023 (UTC)

Sorry, I'm confused by your comment. I didn't change anything in the tables relating to the SI values on Hartree atomic units. I certainly did no translation. Rather, I reported what the sources said. To be sure, maybe we need more content to relate these these historical discussions to modern uses. Since I did not know this was an issue I didn't look for sources to add such content. Perhaps we should discuss this on Talk:Hartree atomic units? Johnjbarton (talk) 16:10, 29 December 2023 (UTC)

As for irresponsibility, the problem with the Hartree atomic unit page is lack of verifiable references. If the page had reliable references explaining the historic and modern usage issues, then I would not have changed the page. Asserting the modern values in place of what the sources say is also not responsible. So the right fix is to have both the historic references and the modern changes with sources. Johnjbarton (talk) 20:49, 29 December 2023 (UTC)

I apologize: I'm overreacting, especially given what you are doing. And yes, that talk page is the place to discuss it. But, for the next little while, I had best take a break from units and unit systems – I'm clearly being overly cranky at the moment. —Quondum 21:13, 29 December 2023 (UTC)

The topic is much more intricate than I expected. Very specific concerns would be helpful so I can research appropriate solutions. Johnjbarton (talk) 00:15, 30 December 2023 (UTC)

It confounds the majority of people, in my experience, although few are aware of it. Give me a few days to get myself on an even keel, and I should be able to contribute some interpretation of specifics. —Quondum 01:37, 30 December 2023 (UTC)