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I think that "atomic mass" is not dimensionless and should be removed from the list. Atomic mass is measured in amu, atomic mass units. I am not knowledgable to know for sure. Can someone correct me on this if I am wrong, or correct the article if it is wrong? Thanks. --Atraxani
Everyone I've said this to has disagreed entirely, but I'm not going to give up.
People like to elevate Avogadro's number as a "magical" number.
It is just the conversion factor between amu and g, nothing more. Both grams and amu are just arbitrary units of mass.
If you say the number is a dimensionless constant, than you have to say the convertion factor between all other units are too. In which case 2.45 cm/in is a dimensionless constant. And 4.45 lb/N is also a dimensionless constant.
There is a reason we don't include unit convertion factors here and instead on another page (see unit conversion); they are expressed in units over units, yet mass over mass should cancel out, but we aren't using the same units, so they're here to stay.
In other words, 2.45 isn't a dimensionless constant because it is expressed in cm/in. Similarly 4.45 isn't a dimensionless constant because it is expressed in lb/N. Finally, Avogadro's number isn't dimensionless either because it is expressed in amu/g. GWC Autumn 57 2004 13.20 EST
Avogadro's number may also be considered dimensionless, although Avogadro's constant is definitely not.
Avogadro's number redirects to Avogadro's constant. pick one, would you? --178.251.171.178 (talk) 12:59, 17 March 2017 (UTC)
Amount of substance is also dimensionless or pseudo-dimensional, although it appears dimensional. It can be compared to angle whose unit radian is a dimensionless unit. Mole has a similar dimensional status with radian. Amount is the ratio of two masses: a given value of mass of a substance divided by the molar mass which is a material/substance constant. Molar mass itself is the expression in units of mass of relative molecular mass which contains Avogadro number of particles.--188.26.22.131 (talk) 11:09, 24 February 2014 (UTC)
The article contains the following two statements:
How can these two statements be reconciled? -- The Anome 23:57, Jan 5, 2005 (UTC)
Our definition says: "a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units". This is only superficially true. Beside the example given by The Anome there is an easier case, as Pdn pointed out on Category_talk:Dimensionless numbers:
One might object that pH should be measured in bel, but we can't set standards for chemistry here. Fact is that our intruduction contains a wrong statement. If you're a quantity, having dimension 1 (or 0?) is not equivalent to being "pure" – you may still have physical units in your definition. — Sebastian (talk) 18:18, 2005 May 21 (UTC)
Isn't any cardinal number dimensionless? For example, four, or twenty six? If "dimensionless numbers" refers to ratios which have been found to be useful in some discipline, wouldn't pi count? Perhaps someone can write an introductory paragraph to this article, which would explain this category of numbers a little better? Thanks! --24.190.141.119 14:37, 19 Apr 2005 (UTC)
Ooops! I forgot to log in! Sorry about that! --Keeves 14:40, 19 Apr 2005 (UTC)
That's not a dumb question at all. You're making three valid points:
For all i know, dimensionless numbers are rather measured in m0 than in m1. But it's in such a prominent place in this page and this whole term is so fraught with inconsistent usage anyway that i rather ask before changing it. — Sebastian (talk) 18:55, 2005 May 21 (UTC)
Maybe this was meant as dimension(dimensionless numbers) = dimension(1) = 0 ? Still, the wording is misleading. — Sebastian (talk) 00:06, 2005 May 22 (UTC)
I don't know if this will help, but in my experiance a simple example often lends to better understanding of concepts. Consider for example Strain. Strain is considered to be a dimensionless quantity (as opposed to a dimensionless constant such as pi), and is defined by , with L being a unit of length. So long as the units are kept the same in the numerator and denominator, then it doesn't matter whether you measure in metres, feet, or even snorkles, all that matters is that A), the units are identical in the equation, and B), that the unit used is well defined.
Another property which I feel has been neglected here, is what happens to other quantities and specifically their units when multiplied/divided by a dimensionless quantity. For example: If we take one unit (length) and divide it by another unit (time), the result will be in a unit (in this case speed) which is defined as . However if we do the same thing, but replace one of the units with a dimensionless quantity, this no longer happens.
A simple example of this is in the equation for determining the Modulus of Elasticity of a material, which is defined as . Stress here can be defined as load/area, which has dimensions to it. Going back earlier, I pointed out that strain is a dimensionless quantity, so therefore when we divide stress/strain, the resulting unit remains the very same stress unit that was used in the formula.
Any mathamaticians out there would be able to clarify this in a way that follows a bit more convention (my math is pretty poor), but nonetheless I feel that these simple examples would help out the conceptual understanding. --Sjkebab 01:39, 3 Jun 2005 (UTC)
Encouraged by the comment of one contributor above, who suggests that "quantity" should be referred to in place of "number" in the introduction to this article, I propose that in fact the entire article (including its title) should be revised to refer to dimensionless quantities. All numbers are dimensionless. It is the physical quantity, expressed by a number and its unit, that may be dimensionless. Contradictions invited.
I concur
I agree with the move
I would argue that Rockwell Hardness is not a true dimensonless quantity because without knowing the scale used it is useless. For that reason the scale itself becomes a dimension. For example the hardness number is referred to by the scale used, e.g. 60 HRB, which becomes a unit itself. Reading the way these are derived, the actual number is a constant minus a depth in mm, so the actual unit seems to be mm. If others concur we should remove this from the list.
Without being an expert on E&M, in regard to
However, a physical quantity may be dimensionless in one system of units and not dimensionless in another system of units. For example, in the nonrationalized cgs system of units, the unit of electric charge (the statcoulomb) is defined in such a way so that the permittivity of free space ε0 = 1/(4π) whereas in the rationalized SI system, it is ε0 = 8.85419×10-12 F/m.
I would say that you must be measuring different things here. In other words, these two quantities must be defined in different ways that give them different dimensions. There is no mathematical reason to explain how one physical quantity could have 2 different dimensions. The reason must be something to do with the physics.
Please, 217.84.175.39, stop messing around in the several "dimension" related articles. The square brackets mean "dimesion of" and in the articles where we have used italics, it is because they have been so used, at least, in the last 50 yrs. If there are "new" rules, show them . --Jclerman 11:03, 28 July 2006 (UTC)
In my understanding, this section is completely wrong. In the Planck system, constants like c are used as units, but this does not make them dimensionless. If you look up the Planck units article, the dimensions of all constants are even indicated. In case of c, the dimension is L/T. Therefore, those constants are by no means dimensionless and the section should be deleted.
What happens is the following: instead of the "normal" system of base quantities (which you find in the article about physical quantity) the Planck system uses another system of base quantities which is based on natural constants. That's all. It is also not true that the quantities have no units, as many people think. They have units but they unfortunately are not used. For example, when indicating a velocity v in Planck System the unit of v is c ([v] = c). Most people, however, do not say "v = 0.8 c", they only say "v = 0.8" which is convenient but lazy and inaccurate.
The notion that in the Planck system the constants are "eliminated" is also inaccurate. What in short is called a physical constant is more precisely a constant physical quantity. A physical quantity Q, however, consists of two things, a numerical factor {Q} and a unit [Q]. In the case where the numerical factor {Q} = 1 the quantity Q is by no means eliminated, it still has the unit [Q]. (Otherwise one could say that the original meter in Paris would be "eliminated" because its numerical factor is also 1, but in fact we need it because of its unit, the meter.)
--Kehrli 12:56, 31 July 2006 (UTC)
I had never heard the term "pure number" until about a month ago (I had heard of dimensionless though), the mark scheme for a CCEA A level physics question "explain why the quantity x (or whatever it was actually called) does not have units" said that the correct answer was the obvious "it's in a log" and the weirder terminolgy "it is a pure number", so I assumed pure = dimensionless. So now pure number redirects here. Stuart Morrow 00:11, 30 December 2006 (UTC)
Would it be correct to add normalized moments (see moment) to the list of dimensionless quantities? EverGreg 13:08, 20 September 2007 (UTC)
The example, given at the article's beginning, of radians as a dimensionless quantity is very confusing. While technically expressing a ratio, radians function a lot like units and are often seen combined with units (e.g. rad/s rather than Hz). It seems like the example is more complex and confusing than the concepts it's trying to clarify. jdg (talk) 19:40, 29 February 2008 (UTC)
Cannot radians be expressed with a small "r". I know it's optional, but couldn't one be put in parens or something. Asmeurer (talk ♬ contribs) 15:15, 16 October 2008 (UTC)
Should not Chandrasekhar number be a part of list? ~Divij (talk) 11:17, 25 March 2009 (UTC)
I removed Berchak number from the list, since both an article on the subject and reliable sources are missing. It can be re-instated once this entry is verifiable. -- Crowsnest (talk) 19:03, 15 April 2009 (UTC)
Regarding the table, entry "Decibel", "ratio of two intensities, usually sound". 1) There is a non-linear transformation involved (log, base 10), not just the ratio 2) dB is also commonly used for ratios in electronic systems, e.g. -3 dB frequency cutoff (ratio between input and output signal, possibly normalised) and signal-to-noise ratio. --Mortense (talk) 18:27, 15 November 2010 (UTC)
Wouldn't the dimension of the number people in a room be "people" or "persons"?
If I were calculating the ratio of apples to people in a room, and I had, say, 10 apples and 5 people, I would have 2 apples/person. Ktwombley (talk) 17:49, 4 February 2011 (UTC)
People seem to be confused by the difference between these two related concepts. Any suggestions for how to make the article address this better?--217.84.29.188 (talk) 13:17, 20 July 2011 (UTC)
Reference 26 (to Strouhal Number) is broken. Please fix. Tkemp (talk) 16:17, 21 February 2013 (UTC)
The list of dimensionless quantities has become large enough that I think it would be best to have the list moved to a page of its own. I feel it is necessary and useful for wikipedia to include the information together as a list, but the list is significantly larger that the article itself, and I think that for a list size detracts from the article. We might keep a short (10-15 item) summary list to show the variety of dimensionless quantities throughout science (see the way the list looked c.2006), but otherwise the bulk of the information would only be in the new List of page. Thoughts? Rememberlands (talk) 05:16, 26 November 2013 (UTC)
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According to the Buckingham π theorem the space spanned by a set of fundamental dimensions, scaled in some units can be spanned by any appropriate set of dimensions with units, suitably selected. So dimensions, as well as units, are are not inherently affixed to physical quantities, but assigned in a reasonable act of caprice, making up a useful set of dimensions with units (see atomic units, natural units, Planck units, ...). As a consequence, physical quantities do not have innate dimensions, but these are assigned notions, to the taste of the current theory. Purgy (talk) 10:21, 14 July 2018 (UTC)
why the modal "may"? Either it is or isn't. --Backinstadiums (talk) 22:45, 9 August 2019 (UTC)
Hello,
I wonder if albedo and reflectance should be added to the dimensionless quantities list.
2A02:2788:22A:100D:4169:D178:FCCC:5DDD (talk) 12:22, 9 October 2020 (UTC)
A note for future reference: it seems that the term "quantity of dimension one" will be replaced by the term "quantity with unit one" in VIM4 (draft) §1.8. An explicit symbol for the dimension of such a quantity (previously taken to be 1) becomes unmentioned, so it becomes unclear what symbol will be used. —Quondum 18:22, 13 May 2021 (UTC)
In most of the examples the actual quantities do not become unitless: what happens is that the denominator becomes the new benchmark for measurement, which is often context dependent. Strain as described in the above example is still a quantity which has a dimension of type 'length' and its unit of measure is 'the original length'. What happens here is similar to when we divide the distance of 'jupiter and sun' with the distance of 'earth and sun' both expressed in kilometers, and the resulting ratio of 5.2 is not considered a unitless number but it is the 'jupiter - sun' distance in astronomical units (i.e. multiples of 'earth -sun' distances).
I think it is worth mentioning this alternative interpretation somewhere in the article. Gyomaigy (talk) 18:15, 11 April 2023 (UTC)