# Talk:Boltzmann constant/Archive 1

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## Units

The 1.99 cal/mole-K is the gas constant, not Boltzmann constant. [[[User:129.215.232.41|129.215.232.41]] 13:37, 31 May 2007 (UTC)Mark]

k is not one of the Planck units - it is one of the physical constants on which the Planck units are based. At least, that's what our current article says - I'm not arguing the physics of this situation. To maintain the information content, I'll put in links from energy, temperature, etc. to Planck units. -- Tim

Sorry. I wanted to put a link in to Planck units; I was hoping someone would corrent my phrasing rather than just remove ... :) -- Tarquin

## Edits

I have to say, CYD, I disagree with just about every change you made to my text in your latest edit. Apparently k is now "a fundmental quantity which relates temperature to energy". What were the other quantities you were thinking of? And is k really a quantity? What is it a quantity of? It seems to me that it's a proportionality constant -- you can't produce 3.6k of something, but you can use it to say 1K is equivalent (in some sense) to 1.38×10-23J.

Why did you change the HTML specification of the value to [itex]? The only visible difference is that it's not wikified anymore.

In my section on characteristic energy, I was attempting to hint at nomenclature used in solid state physics. I deliberately left out a specific example of what the characteristic energy is, because it shows up in both statistical mechanics and solid state/quantum. I wanted to give a sense that k is used in almost any field of physics involving temperature (which it is).

What's wrong with meV? 25.9 meV is so much nicer than 0.00259 eV.

Entropy is important, and I appreciate your new section on it.

"Historically, the units of energy and temperature were defined before it was discovered that they were related." True. "As a result, the Boltzmann constant is expressed using the unit of temperature, and not the other way around." You've lost me. Which other way around? "Conceptually, however, the Boltzmann constant is the more fundamental quantity." Nope, still lost. More than what?

I think I can see what you're trying to get at with those last few paragraphs. My interpretation of the physical situation is that the relationship between energy and temperature is similar to the relationship between distance and time. In both cases, there are two sets of units originally defined in terms of physical quantities (e.g. orange-red radiation and triple points). Theoretically though, it would be much more sensible to define c=1, or c=α (the fine structure constant), in just the same way as it would be more sensible to set k = 1 and use Planck temperature. We can't necessarily argue that physically, k should be 1, but it should definitely be dimensionless.

-- Tim Starling 05:34 May 3, 2003 (UTC)

I'm not particularly concerned about most of the changes, so I have tweaked them to suit your objections. --CYD
Thanks. -- Tim
As for the relationship between energy and temperature, the key idea is this: energy is a microscopic (mechanical) quantity, and temperature is a macroscopic (thermodynamic) one. The main reason Boltzmann's definition of the entropy is so important is that it shows us how this macroscopic property of a system emerges from the microscopic details of its constituents. If you know enough about the mechanical properties of atoms, Boltzmann's equation shows you how to define a quantity, the "temperature", of large assemblies of atoms. In this sense, Boltzmann's constant defines the temperature, and not the other way around. -- CYD
The distinction between Boltzmann's constant defining temperature and temperature defining Boltzmann's constant seems rather arbitrary to me. Temperature is defined either macroscopically, by the properties of gases, or microscopically, with 1/(dS/dE) and Boltzmann's formalism. But in either case, k is merely a proportionality constant, and tells you about the units used to keep the books, not the physics involved. By itself, it tells you very little about the concept of temperature. It is Boltzmann's formalism (or the properties of gases), not k itself, that defines temperature.
But I'm getting distracted by a discussion of physics, and forgetting our main goal. Would it be fair to say that if your final paragraph confused me, it's going to confuse the general public? If you can think of a more eloquent way to put your ideas, in such a way that seems intuitive and correct to me, I'll be happy. I know my current final paragraph says something completely different to what you were getting at, but I think some reference to Planck units is warranted. Tarquin tried to include something about them a while back, but I cut it out. -- Tim Starling 00:15 May 5, 2003 (UTC)

I am a physics student at a community college. the fellow who talked about botzmanns constant k, tim. did a very well job explaining the concept of k. thank you. —Preceding unsigned comment added by 71.103.70.145 (talk) 04:21, 13 February 2008 (UTC)

## Relation between charge and thermal energy

k is a relation between temperature and energy for a single atom (or single mole). There are a lot of equations in electrochemistry where you want to relate temperature to energy for a unit of charge (because in electrics we are more interested in units of charge than in number of atoms). So I was wondering if there is any defined symbol for the quantity e / k or k / e (equivalently F / R or R / F)? --Chinasaur 01:51, 14 Sep 2004 (UTC)

The relationship between temperature and energy is special. At a certain (constant) temperature ${\displaystyle T}$ there is a corresponding thermal energy ${\displaystyle k_{B}T}$. Roughly speaking, the thermal energy sets the bar for the energy of microscopic energy fluctuations; if the thermal energy is higher, the fluctuations get correspondingly stronger. This is a fundamental part of statistical mechanics. One could, in fact, completely do away with the Boltzmann Constant and express temperature solely in terms of thermal energy. We're used to Kelvins, though (thermal energy is currently ${\displaystyle 3.92\times 10^{-23}J}$ outside my place).
There is no such fundamental relationship between charge and temperature. The closest thing there is, is the unit charge, but some ions are 2+ or 2- or more.

## Boltzmann's constant and Entropy

Quote:

With 20:20 hindsight however, it is perhaps a pity that Boltzmann did not choose to introduce a rescaled entropy such that
${\displaystyle {S^{\,'}=\ln \Omega }\;;\;\;\;\Delta S^{\,'}=\int {\frac {dQ}{kT}}}$
These are rather more natural forms; and this (dimensionless) rescaled entropy exactly corresponds to Shannon's subsequent information entropy, and could thereby have avoided much unnecessary subsequent confusion between the two.

I know some physics researchers have jumped the gap regarding this, and as a natural consequence, they will express temperature in the same unit as energy. I'll try to find a reference for that.

What is ${\displaystyle \Omega }$ and what is Q? The article makes no mention of what these represent. GoldenBoar 00:21, 8 January 2006 (UTC)
-- For example, the Planck system, mentioned at the end of the article. But I think you're right, it's not just in those units that people "drop the k". Jheald 10:25, 5 November 2005 (UTC)
-- the great Landau and Lifshitz adopt this convention, using an energy scale for T so k disappears (Statistical Physics, Part 1 (3e, 1980), Oxford: Pergamon Press). Jheald 21:52, 8 November 2005 (UTC)
although that is probably not a good idea to adopt these conventions in an article, with a reference to quote that might be worth mentioning, either in here or in the temperature article. ThorinMuglindir 22:31, 8 November 2005 (UTC)

I am of the opinion that k is arbitrary, precisely that cutting kT into k and T is arbitrary, so that T is just as arbitrary. Because temperature is an energy scale. Think of it this way: I don't understand why temperature is given in here as a base unit of SI system. Because, if you get rid of charge, or mass, then you can't have the same physics anymore, you completely lose the corresponding parts. But, if you count temperature as energy, and remove all occurrences of Boltzman's constant in expressions where you meet it, then this doesn't change anything to the objective meaning of your equations. You retain exactly the same physics. ThorinMuglindir 01:28, 5 November 2005 (UTC)

Boltzmann's constant k is the bridge between the macroscopic and microscopic physics. Macroscopically, the amount of matter is measured in joule per kelvin, according to the ideal gas law: volume×pressure/temperature. Microscopically, matter consists of molecules. k tells how many J/K make a molecule. You may say that k is the size of one molecule. The kelvin temperature scale is somewhat arbitrary, being based on the triple point temperature of water, which is not of fundamental physical significance. Measuring gas in molecules give the temperature unit joule per molecule. k joule per molecule = 1 kelvin. Bo Jacoby 22:24, 29 January 2006 (UTC)

## eV/K value

Is there any reason to mention the value of 1/k in K/eV instead of simply listing k in eV/K. I would change it, but I suppose there is a good reason to give the value of 1/k instead of k Glaurung 15:09, 18 January 2006 (UTC)

I agree. I think it should be changed. It is just as easy to divide by k as it is to multiply by 1/k. In addition, it is clearly more consitent to use dimensions of energy per absolute temperature regardless of the units of measure (joules/kelvin versus electron-volts/kelvin). -- Metacomet 00:34, 20 January 2006 (UTC)
I went ahead and made the change, along with a few other things. -- Metacomet 00:49, 20 January 2006 (UTC)

Why is eV/K even given? It's a simple enough conversion, and the aside about the conversion factor is especially asinine; it follows naturally from the definitions of the units! --Belg4mit 16:13, 21 August 2006 (UTC)

## Measurement

Has the measurement changed over time? My calculator (a Casio from about 10 years ago) lists k as 1.380662E-23, while the google calculator and this page both say 1.3806505E-23

Ojw 14:52, 23 January 2006 (UTC)

My calculator(HP 49G+) also shows the order as being 10^-23. It's fairly important that this gets fixed, so if nobody objects I'll change it.

66.189.211.162 07:19, 1 February 2007 (UTC)

Ahem ... I love calculators, but when it comes to looking up constants, why not use the CODATA reference that is clearly given in the article? --DrTorstenHenning 08:56, 1 February 2007 (UTC)
66.189: Looks like the article had been sneakily vandalised about 2 hours before you read it. Thanks for spotting it & flagging it up.
In future, if you see something like this that looks odd, look back a few revisions in the history tab and do see if it's a recent change. If no explanation's been given, and it looks like vandalism, then it probably was - feel free to correct it back again, and stop people being misled. Jheald 14:13, 1 February 2007 (UTC)

## Physical meaning

A long section of this article is called 'Physical significance'. However it has always seemed to me that this constant has none - it is simply (like Avogadro's number) a dimensionless conversion factor. The paragraph that starts 'In hindsight however, it is perhaps a pity ...' doesn't really make sense, because there is exactly the same justification for measuring entropy in macroscopic units as there is for measuring temperature in such (i.e. K, rather than J or ev). Should this be rewritten? The way, the truth, and the light 23:14, 1 May 2007 (UTC)

## Precision

The article lists boltzman's constant as 1.380 6504(24)×10−23. That is very precise. How is it measured? (Also, what is the source for this that is claiming such accuracy?) RJFJR 15:05, 16 November 2007 (UTC)

The sources are given at the bottom of the article. You might find it useful to follow the link to the CODATA site where you can find an article on the history of the measurement of the physical constants for non-experts. A better place to ask questions is the Reference Desk. This page is intended for discussion of the article and how to improve it. -- Spinningspark (talk) 20:19, 16 November 2007 (UTC)

## k not fundamental?

I have serious doubts about this assertion (I quote from the section 'Value in different units'): The numerical value of k has no particular fundamental significance in itself: It merely reflects a preference for measuring temperature in units of familiar kelvins, based on the macroscopic physical properties of water. What is physically fundamental is the characteristic energy kT at a particular temperature.

Boltzmann's constant is a constant of proportionality and it is about as fundamental as h-bar. Who would say that h-bar is not really fundamental and that only energy is fundamental? Nobody. Then why say this about k?

Also, the kelvin scale has nothing to do with water - that's the Celsius scale.

The triple point of water has nothing to do with water? How odd. SpinningSpark 10:47, 2 May 2008 (UTC)

I include here a link to a site that gives a very good overview of how the kelvin scale and Boltzmann's constant were derived from the ideal gas law by scientific graphing of experimental stats: [1]. Anyhow, that's my input for the moment. It took me quite a while to work out exactly what the quoted passage was trying to say. Lucretius (talk) 10:04, 2 May 2008 (UTC)

Hi Spinningspark and thanks for the correction. If you look at the article kelvin it declares that the kelvin scale is defined according to 2 points - absolute zero and the triple point. However, it's a matter of historical fact that the kelvin scale is defined by absolute zero in relation to an ideal gas. Of course absolute zero is a statistical ideal and a physical impossibility and therefore the scale can't be adequately calibrated from the zero point. The triple point was subsequently used in order to allow the scale to be calibrated backwards to zero. The scale is based on the concept of absolute zero and it is not based on the macroscopic properties of water. It is based on 0, not on 273.16.

I was exaggerating a little when I said that kelvin has nothing to do with water. However, the article is completely wrong to assert that kelvin is based on the macroscopic properties of water. That assertion misrepresents the significance of kelvin and the significance of Boltzmann's constant. Lucretius (talk) 23:25, 2 May 2008 (UTC)

Incidentally, it's bad manners to insert a comment into someone else's text. It turns any rational argument into a shouting match. However, I do appreciate your willingness to respond. (;}) Lucretius (talk) 23:30, 2 May 2008 (UTC)

Deletion - for reasons given above, I intend deleting the last paragraph in the article, as follows:

The numerical value of k has no particular fundamental significance in itself: It merely reflects a preference for measuring temperature in units of familiar kelvins, based on the macroscopic physical properties of water. What is physically fundamental is the characteristic energy kT at a particular temperature. The numerical value of k measures the conversion factor for mapping from this characteristic microscopic energy E to the macroscopically-derived temperature scale T = E/k . If, instead of talking of room temperature as 300 K (27 °C or 80 °F), it were conventional to speak of the corresponding energy kT of 4.14×10−21 J, or 0.0259 eV, then Boltzmann's constant would not be needed.

Anyone object? I'll hold off for a few days to give others a chance to put the opposite case. Lucretius (talk) 03:05, 4 May 2008 (UTC)

I object, because it's true and relevant. The way, the truth, and the light (talk) 03:21, 4 May 2008 (UTC)

Hi The way, the truth and the light! I have 4 questions for you:

1)Are you able to refer me to a scientific text that says k has no fundamental physical significance?
2)Can you refer me to a text that says some indeterminate energy kT is physically fundamental?
3)Can you tell me how the concept of entropy, with units joules/kelvin, fits into your definition of k as really some indeterminate energy kT?
4)Can you refer me to a text that says kelvin is based on the macroscopic physical properties of water?

The quoted passage looks to me like someone's personal viewpoint. However, I myself am no expert and I'd be happy to be proved wrong. Lucretius (talk) 07:42, 4 May 2008 (UTC)

Lucretius: Let's take your questions in reverse order:
(4) The definition of the kelvin is "precisely 1 part in 273.16 parts the difference between absolute zero and the triple point of water"; (see references at kelvin.
(3) The most natural definition of Entropy - in a natural system of units - is as a dimensionless quantity
${\displaystyle S=-\sum p_{i}\ln p_{i}}$
For thermodynamic systems in equilibrium, one can then find for entropy defined on such a scale that
${\displaystyle \Delta S={\frac {\Delta Q}{kT}}}$
-- where the constant k is required solely to compensate for the scale of units (kelvins) we happen to have chosen for T.
(2) A more fundamental approach to temperature is to invert the above equation, and define temperature in terms of the corresponding energy ΔQ/ΔS.
This gives an energy scale for temperature, the energy equivalent to kT if T were measured on the kelvin scale. But it is energy, rather than kelvins, which is really the more natural scale. Which is why eg Planck units do exactly this, and take that energy as their temperature scale.
(1) The situation is analogous to the equation of motion,
${\displaystyle F\propto ma}$
If one measures the force F in units of pounds force, ie as a multiple of the gravitational force exerted on 1 lb of material at the surface of the Earth, then the equation needs a nasty constant of proportionality.
What is significant, physically, is that there is a proportional relationship between the two sides of the equation. But the numerical value of the constant of proportionality has no fundamental significance, because the numerical value is not telling us something about the physics, but rather about the particular scale of units (eg pounds force) that we have chosen for measuring force.
Instead, we can choose to measure the force in newtons, and then the constant of proportionality will just be 1.
Similarly for Boltzmann's constant. What is significant physically, is that there is a direct proportional relationship between temperature and a particular amount of energy which is characteristic of that temperature. But the numerical value of the constant of proportionality has no fundamental significance (in the way that eg, at least at present, the fine structure constant does have fundamental significance), because the numerical value is not telling us something about the physics, but rather about the particular scale of units (Kelvins) that we have chosen for measuring temperature.
We could instead choose to measure the force in joules, and then the constant of proportionality would just be 1.
I hope this helps to clarify a bit what that paragraph of the article is trying to communicate. Jheald (talk) 11:52, 4 May 2008 (UTC)

... to be continued. Jheald (talk) 11:23, 4 May 2008 (UTC)
Lucretius was asking for references, not for the reasoning. However right your reasoning is, this strange place Wikipedia requires sources to quote before you can say it. SpinningSpark 11:46, 4 May 2008 (UTC)
I thought I'd set the argument out first. References for each section of it shouldn't be too hard to find, though I don't have books to hand at this precise moment.
But Landau and Lifshitz is one text which systematically uses units such that k=1 throughout; as do most works in gravitation/cosmology. Jheald (talk) 11:57, 4 May 2008 (UTC)
Not sure that is significant. Einstein commonly set C=1, but nowhere does he say that C is not a fundamental constant. Planck units set all the constants to one, but again, no argument that the constants are not fundamental. I wandered over to the Entropy (statistical thermodynamics) article thinking that if anywhere, that should have a reference to this issue. Sadly, it has no references at all. This reference[1] while talking of applications of entropy to systems other than thermodynamic ones says, "For these other applications, the connection with temperature is unimportant, and we do not need to make use of Boltzmann's constant". Instead of using kB, the constant kS=1/log(2) is used. This gets kind of close to your point but may not say it unequivocally enough to satisfy Lucretius (sorry if I am putting words in your mouth). I have seen elsewhere the argument that entropy is most naturally defined without reference to temperature or Boltzmann's constant and that if Shannon had got there first before the thermodynamicists then that is the way it would be defined now, but I no longer remember the source. SpinningSpark 13:05, 4 May 2008 (UTC)

Hi All - your responses are much appreciated. I'm beginning to think much of the problem here is linguistic rather than conceptual. Let's look at the paragraph piece by piece:

The numerical value of k has no particular fundamental significance in itself:

In my opinion, the choice of units has no particular fundamental significance (e.g. in Planck units k=1) but the numerical value is extremely significant within each system of units. But notice also that the clause terminates with a colon, indicating that the meaning is to be understood by what follows. Yet this is what follows:

It merely reflects a preference for measuring temperature in units of familiar kelvins, based on the macroscopic physical properties of water.

To my mind this is even more objectionable than the opening clause. Celsius is based on the macroscopic physical properties of water (frozen is 0, boiling is 100). Kelvin is linked to Celsius for reasons of convenience not because it is based on the properties of water. Anyhow, the wording in the paragraph creates confusion and could well lead the reader to suppose that there is no real difference between Celsius and kelvin, whereas the difference between them is in fact enormous. Next we have this sentence:

What is physically fundamental is the characteristic energy kT at a particular temperature.

In my opinion kT here could refer to any energy - 1.3 joules, or one billionth of a joule, or anything at all. How is 1.3 joules fundamental? It's nonsense. I think the author is trying to say that k is a constant of proportionality and that it has no other physical significance. But such an observation, while true, is so trivial I can't see the point.

Finally, the paragraph goes on to detract from the significance of temperature as a unique dimension. It argues that the real dimension is energy. It's true that temperature measures energy - but it measures a particular kind of energy (the average kinetic energy of a molecule). The question whether or not this kind of energy deserves a separate dimension is one that is beyond the intellectual equipment of anyone here, let me dare suggest. I suggest we just cut it out altogether. Either that or the debate, if it exists in scientific circles, should be properly referenced - it shouldn't be stated in a partisan manner by an anonymous Wiki editor. Lucretius (talk) 02:06, 5 May 2008 (UTC)

To respond to a few points:
Celsius is based on the macroscopic physical properties of water (frozen is 0, boiling is 100). Kelvin is linked to Celsius for reasons of convenience not because it is based on the properties of water.
To be sure, the zero-point on the kelvin scale is defined by absolute zero, which is as fundamental as things get. But it's simply a fact that the other reference point on the scale is defined by the macroscopic properties of water. The size of a degree interval on the scale, therefore, is not some fundamental quantity. Instead, like the pound force, it's a historical convention.
What is physically fundamental is the characteristic energy kT at a particular temperature.
This sentence could perhaps be better expressed
• What is physically fundamental is the characteristic energy kT of a particular temperature.
What it says is that, whatever scale you choose for measuring temperatures, the fundamental thing is to be able to map it to an energy which is charateristic of the temperature.
1.3 J is the fundamental energy that is characteristic of a temperature of 1.3/k K. 10-6 J is the fundamental energy that is characteristic of a temperature of 10-6/k K.
It argues that the real dimension is energy.
Perhaps.
A clearer way to think about it might be that, rather than the kelvin, a more fundamental SI-esque unit of temperature would be to measure it in units of joules per nat -- i.e. the energy in joules required to increase the dimensionless entropy one nat. This is a temperature scale that is fundamental in the sense that its reference points are not defined by the macroscopic properties of any particular arbitarily-chosen substance.
The truth is that, every time k appears in an equation, it is there because it is needed to map temperatures from the traditional kelvin scale to a more fundamental joules/nat scale.
That is why it is appropriate to say that
• the numerical value of k can be seen as telling us more about the definition of the kelvin than about any more fundamental property of the physical universe;
-- in much the same way that the constant 4.4482216... would tell us more about the definition of the pound force than about any more fundamental property of the physical universe;
Either that or the debate, if it exists in scientific circles, should be properly referenced - it shouldn't be stated in a partisan manner by an anonymous Wiki editor.
I'm not sure I'm aware of anything that could be contrued as a "debate" in scientific circles - I think everything I've set out above actually is taken as fairly obvious. Can you provide a reference which disputes it?
One paper you might like to look at which looks at the question from a pedagogical standpoint is
Harvey S. Leff, What if entropy were dimensionless?, American Journal of Physics 67 (12), December 1999
Note that the paper uses the uglyism "tempergy" for "temperature measured on an energy scale" -- (i.e. temperature measured in units of joules per nat).
I dare say more sophisticated references could be found. I came across this one because Harvey Leff (amongst other things, editor of a standard book of papers on Maxwell's Demon) happened to be a personal friend of the person I was discussing with at the time, and so this seemed an appropriate paper to refer him to. Jheald (talk) 11:02, 6 May 2008 (UTC)
I've made the change at -> of, and hope this settles things. Jheald (talk) 11:17, 6 May 2008 (UTC)

Thanks for your efforts. Unfortunately you haven't settled my personal disquiet about that paragraph (quoted again in italics below). Your point-by-point response only sidesteps the issues I raised. The paragraph features vague and inappropriate use of the word 'fundamental', it confuses kelvin with Celsius, it glibly asserts that temperature is a dimension without unique significance, it asserts that the numerical value assigned to k is non-essential when in fact the numerical value is determined by the choice of units (the choice of units is non-essential, eg J, eV, erg, Planck units etc), and it provides no citations for its quite shocking assertions. Since the debate is getting rather long, I'll copy and paste the paragraph here, in case anyone forgets or doesn't know what we are talking about:

The numerical value of k has no particular fundamental significance in itself: It merely reflects a preference for measuring temperature in units of familiar kelvins, based on the macroscopic physical properties of water. What is physically fundamental is the characteristic energy kT at a particular temperature. The numerical value of k measures the conversion factor for mapping from this characteristic microscopic energy E to the macroscopically-derived temperature scale T = E/k . If, instead of talking of room temperature as 300 K (27 °C or 80 °F), it were conventional to speak of the corresponding energy kT of 4.14×10−21 J, or 0.0259 eV, then Boltzmann's constant would not be needed.

I want this paragraph deleted from the article for the reasons given above. Either that or it must be rephrased and even then it might still need citations to support its claims. I think the rephrasing is going to cause a lot of problems because the underlying meaning is so confused. Try this for example:

"The numerical value of k has no particular fundamental significance in itself: It merely reflects a preference for measuring energy in units of joules, electron volts, ergons etc, and temperature in familiar kelvins, based on zero energy and the macroscopic physical properties of water (i.e. the triple point of water is arbitrarily defined to be 273.16 kelvin, which doesn't really mean that the kelvin scale has any significant association with water since we could equally well define the triple point as 432 609 kelvin or 35.8761 kelvin). What is physically real is the characteristic energy kT at a particular temperature, though of course an alien civilization might argue that energy is not a real entity compared for instance with mass, and yet it must be admitted that there could be a civilization somewhere in the universe that regards energy/temperature as a real entity, while energy on its own is a mere fiction etc etc."

As you see, a rephrasing is going to require a lot of ifs and buts and maybes and also lots of citations because the original paragraph is a pot-pourri of nonsense. Lucretius (talk) 05:00, 7 May 2008 (UTC)

I'm sorry, IMO the paragraph in the article is both accurate and justified. Apart from restating what's already been said above, I'm not sure there's much more I can add to take this forward. But I've put up a request at WT:PHYSICS to try to get some more editors to come and have a look at this. Jheald (talk) 09:48, 7 May 2008 (UTC)

This dispute is just the good old dispute about the role of units/dimensional constants in physics. Contrary to what is claimed above:

Who would say that h-bar is not really fundamental and that only energy is fundamental? Nobody. Then why say this about k?

Many theoretical physicsis I know do regard h-bar as a mere conversion factor that arises because we defined our units before we knew about quantum mechanics. The same is true for the value of the speed of light and the gravitatonal constant. Now not everyone agrees with this way of looking at dimensional constants, see here for three different views. The view expressed by Michael Duff makes the most sense to me.

If you do consider dimensional constants to be fundamental, then what about trying to measure the time variation of such constants? But, as Duff points out here, that doesn't make sense. If you read this article you do see that this subject, simple as it is (a high school student should be able to understand it), is very controversial. This is because in high school we are taught units in a flawed way.See also point 1 raisd on this website Count Iblis (talk) 16:05, 7 May 2008 (UTC)

Seems to me like "fundamental" and "water" are big sticking points, and the same sentiment could be expressed equally well in an uncontroversial way. Let me try:
The numerical value of k is important insofar as it essentially provides a conversion factor between the units of temperature and the units of energy. In fact, in some unit systems (such as Planck units), temperature is always measured in the same units as energy, and Boltzmann's constant is not needed. (Equivalently, it is said that k=1.) Most of the time, however, temperature and energy are not measured in the same units, and Boltzmann's constant provides a way to find the characteristic energy kT at a particular temperature T, or likewise the characteristic temperature E/k for a particular energy E.
In this way, k serves a similar role in physics as the speed of light, which in light of special relativity can be seen as a natural conversion factor between units of length and units of time; and Planck's constant, which in light of quantum mechanics can be seen as a natural conversion factor between units of energy and units of frequency.
Eh? :-) --Steve (talk) 17:25, 7 May 2008 (UTC)

Hi Steve and Count Iblis! And thanks! There are now three of us here who know the deep waters that the disputed paragraph has ventured or blundered into. This article is not a place to address those profound issues, in my opinion. Maybe the use of links would be effective. But there are other problems with the disputed paragraph in addition to the philosophical ones you've both touched on. Lucretius (talk) 02:52, 8 May 2008 (UTC)

### Outside view

• I think the paragraph as originally written is correct; however, we ought to be able to find a source that makes the statement. Has anyone looked for one? In any case, the analogy with c or ${\displaystyle \hbar }$ is a red herring; certainly the relationship between energy and temperature is a more direct one than the relationship between space and time. -- SCZenz (talk) 17:45, 7 May 2008 (UTC)

k is usually regarded as a fundamental physical constant, same as c and ${\displaystyle \hbar }$ and that's no red herring. You won't find any source that says something like:kelvin is based on the macroscopic properties of water (because that's a definition of Celsius). You won't find any source that says something like the numerical value of k merely represents a preference for measuring in kelvin (because that overlooks the other dimension, energy, whose units also contribute numerically). You won't find any source that says something like kt is fundamental and temperature isn't (because nobody actually knows which dimensions are physically real and which aren't - it's a difficult question and professional physicists just don't go there). The paragraph needs to be rephrased and yet I find it very difficult to rephrase it because the meaning is so confused. In the end, it'll probably end up something like this: "k is a constant of proportionality that mediates between the dimensions of energy and temperature. If we assume that these two dimensions are in fact the same dimension then k is no longer necessary." Not much, is it! But that's all I can find in it that makes sense. Lucretius (talk) 02:08, 8 May 2008 (UTC)

Well, how about just the first paragraph I wrote above (and not the second)? SCZenz, I still think the analogies with c and hbar are physically sound, but I concede that it would confuse the average reader. Certainly the "conversion" aspect of k is more obvious and straightforward. So yeah, I'd be happy to leave that part out. Lucretius, I think that the paragraph I'm proposing is very similar to the quote you offer above. By the way, one could also apend a sentence to the end of it: "The very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule. Physically, for example, a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller." --Steve (talk) 02:54, 8 May 2008 (UTC)

I like the look of this 'appended' sentence better than the Planck sentence. I don't think you can say that temperature and energy are measured in the same Planck units, unless you are talking about the non-dimensionalized form, and this is getting a bit out of the way, though you could link to Planck units easily enough. We have to remember that the disputed paragraph features in a section about conversion to other units such as eV. You could add Planck units to the table and then link to the Planck article. But over all, yes, I think you are making the right moves at the moment. In fact, if you are eager to shoulder the work, why not copy the relevant section, redraft it the way you think would best represent the consensus view, then paste it here or on your user page, for comment? At the very least, it could get things moving here. Otherwise we are waiting endlessly for the others to come up with citations that aren't out there. Lucretius (talk) 03:31, 8 May 2008 (UTC)

<ref>Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005</ref>
The paper discusses the scope for redefining the temperature measurement unit. Boltzmann's constant is naturally related to the temperature, and therefore the unit of temperature measurement can be an energy unit. quoted from abstract. SpinningSpark 18:27, 8 May 2008 (UTC)

Hi Spinningspark. You've been busy and thanks for the effort. However, this quote doesn't change anything in my opinion. This quote says that temperature units can be understood to measure energy. The disputed paragraph on the other hand says that temperature is somehow less real or 'fundamental' than energy and it says we can scrap temperature units and Boltzmann's constant. You need to find citations for that radical view. Also, the paper you refer to here seems to be arguing for revision to existing practices and that's not really ideal as an authoritative source.

I'm hoping somebody is going to come up with a new draft of the paragraph - a draft that everyone can agree to. The disputed paragraph should not be regarded as Holy Writ and I really can't understand the determination to defend it. Whatever it is trying to say can be said better. Here's my redraft, incorporating contributions by Steve:

New draft
The numerical value of k has no particular significance in itself: It merely depends on the choice of units for energy and temperature. Thus for example the very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule (a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller). In Planck units, on the other hand, the Plank unit of temperature and the Planck unit of energy are defined in such a way that k=1.

Spinningspark, is there anything you want to change or add to this? Lucretius (talk) 05:16, 9 May 2008 (UTC)

No, you're still missing the point. The point is that k is less fundamental than h or c.
h and c describe fundamental properties of the universe. k on the other hand is a just a conversion factor, on a level with the number of pounds force per newton. (And I don't think you'd argue that was fundamental?). The reason for the difference is that when it comes to temperature, there is a single natural starting point for building a natural system of units; one that even your hypothetical aliens would regard as a most natural place to begin.
It is to start with the nat as the unit of entropy.
That then leads to the number of energy-units per nat as the unit of temperature. In any such system there is no need to introduce a constant k. That's why the J K-1 value of k is best seen as a measurement, fixing the convenient kelvin scale; but not a property which is a fundamentally necessary to build a model of the universe. Jheald (talk) 06:41, 9 May 2008 (UTC)
I think it's wrong to say that k is really any different from h or c. All of them are normally considered conversion factors, often explicitly referred to as such in the scientific literature. (Note, for example, that c is a defined quantity, not a measured one.) When I took stat mech, I remember our instructor going over this and explicitly comparing k to h and c.
I found Frank Wilczek's discussion of fundamental constants quite illuminating. The preliminary section is especially appropriate to the discussion here, although (sadly) it doesn't mention k:
If we keep additional units then we will need additional fundamental constants to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open.
--Starwed (talk) 08:42, 9 May 2008 (UTC)
Yes, I think that it quite a useful quote. Boltzmann's constant is needed only if we insist on a temperature scale distinct from an energy scale. But the definition of temperature is so well established, that most physicists are prepared to regard the link between temperature and the energy required to increase the entropy one nat, as indeed a definitional a-priori part of the world model -- just as no separate scale is needed for force, compared to mass x acceleration. This is different to the sort of quantities with physical meanings that Wilczek describes in his abstract. Jheald (talk) 09:29, 9 May 2008 (UTC)

Jheald, if you can find a quote by an authoritative figure saying that c and h are more fundamental than k, it would be useful in an article about scientific controversies. I don't think it would be useful here unless we couple it with quotes about the fundamental significance of k. I've offered a redraft of the disputed paragraph (see above). What do you want to add to it? Please don't be obstructive but help draft a non-controversial, error-free paragraph. I'd be happy to include Starwed's quote from Wilczek, so long as it is included in a sensitive manner. Lucretius (talk) 21:53, 9 May 2008 (UTC)

I note that throughout this discussion you continually demand references from others (and then dismiss them as irrelevant when they are provided - even going so far as to dismiss them in advance in your comment above) but on the other hand you have provided none whatsoever for your side of the argument. SpinningSpark 22:24, 9 May 2008 (UTC)

Do I need references to support the case that k is a physical fundamental constant? It's the common position in science. However, you'll find k listed as a fundamental physical constant by NIST CODATA, for example (Boltzmann's constant CODATA value at NIST). I have no personal agenda here. I want to make sure that the Boltzmann article is balanced, non-controversial and error-free. The disputed paragraph is none of those. I think Starwed's quote is perhaps our best opportunity for a consensus. Does anyone want to try working that into the redrafted paragraph above, or would you rather look for quotes saying k has no fundamental significance? Lucretius (talk) 22:55, 9 May 2008 (UTC)

Here's a suggestion, Spinningspark - how about using the quote that you came up with as an example of the thing Wilczek is saying about 'keeping issues open'. The idea that k is not fundamental may be treated as one such open issue.Lucretius (talk) 23:24, 9 May 2008 (UTC)

2nd redraft
The numerical value of k has no particular significance in itself: It merely depends on the choice of units for energy and temperature. Thus for example the very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule (a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller). In Planck units, on the other hand, the Plank unit of temperature and the Planck unit of energy are defined in such a way that k=1.
Boltzmann's constant, like other fundamental physical constants, is merely a scientific tool for understanding the physical universe. As observed by Frank Wilczek, there are important issues surrounding any choice of units and constants:
"If we keep additional units then we will need additional fundamental constants to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)
Some would argue that temperature is not a significant dimension and that units of temperature can be replaced by those of energy (eg "...the unit of temperature measurement can be an energy unit." (:<ref>Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005</ref>). If units of temperature are made unnecessary then Boltzmann's constant would no longer be needed.

Any disagreements about this draft? This draft has 4 sets of fingerprints on it - Steve, Starwed, Spinningspark, my own, and those of the original author - and I think maybe this will be enough, though it could still do with some final polishing perhaps. Lucretius (talk) 00:04, 10 May 2008 (UTC)

(ec)Yes you do need references, you demand them of others, you should be prepared to provide them yourself;

The burden of evidence lies with the editor who adds or restores material. All quotations and any material challenged or likely to be challenged should be attributed to a reliable, published source using an inline citation (WP:V)

CODATA - come on, that is not a scientific paper or text, it is what it says on the tin - data. They give no dissertation on the significance of any of the constants they list. But as you have mentioned it, you might want to note that CODATA puts Boltzmann's constant in the category "Physico-chemical" rather than the "Universal" category that C and h belong to [2]. I suspect they might have a reason for doing that.
I support your idea of wording the paragraph as an open issue in order to gain consensus. My personal opinion is that temperature is not a primary unit in the same way as length and time are. However, it is not my view that counts as far as Wikipedia is concerned, but the views expressed in the literature. SpinningSpark 00:13, 10 May 2008 (UTC)

Only a few disagreements about the content, the part about k being fundamental and "a scientific tool for understanding the physical universe", I don't understand how this can be the case. But apart form that, this text is becoming quite large, so I guess it would be better to mention the things earlier in the text.
Now, my style of writing stuff for wikipedia is a bit different than just mentioning some facts/opinions and then reference them to the literature. I'm more in favor of explaining the fundamentals so that a reader who reads it really understands the topic. From this perspective what is missing is a discussion of thermodynamics and statistical physics in a little more detail.
If we do this then it becomes obvious that one can define a temperature that describes macroscopic thermodynamical phenomena and that the link to physics at the microscopic level can remain hidden. You can postulate atoms and develop statistical mechanics as Boltzmann did, but if you only have access to macroscopic observables you cannot determine Boltzmann's constant. You cannot tell the difference between one model in which Avogadro's constants takes one value or another model in which it is different and other microscopic parameters are also rescaled appropriately.
What we need to write in this article is that the conventional units for temperature we use today (Celcius Kelvin etc.) were defined before we could link thermodynamics to the physics at the microscopic level. In the mid 1800s Avogadro's constant was first measured approximately. And in 1910 another independent detemination using Brownian motion was made. Count Iblis (talk) 00:34, 10 May 2008 (UTC)
(ec)I like this version of the final para better,
It has been argued<ref>Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005</ref> that temperature is not a significant dimension and that units of temperature can be replaced by those of energy. If units of temperature are made unnecessary then Boltzmann's constant would no longer be needed.
There is no need for a direct quote when you have already said as much in your owm words. I have put the ref right after the weasel words to mitigate them and changed "some would argue" to "it has been argued" as a) this is slightly less weasely and b) it is more neutral as it "some" could be interpreted as "only some". And, oh my god, I have just followed my own weasel link and seen they use that very phrase as an example!
You also need a sub-head for this as it is now too long for its original position and would swamp the other material in that section. I suggest "The physical meaning of k". SpinningSpark 00:42, 10 May 2008 (UTC)
Count Iblis is right, the second para reads as if that was said by Frank Wilczek. I propose this;
It has been noted by Frank Wilczek that our choice of whether or not to use different units (and a corresponding fundamental constant) for two physical properties says something about our confidence in our theories of the physical world:

### 3rd proposed draft

#### The physical meaning of k

The numerical value of k has no particular significance in itself: It merely depends on the choice of units for energy and temperature. Thus for example the very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule (a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller). In Planck units, on the other hand, the Plank unit of temperature and the Planck unit of energy are defined in such a way that k=1.
It has been noted by Frank Wilczek that our choice of whether or not to use different units (and a corresponding fundamental constant) for two physical properties says something about our confidence in our theories of the physical world:
"If we keep additional units then we will need additional fundamental constants to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)
It has been argued<ref>Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005</ref> that temperature is not a significant dimension and that units of temperature can be replaced by those of energy. If units of temperature are made unnecessary then Boltzmann's constant would no longer be needed.

SpinningSpark 00:59, 10 May 2008 (UTC)

It would have a better logical flow if the paras were in the order 1,4,3,2. SpinningSpark 01:09, 10 May 2008 (UTC)

Personally I think your redraft makes the second paragraph more difficult to understand. How about this: It has been noted by Frank Wilczek that our choice of units and constants says something about our confidence in our theories of the physical world:. I agree that the subheading should be revised to 'The physical significance of k'. I do not agree that we should change the paragraph order. The final paragraph is the controversial idea we are moving towards, that k might be considered unnecessary, and it's best left at the end as a possibility, almost an afterthought. Lucretius (talk) 01:21, 10 May 2008 (UTC)

No, that's not what he is saying. The choice of units means nothing significant, for instance measuring in pounds or kilograms. The choice of measuring inertia and quantity of gravity in the same units - be they pounds or kilograms - is highly significant in that it reflects our confidence in the principle of equivalence. Likewise measuring temperature in joules would be making a similar kind of statement. SpinningSpark 01:46, 10 May 2008 (UTC)

You're interpreting Wilczek too narrowily. Here's a fuller quote from the same article:

Thus we clearly see that identifying fundamental constants, or even counting their number, involves an element of convention. It depends first of all on how many units we wish to keep. If we keep additional units (such as Q) then we will need additional fundamental constants (such as ${\displaystyle \varepsilon _{0}}$) to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)

He's talking simply about units and constants and our choices about which to keep and which to reject. The two positions he identifies are both provisional but one is more provisional than the other i.e some constants and units enjoy greater confidence than others. I don't care how you phrase that second paragraph so long as it is simple and clear. Your present phrasing makes my brain flicker as if I've missed a signal. I think we're almost there. Lucretius (talk) 06:41, 10 May 2008 (UTC)

You are wrong, he does not say "choice if units", he says "units we wish to keep". The example is the same principle as I gave for mass, choosing to eliminate ${\displaystyle \varepsilon _{0}}$ expresses our confidence in Coulombs Law and equivalently results in electric flux density and electric field strength being measured in the same units. If he were only talking of choice of units it would have little bearing on this debate, but he is not. It is the second part where he points out the profound implications of that choice that is most relevant. SpinningSpark 07:10, 10 May 2008 (UTC)
And also, your problem with digesting the second para is precisely why I suggest putting the (currently) last para before it. The concrete example of eliminating Botzmann's constant fixes the idea in the mind that is subsequently discussed in general terms by Wilczek. SpinningSpark 07:21, 10 May 2008 (UTC)

Actually I don't really care about the paragraph order (I don't want to make an issue out of it). Given the existing order, here's my suggestion for the 2nd paragraph. It involves using the larger quote I've taken from Wilczek's paper. The 2nd para in this case is virtually no more than an intro to the 3rd paragraph:

(Para2)There is considerable debate in scientific circles about which physical constants should be regarded as truly fundamental and which should not.Frank Wilczek expresses the issue in this way:
(Para3)...identifying fundamental constants, or even counting their number, involves an element of convention. It depends first of all on how many units we wish to keep. If we keep additional units (such as Q) then we will need additional fundamental constants (such as ${\displaystyle \varepsilon _{0}}$) to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)

We've almost reached a good co-operative result, in my opinion. Can we please just go that extra yard and finish this off simply and clearly? Lucretius (talk) 10:11, 10 May 2008 (UTC)

Lucretius, I am on the verge of simply withdrawing my support for any change. As far as I can see no-one else is unhappy with the article and this debate has become a monster. The paragraph as it currently stands in the article at least has the benefit of brevity. Everyone else seems to have gone away for the moment (I am not surprised, it takes stamina to stick with this). You simply cannot say "there is considerable debate" without backing it up. I have seen no evidence so far that the statement in the article as it stands is actually controversial in scientific circles. Furthermore, widening the discussion to physical constants in general, which is what your latest draft is doing, is turning the article into a monster as well. SpinningSpark 10:40, 10 May 2008 (UTC)

k is a constant of proportionality much like c. We could discard c and measure length in seconds, or alternatively measure time in meters. But c is useful because, historically and intuitively, time and length are two different things that we measure differently. Energy and temperature are also measured differently, but both energy and temperature are somewhat more nebulous and unintuitive concepts than length and time, so there's less urge to separate the two. This, combined with the fact that T always appears as kT or RT in physical laws means that it's less useful to treat temperature as a separate quantity. So, I think c is a little more useful than k, which is in turn a little more useful than epsilon0 and mu0, which serve only to bastardize equations. Ken —Preceding unsigned comment added by 128.83.61.196 (talk) 16:51, 31 October 2008 (UTC)

## 4th draft

Sorry to hear about your disillusionment, Spinningspark. I think the issue is important and I've already pointed out the errors in the original text. I disagree that the revision is a monster. It can be drafted in a succinct form. Here is my choice (it may be a futile gesture if nobody else is interested but at least I've put it on the record).

## The physical significance of k

Values of k Units Comments
1.380 6504(24)×10−23 J/K SI units, 2002 CODATA value
8.617 343(15)×10−5 eV/K 1 electronvolt = 1.602 176 53(14)×10−19 J
6.336 281(73)×10−6 Ryd/K 1 Rydberg = 13.6 eV
1.3807×10−16 erg/K
The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value. k can also be expressed with the unit mol (such as 1.99 calories/mole-kelvin); for historical reasons it is then called the gas constant.
The numerical value of k has no particular significance in itself: It merely depends on the choice of units for energy and temperature. Thus for example the very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule (a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller). In Planck units, on the other hand, the Plank unit of temperature and the Planck unit of energy are defined in such a way that k=1.
There has been considerable debate in scientific circles about which physical constants should be regarded as truly fundamental and which should not (e.g. Comment on time-variation of fundamental constantsand Trialogue on the number of fundamental constants). Frank Wilczek expresses the issue in this way: "...identifying fundamental constants, or even counting their number, involves an element of convention. It depends first of all on how many units we wish to keep. If we keep additional units (such as Q) then we will need additional fundamental constants (such as ${\displaystyle \varepsilon _{0}}$) to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)
One such open issue is the question whether or not Boltzmann's constant is truly a fundamental physical constant. It has been argued that temperature is not a significant dimension and that units of temperature can be replaced by those of energy (*Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005). If units of temperature are in fact replaced by units of energy then of course Boltzmann's constant would no longer be needed.

Something like this is quite concise, it presents the facts, it contains no errors. I don't regard it as a monster. Anyhow, that's enough from my end. (:}) Lucretius (talk) 14:29, 10 May 2008 (UTC)

I'm not sure. I've never actually believed that Boltzmann's constant is fundamental in the sense that c and h are; do you have any source that both believes in dimensionful fundamental constants and that k is one?
Saying that it is an 'open issue' whether k is fundamental - or better, whether temperature and energy are different physical dimensions - seems to imply that it is a scientific question. But it is not; no experiment or observation could tell us whether they are or not. The way, the truth, and the light (talk) 17:13, 10 May 2008 (UTC)

The original text (which is still there on the article page) says: "What is physically fundamental is the characteristic energy kT of a particular temperature." Ask yourself this: What's the theoretic context for that judgement, where are the citations and why was the author so dogmatic? The redraft above was written to correct those omissions. The original text also says things like "The numerical value of k merely reflects the preference for measuring in kelvin". Ask yourself this: what about the numerical contribution made by units of energy? The redraft above corrects that error too. The original text says things like "kelvin is based on the macroscopic properties of water". Ask yourself this: if that's kelvin then what's Celsius? The above redraft removes that error also. The redraft is there for you guys to use or adapt when and if you decide that the original text is inadequate and/or wrong. Many thanks to Steve, Starwed, Spinningspark and others for providing the material for the redraft. Cheers. Lucretius (talk) 02:03, 11 May 2008 (UTC)

This counterposing of Kelvin and Celsius shows a fundamental misconception of what the Celsius scale is. Celsius is the same scale as Kelvin but with an offset. They both take absolute zero and the tp of water as their references points. It is the Centigrade scale that takes mp and bp of water as its references points. In any case, all three have at least one reference point which is dependent on a physical property of water so I cannot see how that is an error in the article. SpinningSpark 07:19, 11 May 2008 (UTC)

## The physical significance of k

Values of k Units Comments
1.380 6504(24)×10−23 J/K SI units, 2002 CODATA value
8.617 343(15)×10−5 eV/K 1 electronvolt = 1.602 176 53(14)×10−19 J
6.336 281(73)×10−6 Ryd/K 1 Rydberg = 13.6 eV
1.3807×10−16 erg/K
The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value. k can also be expressed with the unit mol (such as 1.99 calories/mole-kelvin); for historical reasons it is then called the gas constant.
The numerical value of k has no particular significance in itself: It merely depends on the choice of units for energy and temperature. Thus for example the very small numerical value of the Boltzmann constant in SI reflects the fact that the SI unit of temperature, 1 Kelvin, corresponds to a much smaller energy than the SI unit of energy, 1 Joule (a single molecule in a cloud of gas at 1 kelvin would have an average kinetic energy which is not 1 joule, but rather is around 23 orders of magnitude smaller). In Planck units, on the other hand, the Plank unit of temperature and the Planck unit of energy are defined in such a way that k=1.
There has been considerable debate in scientific circles about which physical constants should be regarded as truly fundamental and which should not (e.g. Comment on time-variation of fundamental constantsand Trialogue on the number of fundamental constants). Frank Wilczek expresses the issue in this way: "...identifying fundamental constants, or even counting their number, involves an element of convention. It depends first of all on how many units we wish to keep. If we keep additional units (such as Q) then we will need additional fundamental constants (such as ${\displaystyle \varepsilon _{0}}$) to mediate equations in which they appear. More profoundly, it depends upon where we choose to draw the dividing line between facts so well established that we are comfortable to regard them, at least provisionally, as a priori features of our theoretical world-model, and issues we choose to keep open." (discussion of fundamental constants)
One such open issue is the question whether or not Boltzmann's constant is truly a fundamental physical constant. It has been argued that temperature is not a significant dimension and that units of temperature can be replaced by those of energy (*Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005). If units of temperature are in fact replaced by units of energy then of course Boltzmann's constant would no longer be needed.

Something like this is quite concise, it presents the facts, it contains no errors. I don't regard it as a monster. Anyhow, that's enough from my end. (:}) Lucretius (talk) 14:29, 10 May 2008 (UTC)

I'm not sure. I've never actually believed that Boltzmann's constant is fundamental in the sense that c and h are; do you have any source that both believes in dimensionful fundamental constants and that k is one?
Saying that it is an 'open issue' whether k is fundamental - or better, whether temperature and energy are different physical dimensions - seems to imply that it is a scientific question. But it is not; no experiment or observation could tell us whether they are or not. The way, the truth, and the light (talk) 17:13, 10 May 2008 (UTC)

The original text (which is still there on the article page) says: "What is physically fundamental is the characteristic energy kT of a particular temperature." Ask yourself this: What's the theoretic context for that judgement, where are the citations and why was the author so dogmatic? The redraft above was written to correct those omissions. The original text also says things like "The numerical value of k merely reflects the preference for measuring in kelvin". Ask yourself this: what about the numerical contribution made by units of energy? The redraft above corrects that error too. The original text says things like "kelvin is based on the macroscopic properties of water". Ask yourself this: if that's kelvin then what's Celsius? The above redraft removes that error also. The redraft is there for you guys to use or adapt when and if you decide that the original text is inadequate and/or wrong. Many thanks to Steve, Starwed, Spinningspark and others for providing the material for the redraft. Cheers. Lucretius (talk) 02:03, 11 May 2008 (UTC)

This counterposing of Kelvin and Celsius shows a fundamental misconception of what the Celsius scale is. Celsius is the same scale as Kelvin but with an offset. They both take absolute zero and the tp of water as their references points. It is the Centigrade scale that takes mp and bp of water as its references points. In any case, all three have at least one reference point which is dependent on a physical property of water so I cannot see how that is an error in the article. SpinningSpark 07:19, 11 May 2008 (UTC)

Can first just say: Wow! Thats a long discussion! Its longer than the article itself. That said, I think its great that you are all so motivated and are willing to put so much time into it. As a newcomer to this discussion perhaps I can offer some insights and a compromise. The discussion as to which physical constants are significant and which are not, is a very tricky one as it inevitably depends on one's own perspective (My thermometer reads Celsius, maybe yours reads eV?). This discussion would perhaps feel more at home at Physical_constant. I would propose to leave out the whole discussion of how fundamental k is and move it there.

The second paragraph starts out stating that k is not significant. I can imagine this causes some resistance since this is a value statement. But since we all use k all the time, clearly it is of importance. Its numerical value depends on the system of units that you choose, one can even go so far as to pick a system of units such that k=1 (just like one can for c and h). Let's just say this and let the reader decide how this affects how significant or fundamental k is. I would propose this following

## The numerical value of k

Values of k Units Comments
1.380 6504(24)×10−23 J/K SI units, 2002 CODATA value
8.617 343(15)×10−5 eV/K 1 electronvolt = 1.602 176 53(14)×10−19 J
6.336 281(73)×10−6 Ryd/K 1 Rydberg = 13.6 eV
1.3807×10−16 erg/K
The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value. k can also be expressed with the unit mol (such as 1.99 calories/(mole * kelvin)); for historical reasons it is then called the gas constant.
Since k is a constant of proportionality of temperature and energy, the numerical value of k depends on the choice of units for energy and temperature. The very small numerical value of the Boltzmann constant in SI units reflects how the energy associated with thermal motion of particles at room temperature is exceedingly small compared to the kinetic energy of macroscopic objects, measured in Joule. On the other hand, the Plank units of temperature and energy are defined in such a way that k=1. If we choose to measure temperature in units of energy then of Boltzmann's constant would not be needed at all.

(*Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005).

--V. (talk) 01:24, 13 May 2008 (UTC)

Room temperature has nothing to do with it. SpinningSpark 18:52, 14 May 2008 (UTC)
k is a conversion factor. If we would just pick our units in a sensible way it would not be needed. So why does everybody use it? Why did we pick out unit of temperature to be the Kelvin or the Celsius and our unit of energy to be Joule? It is because those units are natural to use in the environment that we actually experience. As I said before my thermometer reads Celsius. Tomorrows temperature forecast tells me about 25 Celsius, not 4*10^-21 Joules. The kinetic energy of a baseball is about 100 Joules. We picked out units for practical considerations at roughly room temperature. That means k has to be really small. That is why we bother with a conversion factor rather than to report the weather in Joules. But please rephrase if you like. --V. (talk) 22:47, 14 May 2008 (UTC)

Since there were no more comments. I changed the page. --V. (talk) 16:14, 4 June 2008 (UTC)

Lack of further comment was not a sign of agreement, it was a sign of exhaustion after the debate with Lucretius. Neither the Joule nor the Kelvin have anything to do with room temperature or the properties of anything at room temperature. The Kelvin on the other hand has a lot to do with the properties of water, as stated. k is small because it is small relative to a Kelvin. It is still small relative to 1 deg K difference at 50oK as much as it is at 300oK. SpinningSpark 19:11, 4 June 2008 (UTC)

I'm baaaaaack! No just kidding. I'm sorry you guys didn't get around to changing the paragraph but such is life. According to PV/N=kT, temperature can be a way of measuring volume under constant pressure, or pressure within a constant volume. It can even be taken to measure N number of particles, everything else being constant. Yet the paragraph says that temperature is fundamentally a measurement of energy. Who is to say the energy is more fundamental than volume or pressure or number of particles? If you really know what is fundamental and what isn't then you know something that science doesn't.

As for the properties of water, I could tie the Kelvin scale to the tp and bp of any substance, even pea soup, and it would still be an absolute temperature scale based on zero energy/0 volume/0 pressure/0 number of particles. Kelvin is not based on the macroscopic properties of water. Kelvin is conveniently tied to water simply to allow for an easy translation to and from the older temperature scale.

I could go on and on and on. But fear not! I am silent. Lucretius (talk) 02:06, 5 June 2008 (UTC)

SpinningSpark: If you don't like the current draft, please make a revision. It would greatly help this process along if we could work together to come to some compromise that everyone can agree to.

Lucretius: The ideal gas law only applies to ideal gasses. In addition to that, it follows from the microscopic (ie. particle level) description of matter that kT should have units of energy.

One thing we do all agree on is that k is small because of the units that we chose for temperature and energy. I think it would be worthwhile to make a statement about why these units were chosen, and what it means for k to be small. I agree that the use of the term room temperature is awkward, once again, I welcome a better phrasing. --V. (talk) 21:49, 5 June 2008 (UTC)

Sorry for appearing unco-operative. I had a bad experience earlier in this debate (along with many others I suspect) of suggesting a draft only to have it re-injected with an agenda and then claiming I was in support. I will work on it tomorrow. SpinningSpark 22:39, 5 June 2008 (UTC)

## Value in different units

Values of k Units Comments
1.380 6504(24)×10−23 J/K SI units, 2002 CODATA value
8.617 343(15)×10−5 eV/K 1 electronvolt = 1.602 176 53(14)×10−19 J
6.336 281(73)×10−6 Ryd/K 1 Rydberg = 13.6 eV
1.3807×10−16 erg/K

The digits in parentheses are the standard measurement uncertainty in the last two digits of the measured value.

The constant can also be expressed in terms of energy per mole instead of energy per entity (such as 1.99 calories/mol-K); for historical reasons it is then called the gas constant and given the symbol R.

Since k is a constant of proportionality of temperature and energy, the numerical value of k depends on the choice of units for energy and temperature. The Kelvin temperature scale was chosen to conveniently divide up the liquid range of water into one hundred intervals. The very small numerical value of k merely reflects the small energy in joules required to increase a particle's energy through 1oK. The physically fundamental idea is the characteristic energy kT of a particular temperature.

The numerical value of k provides a mapping from this characteristic microscopic energy E to the macroscopically-derived temperature scale T = E/k. On the other hand, the Plank units of temperature and energy are defined in such a way that k=1. If we choose to measure temperature in units of energy then Boltzmann's constant would not be needed at all.[2]

I support the above version, which, I think, includes the ideas V wants to get across. I have taken out all the stuff about room temperature which really is a red herring. I have left in that characteristic energy, and not arbitrary temperature scale, is fundamentally significant. Also a few minor tidies. SpinningSpark 13:01, 6 June 2008 (UTC)
Good work! I would suggest some small changes to the second paragraph, how about this:
Since k is a constant of proportionality of temperature and energy, the numerical value of k depends on the choice of units for energy and temperature. Physically fundamental is the characteristic energy kT of a particle at a particular temperature. The Kelvin scale was chosen to conveniently divide up the temperature range over which water is liquid into one hundred intervals. The very small value of k in SI units reflects the small energy in joules required to increase a particle's thermal energy by 1 Kelvin.
The numerical value of k provides a mapping from this characteristic microscopic energy E to the macroscopically-derived temperature scale T = E/k. If we choose to measure temperature in units of energy then Boltzmann's constant would not be needed at all. For example, the Plank units of temperature and energy are defined in such a way that k=1. [3] —Preceding unsigned comment added by V81 (talkcontribs) 23:16, 6 June 2008 (UTC)
I prefer Spinning spark's version - it's more economic and it also happens to be sweeter prose. However I've never before seen the word 'fundamental' used in relation to a dimension and it represents a value judgement open to much dispute (PV/N contains even more fundamental fundamentals from my perspective, and temperature measures a particular kind of energy that probably deserves to be recognized independently - these are all value judgements of course). But I'm prepared to let that objection go in the interests of world peace. Oooops. I'm supposed to be silent. Anyhow, I accept Spinning spark's version.
PS - maybe this is a small issue but 'to conveniently divide' is a split infinitive, a solecism that used to result in detentions in the traditional classroom. Admittedly it is less cumbersome than 'conveniently to divide' or 'to divide conveniently'. Generally in such cases it's best to find another way of phrasing the matter. So how about this sentence instead: The Kelvin temperature scale was chosen for the convenient division of the liquid range of water into one hundred intervals. But now I shall go back to my corner on the Naughty Chair. I am silent. Lucretius (talk) 01:31, 7 June 2008 (UTC)
I've now pasted Spinningspark's edit into the article. It's not all I wanted but it's a whole lot better than the original. Thanks for your willingness to compromise, Spinningspark, and thanks V81 for mediating. My apologies if I've stepped on any toes. I behaved like a jerk at times. But at least now the article doesn't annoy the hell out of me. I only hope I'm not stepping on any toes now by making this change. We'll find out! (:}) Lucretius (talk) 01:19, 8 June 2008 (UTC)

I'm ok with this. --V. (talk) 18:48, 8 June 2008 (UTC)

1. ^ Sethna, James P, "Statistical Mechanics: Entropy, Order Parameters, and Complexity", p87 ,Clarendon Press Oxford, 2008, available online here
2. ^ Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005.
3. ^ Kalinin, M; Kononogov, S, "Boltzmann's Constant, the Energy Meaning of Temperature, and Thermodynamic Irreversibility", Measurement Techniques, pp632-636, vol 48, no 7, July 2005.