Talk:Planck constant/Archive 1

Parentheses in the equations
Am i correct in assuming that the parentheses in the equations for h are values related to uncertainty? Someone DEFINATELY needs to explain how that works - or better yet, write it in a more intuitive systm - because (35) looks like multiplication to me. User:Fresheneesz

Limits of Energy and Time
h means: energy is related to time. Is there an upper or lower limit of energy or time? ErNa 09:17, 9 Jun 2005 (UTC)

"slowing" of light
Article says:
 * Similarly, the amount of time it takes a photon to travel one Planck length is Planck time: 10^-43 seconds. This is the smallest meaningful division of time.

Shouldn't that be more accurately the amount of time it takes for a particle travelling at the speed of light in a vacuum one Planck length? Photon's can travel slower than the speed of light in a vacuum in some circumstances, can't they? -- SJK

I don't think that the photons actually slow down. I believe that the slow down in a refractive material is due to the absorbtion and re-emission of the photons; slowing down the wave as a whole. I may, of course, be wrong. --BlackGriffen


 * You are correct. Incidentally, the unqualified phrase "speed of light" aelmost always refers to the speed of light in a vacuum. -- CYD

apostrophe?
Shouldn't the title of the article contain an apostrophe, or is that not possible? --BlackGriffen -

equation for planck's length
Also could someone post the equation for Planck's length and explain in detail why two points separated by less than Planck's length are indistingushable? I think it has something to do with heisenberg's uncertainty principle?
 * Moved --User:maveric149

Thanks for the suggestion! The formula for the Planck length is:

SQRT(h-bar G/c3)

There is currently a buzz in physics surrounding this length because general relativity and quantum mechanics are glaringly incompatible at Planck scale. This is a temporary condition. The theories of gravity and matter will be adjusted so they don't contradict each other, the buzz will stop or be about something else. The Planck units will still be there as natural units implicit in light and gravity explainable in simple terms without all the heavy talk about theories breaking down, just as they have been there for a hundred years. They're nice because they make the constants you use all the time come out to be one.

But yes!!!! maveric. The current clash of theories DOES have to do with HUP! The prevailing theory of gravity (Gen. Rel.) allows for black holes of any mass, consisting of a point of singularity surrounded and hidden by an event horizon whose size (the halfradius) is proportional to the hole's mass. For a non-rotating black hole of Planck mass the halfradius would be Planck length.

But in the prevailing theory of matter (Qua. Mech.) every mass has a Compton wavelength which imposes a limit on localization and the Compton for something with Planck mass is also equal to Planck length. This trashes the model of a black hole because how can the point of singularity be surrounded and hidden by the event horizon when the point is so spread out that it barely fits inside? there is not enough ability to localize for the trim geometry of the black hole model to work convincingly.

So physicists (as a professional class very subject to tunnel vision, thinking only about the Problem of the Day) tell you that Planck scale IS where the theories break down. Right now that is the significance of the Planck scale for them. I think in the long run it is more significant that the people who seem to be making the most progress at FIXING the problem (String Theorists) actually do their work in Planck units. In other words they are handy units to work in when you are trying to unify gravity and the other forces of matter and build a general theory, so that when there finally is some theory that works it will very likely be written in Planck units. I see them as the units of the future rather than as the place where current theories collide. But you are right to point out that aspect.

Updated 2002 CODATA values
I've replaced the old 1998 CODATA-recommended values with the new 2002 CODATA-recommended values. These values became available in December 2003, and are the new internationally-recommended values for these constants.

The U.S. National Institute of Standards and Technology's excellent reference site has the updated CODATA international data.

References to 2002 CODATA Values: --Alan Eliasen
 * CODATA value for h
 * CODATA value for hbar

Physical Unit
Angle is measured either in radian or in 'cycle'.

The conversion factor is $$2\pi$$ radian per cycle.

Frequency is measured either in radian per second or in cycle per second, hertz.

Energy is measured in joule.

The essence of quantum mechanics is that energy is actually the same thing as frequency.
 * Not at all! ErNa 10:09, 7 November 2005 (UTC)

The conversion factor is the planck constant h joule per hertz.

The conversion factor between joule and radian per second is the 'reduced planck constant' h-bar.

When omitting the angle unit and just stating the unit Js, joule-second, you cannot tell the difference between joule-second per cycle and joule-second per radian.

When stating the angle unit, cycle or radian, you don't need different symbols 'h' and 'h-bar'.

When stating the energy unit, joule or hertz, you don't need the symbol h, just as you don't need a special symbol for the conversion factor between inch and metre.

Bo Jacoby 13:43, 12 September 2005 (UTC)


 * Mathematics give us a feeling, that something is a single event, expressed by an infinite line or it is periodical, symbolised by an circle. Nature only makes sense, if there is something periodical within the singularity of existance. The question h or h-bar can be answered: it depends on the actual point of view. Use it just the way, it makes live comfortable. Anyway, it is easy to switch! ErNa 10:09, 7 November 2005 (UTC)


 * Having taken physics at A level, it seems to me intuitively that "joules per herz" (J/Hz or J s) and "joules per (radian per second)" (J/(rad/s), J/(rad Hz) or (J s)/rad) are different units, and that the relationship between Planck's and Dirac's constants is really $$\hbar = \frac{h}{2 \pi {\rm rad}} \ $$. However, other sources I've found on the web seem to give a value for Dirac's constant in joule seconds, and the relationship as in this article. I don't think you can mix them up. In fact we contradict ourselves here, as we say in one place that Dirac's constant has units (J s)/rad, and elsewhere that it has units J s. What is going on here? Hairy Dude 19:59, 12 April 2006 (UTC)


 * The dimensions are arguably the same in J/Hz and J/(radian/s). Radians are dimensionless numbers (they are essentially defined as length/length.)  While the SI had radians as their own base unit up until 1974 or so, they dropped it as a unit because it introduced artificiality and incorrectness into calculations.  Think of radians as dimensionless numbers, as they truly are, and the confusion disappears.  --Eliasen 23:22, 18 July 2006 (UTC)

How was it found?
I went through the article and I don't think there's any mention of how the constant was first derived and why exactly it was named after Max Planck. It would be nice if a journal reference were available too. -- Rune Welsh &tau;&alpha;&lambda;&kappa; 19:59, 4 October 2005 (UTC)
 * See the article Max_Planck . Bo Jacoby 13:52, 5 October 2005 (UTC)
 * I've added a short section on the origins of Planck's constant and the more common use of Dirac's constant. Hopefully this helps. Deklund 02:15, 14 November 2005 (UTC)

Constants
It always bothers me a little when somebody uses a symbol to represent a unit of measure without defining it. Strangely, this article take the trouble to tell the average well-informed reader that π is pi, which every grade school child should know. But it uses symbols like J without a hint. It happens that I already know what that represents, but probably only because I sat in the physics lecture hall five days a week for a couple of semesters. It is hard enough to understand any of these things without unintentionally making everything more mysterious than it needs to be. P0M 01:31, 28 October 2005 (UTC)
 * The letter J is explained to mean joule, and you may click on joule to get an article on it, in precisely the same way as pi is explained. Have you got any suggestion for improvement? Bo Jacoby 15:32, 14 November 2005 (UTC)
 * I think he was referring to the use of J in the sense of the angular momentum operator, in the Usage section. I think right now it's explained as best as it can be in context (without going into unnecessary detail), and it is a nice example of how h pops up as the quantization factor in more than just the well-known position-momentum uncertainty relationship. Q.M. Deklund 03:40, 15 November 2005 (UTC)

Dirac's constant
From article:
 * The unit of measurement of Planck's constant is joule per hertz, or joule per (turn per second), while the unit of measurement of Dirac's constant is joule per (radian per second). The two constants are merely conversion factors between energy units and frequency units. Physicists tend to omit the unit names for angle, and so they need two constants for the same concept.

This explanation doesn't seem to do justice to the role Dirac's constant plays in the context of quantum mechanics. The historical root of Planck's constant is of course in the fact that Planck proposed it in the context of the equation $$E = h\nu$$, but the fact that Dirac's constant just happens to fit in nicely in the variation of $$E = \hbar \omega$$ is only secondary to its true definition. The root of Dirac's constant, as I understand it, is not in a difference of units, but rather that if you extrapolate back to the basic postulates of quantum mechanics, there is some constant, which we call $$\hbar$$, which plays the role of the (magnitude of the imaginary component of the) commutator relationship between the position and momentum operators. The fact that this completely separate constant also happens to only differ from Planck's constant by a factor of $$2\pi$$ (in the context of the Planck equation), and provides a convenient alternative in terms of the angular frequency, is only coincidental. Deklund 05:33, 15 November 2005 (UTC)


 * This discussion can go on and on. To me, Planck discovered: action is quantisised. The problem is: what the hell is "action"? What is energy times time? We accept, that energy is voltage times charge, or, force times distance. But action? Why dont we ask the question why meter times meter is squaremeter? Whe say: 1.:plancks constant is a proportionality factor between energy and frequency. 2: Diracs constant has do do with quantum mechanics. To me, it is very clear: statement 1 is just wrong! What is the frequency of an photon? Did someone else ever analyse the fourier spectrum of a wavelet-like event? Frequency is not a property of photons, but a property of an electro magnetic wave, i.e. Laser light, broadcasting, etc. ErNa 06:40, 15 November 2005 (UTC)

Hey ErNa. Electromagnetic waves consist of photons - the frequency of the photons is the same thing as the frequency of the field. When the frequency &nu; is well defined, then the time-dependence of the field is of the form e2&pi;i&nu;t. The derivative is (d/dt)e2&pi;i&nu;t=2&pi;i&nu;e2&pi;i&nu;t. So the differential operator is d/dt=2&pi;i&nu;. The commutator between differentiation and multiplication, acting on an arbitrary function y, is ((d/dt)t-t(d/dt))y=dty/dt-tdy/dt=tdy/dt+y-tdy/dt=1y so that (d/dt)t-t(d/dt)=1. That gives &nu;t-t&nu; = 1/2&pi;i. Inserting E=h&nu; gives Et-tE=h/2&pi;i. So the commutator relationship is merely an elementary consequence of the fundamental quantum mechanical equivalence between energy and frequency. Bo Jacoby 11:55, 15 November 2005 (UTC)


 * If you look to Photon You see, it is not realy clear, what a Photon is. E-m-waves are not photons. We know, that e-m-waves of a certain frequency can exchange energy with matter, and they can be quantisized. ErNa 16:44, 15 November 2005 (UTC)


 * Could you explain why "we" "know" that electromagnetic waves are not photons? You're simply being incoherent. -- CYD
 * Yes. First we have to accept: we don't know, how photons "look" like. What do we know: There is matter, carrying electric charge. There is an electromagnetic field. Both, matter and field show properties energy and momentum (at least). Matter is something, that consists of dicriminated "particles", fermions. There is one value of energy and momentum for all the matter in universe(simplified, no relativistic effects). e-m-field is the superposition of "photons". Again there is one value of energy an momentum for the whole field. The interaction between the particles of matter is established by the field. Energy and momentum is transfered from matter to the field and again from the field to matter. And, the only way to describe this transfer is: all the matter particles could be represented by a vector in a phase space. (ok, this space will have many dimensions.) But: if there is interaction between field and matter, the vector changes exactly be h. We don't know, why this interaction is quantized. That is, what we call a photon. Now, we created an excitation, that moves through the field and doesn't change its "shape" (a shape, we can't measure, we don't know). But why doesn't it make sense, to call this a photon? Matter can be seen localised in area of space. The field is a superposition of all excitations and, whenever matter "sees" a photon and gets energy and momentum from the field, this "photon" can be the momentary superposition of billions of "photons" at this place. The propability to "see" a "photon" increases, when we send a stream of "photons" from a source to the "detector". Only by accident "photons" form a monochromatic electromagnetic wave. We somehow provoke this with help of resonators, for example paralleled mirrors. t.b.d ErNa 08:55, 16 November 2005 (UTC)


 * That's a very sketchy explanation at best (t and d/dt are not operators in the usual quantum mechanical sense, so the energy-time uncertainty principle doesn't arise from a fundamental commutation relation; its origins are more subtle than that). The way to answer ErNa's question is simply the good old photoelectric effect. -- CYD

Nobody talked about the uncertainty relation. Deklund referred to commutation relations as more fundamental than the equivalence between energy and frequency, and I argue against that. t and d/dt are linear operators in the mathematical sense: they map functions to functions.
 * t&middot;(Af+Bg)=Atf+Btg and (d/dt)(Af+Bg)= Adf/dt + Bdg/dt Bo Jacoby 15:37, 15 November 2005 (UTC)


 * The point is that they are not observables. So your commutation relation has no physical significance in the usual quantum mechanical sense. This is equivalent to saying that it does not specify an uncertainty relation, which is the usual physical content of saying that two operators (corresponding to observables) do not commute. That's why the point you're making is not a very good one.


 * I understand the point you are trying to make, but it's really not as complicated as you're making it out to be. It suffices to say that the Schrodinger equation H&psi; = i hbar d&psi;/dt relates energy to time (inverse frequency). And the Schrodinger equation applies to all quantum mechanical systems. -- CYD


 * I get your point, Bo, on how the commutator relationship isn't really fundamental, but I'm still not convinced by your point that h and hbar only differ in terms of units in the context of the Planck equation. Clearly Planck's constant plays the role of the proportionality factor between energy and frequency in quantum mechanics, but it also plays the role between, for example, angular momentum and quantum number, or between linear momentum and spatial derivative($$p = \frac{\hbar}{i} \frac{\partial}{\partial x}$$).  In these contexts measurements the units rad^-1 don't seem to make as much sense.  Furthermore, if you look at other "fundamental" equations in physics, you don't seem this same "dual-definition" in terms of "turns" or radians; e.g., one can relate the frequency of a photon to its wavelength through the trivial $$c = \lambda \nu$$, but no one in their right mind goes and defines a new constant "c-bar" such that $$cbar = \lambda \omega$$.  To me, this suggests there's a more fundamental justification for the use of hbar instead of h. Deklund 03:56, 16 November 2005 (UTC)

To CYD and ErNa. The time of arrival of single high-energy photons, and their energy, are actually observed in CERN with very high precision, but of cause subject to the uncertainty of Heisenberg, so I fail to understand your objection that they should not be observables. The Schrödinger equation is a consequence of E=h&nu; and 2&pi;i&nu;=d/dt

To Deklund. The frequency &nu; measured in turn per second (or waves per second) relate to the wavelenght &lambda; measured in meter per wave, and the speed c measured in meter per second, by your formula $$c = \lambda \nu$$. You may measure wavelength lambda-bar in meter per radian and 'angular' frequency &omega; in radian per second, and the speed is unchanged. There is no 'c-bar' because speed is not related to angle. The wave vector k, measured in radian per meter, relate (quantum mechanically) to the momentum p by p=h-bar k, and (classically) to the differentiation operator by ik=d/dx, (because the spatial dependence is eikx). Classical angular momentum is measured in joule second per radian, and so its connection to quantum mechanics is via h-bar having also unit joule second per radian. Bo Jacoby 14:14, 16 November 2005 (UTC)


 * Thanks for the explanation, Bo. I have one more question, though it's getting more into math rather than physics.  So when you apply an operator like d/dx or d/dt to a state function &psi; (or any "wave-like" function), you're really "bringing down" not just a factor of inverse length or frequency, but also an extra factor of radians, e.g. d/dx(e^ikx) = ik e^ikx = [rad/m].  Which is why you use hbar in Schroedinger's equation, H&psi; = i hbar d&psi;/dt, instead of h.  First of all, this seems a bit counter-intuitive: shouldn't differentiating a function with units [x] with respect to a variable with units [y] result in a function with units [x/y], regardless of the form of the original function?  And is there some way you could reformulate Schroedinger's equation in terms of "turns" per time instead of radians per time, so that H&psi; = ih d&psi;/dt?  Or is this some fundamental quality of a wave-like solution?  I'm trying to understand how taking a basic differential equation f(2)(x) = - f(x) (resulting in f(x) = e^ix) leaves you with a function that acts on units of radians (with factors of pi popping up all over). Deklund 03:00, 18 November 2005 (UTC)

Draw the unit circle in the complex plane. The direction ei=cos(1)+i sin(1) corresponds to the angle 1 rad. The direction eix=cos(x)+i sin(x) corresponds to the angle x rad. The direction e2&pi;i=cos(2&pi;)+i sin(2&pi;)=1 corresponds to the angle 2&pi; rad = 1 turn. The direction e2&pi;ix=cos(2&pi;x)+i sin(2&pi;x) corresponds to the angle 2&pi;x rad = x turn. (I like the notation 1x meaning e2&pi;ix, but that is nonstandard). The differentiation operator d/dt has the eigenvalue 2&pi;i&nu; because de2&pi;i&nu;t/dt=2&pi;i&nu;e2&pi;i&nu;t, (or d1&nu;t/dt=2&pi;i&nu;1&nu;t). Here the unit of &nu; is turn per second, such that the unit of &nu;t is turn, and the unit of 2&pi;&nu;t is rad. The eigenfunction is &psi;(t)=e2&pi;i&nu;t (=1&nu;t). Substitute the quantum mechanical equivalence between energy and frequency: E=h&nu;, and obtain the Schrödinger equation: E&psi;=(h/2&pi;i)(d&psi;/dt), saying that the energy is an eigenvalue of the operator (h/2&pi;i)(d/dt) Bo Jacoby 14:23, 18 November 2005 (UTC)

hbar-c
Can I get someone to add a correct value of hbar-c to the article? (hbar times speed of light). My back-of-the-envelope calculation shows that


 * $$\hbar c= 0.197 \;\rm{ eV \cdot \mu m}$$

where &mu;m is a micron. I find this interesting, since semiconductor manufacturing is sub-micron thse days, and one electron-volt is typical of light wave frequencies, and of chemistry (e.g. AAA-size batteries etc, neurons in retina, etc.). I'd like to say the above in the article in some more formal fashion, but not sure how ... linas 00:58, 14 January 2006 (UTC)

Symbol for frequency?
The symbol for frequency was the nu (letter), &nu;. Somebody changed it to f in the beginning, but not throughout.

Niels Bohr used &nu; in the formula $$E=h \nu$$. So did Richard Feynman and Sin-Itiro Tomonaga.

The article on frequency uses f.

Anybody know a reference supporting the use of f ?

Bo Jacoby 19:43, 17 April 2006 (UTC)


 * You have got to be kidding. I see f for frequency *everywhere*. I've seen v only once or twice. Look up frequency physics on google. You'll have a hard time finding v. Fresheneesz 02:01, 20 April 2006 (UTC)


 * Does it matter it's just a symbol. Nu is I think more widely used by physicists and was the original used by Bohr as mentioned above. f is probably more accessible as it's used more in schools and is more easily seen as being the first letter of frequency to those who don't know greek letters. The important thing is to be consistent.Jameskeates 11:05, 14 September 2006 (UTC)


 * I agree on the point of consistency. On the point of $$\nu$$ versus $$f$$, I went through all of the high school only seeing $$f$$ (including AP physics, advanced mechanics, and some general relativity).  However, the current course I'm in dealing with quantum mechanics uses $$\nu$$.  Not sure what any of that means to the decision, if anything, but I do agree the most important point is consistency. Archmagusrm 16:41, 14 September 2006 (UTC)


 * I think the &nu; character looks too much like a 'v'; at least on my system. I first mistook the E=f&nu; equation for E=fv, which looks like it could be possible but obviously doesn't work. It says on the article f that it is a common variable name for frequency. On the other hand, nu (letter) does say that it is the frequency too. However, I think Wikipedia should be accessible to those who are not quantum physicists, too. I, too, have only seen the letter f denoting frequency everywhere, and I have read university physics. As has already been pointed out, f is a lot more common in general. So, would anyone oppose changing all instances of &nu; into f? --ZeroOne 11:32, 19 September 2006 (UTC)


 * Do not change it. In the field of quantum mechanics it is standard. The most important point is not consistency, but communication. If Wikipedia were the only source of knowledge, then yes, change it, but someone reading these articles will have to be translating from Wikipedia's eccentric use of f to the &nu; used by every book and article written on this particular subject since the dawn of quantum mechanics. Its like saying "lets change E=mc2 to U=mc2 to be consistent with the use of U as energy in thermodynamics. It's simply should not be done. Do not change it. PAR 15:16, 19 September 2006 (UTC)

"quantized time" entry in "trivia"
This paragraph contains several statements such as "Well, if time is quantized, then time can be stopped" that definitely need supporting references and further explanation. Moreover, the whole paragraph is pretty vague; I can't tell what point it's trying to make. Is it alluding to the Planck time and energy being on such different scales, since hbar, as the constant of proportionality, is so small? Is it saying something about the uncertainty principle? Is this the right article for speculative musing about the nature of time, which is not an observable in either the Standard model or many of its proposed successors? Certainly, this particular material is far from "trivial"!

As an aside, the paragraph's tone is somewhat philosophical, and comments like "as we all now, people like to pigeonhole theories ever since the dawn of civilization" seem out of place in a serious scientific article.

Could someone who understands this paragraph's intent revise it, please? —Preceding unsigned comment added by Varuna (talk • contribs) 00:22, 15 June 2006

Reasoning for units
The reasoning given for eV units ("because of the small energies that are affected by the uncertainty principle") seems too specific. The reason for using electron volts isn't just for the small energies affected by the uncertainty principle, but rather the small energies found so often in quantum theory. --Archmagusrm 16:07, 10 July 2006 (UTC)

About planck's constant
It has been mentioned in the article that the constant introduced early in 1899 but no hints about its first introduction in the literature and its purposeBaiju George 10:37, 26 July 2006 (UTC)

Trivia section
I think that the information on h-bar should be removed from the article. It's a cool name for a bar in a physics department, but it doesn't add anything to the article. What do other people think? --Apyule 12:47, 2 August 2006 (UTC)


 * As no one has objected, I will move the section to this page in case anyone wants to discuss it.
 * Trivia
 * The coffee shop in the physics and astronomy building at the University of Washington is called the h-bar (usually denoted by the symbolic representation), an obvious play on words.

h/4π or h/2π
See: AvB &divide; talk  00:49, 31 October 2006 (UTC)
 * http://en.wikipedia.org/wiki/Wikipedia:Errors_in_the_Encyclop%C3%A6dia_Britannica_that_have_been_corrected_in_Wikipedia#Uncertainty_Principle
 * http://nostalgia.wikipedia.org/wiki/Uncertainty_Principle/Talk

To plonk or not to plonk
I've removed the unsourced statement pronounced "plank" or "plonk"; from the intro: "plank" is alright for all types of English, but "plonk" (presumably German) has been met with some disagreement recently. To me, the "a" in "Planck" sounds like as in body, pod, father. FWIW, I tried to find a written source myself but couldn't find one in the few minutes I wanted to spend on this. However, for anyone wishing to pursue the issue, there's a sound file at http://www.answers.com/topic/max-planck - the same dictionary also has a sound file for "plonk". AvB &divide; talk  10:48, 20 November 2006 (UTC)

Vandalism of Planck's Constant article
Hi! I believe this article has been vandalised due to repeated ocurrences of junk text interspersed with the article .eg

"Also Electronvolts archenemy megatronobohravolt/einstein is used because of the nermous amount of crap occured in quantum astrophysics which does not even exist."

(Bottom of second pargraph)

I am not qualified to fix without possibly breaking something else, but would like to see if fixed !

Many thanks ! !
 * ) —The preceding unsigned comment was added by 203.89.165.242 (talk) 03:39, 3 March 2007 (UTC).

Title
Surely the title of the article should be Planck constant. Possessive forms are not usually used for the names of physical constants: see. Physchim62 (talk) 16:57, 18 June 2007 (UTC)

Put constant's value in text
One of the uses of this page is as a reference to find the value of the constant. People will come here to pick up a copy of the value of the constant to put into computer programs or documets of their own. So the value should be there on the page in plain text, and not as part of a pretty looking formula that may appear as a graphic. A graphic forces people to retype the value and possibly mistype the value. I don't want to imply that somebody's satellite will go drifting out into space as a result of not being able to copy paste a value from here, but I think you'll get the idea of what I'm saying. Crysta1c1ear 13:59, 25 June 2007 (UTC)

Simple and wrong unity
dim h: Js = wrong! dim h_: Js = wrong! correct: dim Hz = 1/s but what? For frequenzy you mean 1 circle with 2 pi rad. 1 Hz(c) = 2 pi rad/s. dim h: J/Hz(c) ~ J/Hz = Js/(2pi rad) dim h_ : J/(rad/s) = Js/rad. h/h_ = 2 pi —The preceding unsigned comment was added by 87.175.78.31 (talk • contribs) 02:23, 7 July 2007 (UTC)

Heisenberg: dp*dx>h = Js>Js/rad = big NONSENS. dE*dt>h = Js>Js/rad = big NONSENS. df*dt>1/2 = also big NONSENS. And 70 years of some quantum physics too. —The preceding unsigned comment was added by 87.175.99.7 (talk • contribs) 22:56, 19 July 2007 (UTC)

Please sign your talk page contributions. 87.175.99.7, I can't make head or tail of your comment (maybe TeX markup would help you make your point?). Anyway, this was discussed above. I've tried to clear up the confusion in the text by mentioning that the conversion factor is dimensionless. Hairy Dude 23:45, 19 July 2007 (UTC)

Assessment comment
Substituted at 21:55, 3 May 2016 (UTC)