# Talk:Planck units/Archive 3

## The new section on linear solution to get Planck units

We know, literally by definition, that expressed in any system of units, that the 3 principal Planck units (time, length, charge) must satisfy these 3 equations:

${\displaystyle F_{P}=G{\frac {m_{P}^{2}}{l_{P}^{2}}}\ }$
${\displaystyle E_{P}=m_{P}c^{2}\ }$
${\displaystyle E_{P}=\hbar {\frac {1}{t_{P}}}\ }$
along with the fact that in any consistent system of units
${\displaystyle E_{P}=F_{P}\cdot l_{P}=m_{P}{\frac {l_{P}}{t_{P}^{2}}}\cdot l_{P}=m_{P}{\frac {l_{P}^{2}}{t_{P}^{2}}}\ .}$

Those are the equations to solve and, viola, you get the Planck units. If those equations above have the logarithm function applied to both sides, then the powers turn into scalers, multiplication and division turn into addition and subtraction, and you get linear equations:

${\displaystyle \log(F_{P})=\log(G)+2\log(m_{P})-2\log(l_{P})\ }$
${\displaystyle \log(E_{P})=\log(m_{P})+2\log(c)\ }$
${\displaystyle \log(E_{P})=\log(\hbar )-\log(t_{P})\ }$
${\displaystyle \log(E_{P})=\log(F_{P})+\log(l_{P})=\log(m_{P})+2\log(l_{P})-2\log(t_{P})\ }$

So, instead of solving for the Planck units directly (in the unit system of your choice), you are solving for the logarithms of the numerical values of the Planck units in terms of the units of the system of your choice. That recently added section Planck_units#Derivation_by_linear_equations is that. That is all that it is. I am not sure what it adds, but if it is to be added, shouldn't some context (similarly to the above text and math, but better) come with it? Otherwise that section does nothing to add understanding to the concept of Planck units. Also, for a system so small (3 equations, 3 unknowns), why bother to transform it into the log domain just so one can express it as a simple set or 3 linear equations? The Planck unit equations above are solved simply enough.

Can IP user 76.220.108.235 provide a little context and justification for the addition? Why is it needed? What does it add? 96.252.13.17 (talk) 01:51, 2 October 2009 (UTC)

I'm in complete agreement. The article about Planck units need not show exactly how their values (in SI) are determined. It could show how the equations are set up (as above), but that is not necessary. In all sorts of physics articles in Wikipedia, it appears to be beyond the scope of many or most of them to derive all of the theorems. The method recently added in the section that I deleted is cruft. It refers to all manner of unnecessary concepts, such as augmented matrix. There is absolutely no need for it and I see nothing like such discussion in any source regarding Planck units. 162.83.247.140 (talk) 16:52, 14 October 2009 (UTC)
It appears that User:An Justified Wikipedian may be the same as User:76.220.108.235 and immediately reverted the deletion of the cruft with no explanation at all. Just as User:76.220.108.235 never justified the addition of it in the first place. 162.83.247.140 (talk) 16:58, 14 October 2009 (UTC)
Concur that this is a bit of a digression for this article. Any more detail on why it might belong? - 2/0 (cont.) 05:17, 15 October 2009 (UTC)
That section is a trainwreck, so I took it out. More cutting would probably do this article some good. mislih 15:22, 15 October 2009 (UTC)
The linear equations provide a direct algorithm for the derivation. That means that there is no algebra required on the part of the reader. For the average reader, the algebra is likely to represent "guesswork" but the linear equations can show them that there is no guesswork required. On top of that, it expresses the idea in *one equation*. I think that such is helpful. From wikiquote:Stephen Hawking#A Brief History of Time (1988) "Someone told me that each equation I included in the book would halve the sales." It is just there is re-assure the reader that they can understand the derivations if they want or need to.--Popovvk (talk) 16:57, 1 November 2009 (UTC)
Without first setting up what Planck units are (as done above), then applying logarithms to both sides, there is no "derivation", much less a "direct derivation". It is entirely unnecessary, adds cruft, being incomplete mathematically adds nothing to understanding (it's like someone pulled these equations out of their ass). Without logging both sides, it's pretty easy deriving the Planck units from the first principles, there is no need whatsoever to convert the problem to the log domain. As misli says, it's little more than a trainwreak, and you've done nothing to justify it. 96.252.13.17 (talk) 18:23, 1 November 2009 (UTC)

## English variety

This edit made me notice that the article is spelling meter/metre inconsistently. Per WP:ENGVAR (see also WP:SPELL), I suggest deciding upon the variety to be used. Regards, Paradoctor (talk) 00:31, 30 January 2010 (UTC)

## Planck units based on natural constants or natural constants based on Planck units?

Whereas the article broadly discusses the first alternative I'm missing a serious discussion about the second one. I would highly appreciate contributions to that aspect. Thanks. —Preceding unsigned comment added by 79.212.64.5 (talk) 04:22, 24 February 2010 (UTC)

An earlier version of the article had the constants expressed in terms of Planck units, e.g. ${\displaystyle c={\frac {l_{P}}{t_{P}}}}$ but it was taken out. Really, all the issue is how the Planck units relate to the anthropometric units and from that c would be pretty fast. 96.252.13.17 (talk) 06:39, 24 February 2010 (UTC)

My question of course was also looking for expression of the natural constants by Planck units (would appreciate to find them in the article to make it more complete). However, I was also looking for some kind of a discussion on why the Planck units carry the values they are carrying and thereby determine the values of the natural constants. —Preceding unsigned comment added by 79.212.125.159 (talk) 17:11, 28 February 2010 (UTC)

By "natural constants", do you mean these non-dimensionless constants like c, G, ħ, ε0, kB? Those constants are easily solved for in terms of the base Planck units and their numerical values depend solely on the particular units one chooses to use to represent the Planck units, which is essentially an accident of history. If you express your Planck units in terms of SI units, then you will get the values for those dimensioned constants that we see at the NIST site. If you express your Planck unit quantities in terms of Planck units, then the numerical values of all those numbers is 1 (except ε0 which is 1/(4π), and that is simply because of another human convention in defining Planck units).
There is nothing physically deep about those numbers. They are the result of the units we started with to measure things. Then, in terms of those units that we historically decided to use, the values for c, G, ħ, ε0, kB got measured.
Take a look at Fundamental physical constant. I am not sure that you're understanding what's important to Nature and what's just important to mere humans. 96.252.13.17 (talk) 00:40, 1 March 2010 (UTC)
Just for your verification, are these the expressions for these "natural constants" you seek?:
${\displaystyle c={\frac {l_{P}}{t_{P}}}\ }$
${\displaystyle \hbar ={\frac {m_{P}l_{P}^{2}}{t_{P}}}\ }$
${\displaystyle G={\frac {l_{P}^{3}}{m_{P}t_{P}^{2}}}\ }$
${\displaystyle \epsilon _{0}={\frac {q_{P}^{2}t_{P}^{2}}{4\pi m_{P}l_{P}^{3}}}\ }$
${\displaystyle k_{B}={\frac {m_{P}l_{P}^{2}}{t_{P}^{2}T_{P}}}\ }$
They were removed from the article 4 years ago.
A legit question is whether this should have been removed. These equations don't mean much more than a tautology. 96.252.13.17 (talk) 00:53, 1 March 2010 (UTC)

Yes, I mean those constants. May I invite you for the following tautologies:

- take Newton's law of gravitation

- replace G by the Planck units

- set the masses as proton masses (it has been shown that Newton's law also applies to particles like protons)

- re-group the fractions in a way that masses build one fraction, lengths another one and time a third one.

- expand the mass fraction by Planck mass

- transfer the Planck mass out of the denominator of the mass fraction and one Planck length out of the denominator of the length fraction into the denominator of the time-fraction and express the resulting fraction as Planck force.

- in the fraction of masses, substitute them by lengths (based on m=hc/wavelength).

- split the fraction of lengths into two fractions, one related to the square of the size of the protons and one related to the square of the size of the distance between the protons, with squares of Planck length in each denominator.

You will recognize that the gravitational force emerges as a fraction of the Planck force, determined by geometry (the fractions with the squares of sizes can be seen as ratios of sphere surfaces. I.e. sphere surface of a Planck size object related to a proton sphere size and sphere surface of a Planck size object related to the surface of a sphere built by the distance of the photons in Newton's equation).

As I'm not experienced to build formulae with this software I would appreciate if you could display your findings, here. Thanks a lot.

Expressed in words it should read like:

Gravitational force = Planck force * square of Planck length/square of Proton diameter * square of Planck length/square of proton distance.

Want to learn more? Let me know. —Preceding unsigned comment added by 79.212.79.100 (talk) 18:20, 7 March 2010 (UTC)

I really doubt that there is anything in what you mentioned above of which there is anything to learn. "If you can't dazzle them with your brilliance, then baffle them with your bullshit." 96.252.13.17 (talk) 19:49, 7 March 2010 (UTC)

Hm. What nourishes your doubts? Anything wrong? —Preceding unsigned comment added by 79.212.76.83 (talk) 19:49, 8 March 2010 (UTC)

Listen, I know that you would like to think that you discovered something. It is only saying that, measured in Planck units, the gravitational force between two protons is very small. And that is because the masses of the protons (in terms of the Planck mass) is very small. It doesn't have anything to do with the proton diameter, when didn't go into your explanation but somehow appeared in your conclusion. 96.252.13.17 (talk) 23:54, 8 March 2010 (UTC)

No. I don't think I discovered something. Also I don't claim it must be as sketched. I only applied some math. But what makes folks so sure that it has not to do anything with the proton diameter or, better, geometry, or, even better with the ratio of surfaces (the ratio of different ball surfaces mathematically is the ratio of the squares of their diameters, i.e. of lengths, as appearing in the equation). To be clear: I'm not saying that the proton must be a ball, neither that an object sized of a Planck length must be a ball. Nevertheless, I personally think that such a ratio as appearing in the equation simply tells us that only a tiny spot (square of Planck length) on the "surface" of a mass makes a mass (proton, neutron) susceptible to Planck-force coming to bear. And that only a tiny spot of the same size on the surface of a (virtual) ball around a proton (the other proton sits on the surface of the virtual ball at distance d) also determines the susceptibility of a proton for Planck force come to bear.

Net, mathematically it appears that geometry may be the reason why gravitation is such a weak force and thereby probably answers the question Wilczek refused to ask: "Why is gravity so feeble?". —Preceding unsigned comment added by 79.212.88.128 (talk) 20:32, 10 March 2010 (UTC)

Gravity is feeble compared to what? I guess that there likely a nearly equal number of positive and negatively charged fundamental particles in astronomical bodies, because gravity is king there. But compared to the other fundamental forces at work in the atom, it's very weak. EM and gravity are both inverse-square so two protons would repel each other with 1040 times more force than gravity attracts them at any distance. So why then is gravity so feeble compared to EM (at least now you are comparing two forces in a well-defined experiment)? It's because the proton charge is in the ballpark of the unit charge (in Planck units) and the proton mass is much, much less than the unit mass. That's why gravity is weak.
Because the electron mass is even smaller, you can also say that most of the reason that atoms are much larger than the Planck length is because fundamental particles have such small mass (compared to Planck mass). Don't know the answer, but the reason gravity is weak is the same reason that fundamental particles have so small mass which is the same reason that atoms are so large. 96.252.13.17 (talk) 00:36, 11 March 2010 (UTC)

Thanks. The fraction of masses I mentioned in the 7th bullet point early above reads: (Proton Mass)^2/(Planck Mass)^2 which I think is what you are referring to as "the proton mass is much, much less than the unit mass". So, I fully agree to your view that this huge difference makes gravity so small. But let's take that a bit further: as mass equals hc/wavelength we can also state that gravity is so weak because of the huge difference between Planck length and proton (or neutron) "wavelength". But in fact, gravity is not really small per se. As shown in the 6th bullet point above, Planck force (the strongest possible force) obviously plays a fundamental role in gravity as it appears in the law of gravity. It's just the incredibly small probability that the Planck force comes to bear which makes gravitational attraction so small. I hypothesise that this probability is determined by the geometric factor [square of Planck length/square of Proton "wavelength"] * [square of Planck length/square of proton-proton distance]. Now, what does it mean that Planck force comes to bear, although with extremely low probability? I hypothesise that the geometric factor means the following: As a force is the number of impulses * frequency of impulse transmission, the transmission of a Planck impulse only happens if a Planck area (Planck length^2) on the surface of a proton (or neutron) is hit. If it is not hit, no impulse will be transmitted. Also impulse transmission only will happen, if a Planck area on the surface of a virtual ball (radius = proton-proton distance) is hit. If it is not hit, no impulse transmission happens. Hence the geometric factor as described can also be seen as a measure of the - extremely small - probability that transmission of Planck impulses happens. Maybe this is the answer you reported not to know. While the proton-to-proton (or neutron-to-neutron or proton-to-neutron) gravity is extremely small (but not zero), the huge number of such particles involved, e.g. in the earth and in human beings, makes that we directly experience gravity. —Preceding unsigned comment added by 79.212.83.131 (talk) 22:08, 11 March 2010 (UTC)

## Excuse the naivete of a non-physicist

... but since space and time are actually just features of a single phenomenon, spacetime, shouldn't a theory of quantum gravity posit a "quantum" of spacetime that relates the Planck length to the Planck time? —Preceding unsigned comment added by 128.114.162.239 (talk) 18:36, 18 March 2010 (UTC)

Planck length/Planck time = c. c is not only a natural constant but also an upper limit. I.e. speed can take any value between 0 and c but not beyond. And a quantum of speed is 1 Planck length per 1 Planck time. This is because Planck length is the smallest possible distance and Planck time is the smallest possible time interval. —Preceding unsigned comment added by 79.212.79.5 (talk) 02:20, 23 March 2010 (UTC)
Another thing is that i don't think that physicists entirely view space and time as the same exact thing. There is this arrow of time but no corresponding arrow of position, unless maybe you're at or inside the event horizon of a black hole. 70.109.180.126 (talk) 02:52, 23 March 2010 (UTC)

Considering that Planck time^2 is hG/c^5 means that the root of that positive expression, i.e. Planck time, can be positive or negative. Which arrow of time do you want to look to? —Preceding unsigned comment added by 79.212.105.113 (talk) 20:01, 23 March 2010 (UTC)

You can say the same thing about the Planck length or Planck Mass. It doesn't matter. 70.109.176.20 (talk) 21:52, 23 March 2010 (UTC)

## Repeat of 10^60 not really a coincidence

I thought a bit about "The recurrence of the large number 1060 in the above table is a coincidence that intrigues some theorists." Actually, the fact that the diameter and age of the *observable* universe are about the same is just related to the finite speed of light (light must reach us from an object in order for it to be observable), which has been set to 1. The fact the mass and diameter are related is exactly the same "cosmic coincidence" that makes the universe spatially flat to a high precision (this requires general relativity, and here G=1!), this is well-known in cosmology and I believe the theory of inflation in the early universe attempts to explain it. So in fact there is no additional "coincidence" in the fact these numbers are roughly equal in Planck units. —Preceding unsigned comment added by 130.246.135.176 (talk) 17:07, 10 August 2010 (UTC)

## Suggestion: In Table 1 switch columns 2 and 3.

This will match the layout of the other tables in the article. —Preceding unsigned comment added by 173.58.180.116 (talk) 20:07, 10 October 2010 (UTC)

## Planck Epoch

The article reads: "Our understanding of the Big Bang begins with the Planck Epoch, when the universe was 1 Planck time old and 1 Planck length in diameter, and had a Planck temperature of 1."

This is impossible. I understand that the Planck Epoch is determined by a threshold where Planck units are said to have started to apply. This means that also the derived Planck units must have started to apply. One of those is Planck Density. Consequently the today's mass/mass equivalents of the universe must have been compressed into Planck Density. This inevitably means that the diameter of the universe at the end of the Planck epoch cannot have been 1 Planck length.

This leads to the question why an object of Planck density with the mass of the universe "exploded". Black holes of that density do not explode. Answer? —Preceding unsigned comment added by 79.212.55.112 (talk) 08:05, 13 March 2011 (UTC)

## So Mike9110, would you like to justify your edits?

Beginning with this one:

"Planck units are not based on properties of free space, even if some people claim so - statement taken out. ("c" for example is the speed of light; and there is no way to determine G or Hbar without objects."

c is the speed of EM, strong force, and gravitation in what? Some specific material?

Regarding what specific objects is G or ħ measured with? Are you saying that c, G, or ħ are measured with respect to specific objects that have to be defined in advance? That these constants of nature are properties of specific objects? What specific objects would those be?

Did you create your account specifically to take on your perceived "nonsense" in the Planck units article? 70.109.187.84 (talk) 03:15, 17 April 2011 (UTC)

## Planck charge?

What is Planck charge? I think it has no real meaning because it's dimensionless. And why it's definition contains ${\displaystyle 4\pi \epsilon _{0}}$ while others contain only ${\displaystyle G\hbar c}$ (and optionally k)?--Semenov Roman (talk) 18:37, 20 February 2008 (UTC)

It has the same dimension of physical quantity that the elementary charge has. Why it contains ${\displaystyle 4\pi \epsilon _{0}}$ is because that how the math works out. Two Planck charges spaced apart by one Planck length, will exert a force of one Planck force on each other. Also who says that the Planck charge has any G in it? If that's the gravitational G, it does not belong in any expression of the Planck charge. The article is pretty clear about what the Planck charge is and what it isn't (it wasn't defined by Planck originally). 207.190.198.130 (talk) 02:41, 22 February 2008 (UTC)
As with the Boltzman constant, the permittivity was added after the fact and extends the tables only slightly. Both are expendable, but I am tolerant of leaving them in. I added a helpful new section in that article: Planck charge#Physical significance.--Truthnlove (talk) 10:41, 5 March 2008 (UTC)
While I agree that the planck charge has "real meaning," I think that the statement "the charge on the protons is approximately the Planck unit of charge" needs to be corrected, as the charge of a proton is about 1.602 x 10^-19 Colombs, while the planck charge is 1.875 x 10^-18 Colombs, a whole order of magnitude apart! Shouldn't that be clarified? Curious George 334905 (talk) 02:36, 10 July 2011 (UTC)
In the context of the sentence it's in, "approximately" is sufficient. The issue is that the masses of the protons (or any other elementary particle is about 17 orders of magnitude less than the Planck mass while the charge of the protons are 1 order of magnitude less than the Planck charge. And when you consider that, perhaps, a more natural definition of Planck units would be such that normalize 4πG and ϵ0 rather than G and 4πϵ0 as Planck units are normally defined, in that case the elementary charge expressed in these natural units is about 0.30282212 which is not an entire base-10 order of magnitude different. I think the statement stands well as is and "clarification" might just be obfuscation. 71.169.179.85 (talk) 03:32, 10 July 2011 (UTC)

## Recent changes

Recent changes include some arguments that seem dubious to me, such as:

Originally proposed by Max Planck, these units are also known as natural units because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are only one system of natural units among other systems, but might be considered unique in that these units are not based on properties of any prototype, object, or particle (that could be thought of as arbitrarily chosen) but are based only on properties of free space.

Any distinction between a 'property of nature' and a 'human construct' is difficult to maintain since it includes philosophical assumptions that are questionable. Also the distiction is by no means self-evident. A Planck length, for example, could be considered as both a human construct and a property of nature, or even as a human construct without any real physical significance (how do we know length is a natural dimension - it could be how humans interpret things). The distinction is also at odds with the fact that the universe looks well suited to human existence, a fact that some physicists try to explain in terms of the 'Anthropic' argument, while others explain it in terms of 'Intelligent Design'.

Also I don't know how Planck units can be defined as uniquely based on properties of free space. I don't know what is meant by an 'arbitrarily chosen particle' and I don't know what is meant by a 'prototype' etc. I'm sorry but it all looks like gobblygook to me. Does anyone agree with me that the quoted paragraph should be removed? Lucretius (talk) 23:15, 4 March 2008 (UTC)

A prototype is a human-made object that is used as the standard of measurement of some physical quantity to base all measurement of that physical quantity against. Sometimes this standard object is called an artifact.
"Arbitrarily chosen particle" ... So if you are going to define the mass of the electron as your unit mass, why choose the electron? Why not the proton, or neutron, or some quark or boson?
"Property of nature" vs. "human construct". The precise size of our planet is an accident of history. It could have been smaller or bigger by a percent or two and little would have been significantly different, except the metre would have been smaller or bigger by a percent or two. Also why divide the polar circumference of the Earth by 40,000,000? Why not some other number? Who chose that number? Nature or humans?
Finally, I don't know what the anthropic principle or intelligent design has to do with this at all. 207.190.198.130 (talk) 23:38, 4 March 2008 (UTC)

Hi 207 - I get the feeling that you are probably the contributor 'Truthnlove' and that you are defending your own contribution. With all respects, I don't think you have answered my objections. The dictionary meanings of 'prototype' and 'arbitrarily chosen particle' are not in question. I am questioning the validity of their use in the definition of Planck units and I am saying they don't make sense in that context. The paragraph says that Planck units are not the property of a prototype, object or arbitrarily chosen particle - this is to assume that there are no such objects as Planck particles, that the Planck mass is not the prototype of masses, and that it is not an object. How do you know all this? Again, how do you know that Planck units are properties of free space? This is to define free space in terms of the Planck scale. If by 'free space' you mean the energy vacuum, then you have some support for that idea, since many theorists define the vacuum in terms of the Planck scale, but that's still only a theory. The paragraph makes a distinction between natural and human and I am saying this distinction is vague and almost meaningless, particularly in a universe that appears geared to human needs - theorists try to understand this human-centred universe in terms of the anthropic principle and intelligent design, and in this universe the distinction between human and natural is not self-evident. In short, the paragraph is somebody's personal interpretation of Planck units yet it is being presented as orthodox thinking. It is not appropriate. Lucretius (talk) 00:12, 5 March 2008 (UTC)

No, no, no! I ain't Truthnlove (I just undid nearly every change he/she made). I can't tell you who I am, but you know me from before. The issue for Planck units or natural units is that they are defined without measuring the distance from tip of nose to the end of thumb of some monarch that physical reality does not give a rat's ass about. It is not controversial that Planck units normalize quantitative properties of free space because these constants that are normalized exist fundamentally in field equations of free space that make no reference to any particular particle or object.
But if you were to compare to other sets of natural units, you would find that some property (like mass or charge) of some particular particle was chosen (by a human being) as the unit definition (and some other human being might arbitrarily choose something else). Now these other definitions of natural units (like atomic units) might be just as "good" or just as "natural" as Planck units, but they picked a particle and defined the set in terms of that particle. It's no better or no worse than Planck units, but only Planck units (or some variation of it with factors of 4π slipped in) do not require one to pick a "special" particle, object, or "thing" to base it on. Lucretius, this is not controversial stuff, and excluding the [German page], this article has been adopted and translated nearly verbatim by several other Wikipedias. I don't think that would have happened if it was not appropriate. 207.190.198.130 (talk) 01:09, 5 March 2008 (UTC)

I do not care about any of my intermediate changes except ensuring that the order of the dimentions are listed as L M T and that the emphasis on the derivation of the exquations in the second table is clear.--Truthnlove (talk) 01:37, 5 March 2008 (UTC)

Hi 207. Yes I know who you are and I forgive you your sins. But I disagree with your observations. What term in the field equations has any necessary association with Planck units? Do you mean c^4/G ? That is often called 'Planck force' but it is in fact the force associated with any mass self gravitating around its Schwarzscilde radius - in other words, it's typical of any black hole, whatever the mass or scale of the hole. Einstein was not thinking of Planck units when he devised his equations. The association between those units and equations is coincidental and cannot be considered fundamental until science proves that free space is structured according to the Planck scale. Science is a long way from understanding that much!

If the paragraph has been translated into Bulgarian or French or whatever, that merely proves that the translators are not thinking critically about the content - they are probably students of English rather than students of science. Lucretius (talk) 01:52, 5 March 2008 (UTC)

The system of linear equations does not need to be "developed". We do not need to waste space explaining how to solve a 3x3 system of linear equation in the prose because it is handled adequately over in the other article. We do need to show the reader where those formula come from. True, the select group of those who are graduate students "already know that", but it is not obvious to the bright high school student or the below-average college student.--Truthnlove (talk) 02:43, 5 March 2008 (UTC)

I think the current revision looks better. However, I would still delete this bit:

Planck units are only one system of natural units among other systems, but might be considered unique in that these units are not based on properties of any prototype, object, or particle (that could be thought of as arbitrarily chosen) but are based only on properties of free space, as measured by anthropometric units, such as SI. Note that, to have meaning, the Boltzmann constant and the concept of temperature require more than just free space; they require matter.

I think Stoney units could just as well be derived from 'free space', simply by substiting charge for h-bar, and that takes away the Planck uniqueness asserted in the paragraph. Also the inclusion of Boltzmann's Constant indicates that free space is not really a significant context for Planck units. Anyhow, has science actually decided that there is a specific set of constants that define free space? Free space is more a vague ideal than a clearly defined physical reality, as far as I know. The only adequate definition of Planck units is within the traditional context of the equivalence of quantum and gravitational effects. Either that or it should simply be defined in terms of the given constants. But not free space. Lucretius (talk) 04:03, 5 March 2008 (UTC)

I've made a few changes to the article to overcome the objections I raised above. I notice that Table 3 has dimensions listed MLT, yet Truthnlove has changed the order to LMT as in Table 1. Truthnlove might know some good reason for the order he has given (convention in dimensional analysis?) but on the other hand MLT is more like the order for listing SI quantities such as momentum Kg.m./s etc. I don't know enough to decide which order is best and I'll leave it to others. However, I have to agree with 207 that the tour into 'linear equations' seems unnecessary and seems merely to interrupt the flow of things. Surely the idea can be more simply explained as an arrangement of given constants so as to cancel out unwanted dimensions, and then maybe we could add a separate section for derivation from linear equations. I've retained the linear equation explanation in my revision but only out of courtesy to Truthnlove, because Truth and Love are beautiful concepts and I don't want to offend him. Lucretius (talk) 06:07, 5 March 2008 (UTC)

Hi Truthnlove. I'd like to revise this paragraph that you recently included:

Each constant in Table 1 is the primary constant for an important aspect of our universe. c is an aspect of space and time, G is about gravitation of matter, h is about the quantum nature of energy. Epsilon is about the electromagnetic force of static charge. k is the primary physico-chemical constant which describes the conversion of other forms of energy into thermal energy in matter, which is measured as temperature. This latter process will likely lead at some later time to the heat death of the universe. There are other physical constants that could be used to slightly expand this table.

I don't think the heat death of the universe is relevant. I think the constants might best be associated with scientific theories rather than with 'aspects' of the universe. Hence this revision looks right to me:

Each constant in Table 1 is a constant of proportionality associated with one or more scientific theories of fundamental significance for our understanding of the universe. Thus for example c can be associated with Special Relativity, G with General relativity, h with quantum physics, ${\displaystyle \epsilon _{0}}$ with classical electromagnetism and k with Thermodynamics.

Anyhow, that's what I'll revise your edit to unless you have some objection or some better idea Lucretius (talk) 08:29, 5 March 2008 (UTC)

The heat death of the Universe is "an important aspect" of our Universe and is *why* the Boltzman constant gets to be included. It is the "big picture" issue of the nature of heat and temperature and entropy. Entropy is confusing to the layman and death is not confusing. As far as I am concerned, the Boltzman constant is expendable because only two entries to the latter tables: the Planck temperature and that "degrees of freedom" item, but I realize that we are gonna keep it because amateurs love to talk about the temperature of the Universe after the Big Bang, so we might as well explain what it *really* means.--Truthnlove (talk) 10:18, 5 March 2008 (UTC)

This isn't exactly as "in depth" as the rest of the discussion, but while we're talking about the first couple paragraphs of the article...
Originally proposed by Max Planck,"
Planck didn't invent Planck units so much as he laid the groundwork for them. Early on, he didn't even believe that matter was made up of indivisible atoms.(source: Quantum, a Guide for the perplexed, written by Jim Al-Khalili, published by Weidenfeld &Nicolson in 2004. The relevant passage is on page 35.)
The Wikipedia article on Max Planck says that:
At first Planck considered that quantisation was only "a purely formal assumption ... actually I did not think much about it..."
and:
As Planck was deeply suspicious of the philosophical and physical implications of such an interpretation of Boltzmann's approach, his recourse to them was, as he later put it, "an act of despair ... I was ready to sacrifice any of my previous convictions about physics."[8]
He established that energy comes in indivisible units, no one questions that. But I rather doubt that he understood the magnitude of his contribution to science as a whole, let alone that space and time would be subject to the same quantization.Curious George 334905 (talk) 20:53, 10 July 2011 (UTC)
So is it this text in the intro: "Originally proposed in 1899 by German physicist Max Planck, these units are..." or is it the text in the History section that you are taking issue with? If these units were first proposed by someone else before 1899, or even by Planck during some other year, the intro sentence is wrong factually. But I don't think that's the case at all. Otherwise, how do you suggest to make to make it better (more factual, more informative)? Nothing you've typed about whether Planck believed "matter was made up of indivisible atoms" or the "Boltzmann's approach" is particularly relevant to the Planck units. 71.169.189.228 (talk) 00:58, 11 July 2011 (UTC)

It would appear I was wrong. Looking at one of the quotes in the history section, and searching for it with Google, I got the following: http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=APCPCS000676000001000370000003&idtype=cvips&gifs=yes&ref=no
The very same quote shows up in a peer-reviewed scientific article. It would thus appear that Planck did indeed propose the system of units that bears his name.
Though I do retract my original statement, I feel it would be impolite to leave your questions unanswered.
"So is it this text in the intro: "Originally proposed in 1899 by German physicist Max Planck, these units are..." or is it the text in the History section that you are taking issue with?"
I was taking issue with the former. Having read the latter in more detail, it would appear that I was incorrect to take issue with that statement.
"Otherwise, how do you suggest to make to make it better (more factual, more informative)?"
Before I realized that I was incorrect, I would have likely stated that a better sentence would be something along the lines of "The groundwork for these units was laid by Max Planck in 1899 when he established that energy is not arbitrarily divisible..." However, having researched the issue more thoroughly (something I probably should have done before posting... : / ), it would appear that the current sentence is completely accurate/factual/informative.
" Nothing you've typed about whether Planck believed "matter was made up of indivisible atoms" or the "Boltzmann's approach" is particularly relevant to the Planck units. "
Looking back on my post, it would appear that I did stray far from the topic, and I apologize.
Long story short, I was wrong. I retract my previous suggestion that the text in the intro needs any modification.
BTW, I'm here to learn, not to edit the encyclopedia, so the sort of constructive criticism you've been giving me is much appreciated.; ) Curious George 334905 (talk)17:14, 11 July 2011 (UTC) — Preceding unsigned comment added by 70.92.237.225 (talk)
No sweatsky. There was some input recently by some editor who was saying that some particular content was a bunch of crap. The article could certainly be better and some cruft removed, but I do think that it's perfectly factual. Don't confuse Planck units with the Planck constant. 71.169.189.228 (talk) 21:11, 12 July 2011 (UTC)

## SI units of physical constants are out of date

Using the equations and the values of SI units shown in the table produces values for Planck units that do not agree with the values that are shown. For example, using the values of h_bar, G and c to calculate the Planck length l_p gives 1.616252e-35 m. The value shown is 1.616199e-35 m. The reason for the discrepancy is that the SI unit values are wrong (or at least out of date) while the value of the Planck unit is correct. If the current values of the SI units (available at the NIST web site cited in the footnote) are used the correct value is obtained.154.5.32.113 (talk) 03:16, 12 June 2011 (UTC)

It's easily fixed. 71.169.178.122 (talk) 07:29, 12 June 2011 (UTC)

## Planck space-time unit

Multiplying the Planck time unit tP and the Planck volume lP3, we get the fundamental 4-dimensional Planck space-time unit:

${\displaystyle t_{P}\;l_{P}^{3}={\sqrt {\frac {\hbar G}{c^{5}}}}\;{\sqrt {\frac {(\hbar G)^{3}}{c^{9}}}}}$

which reduces very nicely to:

${\displaystyle t_{P}\;l_{P}^{3}={\frac {(\hbar G)^{2}}{c^{7}}}}$ = 2.27728 × 10−148 m3s

Interestingly, this is also equivalent to:

${\displaystyle {\frac {(\hbar G)^{2}}{c^{7}}}=\hbar {\frac {\hbar G^{2}}{c^{7}}}={\frac {\hbar }{p_{P}}}}$

where pP is the Planck pressure.

I'm not sure if this is noteworthy enough to go into the tables or not. — Loadmaster (talk) 20:27, 25 August 2011 (UTC)

## Question about Planck Units in 11 Space-Time Dimensions

What if Law of Gravitation is different on subatomic scale where all 11 dimensions are flat?

${\displaystyle F=\Gamma ^{*}\cdot {\frac {Mm}{r^{9}}}}$

Will it change Planck units?

Mikhail Vlasov
Korablino (talk) 03:24, 20 October 2011 (UTC)

What means "mass" on subatomic scale? Is it the same as on atomic scale? If not, the equation cannot be solved. The real question is: do the natural constants apply on subatomic scale? If not, all equations based on natural constants become meaningless in the subatomic world.

What supports the assumption that natural constants also apply on subatomic scale? The fact that not only the natural constants define the Planck units but that the Planck units, which are really subatomic, in turn define the natural constants. I.e. if the Planck units are defined by whatever real conditions which build the subatomic world, this subatomic world also would define the natural constants and thereby the atomic world. I.e. if e.g. Planck Particles, based on Planck units, build the subatomic world, their properties also define the atomic world via Planck units and the natural constants. — Preceding unsigned comment added by 79.212.29.214 (talk) 03:02, 26 October 2011 (UTC)

But Planck mass does not belong to subatomic scale. It is too big.
That is why I am questioning the Law of Gravitation for distances less than Bohr radius. If Law of Gravitation is different on this scale – all Planck units will change.
Mikhail Vlasov
Korablino (talk) 23:10, 28 October 2011 (UTC)

Don't think that numerical values determine whether a Planck unit belongs to atomic or sub-atomic scale. Think we have to view the Planck units as a whole. We cannot say Planck length belongs to the sub-atomic scale because it is so short and Planck mass belongs to atomic scale as it is so big. — Preceding unsigned comment added by 79.212.44.21 (talk) 08:18, 30 October 2011 (UTC)

Agree. Planck units do not belong to any scale.
Still think Planck Units have this property because they are derived from the Law of Gravitation measured only on human scale and above. No data on gravitation on smaller scale.
Mikhail Vlasov
Korablino (talk) 00:40, 1 November 2011 (UTC)

The usual view is that Planck units are determined by the natural constants. The unusual view is that the Planck units determine the natural constants. I.e. whatever determines the properties of the Planck units it thereby also determines the properties of the natural constants, derived from Planck units like e.g. c = Planck length/Planck time. — Preceding unsigned comment added by 79.212.36.40 (talk) 20:54, 3 November 2011 (UTC)

## Other possible normalizations

35G = 1. This would simultaneously approximate the Rydberg constant, the unified atomic mass unit, the Bohr radius, charge and mass of an electron to integer powers of twelve. Of course, this is simply accidental and does not have theoretical meaning. However, I think that there is educational merit because this relation is effective to recognize scale of nature (or fundamental physical constants). — Preceding unsigned comment added by SGB02104 (talkcontribs) 21:44, 6 December 2011 (UTC)

These are examples.

Item Expression Error from
Maximum density of water 1.064321×12^(-84) 6.432% 1
Rydberg constant 1.000955×12^(-25) 0.095% 1
Typical photon energy (at 540THz) 1.032317×12^(-25) 3.232% 1
Electron mass 0.949265×12^(-20) -5.074% 1
Unified atomic mass unit 1.001391×12^(-17) 0.139% 1
Proton mass 1.008678×12^(-17) 0.868% 1
Elementary electric charge 1.025095×12^(-1) 2.509% 1
Stefan-Boltzmann constant 1.973921×12^(-1) -1.304% 2
Planck length 2.028370×12^(-1) 1.419% 2
Specific heat of water 0.502520×12^(+17) 0.504% 1/2
GCD of a year and a day (11minutes15seconds) 0.999961×12^(+42) -0.004% 1
The age of the solar system (4.6 billion years) 2.009906×12^(+55) 0.495% 2
The age of the universe(13.75 billion years) 0.500301×12^(+56) 0.060% 1/2

--SGB02104 (talk) 12:45, 8 December 2011 (UTC)

## Two Pi or Not Two Pi?

One question I don't see addressed in the article or the talk page is whether the 2pi component should or should not be included in the definitions of the Planck parameters, i.e., whether to use Planck's constant as is or in its "reduced" form. I have seen the question dismissed as irrelevant because it has no dimensional impact, but it does in fact make a difference, not only in numerical values. My observation is that 2pi is included more often than not, but there are examples without it, e.g., as I recall Chris Isham's article in "The New Physics" (1992, editor Paul Davies). The reason why I think the 2pi should be omitted is that doing so makes the Planck energy the same independently of whether it is defined as h*Planck_frequency or Planck_mass*c^2. That relationship is lost if the 2pi is included.

A side point: it might expand the article in a useful way to add the Schwarzschild radius for the Planck mass, which is twice the Planck length with or without the 2pi, and the Compton wavelength for the Planck mass, which is equal to the Planck length if you leave out the 2pi, otherwise it is 2pi times the Planck length. I don't claim that there's necessarily any compelling evidence from that whether the 2pi is a good or bad idea.

I found Mikhail Vlasov's point interesting about gravitation being measured only on macroscopic scales. My feeling is that Einstein did not expect its value to depend on scale, but that is because he considered spacetime to be a continuum, and while it is generally agreed that GR "breaks down" at the Planck scale, that does not imply that the numerical values of its constants change, just that the continuum geometry loses relevance.

I believe that the Planck parameters are more than just a curiosity. I agree with R. Sorkin's remarks (1998, "Black Holes and Relativistic Stars", editor R.M. Wald) that the relationship between the entropy of a black hole and the number of Planck-length-sized tiles covering its event horizon is a clue in the search for Quantum Gravity analogous to the relationship between thermodynamic entropy and statistical mechanical entropy, part of another transition from continuum physics to discrete-granularity physics.

John W. Fowler IPAC, Caltech 71.119.249.126 (talk) 21:02, 13 February 2012 (UTC)

I'm surprised and skeptical that you'll find anyone who says "h=1 in Planck units" rather than "hbar=1 in Planck units". It would be great if you could double-check the citation. For example, CODATA agrees with the value of Planck mass based on hbar.
A photon oscillating with angular frequency 1 in Planck units has an energy of 1 in Planck units. A photon oscillating with ordinary frequency 1 in Planck units has an energy of 1/2pi in Planck units. With h instead of hbar, the ordinary frequency would be 1, but the angular frequency would be 2pi. They can't both be 1 of course. In particle physics, angular frequency tends to be a more natural thing to think about than ordinary frequency, so it makes sense that they chose to focus on the photon with angular frequency = 1, not ordinary frequency = 1. --Steve (talk) 00:01, 14 February 2012 (UTC)
Of course it is and should be ħ rather than h. Using ħ it's energy E = ω = m as it should be. The idea is to simplify the fundamental equations of interaction, in this case Schrödinger equation or the "Planck's relation for energy and angular frequency". The only mistake that Planck made in 1899 was to normalize G instead of normalizing 4πG. And he should have explicitly defined the Planck charge as qP = (ε0ħc)1/2. But normalizing h instead of ħ is not a good idea. 70.109.182.97 (talk) 03:57, 14 February 2012 (UTC)
> "I'm surprised and skeptical that you'll find anyone who says "h=1 in Planck units" rather than "hbar=1 in Planck units".
Isham didn't say that exactly; he was not dealing with normalized units of that type. He just made the fundamental definitions in terms of h (not hbar), G, and c. I'll be at my office tomorrow and get more information from the book, but you can probably see the page(s) of interest by going to Amazon.com, search books for "The New Physics" (Paul Davies, editor), and search inside the book for "Planck length". It's the first reference found; you might have to zoom in to see whether there's a slash on the h.
I am always uncomfortable with defining certain constants to be unity; as soon as some GR text says "We will work in units of G=1", I start worrying that twelve pages on there's going to be some equation that is not fully general and we'll have lost track. I don't find it at all off-putting to keep all the constants in the equations by name. But in any case, my point was just that if you define the Planck length, time, and mass with h instead of hbar (with no setting anything equal to 1), then the Planck energy defined as h/Planck_time is the same function of h, G, and c as the Planck energy defined as Planck_mass*c^2. That does not happen if you use hbar consistently throughout.
I don't doubt that NIST uses hbar; Chandrasekhar used hbar. But I don't recall seeing the Planck energy defined elsewhere as anything other than Planck_mass*c^2, so I can't rule out the possibility that no one ever noticed that it's also h*Planck_frequency if and only if you use h instead of hbar,
Sorry to break in, but John, it is ħ*Planck_frequency if the frequency is angular frequency. And, if you've had a course in calculus, you'll understand that angular frequency is more fundamental. There's a reason they came up with ħ to replace h. And there's a reason why it's ε0, and not 4πε0. But if they were thinking, it would not be G as it is presently presented. 70.109.182.97 (talk) 04:44, 15 February 2012 (UTC)
Yes, it is either E = h*nu or E = hbar*omega. My point is: look at the Planck energy expressed in terms of G, c, and either h or hbar, and see which of the latter gives you Planck_mass*c^2 = h*Planck_frequency, where I mean 1/Planck_time by Planck_frequency, not 2pi/Planck_time.
You still don't get it, John. They both satisfy Planck_energy = Planck_mass*c^2 = ( h | ħ )*Planck_frequency. And in both cases Planck_frequency = 1/Planck_time. It's just that in one case, the "1" is 1 cycle and in the other the "1" is 1 radian. I am now becoming convinced that you haven't learned what you should have learned in calculus. Do you know why the natural measure of an angle is in radians? Do you understand how the derivative of sin(x) is cos(x) with no scaling, but only if x is in radians? Not degrees, not grads, not cycles, not turns, but the angle is in radians. And "radian" is not a dimensionful unit. When angles are in radians, it's just a number with no units at all attached.
You have to figure that out. Because nothing else you say here about h vs. ħ has any consequence at all until you get the concept of the mathematically pure and natural measure of an angle. Since Wikipedia talk pages is not really the place for this, you should take this to Wikipedia:Help desk for help in understanding this, or better yet to a web site like http://physicsforums.com/ to ask about this, because there is clearly something fundamental that you are not understanding.
In other words, let me do it my way, with h, not hbar; then (sorry for the ASCII equations) Planck_time = sqrt(G*h/c^5), Planck_frequency = 1/Planck_time, Planck_mass = sqrt(h*c/G); then if we say the Planck energy is Planck_mass*c^2, we get sqrt(h*c^5/G), and if we say that the Planck energy is h*Planck_frequency, we get sqrt(h*c^5/G), the same as before. If instead you use hbar throughout, you don't get h*Planck_frequency = Planck_mass*c^2.
And that is wrong and is missing some very fundamental concept.
I don't expect to be dealing with this anymore. Check out the physicsforums.com site. Or go to the sci.physics.foundations USENET newsgroup. They can help you there. 70.109.182.97 (talk) 19:43, 15 February 2012 (UTC)
> that is wrong and is missing some very fundamental concept.
Sorry, but "some very fundamental concept"?! I gave my argument in mathematical terms, so if it's wrong, it should be refutable in mathematical terms, not as "missing some very very fundamental concept". It seems to me that you are saying that E = h*nu AND E = hbar*nu. The latter is what you get with the use of hbar in all the fundamental definitions of Planck parameters; I claim that it is wrong. The definitions of the Planck parameters are unequivocal about where the 2*pi factors do or do not go. And if these definitions are anything other than purely arbitrary with respect to the use of h vs. hbar, I would appreciate a reference to where the compelling arguments are, because in 40 years as an astrophysicist I have not seen them. The only thing approaching a compelling argument of which I am aware is the one I am making here. I apologize if I have been unable to make it clear. It seems very simple to me. If you use hbar consistently in the definitions, then you get the Planck energy as hbar*nu, which is incorrect; you don't get hbar*omega (where omega is 2*pi*nu), nor do you get h*nu, both of which are correct. I have never seen a reference that claims E = hbar*nu; it is simply wrong. And whether the Planck frequency is 1/Planck_time or 2*pi/Planck_time is not ambiguous and subject to interpretation, it is unequivocally determined by the definitions of the basic Planck parameters. There are no factors of 2*pi floating around that one can attach or not as one desires.
>the angle is in radians. And "radian" is not a dimensionful unit. When angles are in radians, it's just a number with no units at all attached.
And therein lies the fundamental issue that I raised in the first place (assuming that "dimensionful" is actually a word).
>I don't expect to be dealing with this anymore.
I agree that we have flogged this one to death. Besides, if we go on much longer, we seem to be in danger of indenting ourselves into a black hole. I'm getting the impression that Wikipedia is not the place to publish original ideas, just established orthodoxy that has been published in the professional literature, and that's OK with me, I suppose that's the function of encyclopedias. But in closing, I would like to say that in my opinion, my argument that one should get the same answer for the Planck energy using either E = Planck_mass*c^2 or E = h*Planck_frequency (or hbar*2*pi*Planck_frequency, but no other combination) based on the fundamental definitions of the Planck time, length, and mass, is checkmate. Troublemakers are welcome to contact me via my Caltech email address, jwf@ipac.caltech.edu. John W. Fowler, IPAC, Caltech 71.119.249.126 (talk) 22:27, 15 February 2012 (UTC)
I think you should get the same answer for the Planck energy no matter which of Einstein's two equations you use, E = h*nu or E = m*c^2, applied to the Plank parameters.
--- John W. Fowler 71.119.249.126 (talk) 06:36, 15 February 2012 (UTC)

and that fact carries more weight with me than arguments based on the behavior of "normalized" units, with which as I say I am not comfortable and which may therefore be tripping me up, but if the only correct definitions are those using hbar instead of h, I won't understand why until the reason is expressed in terms of the Plank energy. Thanks for your thoughts! — Preceding unsigned comment added by 71.119.249.126 (talk) 21:34, 14 February 2012 (UTC)
Sorry, forgot to sign.....
John W. Fowler, IPAC Caltech 71.119.249.126 (talk) 21:38, 14 February 2012 (UTC)

Well, this was a poorly organized series of comments. Anyways, what's being missed here seems to be that the 'Planck frequency', defined as 1 over Planck time, is already an angular frequency, and therefore corresponds to omega rather than nu. John seems to have interpreted E=h*nu to be the same as E=h*Planck_Frequency, based on the statements "[it should be that] E = h*Planck_frequency" and "...you should get the same answer for...E = h*nu or E = m*c^2, applied to the Plank parameters." 150.35.244.246 (talk) 04:57, 15 June 2012 (UTC)

Well, you're right and I think that John is wrong. A radian is not a dimensional unit of measure, it's hardly (IMO) in the same class of concepts as units of measure. By normalizing ħ instead of h, equations such as the Schrödinger equation is most simplified (no silly factors of 2π in there) and then the Planck frequency is one radian per Planck time, not one cycle per Planck time. The issue is no more complicated than that. 70.109.182.206 (talk) 20:35, 15 June 2012 (UTC)
Well thanks for un-indenting! But you all are still missing the point, or making incorrect ones. "what's being missed here seems to be that the 'Planck frequency', defined as 1 over Planck time, is already an angular frequency": sorry, absolutely wrong. What's so hard about understanding the difference between 1/T and 2pi/T? Given that "T" is the period (which it is), the former is a frequency measured in Hertz, the latter is an angular frequency measured in radians/s. If someone thinks that frequency defined as 1/T is already an angular frequency, then what is 2pi/T? And I never said that a radian was dimensional, but it still matters where you place factors of 2pi. Suppose that we agree that you will pay me $10/week for my clarifications; would you agree that I can then legitimately claim that you should pay me 2pi*$10/week because that is the same thing? After all, a frequency is a frequency, independently of factors of 2pi, right? (Yes, I'm kidding). "John seems to have interpreted E=h*nu to be the same as E=h*Planck_Frequency": you DID get that right, assuming that like me, by Planck_Frequency you mean 1/Planck_Time. "By normalizing ħ instead of h, equations such as the Schrödinger equation is [sic] most simplified (no silly factors of 2π in there) and then the Planck frequency is one radian per Planck time, not one cycle per Planck time." That would be wrong if it weren't "not even wrong", since the Planck frequency would have to be 2pi radians per Planck time to make your argument work, not just a single radian per second. But again, even 2pi radians per Planck time has to be multiplied by hbar, not h. And incidentally, I'm not objecting to the use of hbar in the Schroedinger equation(s); I agree that there are merits to that, but it's irrelevant to the question of defining the basic Planck parameters. Deciding whether to divide Schroedinger's equation (any one of them, as long as you do it to both sides) by 2pi has no bearing on the Planck parameters. I'm just pointing out an issue of internal consistency in those definitions, and with h throughout they are self-consistent, and with hbar throughout, they are not, plain and simple, because of the latter's failure to get the two expressions for Planck energy to be the same. -- John W. Fowler 71.107.59.217 (talk) 00:20, 23 June 2012 (UTC)
I really wish you would stop discussing what Planck units should or shouldn't be, and start discussing what Planck units actually are. In Planck units---at least Planck units as defined in every reference and textbook I've ever seen---the photon whose period is 1 planck time has an energy of 2pi/c^2 Planck masses, not 1/c^2. This is not an "inconsistency" unless you had some reason to expect otherwise. Maybe you have seen some textbook that says "the photon whose period is 1 planck time has an energy of 1/c^2 planck masses"? If you've seen that, can you please tell us what textbook it is that says that?
If you are defining "John W. Fowler units" you can think hard about whether you would prefer to normalize hbar or h. I have no opinion, you can choose to normalize whatever you please in your own personal system of units. But on this webpage we should really be discussing Planck units---i.e., Planck units as the term is used by physicists, defined in textbooks, etc.---not John W. Fowler units. --Steve (talk) 03:17, 23 June 2012 (UTC)
And I also can think of better normalization choices than Planck. The bestest, mostest naturalest physical units are those that normalize c (not αc as the unit speed), ħ (not h), 4πG (not G) and ϵ0 (not 4πϵ0 and not e). And, John, to use your rhetoric, "What's so hard about understanding the difference" between angular frequency and the common notion of frequency? And that, if you're doing physics, you're doing calculus and then angular frequency is more fundamental. A wheel, with radius r that spins at an angular frequency of ω will roll on the ground at a speed of ω×r (not at ν×r where ω=2πν). Sorry John, but your case holds no water. And that makes it hard to be persuasive. Even if we were free to redefine "Planck units" however we wanted. 70.109.186.162 (talk) 05:53, 23 June 2012 (UTC)
"But on this webpage we should really be discussing Planck units---i.e., Planck units as the term is used by physicists, defined in textbooks, etc." Physicists certainly also talk about Planck PARAMETERS, as they are shown in Table 2 of the main page; the actual values are given there in mks units. It is only when you proceed to redefine units to make one of these 1.0 that you get into Planck UNITS, a much less interesting subject to me. Leaving the Planck PARAMETERS in mks or cgs units is the natural thing to do when one's purpose involves relating these parameters to the real physical world. For example, in a 4-D spacetime composed of granules that are one Planck length in each dimension, one cubic centimeter of space propagating through 1 second of time involves about 1.0e144 granules (using my preferred h instead of hbar); if the propagation is subject to noise, let's take Poisson noise as an example, then the number of granules is 1.0e144 plus or minus 1.0e72. Thus you would have to measure the energy in that cubic centimeter of "vacuum" with an instrumental precision of 72 decimal digits to detect a one-sigma fluctuation. We would not know whether energy conservation is more than a holdover from classical thermodynamics unless we could perform measurements with 72 decimal digits of precision and accuracy. THIS has some relevance to quantum gravity. It is not affected critically by whether you use h or hbar in your definitions, but that does matter more than I would like to ignore. Do you see what I'm getting at? I don't care a fig about "normalizing" to Planck units, I want to use the PARAMETERS to do physics, and there is reason to suspect that spacetime IS granular, and there is reason to suspect that the granule size may be 1 Planck length (to within some possible fluctuations in the 4-D sphere-packing model).
"if you're doing physics, you're doing calculus and then angular frequency is more fundamental." Neither is "more fundamental"; the proper one is determined by the problem you're solving. And every one agrees that in quantum mechanics, E = h*nu, not hbar*nu, not h*omega (hbar*omega is OK, but it is much more rarely seen than just h*nu).
So in conclusion (I hope): the Planck time is how long it takes light to travel one Planck length, NOT one Planck length divided by 2pi. So its inverse is a frequency in Hertz, not an angular frequency in radians/s. It follows that the Planck energy should be h*Planck frequency, and if and only if you used h instead of hbar throughout your definitions, then h*Planck frequency will be the same combination of G, c, and h as Planck mass times c^2. QED -- John W. Fowler 71.107.59.217 (talk) 08:40, 23 June 2012 (UTC)
"Neither is 'more fundamental'..."
This is an indication that you don't do calculus. There is a fundamental reason that the sinusoidal functions, that is sin(θ) and cos(θ), are defined mathematically with their argument in radians and not in terms of "turns". And it is the same reason that the natural exponential function has e as its base. There is a fundamental reason why, when you compute the complex logarithm that the real part of the result is the natural logarithm (that is base e) of the modulus of the argument and the imaginary part of the result is the angle of the argument in radians. Not degrees, not grads, not turns.
John, you're only demonstrating ignorance and WP:IDHT. It is you, who do not get it. You're simply wrong and you evidently do not understand it. 70.109.186.162 (talk) 17:36, 23 June 2012 (UTC)
Sorry, whoever you are, but your rant is irrelevant to the subject of this talk section. In my 40 years as a professional astrophysicist, I not only "do calculus" but have contributed fundamental theorems.
What fundamental theorems of calculus have you contributed to? What record of work as a professional astrophysicist do you have? There is a "John W. Fowler" at Arizona State but he's an engineering prof. and there is a LinkedIn page with a "John W. Fowler" in the Atlanta area. and your IP puts you in Los Angeles.
"What fundamental theorems of calculus have you contributed to? What record of work as a professional astrophysicist do you have?" You surely don't think this talk section is the appropriate place for that do you? We've already been criticized for flogging irrelevant points. My email address is above; send me a request there, and we'll continue this offline. But let's be clear: I never claimed to have invented the Fundamental Theorem of Calculus. I have contributed original theorems USING calculus, which addresses the charge that I am unfamiliar with calculus. The areas in which I have made original contributions include statistical mechanics, probability and statistics, estimation theory, and (drum roll) pure trigonometry. (Please forgive my being facetious, but this whole digression IS pretty ridiculous.) 71.107.59.217 (talk) 03:49, 25 June 2012 (UTC)
I know the difference between the two forms of frequency. If one should eschew the Hertz form of frequency, then someone should have told Einstein that he was demonstrating his ignorance by saying "E=h*nu" (also Planck earlier, but Planck was talking about different oscillators; they were however OSCILLATORs, things that know about sines and cosines). I'll be happy to be judged at the same ignorance level as Einstein. 71.107.59.217 (talk) 19:10, 23 June 2012 (UTC)
Well, you're being judged by someone more ignorant than Einstein. In defining Planck units, he actually did define them in terms of ħ not h. This does not mean that Planck made the best decisions about it. He missed it, in my opinion, by normalizing G instead of 4πG, but unless physicists had, in a widespread manner, evolved the definition from what Planck initially had, then it is inaccurate for Wikipedia to report anything else. But you still don't impress me with your knowledge of calculus and I doubt you're the 40-year professional astrophysicist you say you are. Can you tell me what, in calculus and differential equations, the role of base e for exponential functions are and why expressing the argument of trigonometric functions in terms of radians is? Why do mathematicians define the exponential and trig functions that way? A 40 year professional astrophysicist would have no problem answering that. (And in doing so, would know why angular frequency is more fundamental in physics and mathematics than "ordinary" frequency.) 71.169.181.222 (talk) 02:43, 25 June 2012 (UTC)
"Well, you're being judged by someone more ignorant than Einstein." Thanks; I didn't want to say that myself.
"But you still don't impress me with your knowledge of calculus" That certainly wasn't what I was trying to do; I couldn't care less about impressing you. I merely wanted to end a dead-end discussion. My offer to correspond with you via email is not for the purpose of impressing you either, just to fulfill my obligations as a scientist to answer questions from the public (up to a point!). One need not be much of an expert to know the difference between the two types of frequency, which by the way are more relevant to trigonometry than calculus, but of course appear not only in both but also other places. But please note that the equation "E=h*nu" contains no trig functions, rendering claims based on their arguments irrelevant. Let's continue this via private email. But maybe you'd like to make a wager first about whether I received my Ph.D. in 1972 with a dissertation on the effects of atomic bound-bound transitions on the structure of stellar atmospheres and have worked in astrophysics ever since? -- John W. Fowler 71.107.59.217 (talk) 03:49, 25 June 2012 (UTC)
Your contention is three things (1) There is something called "the Planck frequency" (2) which is the reciprocal of the Planck time, (3) and is also equal to the Planck energy over h [not hbar]. If you believe all three of these assertions, then certainly there is an inconsistency. But I've never seen any textbook or physicist assert that all three of these things are true. Even just (1) is rarely if ever asserted in the literature. Therefore there is no inconsistency after all. ...Unless you can show us some evidence that all three of these things are believed to be true by physicists.
Likewise, can you please direct me to any textbook or reference where the Planck length is ${\displaystyle {\sqrt {\frac {hG}{c^{3}}}}}$ rather than ${\displaystyle {\sqrt {\frac {\hbar G}{c^{3}}}}}$? When you say "You can define the Planck length either way", I emphatically disagree unless textbooks and other reliable sources have actually defined the Planck length either way. You are not personally entitled to decide how the Planck length is defined, any more than you are entitled to make up your own definition of any other widely-used technical term. --Steve (talk) 13:16, 23 June 2012 (UTC)
I do believe the three assertions you listed.
"I've never seen any textbook or physicist assert that all three of these things are true. " You may be right about (3); it may be that it has simply not been considered, which is why it has not been noticed that the hbar definitions yield two different Planck energies, Planck_mass*c^2 and h*Planck_frequency, with different combinations of G, h, c, and pi. It was to probe that possibility that I added this talk section. It seemed obvious to me that the hbar definitions were wrong by virtue of this inconsistency, but it struck me as peculiar that lots of people hadn't noticed. It was exactly because I did NOT want to go off on my own tangent that I looked for provable dissenting opinions.
As for (1), Wikipedia itself has a page on it; however, that page has its own unresolved debate raging on its talk page, and I see that many of the points I made here were made there (by other people!). The core of that debate is the page's arbitrary definition of 1/Planck_time (with the hbar definition) being an ANGULAR frequency (omega below). If that assertion is allowed to stand, then the subsequent evaluation of hbar*omega, which is simply h*nu, does indeed consist of the same combination of G, h, and c as the corresponding Planck_mass*c^2 (where of course hbar was used in the Planck_mass expression). So if that assertion stands, then the hbar definitions have no self-consistency problem. But that assertion cannot stand; it seems that it was made only to ACHIEVE that identical expression for the two Planck energies. The result of that expression does not differ from mine by a factor of 2pi, in fact; the ratio is sqrt(2pi). Now if the Planck time is how long it takes light to travel one Planck length, why is its inverse an ANGULAR frequency? No justification is given. If some process has a period of T, then its regular frequency (as opposed to angular frequency) is 1/T and its angular frequency is 2pi/T. That is the essence of that page's unresolved debate.
As for pointing out references where the Planck length is defined with h instead of hbar: I gave one in my opening paragraph of this section, Chris Isham in "The New Physics". I have also seen it in numerous books, although I'll grant that the hbar definitions are more common. If you'll accept a webpage as a reference, see Eric Weisstein's "World of Physics" definitions (under the Mathworld aegis): http://scienceworld.wolfram.com/physics/PlanckLength.html which gives BOTH definitions (h first,then hbar) and similar pages for Planck time and Planck mass. He gives a reference to a book by Frank Shu, "The Physical Universe", in which Shu derives the Planck mass first by what I consider a slightly hand-wavy argument based on comparing the Compton wavelength to the Schwarzschild radius, and he gets the definition with h instead of hbar. As I pointed out early on, one can define the Planck parameters either way because they were originally constructed purely from dimensional analysis, and factors of 2pi floating around have no effect on that. Presumably the factors should be applied consistently, and that is the case in what I've seen, no mixing h and hbar in the same set of definitions.
"You are not personally entitled to decide how the Planck length is defined, any more than you are entitled to make up your own definition of any other widely-used technical term." I could not agree more strongly with you! Let us end on that amicable note. -- John W. Fowler 71.107.59.217 (talk) 19:10, 23 June 2012 (UTC)

Is there anyone besides the IP editor 70.109.182.120 who thinks that "semi-humorously" needs to have a wikilink to tongue-in-cheek? This seems like a pretty clear case of overlinking to me, but the IP editor seems very insistent on keeping it in the article. Zueignung (talk) 06:02, 5 January 2013 (UTC)

So when a physicist (like in the citations) say that "Planck units are God's units", he or she is kidding because God would never use those units?
Or maybe when a physicist says that "Planck units are God's units", he or she is joking that Planck is God?
Or maybe when a physicist jokes that "Planck units are God's units", he or she means that God is playing jokes on humans leaving us with these Planck units?
Or maybe the physicist is saying it with tongue firmly planted in cheek. 70.109.182.120 (talk) 06:51, 5 January 2013 (UTC)
The definition of wikt:tongue in cheek is not intended seriously; jocular or humorous. Wikilinking the phrase "semi-humorously" to tongue-in-cheek does not serve to disambiguate the meaning of the sentence. This is a textbook example of how not to use wikilinks—you should read WP:OVERLINK, where the very first bullet point says, "Unless they are particularly relevant to the topic of the article, avoid linking everyday English words that are expected to be understood in the general context." Zueignung (talk) 06:58, 5 January 2013 (UTC)
Will you eventually stop patronizing others? Do you actually think that no one else can read? Or derive meaning from what they read?
You're wrong, and it doesn't appear that you can tell which one the physicist means when they say "Planck units are God's units." Don't assume that other people read exactly like you do. Also, even though there are versions of this article in other languages, some are totally different and others are translations of old versions of this English-language article and some non-native English-language readers may be trying to decode this article. They also might wonder in what manner is the humor.
Again, don't assume that because you don't seem to get the connection, that the connection doesn't exist.
And, even though you have made some nice cleanups (that do not go unnoticed nor unappreciated), don't assume that every one of your edits help. Most have, not all. Try not to take yourself so seriously that you just cannot handle an edit of yours getting reverted. That gets sorta anal retentive or micro-controlling. It's not a pun, it's not sarcasm nor mockery, it's not parody nor spoof. When physicists say that "Planck units are God's units", it's tongue-in-cheek.70.109.182.120 (talk) 08:11, 5 January 2013 (UTC)
I've linked this discussion to WT:PHYS so that it may benefit from more input. Zueignung (talk) 08:27, 5 January 2013 (UTC)
I agree with Zueignung. It's partly overlinking, partly over-piping (along the lines of WP:EGG), just in general not useful or relevant. --Trovatore (talk) 09:03, 5 January 2013 (UTC)
Same here. To be fair, the IP appears to be making a huge fuss over nothing. M∧Ŝc2ħεИτlk 09:04, 5 January 2013 (UTC)
I fixed it by removing semi-humorously entirely. Neither of the refs assert that the physicists are joking. If it's obvious that they're joking, let the readers figure it out for themselves. --Trovatore (talk) 09:07, 5 January 2013 (UTC)
I stripped out the entire claim, as it appears to be a misrepresentation of the sources. Not everyone who writes about physics should be referred to as a physicist. — Quondum 10:02, 5 January 2013 (UTC)
Hmm — I take your point, but it strikes me as maybe going a little overboard to remove the entire phrase just because the reference doesn't support the characterization of the users of the terminology as physicists. How about a nice passive voice: "Planck units are sometimes referred to as God's units"? Note by the way that God's units redirects here, and it's likely that users will sometimes use it as a search term, so it would be nice to have some explanation on this page as to why they wound up here. --Trovatore (talk) 10:12, 5 January 2013 (UTC)
I have no objection to my edit being reverted (including reverting the removal of references, of course), while making the change you suggest here. One might even want to refer to the context (e.g. popular science, or whatever). — Quondum 10:52, 5 January 2013 (UTC)
God uses cubits, to say otherwise is a capital offense in some countries. Are we sure this usage isn't the same as in particle physics? Because then it would be fully humorous. Watchwolf49z (talk) 14:22, 5 January 2013 (UTC)
Fair enough. The second cited author, Pickover, appears to have a PhD in some manner of physics, but is listed here as mostly an "author". He might not do physics for a living anymore. The first cited author, Collins, I can't seem to find information on him to know whether or not he's a physicist. I would say it's rather extreme to say that if the statement is made, it is never by physicists, but only one of the two citations say it's from a physicist. 70.109.182.120 (talk) 15:55, 5 January 2013 (UTC)
The intent, in the article, is (should be?) presumably to be nothing more than anecdotal and explanatory about the phrase, and this is in any event not the primary purpose of WP. Since a more accurate humorous description might be "God's units, to within a small factor", I think that at least we should take care not to suggest any uniqueness in this sense by placing undue emphasis upon it. "Natural units" seems somehow more, um, natural. — Quondum 05:12, 6 January 2013 (UTC)

## There are 3 fundamental base units, not 5

I've been attempting to modify the impression given here that 5 base units are needed. The attempt has led to some dispute.The current version is back to asserting that there are five. Here's some discussion, taken from user talk pages, which I initially used out of ignorance of how the system worked.

re the Planck units, you [the IP user who undid my revision] acknowledge that any standard 3-base-unit system already has a temperature unit, i.e. the energy unit. So any Boltzmann constant is a redundant add-on, and is avoided in e.g. Kittel and Kroemer. But you say that some electromagnetic units are needed. Actually, in the very familiar cgs system, on which I was raised (see Purcell's Berkeley E and M book) and in other old rationalized systems, the units for charge etc. were already expressed in the standard 3-base system. For example, one esu (charge) is just sqrt(length*energy) or L^3/2 *M^1/2 *T^-1. --Again, this very common system is a reminder that the unit space is fundamentally 3-D.

-- Mbweissman (talk) 15:11, 5 March 2013 (UTC)

I'm puzzled by your recent comment that some "facts" were wrong in my previous edit. My point, that all units are expressible in terms of three base units, is entirely routine among professional physicists. My attention was drawn to the page because an undergrad was misled by the previous discussion to think that 5 base units were required. Is there some community of which I'm unaware that views things differently? By the way, I agree that the discussion of the charge and temperature units doesn't belong in the lede. It scarcely belongs in the discussion at all, since rationalization of those units is common regardless of whether Planck units are used. However, it seemed best to leave the discussion in as a sort of compromise.Mbweissman (talk) 00:29, 6 March 2013 (UTC)

So again, I don't want to get into an endless oscillation but would like to clarify that the dimension of the units space is 3, not 5.

Most of us involved in editing this article, as well as Natural units, Dimensional analysis, Dimensionless quantity, Fundamental physical constant and Fundamental unit (that article should be deleted, in my opinion, and the what content is good should go into Dimensional analysis), SI base unit, New SI definitions, are well aware of the issue you bring up, but it's still a fundamentally WP:POV issue. SI has 7 base units. You and I know that the candela and the mole are superfluous units that exist not for fundamental physical reasons (as if candelas and moles were measuring a totally different kind of stuff that cannot be described and measured otherwise), but some in the CGPM might see it differently.
Both of us would likely agree about the Boltzmann constant, it is really only an expression of the unit used to measure temperature. Others might disagree, if not about the physics, but about the nature of measurement and the nature of what a physical quantity is. I believe that temperature is a measure of energy per particle per degree of freedom. Energy as a physical quantity exists without a notion of temperature, just as intensity of radiation exists without the notion of luminosity measured in candelas. This gets a little dicey when the number of degrees of freedom begins to change as fluids get heated to very high temperatures. The ${\displaystyle \gamma }$ of diatomic gasses increases when temps get very high. In addition, the Planck temperature was one of the original Planck units derived by Max Planck in 1899.
About electric charge, while it is true that Planck did not originally come up with a Planck charge, what the cgs electrostatic units do with the unit charge is precisely the same principle as what Planck does with four (or three, depending on your perspective) other units. Although defining the Statcoulomb so that ke = (4πε0)−1 = 1, does not mean that electric charge is the same physical quantity as L3/2M1/2T−1. Likewise defining the meter so that the speed of light, c=1, does not mean that length is the same as time. Not in everyone's POV. You insist that "unit space is fundamentally 3-D", but Duff would say it's zero.
It is true that once units for length, time, and mass (or some other combination of three mechanical units) are defined, you can derive all sorts of derived units. But defining speed in terms of length and time does not involve reference to any universal physical constant. Defining force in terms of length, time, and mass does not involve reference to any universal physical constant. However, that is not the case regarding defining the unit to electric charge nor even to temperature (again, it depends on the POV, is kB a universal physical constant or is it just an expression of the unit temperature one chooses to use).
Lastly, the changes you made to the lede of the article only serve to confuse. There is a simple concept that we're trying to get across that there are these five fundamental quantities, four defined by Planck and one later by physicists that have not always been consistent (there were earlier some authors naming the elementary charge as the Planck charge), but consistency has appeared later (nearly all authors using the term now define it as is in this article). The lede should both try to make clear what the major concepts or issues are, but it should also be tight. It does not matter whether one solves a 5×5 system of equations for 5 unknowns directly or if one solves a 3×3 system and from those results solves a simple equation for the unit temperature (since no constant other than kB refers to temperature) and another simple equation for the unit charge (since no other constant, other than ke or ε0 refers to charge). It doesn't matter and splitting that off only muddies the lede. 70.109.182.18 (talk) 15:33, 6 March 2013 (UTC)

Hi- Thanks for the thoughtful comments. I partially agree and partially strongly disagree. The key issue is the one you raise wrt candelas etc. (or it could be BTUs, horsepower, ....). Traditional unit systems have multiple redundancies. The number 3 is special, because you cannot have a complete unit set without making 3 specifications. You need that to specify numbers for all physical measurements. Once you have 3, that suffices, although as you say one can always keep going. Duff may think that the choice of the 3 is so obvious that it goes without saying, but that's another issue. The reason I want to insist on making this distinction is that my bright undergrad student was convinced from this article that 5 were required, although we both know that 5 is no more special than 7 or 12 etc.

On slightly less central issues; The statement "temperature is a measure of energy per particle per degree of freedom" is archaic, especially in the context of Planck! What about thermal radiation? Low temperatures where equipartition isn't close? High temperatures where new dof's are kicking in? Etc. It would be hard to find any physicist in this business who would say something other than "inverse multiplier of E in Boltzmann factor" or "inverse of d(entropy)d(energy)" or maybe "Lagrange multiplier for maximizing entropy with constrained <E>" or something like that. Most of us just don't even think about kb until we have to convert to some practical units, and modern texts treat things that way too.

On electrostatics, all the rationalized versions of CGS (and some versions of MKS) have always used units derived from L, M, T. There are some choices of where to put 4pi, and where to put c (obviously not relevant when c=1) but for those of us raised on rational units, there's no new fundamental constant or law involved.

So the basic point is that in conveying the message about Planck, the current version inadvertently conveys an incorrect message about something even more basic, the number of distinct specifications required. It's 3.--Mbweissman (talk) 20:58, 7 March 2013 (UTC)

The statement "temperature is a measure of energy per particle per degree of freedom" is archaic. Of course it is, but I find it to be pedagogically useful at a level below your undergrad student. Sometimes I leave out the "per degree of freedom" and just talk about monatomic gasses. The point I try to make is that heat is not an energy form different from mechanical kinetic energy except for the random nature of the molecule's motion. Not gonna be explaining entropy to any of these kids in any quantitative manner. The point is that no new physical quantity is being introduced by temperature. It's just a measure of energy and kB is just a conversion factor that converts this measure of temperature in whatever units we happen to be using to energy in whatever units we happen to be using.
I consider electric charge to be different. But that is my POV. Whereas I think you can make this stuff we call "area" out of length and I think we can make "speed" out of length and time, and I think we can make "acceleration" out of length and time, and I think we can make this stuff we call "temperature" out of energy, I don't think we can make electric charge out of mass, length, and time. It's different physical stuff. So with area, speed, acceleration, you can derive "derived units" directly and naturally out of the base units without the need of any universal physical constant. I would say the same regarding temperature but some people would disagree. I don't think kB is really a parameter of nature, it's just an expression of the units for temperature we humans arbitrarily decided to use because we like water (and we have 10 fingers and like powers of 10). You might say the same thing about the Coulomb constant or ε0 and that this constant is not "fundamental" to nature because it's just an expression of what units we humans decided to use to for charge. But as far as Planck units are concerned, that is also the case with G, ħ, and c. They are no more special. They are not parameters of nature, they are merely consequences of the units we decide to measure things with.
You say you cannot have a complete unit set without making 3 specifications. Yes you can, if you're willing to get rid of G, ħ, and c right off the bat (or assign them arbitrary real, positive, and finite values). The only reason you can ditch an arbitrary unit of charge is because you're willing to assign ε0 or μ0 an arbitrary value right off the bat. And only reason you can ditch an arbitrary unit of temperature is because you're willing to assign kB an arbitrary value right off the bat. That is not the case for any of the "Derived units". No additional "fundamental" physical constants are needed to define the Planck pressure or the Planck voltage or a unit for any other physical quantity. But that is not the case for those five base units.
One difference, but I don't consider it compelling, because I don't consider it absolutely necessary to define length, time, and mass to be the base (it could be length, time, and energy, or time, momentum, and energy, I dunno), is that the unit charge can be defined with a single equation, a single relationship given your three "distinct specifications" and one "fundamental" constant. You can simply say "the unit charge is such that two unit charges spaced apart by one unit length results in one unit of force" (and it's not rationalized and flux density is not quite the same as E-field, which I find distasteful) which is no different than saying (in MKS) "the unit charge is such that makes ε0 equal to 1/(4π)". And you can say something similar about temperature. But with a unit time defined, you can do the same thing for length (and the "fundamental" constant, c) and we do that already. So why not just say that "number of distinct specifications required" is 2? Just because it takes a 3×3 system of equations to solve for the Planck length, time, and mass, and from that you can solve for the Planck temperature with one equation and the Planck charge with another single equation, big deal! It's no different from a 5×5 system of equations where there are a few zeros in some of the coefficients. Big deal.
The salient thing is that 5 "fundamental" physical constants (Duff would say that none of them are fundamental, but there are others who insist that G or c or ħ or even ε0 are fundamental parameters of nature) are getting eliminated from expressions of physical law by the judicious definition of, well it has to be, 5 units of independent physical quantity. Saying that the number is 5 or 3 or 2 are all equally archaic. And drawing a distinction of what are the "Big 3" dimensions of stuff is a point-of-view. I think it's 4. Duff thinks it's 0. Someone else who thinks temperature is different "stuff" might think it's 5. Chemists, who want the mole left alone, might think it's 6. I dunno who the candela is supposed to serve, but they might think it's 7. But the simple fact remains the same: Planck units normalize 5 "fundamental" physical constants by defining 5 units initially. Call 'em what you may, but we're calling them "Base units". Once they are defined the "Derived units" can be defined with no other reference to any external parameter. 70.109.182.137 (talk) 04:04, 8 March 2013 (UTC)

This conversation is actually getting more interesting than I expected. Here's some mutterings. As background, you should understand that I'm not just seeing things as a physicist but also was raised by a chemist who routinely thought of dimensionless entropy, i.e.. kB=1, and then learned physics from Purcell, who made things much easier for us all with Gaussian CGS. So seeing kB or ε0 treated as natural facts seems odd. We both see kB the same way, although in light of how respectable modern texts are written, I don't think the POV that it's a physical constant, as opposed to an auxiliary unit definition, is worth catering to. I mean, Boltzmann's famous tombstone wasn't carved yesterday. Your point about charge is more interesting. Intuitively, it feels like different stuff than some combo of L,M, and T. On the other hand, to people who think in terms of gauge symmetries, (not me, usually) maybe it's intuitively obvious the Q^2 is some amount of hbar*c. That line of thought tends to lead partway toward Duff. What terms in what equations are really not a matter of taste, barring real perversity? Maybe that comes down to symmetry groups. You'd have to be nuts to measure different spatial directions in different units, given rotational symmetry. Whoops, given the Lorentz group, you'd have to be nuts not to define c=1. I guess we're down to 2 units. Since allowed angular momenta are defined by the rotational symmetry group, and naturally come in dimensionless units, I guess you'd also have to be nuts not to set hbar=1. Now we're down to 1. I don't know of any symmetry giving a natural G, but maybe somebody knows one or will someday find one. So I sort of see your point, although I hate to encourage people to ignore the rationalizations that preceded Planck just because he took it further. Mbweissman (talk) 03:30, 9 March 2013 (UTC)

...I'm not just seeing things as a physicist but also was raised by a chemist... Here is a funny coincidence: Just 3 days ago, I was helping my local Democrat pol get elected on what we call "Town Meeting Day" and a nice old fellow came up to us (standing outside the polling place holding signs of our candidate) to talk with us because he evidently identified our politics. Anyway he was shaking hands and introduced himself as "Mike Smolin" and, since I knew of only one other "Smolin", I asked him if he knew or might be related to Lee Smolin and he said that Lee is his son and this guy is also a chemist (or maybe he's a retired chemical engineer). Anyway, I dropped my sign with my mouth gaping when he said that. I walked him home (the guy walks a lot for 81 years old). So if you run into Lee Smolin somewhere (I know he's not hanging around UIUC), tell him this Wikipedia anon IP lives about 300 meters from his dad.
My own belief is that length, time, mass, and electric charge are the fundamental dimensions of "stuff" and you can make or measure or describe every other physical quantity out of some combination of those 4. But while I believe that, I do not think that G or c or ħ or ε0 are parameters of nature but are solely expressions of units humans have decided to measure things with. I don't buy into "varying c" or "varying G" or (not that anyone has proposed it) "varying ħ" theories. I think the only fundamental constants are the dimensionless ones, and it's only those constants that would have meaningful variation.
If someone asks "Why is the speed of light the value that it is?", I would ask "Why are there about 1025 Planck lengths in the size of an atom?" and "Why are there about 105 atoms across a biological cell and why are there about 105 of these cells across the width or length of a creature like us?" (The first question is for physicists, the latter two for microbiologists and biologists, I suppose.) That will tell you why there are about 1035 Planck lengths in a meter. You can do a similar song-and-dance regarding how many Planck times go into a second (about 1044) and then you can explain why there are about 109 meters in a light-second. These dimensionless parameters are the only important ones for explaining why things are as they appear to be. Yes, EM radiation appears (to mortal human beings) to be pretty fast, but there are both physical and biological reasons (the latter might be obviated by the former in a sorta Theory of Everything) for that appearance.
The speed of EM propagation, c, need only be real, positive, and finite, and then we may as well say that it's "1". Same for ħ, same for G, same for ε0. Actually, I would rationalize Planck units and have 4πG=1 and have ε0=1. That way, for either EM or gravity (in Euclidean space), field and flux density is the same quantity (in free space) and I would venture to say are exactly the same thing. The characteristic impedance of free space, whether it's EM radiation or gravitational radiation, would be 1. Maxwell's equations (and the GEM equations) would not have annoying factors of 4π in them. Seems pretty natural to me. 70.109.182.137 (talk) 05:12, 9 March 2013 (UTC)

## Changing constants of nature

In the section "Planck units and the invariant scaling of nature" is referred to George Gamov's book where the speed of light in vacuum is decreased. This has an effect on our perception. However, an editor wrote that this "is challenged" by Barrow (2002). This does is not follow. If $c$ is changed, and $e$ and $h$ are fixed, the world is empirically distinguishable from the original. The fixation of $e$ and $h$ are implicitly assumed in the story about Mr Tompkins. This is not challenged by Barrow's text. It is only if $\alpha$ is fixed (consistent with certain combined change of $c$, $e$ and $h$), the world is empirically indistinguishable.

I propose to remove the part with "challenge". Furthermore, we should either remove Gomov's text or put it in a different context.

Note that below the citation (Barrow, 2002) is an explanation on the type of constants (the ones that do and the ones that don't give a distinguishable world). This may need some extra citations and more clarity. Hulten (talk) 12:18, 19 July 2013 (UTC)

No, the Barrow text says that it "would be a mistake...to think that a world in which the speed of light was slower would be a different world." Barrow disputes that "this has an effect on our perception." Directly.
True, he says this. However, if c is changed while e and h are kept constant, the fine structure constant α would change. Most of the discussion I've seen, including Duff's comments, argues that a change in α does result in an empirically distinguishable world.
Absolutely. Virtually everyone agree that a change in a dimensionless "constant" is salient. Most physicists understand that all measurements of physical quantity (including the first, very crude measurements which are anthropometric) are done against a like-dimensioned physical standard, which means those measurements are dimensionless. The issue that this section speaks to is whether the change in this dimensionless physical constant can be attributed to a change in c and not h or e. The point is that it's meaningless to ascribe the change in the dimensionless constant to any of the constituent dimensional constants since the meaningful and salient constant is whatever dimensionless change in quantity that was measured in the first place.
And the Duff stuff are additional citations. 12.226.82.60 (talk) 06:49, 21 July 2013 (UTC)
I've read Duff (2002), the Comment on time-variation of fundamental constants. My impression from the discussion between Duff, the referees and Davies, is that Duff's point of view is not scientific consensus.
I have doubts whether the whole section Planck units and the invariant scaling of nature should be here in the first place, because of several reasons. Firstly, there does not seem consensus on this issue (yes, it is in Discussion making this less of an issue). Secondly, it is not specifically on Plank units but a more general discussion. Maybe part of the discussion should be moved to another page. Or even removed altogether.Hulten (talk) 11:54, 21 July 2013 (UTC)
The issue also is discussed at the Dimensionless physical constant page which was renamed from Fundamental physical constant and the latter redirects to the former. However, both Duff references make specific references to Natural units systems specifically Planck units to make their points. 12.226.82.60 (talk) 16:48, 22 July 2013 (UTC)

## Planck Volume (citation not specified)

This edit → [1], [2]
Provide the source for the Planck Volume value. >> Kron7 (talk) 13:36, 25 June 2014 (UTC)

The volume given is simply the cube of the Planck length. No citation is necessary. (See my comment in the next section below.) — Loadmaster (talk) 22:54, 28 October 2014 (UTC)

## Planck Area (citation not specified)

This edit → [3], [4]

Wolfram contains incorrect (inaccurate) value.

For example, the Wolfram says that the Planck length is:
1.6161×1035 m
Now let's see the correct value on the NIST:
1.616199(97)×1035 m
Rounded to the 4th digit after the point (as on the Wolfram):
1.6162×1035 m
Thus, the values ​​of the Wolfram and the NIST are different. Consequently Wolfram contains not quite correct values​​.

Provide the source for the Planck Area value. >> Kron7 (talk) 14:42, 25 June 2014 (UTC)

Can someone please explain what the fuss regarding the Planck Area and Planck Volume citations are about? The difference between the Wolfram and WP values for Planck area are inconsequential. NIST doesn't seem to show either Planck area nor volume. Of course the Planck area is the square of the Planck length and the Planck volume is the cube. Why is there such a fuss about this when there are no citations required for any of the other derived units like the Planck momentum or Planck energy or Planck pressure or Planck voltage? Or even the Planck charge (which is a base unit)?
This article has a long, slow-burning problem with IP editors (a suspiciously high fraction of whom are registered to a single ISP) aggressively reverting other editors, particularly those who try to alter the language in the lede. The "fuss" here is not due to the editors who are asking for a citation, it's due to the editors who seem to forget that they don't own the article. Zueignung (talk) 05:07, 28 October 2014 (UTC)
The Planck volume is simply the cube of the Planck length. That's how I calculated them when I added it to the table back in Dec 2008 (here). Someone else had already added the Planck area, which is just as obviously the square of the length. No citations are necessary. — Loadmaster (talk) 22:54, 28 October 2014 (UTC)

## Why not begin with basic values ?!

Having studied the subject for quite some time, it occured to me that the complete "Planck world", i.e. all Planck values (and their derivatives) are necessarily wrong, since they all rely on the reduced Planck constant ("h-bar") instead of the true value. Wherever h-bar is used, typically in a square root, the result of the calculation is off by a factor of roughly 2,5 (or roughly 6 when h-bar itself is used). There is no problem introducing reduced constants or some normalisation, mentioning their further application, once the unchanged constant(s) of nature have been used. My suggestion is obviously to begin the corresponding articles with the basic calculations, using especially the Planck constant in the original form. It would not surprise me when it should turn out that a few problems raised in the article just vanish due to this issue. Regards, K. Cormann 80.136.3.251 (talk) 13:10, 24 December 2014 (UTC)

ħ is in no sense less (or more) fundamental or basic than h. If you normalise h to 1 you will lose a few factors of 2π in some places, and gain some in others. It's an arbitrary choice, but if you choose something different to ħ = 1 you need to give it a different name. Djr32 (talk) 18:53, 24 December 2014 (UTC)
This objection to ħ is nonsensical. If the results of your calculations are "off", it means you made a mistake somewhere. Zueignung (talk) 02:11, 25 December 2014 (UTC)

First, ħ is not fundamental, as it is derived from the true fundamental, which is h, the original Planck constant. I don't mind normalisations which may - or may not - become necessary for further use, say, in quantum mechanics. But when calculating basic elements such as the ones in tables 2 and 3 (and considerations as in table 5), the result is simply and evidently off by the factors I've mentioned. So, I don't "choose" anything different to ħ, but return to the unchanged h itself. Second, what really is nonsensical is the use of an arbitrarily changed constant for basic calculations, no matter how it "simplfies" the use in other domains than cGh physics. Before assuming that my calculations are off, just try any of the data in tables 2 and 3 (or re-calculate any in table 5), using h instead of ħ. Given that the results are provided with amazing accuracy, this accuracy even suggests a precision which blurs the issue of a changed basic value, affecting much more than the last decimal places. Just to make sure: I don't mind the normalisation to ħ, when it is required as described in the article. But basic calculations such as the ones in the tables mentioned above need to be done with the basic values to be physically correct. K.Cormann 80.136.18.243 (talk) 08:09, 25 December 2014 (UTC)

ħ is no more or less fundamental than h. If you choose ħ = 1, you get the values given in the tables in the article. If you choose h = 1, you get a different set of values which most physicists would probably not identify as "Planck units". Zueignung (talk) 18:33, 25 December 2014 (UTC)

Neither h nor ħ = 1, the correct interpretation is presented right here in Wikipedia (article on Planck's constant). ħ gets relevant when angular momentum comes into play. The importance of h is not only explained in some detail in the corresponding article, it has been measured by Planck itself to a noteworthy accuracy (esp. for his time). Calculating the physically correct Planck data for esp. time, length and mass is not a matter of "choosing", but of inserting the correct data, which are c, G and h. 80.136.22.25 (talk) 08:36, 26 December 2014 (UTC)

This is why ħ is more fundamental than h. It is what relates angular frequency to particle energy and angular frequency is more fundamental to calculus than is ordinary frequency. This is why you see ħ in Schrodinger's equation and not h (unless h has all that 2π crap attached to it). It is a matter of convention, but your convention, K, is not as good (as simple or fundamental) as the ħ convention. The convention for Planck units could be better, in my opinion. It would be better (more "fundamental") if Planck units normalized 4πG rather than normalizing just G. And if they normalized ε0 rather than normalizing 4πε0. That way, whether it's EM or GEM, the quantities of field strength and flux density are (in free space) exactly the same thing. Nature doesn't have to pull these unit-dependent scalers outa her butt to change flux density (calculated from "cause" like charge or mass density) into field strength ("effect"). But others will say it's better to normalize 8πG as more fundamental (but I think the "2" belongs in the most fundamental form of the Einstien equation).
It's convention. Might not be the best convention, but it could get worse, and frankly K, I think your convention regarding h is worse than the existing convention using ħ. 50.198.99.124 (talk) 04:38, 29 December 2014 (UTC)
Please provide a link to a published, reputable source which explains why one must use h (and not ħ) in order to obtain "physically correct" data (whatever that means). Please include page number, paragraph number, etc. as appropriate. Zueignung (talk) 03:06, 27 December 2014 (UTC)

Why should I bother? After all, you didn't care to rationalise your choice using ħ in basic equations eg. for length, time and mass, although in the article on the Planck constant, it is made explicitly clear that the key issue to use ħ would be an angular momentum (or "angular frequency"). The article is quite exhaustive on the meaning and use of h or ħ. However, here is a simple question: What is the smallest wavelength observed in nature or produced in a lab? Is it the Planck length using h or the one using ħ? (Another issue would be the entropy of a black hole - but that's pretty hard to study.) And, btw: The question above is tightly linked to physical correctness, which means that an equation describes nature. To note that there is always an easy compromise, which would be to just add a column to the tables including the results for the units using h instead of ħ. This way, all possible informations were there. 80.136.19.191 (talk) 11:19, 27 December 2014 (UTC)

It is not for the editors of this article to justify the choice of ħ or h in the definition of the Planck units, that decision was made by the people who invented Planck units, and is reflected in the values of the Planck units in SI units published e.g. by NIST. It would be highly undesirable to add an extra column to the table to give values of something that aren't the Planck units. A number of people above have tried to explain the errors in your arguments, until you have understood these issues then I think that further discussion of the topic would be a waste of time for both sides. Djr32 (talk) 00:00, 28 December 2014 (UTC)

There is a difference between justification and explanation, and the article lacks either one. As for a possible (or hopefully likely) addition to the current publication by the NIST, I've contacted them parallel to the topic here. You tried to re-enforce your point and did not care about the still open question, even contradicting, to some extent at least, the article on Planck's constant itself, which obviously has not been considered once by the "number of people above". Never mind, though. It's not the first time Wikipedia ignores inputs, maintaining a single-sided view on a topic. Of course, the value of the encyclopedia keeps decreasing with this position, as has been noted by quite a number of people around. 80.136.1.79 (talk) 06:52, 28 December 2014 (UTC) Edit (since you've asked): You might be interested that indeed there is a source for the, in our view correct, explanations for Planck length, time and mass, which is the Encyclopedia Britannica (just in case I happen not to provide the links correctly): [1], [2], [3]. Perhaps something at least to think about. 80.136.1.79 (talk) 12:55, 28 December 2014 (UTC)

## "Interchangeable experimental parameters" vs. "human construct".

I have to agree with IP 76 about the description:

"... from properties of the fundamental physical theories and not from interchangeable experimental parameters..." does not really say anything. "... from properties of nature and not from any human construct..." actually says something, and I added links to say specifically what it says. 4.15.65.187 (talk) 23:25, 18 September 2015 (UTC)
From your inability to avoid gratuitous overlinking and violations of WP:EGG, it's obvious that you're the same IP editor who's been reinserting the exact same language into the lede/first section over many years, and who has been curating the nonsensical blahblah section about "Planck units and the invariant scaling of nature". Kindly stop littering this article with your trash. Zueignung (talk) 04:36, 5 October 2015 (UTC)
I am the "76" IP and I am not the IP 4.15.65.187. And it is you that is crapping up the article with your POV. You seem to have a conflict reputation here at Wikipedia to show for it. 76.118.23.40 (talk) 22:41, 5 October 2015 (UTC)