Talk:Planck units

Contents

1 Planck units and fundamental constants

4 What is the rational for "changing dimensions to those of SI base units, changing symbol for temperature"?

Planck units and fundamental constants

There's a long argument over the most fundamental constants to use. I just want to ask, what is that media hyped length at which conventional physics breaks down (ie, can't tell between here and there)? I think it's called Plank length, and whichever one it is, be it the one with hbar or h, 4piG or G, should be the natural length. Doesn't that make a lot of sense? Using the same logic, I would then ask at what time interval can conventional physics no longer tell between simultaneous and non simultaneous events. After that, what was the temperature of the big bang (ie, infinite). If they all use hbar over h, or 4piG over G, or 1/4pi-epsilon0 over epsilon0, then we know which one is more natural, and we can predict the rest of the most fundamental natural base units (ie, charge and mass). If they're all different, then we'll have to determine them like the others. Once we get the base units, the derrived units are a piece of cake. As you can see, I'm just a laymen with no physics background. That's why my reasoning is more of the common sense than sophisticated type. GWC Winter 84 2005 13.45 EDT

Apparently there isn't much debate anymore. The physics community unanimously votes hbar not h. The whole 1/4piepsilon vs epsilon is only relevant one out of five base units. Only one person seems to think 4piG is better than G. But the question is not which of the two simplifies the great formulas more, but which is more fundamental. Either (hbarG/c^5)^1/2 or (hbar4piG/c^5)^1/2 is the planck length, the length where all of physics shifts. That is the place worthy of being "one," because it was always "one". It's not necessarily the length that simplifies formulas more, its just the most fundamental length in existance (practically 0). GWC Winter 84 2005 21.25 EDT.

probably this is best taken to a USENET newsgroup such as sci.physics.research . my only philosophy about Planck units is that they are the units that make these dimensionful physical constants go away. not that anything necessarily special happens at those scales. we know that the Planck length and Planck time are pretty damn small, so small that we know of no physical structures at those scales, but the Planck mass is not that small, about the mass of a speck of dust. many times bigger than an atom. i dunno if ithe the "only one person" you refer to, but my feeling about the (mistaken) normalization of <math> G \ <math> and the Coulomb <math> 1/(4 \pi \epsilon_0) \ <math> is because, in the latter case, with the current definition of Planck units, the speed of propagation of E&M is normalized to 1, but the characteristic impedance is <math> 4 \pi \ <math> and i am convinced that it is more natural if <math> \epsilon_0 \ <math> and <math> \mu_0 \ <math> and <math> Z_0 \ <math> are more fundamental and should all be normalized to one as well as <math> c \ <math>. the same arguement could be raised regarding gravitational radiation. the speed of propagation of gravitational radiation has been normalized to <math> c \ <math>, but the characteristic impedance of propagation is, again, <math> 4 \pi \ <math>, because they normalized <math> G \ <math> instead of <math> 4 \pi G \ <math>. Planck units are what they say they are, but i am not entirely sure they are the most natural choice, and that's what i think they are there for.

Nor do they seem the most natural to me. Were I to be the one choosing the system I'd set the charge on the electron to unity and leave the gravitational constant out all together.

All the other constants are used extensively in ordinary quantum physics but the gravitational constant is only needed when talking about macroscopic scales or enormous densities. The charge on the electron, on the other hand, is of fundamental importance to quantum physics.

As for <math> 1/(4 \pi \epsilon_0) \ <math> verses <math> \epsilon_0 \ <math>, I don't know. I tend towards the latter but maybe the former is the better choice. - Jimp 1Jun05

the most salient concept of the definition of "Natural units" is that these units are not based on some properties of some particular substance or object or "thing". How can we be sure that the aliens from Zog would choose the same substance or "thing"? it might be very natural to choose for us to choose the unit mass to be the kilogram (assuming for the moment that the meter is a natural choice) because the liter is 10 cm cubed and a kilogram was originally intended to be the mass of a liter of water at maximum density. but the aliens on Zog don't give a rat's ass about water.

you are choosing this particular "thing" called an electron to define the unit charge. and there are unit systems that do that, Atomic units and Stoney units. they might also choose the unit mass to be the mass of the electron. but there are other paricles in the universe. not all of them have the same charge or mass. who is to say which particle to base this on?

the vacuum of space has the properties of <math> G \ <math>, <math> c \ <math>, <math> \epsilon_0 \ <math>, and <math> \hbar \ <math>. these constants are universal and are not based on some property of any particular particle or object or "thing" that is arbitrarily chosen. these constants also take on the numerical value that they do only because of the units of mass, length, time, and charge, that we have arbitrarily decided to use. we can argue about whether it is <math> G \ <math> or <math> 4 \pi G \ <math> that is normalized or <math> 1/(4 \pi \epsilon_0) \ <math> verses <math> \epsilon_0 \ <math>. i'm in favor of rationalized Planck units that nomalize <math> 4 \pi G \ <math> and <math> \epsilon_0 \ <math> (as well as <math> \hbar \ <math> and <math> c \ <math>). but, the choice of the electron's properties is an arbitrary choice of some particular "thing" in the universe to base a set of units on. not as natural. r b-j 15:38, 1 Jun 2005 (UTC)

Sure, but this thing is no arbitary one. As far as we know these electrons are to be found throughout the Universe. We have no more reason to doubt this than to doubt that the physical constants are truely constant throughout the Universe.

How can we really be sure that those Zoglings are going to choose the same physical constants as Max Plank did? There's probably a Wikipedia on the Planet Zog in which two Zoglings are having just the same debate as we are.

The charge on the electron is no less fundamental than these constants. They're bound to have electrons on Zog (hey, it could be an Antiplanet with positrons instead but six of half a dozen of the other).

It speaks volumes that a unit regularly in use in quantum physics is the electron Volt (no, not the aitch-bar Hertz). The Zoglings may not care about water but if they're interested in physics they're going to care about elementary particles; they're going to care about electrons. - Jimp 15Jun05

certainly there is a natural usefulness to units similar to eV when one is doing quantum physics regarding atoms and subatomic particles. indeed, there are unit systems, Stoney or atomic units that normalize the elementary charge. Planck units are not the only proposed set of natural units, but they are the only set that is not based on the properties of any particular particle, object, substance, or "thing". a comprehensive reference of different schemes of Natural units is K.A. Tomilin: NATURAL SYSTEMS OF UNITS; To the Centenary Anniversary of the Planck System (http://dbserv.ihep.su/~pubs/tconf99/ps/tomil.pdf).

Zoglings that we could ever communicate with will likely also be doing somthing like quantum physics regarding atoms and subatomic particles. the electrons there will likely have the same properties (mass, charge, etc.) as they do here. the elementary charge is almost certainly a universal quantity.

at one time, i wanted to get around to writing a more general article on Natural units that refer to other definitions other than the Planck units. a reference that i like to look at is the Duff: Comment on time-variation of fundamental constants (http://www.arxiv.org/abs/hep-th/0208093) where he concisely points out exactly what dimensionful universal quantities are normalized by the choice of units.

Planck units: <math> \hbar = c = G = 1 \ \ e^2 = \alpha \ <math>

Stoney units: <math> c = e = G = 1 \ \ \hbar = 1 / \alpha \ <math>

"Schrodinger" units: <math> \hbar = e = G = 1 \ \ c = 1 / \alpha \ <math>

"Dirac" units: <math> c = e = m_e = 1 \ \ \hbar = 1 / \alpha \ <math>

"Bohr" units: <math> \hbar = e = m_e = 1 \ \ c = 1 / \alpha \ <math>

(admittedly, the names for which some of these sets of units are named after is the conjecture of Duff.) the reason that none of these sets do what you would like:

"Jimp" units: <math> \hbar = c = G = e = 1 \ <math>

is because in all of the other sets of units, the unit charge was still defined or arranged in such a way that the Coulomb Force Constant (in SI <math> 1/(4 \pi \epsilon_0) \ <math>) is always implicitly the dimensionless 1. dunno why, but these big time physicists just don't like to have that factor. for them (and the cgs system) the Coulomb's Law always is:

if we used "Jimp" units where <math> \hbar = c = G = e = 1 \ <math>, then you'll have to get

<math> F = \alpha \frac{Q_1 Q_2}{r^2} <math>

and that's fine, but you'll be carrying that <math> 4 \pi \alpha \ <math> around with you throughout the Maxwell's Equations and so on. it will appear in the characteristic impedance of free space. can we expect the Zogians to do that? r b-j 16:23, 15 Jun 2005 (UTC)

We'll be carrying that <math> 4 \pi \alpha \ <math> about iff we're writing dimensionless equations. Gees I hate dimensionless equations: it's so hard to tell what's what. Hey, a more general article would be great even if it only gives the list of normalised constants for each system. By the way my units would be

"My" units: <math> \hbar = k = e = c = 4 \pi \epsilon_0 = 1 \ <math>

I'm ditching the gravitational constant. Jimp 16Jun05

your natural units are perfectly respectable. i have my preference, too, and it's more like Planck, but not exactly. especially if you ditch <math> G \ <math>, you can't call them "Planck units". just for the record, the Gospel of the Most Natural Physical Units according to r b-j are those that make

<math> \hbar = c = 4 \pi G = \epsilon_0 = 1 \ \ \ e = \sqrt{4 \pi \alpha} \ <math>

those are the constants we see in fundamental equations that would disappear. somehow, that's what i think Nature is thinking of. i don't see Nature determining how much flux is diverging from some point and then scaling that with any <math> 4 \pi \ <math> or any other constant and declaring that to be the E field. why would Nature bother to do that? r b-j 01:57, 16 Jun 2005 (UTC)

The thought that had been running through my head had been ditching G and putting e in its place.

"Wrong" units: <math> \hbar = k = e = c = 4 \pi \epsilon_0 = 1 \ <math>

This, of course has the nice consequence of setting <math> \alpha = 1 \ <math>. Great! The whole of mathematics has just collapsed: time for everyone to all go home and have a few tins of beer. That'll teach me to type something up before I've thought it through.

So, if I want <math> \hbar = c = e = 1 \ <math>, which I do, then I'm going to be stuck with <math> \alpha = 1/(4 \pi \epsilon_0) \ <math>. I guess I could live with that. I wouldn't be carrying <math> \alpha \ <math> through all those equations but only because I prefer not to write dimensionless equations in the first place.

If I really want to ditch the gravitational constant, I'll have to throw something else in in its place. The mass of the electron would be a candidate; if it's good enough for Bohr and Dirac, who am I to snub it? However, this is more of an arbitary choice than the charge on the electron. Except for the quarks charge is quantised as whole number multiples of e. Its a different case for mass. So those are my units after all.

"Jimp" units: <math> \hbar = c = k = G = e = 1 \ \alpha = 1/(4 \pi \epsilon_0) \ <math>

Jimp 17Jun05

Jimp, i should have made it clear that the <math> \alpha \ <math> i was referring to was the dimensionless fine-structure constant. ain't no way you can choose units to make it anything other than what it is, about 1/137.03599911 , in the case of Planck units, you end up choosing a unit charge that is independent of the elementary charge so you have little remaining choice to set the elementary charge to 1 or anything else. and it just turns out that the elementary charge is related to the unit charge by the square root of the fine-structure constant. r b-j 01:31, 17 Jun 2005 (UTC)

Jimp, i'm looking at what you said more carefully, and i disagree with your most current point. (i presume <math> k \ <math> is the Boltzmann constant which i don't worry about because i do not view temperature as a dimensionful fundamental physical quantity as i do length, mass, time, and electric charge. these hot-shot physicists to not regard charge as an independent fundamental physical quantity. the see charge as sqrt(force) times length. i don't like that.) anyway, if you set <math> \hbar = k = e = c = 4 \pi \epsilon_0 = 1 \ <math> that does not force <math> \alpha \ <math> to be anything.

it just forces your Coulomb's Law... oh wait, you're right. i thought, without fixing G, you could be free to fix both <math> \epsilon_0 \ <math> and <math> e \ <math>, but you can't, well, i think you should just accept the inevitable wisdom of the "r b-j units": <math> \hbar = c = 4 \pi G = \epsilon_0 = 1 \ \ \ e = \sqrt{4 \pi \alpha} \ <math> . i'll bet money, those are the units E.T. will use when the send us a message. r b-j 01:44, 17 Jun 2005 (UTC)

Yeah, that's why I say "the whole of mathematics has just collapsed". There's nothing left to do but drink beer when you end up with 1/137.03599911 = 1 ... and don't bother trying to count how many centilitres (or cubic giga-Planck-lengths) you're drinking if one equals two. So, to keep e I have to throw out <math> \epsilon_0 = 1 \ <math> I can't just ditch G to make room. I'm willing to bet that E.T. doesn't use feet, pounds and pints. Oh, yeah, k is Boltzmann's constant ... fundamental or not temperature does tend to crop up. Jimp 17Jun05

Now that we know how to relate heat to work and energy, the unit of temperature can be defined naturally from the base units in such a way to make <math> k = 1 \ <math>. it's like defining the unit force to naturally be the time derivative of momentum given the already (naturally) established units for mass, velocity, and time.

especially if you use <math> m_e = 1 \ <math> in your definition of natural units, you really are defining some form of atomic units which are very useful for doing the hydrogen atom (i think the unit energy is the Hartree energy in those units. i still think that, since it is possible to define units without reference to any particular substance, object, particle, or "thing", then to refer to any properties of any particular particle, such as the electron, is not as natural as defining this units to lay out a scaling scheme that is inherent to just absolutely nothing - the vacuum. this is what loses the anthropocentric coefficients in some pretty fundamental laws. where i disagree with Planck units (and cgs) is that the most fundamental expression of any inverse-square law is

i think, because of Gauss's law the most fundamental expression of an inverse square law is the "rationalized" form:

and it's the rationalized constant <math> k_r \ <math> that should be eliminated by judicious choice of units. as i put in my talk page, the criteria that seems clearly to me that defines the most natural physical units of free space, the scaling that is inherent to free space, are these criteria:

1. One unit of mass is equivalent to one unit of energy (or equivalently, the unit velocity is the speed of light).

2. A particle or photon with a wave function of one unit of radian frequency shall have one unit of energy.

3. The force applied to a unit mass in one unit of gravitational flux density shall be one unit of force and a single unit of gravitational flux density shall result from a unit mass distributed over a unit area.

4. The force applied to a unit charge in one unit of electrostatic flux density shall be one unit of force and a single unit of electrostatic flux density shall result from a unit charge distributed over a unit area.

of course, the units of velocity, momentum, force, torque, energy, power, intensity, pressure, density, voltage, current, impedance, etc. are done the same way as derived units are now (say in SI) from these four base units.

those are, in my honest but biased opinion, are the natural units. they express the inherent scaling of nature and our existence and perception of reality are really scaled against these units. i had a big argument with the creator of the Variable speed of light article where i said the following:

now, i don't know why an atom's size is approximately <math> 10^{25} l_P \ <math>, but it is, or why biological cells are about <math> 10^{5} \ <math> bigger than an atom, but they are, or why we are about <math> 10^{5} \ <math> bigger than the cells, but we are and if any of those dimensionless ratios changed, life would be different. but if none of those ratios changed, nor any other ratio of like dimensioned physical quantity, we would still be about as big as <math> 10^{35} l_P \ <math>, our clocks would tick about once every <math> 10^{44} t_P \ <math>, and, by definition, we would always perceive the speed of light to be <math> c = \frac{1 l_P}{1 t_P} \ <math> which is the same as how we do now, no matter how some "god-like" manipulator changes it.

now if some dimensionless value like <math> \alpha \ <math> changed, that's different. we would perceive the difference. but to attribute that change to a change in <math> c \ <math>, that case is not defensible. you could argue that the change in <math> \alpha \ <math> is due to a change in the speed of light, and i could argue it's a change in Planck's constant or the elementary charge and there is no way to support one over the other.

this is what i truly believe is the major significance of Natural units, and, except for a scaling factor of <math> \sqrt{4 \pi} \ <math>, i think Planck got it right. r b-j 20:01, 17 Jun 2005 (UTC)

Misc

Can we fix the h-bar to use the Unicode as seen on the Plancks' Constant page? The display as it is at the moment appears to me as an h with a line through the curved n-like part of the stroke, whereas it should the bar should cross the h in the upper part above the 'n' - EddEdmondson 22:42 Feb 4, 2003 (UTC)

"So the complete set is based on five (not three) fundamental physical constants: G, c, h-bar, k, and e"

The unit "Kelvin" is usually viewed as less fundamental, but of course, if we want to convert it to the other units (or express temperatures as dimensionless numbers), we need to set k=1 (the Boltzmann constant is the only constant from the list that contains Kelvin degrees). On the other hand, it is completely inconsistent to set e=1 once we already set G=c=hbar=1. The reason is simple - the elementary electric charge is simply not independent of the rest hbar,c,epsilon0 (I don't need Newton's constant here) - because the ratio known as the fine-structure constant is equal to a numerical constant, namely 1/137.03604 or so. This is a dimensionless number, and therefore does not depend on the choice of units, and because it is not one, it cannot be set to one. It's a parameter of Nature - that sort of measures the strength of the electromagnetic force in natural units - that even the aliens who use very different units know very well, and therefore it's a number that a very complete theory of Nature - such as string theory - should eventally be able to calculate. (Note that in the SI international units, I had to set the vacuum permitivity epsilon0 equal to one, too.) Note that the smallness of the fine-structure constant is the reason why we are so successful with making perturbative calculations of Quantum electrodynamics.--Lumidek 23:49, 3 Oct 2004 (UTC)

Two issues. First, h-bar is h/2π. h is the more fundamental of the two formulations, because the true value of π is dependent upon the geometry of the universe (i.e. if the universe is non-Euclidian, then you will need to change the value of π used in all physics formulations accordingly so that it still fits the definition 2π = C/r).

This is not correct: the value of Pi has nothing to do with the geometry of spacetime. It is a mathematical constant, defined by some convergent series. In Euclidean space it happens to be the ratio of circumference to diameter, and in non-Euclidean spaces (like our universe), that's not universally true. But the physical equations always use the precise mathematically defined value, not some experimentally determined number. AxelBoldt

I agree with AxelBoldt. In physics, we always consider hbar to be more fundamental, and often set it equal to one, while h=2.pi.hbar is a derived concept. Of course that the value of pi is completely universal (mathematical constant) and does not depend on any physical assumptions. The reason why hbar is more fundamental is related to the fact that we like to measure angles in radians, and we like to express the frequency f in terms of the more fundamental angular frequency omega=f/2.pi. Therefore, E=h.f=hbar.omega, the factors of 2.pi cancel. Moreover, the argument above involving "dependence of pi on politics or at least shape of the Universe" could be also reverted: h=hbar.2.pi, and because pi depends on politics and the weather, it is only hbar that is fundamental. ;-)--Lumidek 23:42, 3 Oct 2004 (UTC)

There's a difference between "more fundamental" and "happens to make some popular formula shorter", I would think. From the POV of complex analysis, the formulation of Schrödinger's equation expressing the time-development operator as e^{2πi Ht/h} seems quite natural, since 2πi is the constant that appears quite unavoidably all the time, anyway. I'd like to express the opinion that it's more natural to have 2πi together rather than artificially ripping the 2π off and putting it into a constant somewhere where no one will find it :-)

I think it might be a good idea to approach the concept of naturalness more carefully, to be honest. For example, arguing that "we like to measure angles in radians" really makes me wonder what's so natural about that. Measuring angles in 1/2&pi radians certainly isn't the only way to do it (I've always considered normalising angles so 1 would correspond to a full circle to be pretty natural). For a slightly more outlandish suggestion, you could ask yourself what the natural unit of area should be, even if you know the natural unit of length. See Hausdorff measure for one argument why normalising squares (which is essentially what the product measure does) is not the only way to do it.

Prumpf 00:53, 4 Oct 2004 (UTC)

Second, e (the charge of the electron, not the base of the natural log, right?), makes for a bad fundamental unit since there are quarks with smaller units of charge. This objection only holds, of course, if the Planck units are intended to represent the indivisible quanta of each measurement type.

Thanks for the nice questions. You say:

<<objection only holds, of course, if the Planck units are intended to represent the indivisible quanta of each measurement type.>>

That is right! What you say is correct. Therefore the objection does not hold. Because when Planck defined them in 1899 (and Stoney did part before him in the 1870s) the units were only intended to be universal natural units (making the most widely used universal constants unity) and were NOT intended as "indivisible quanta". e is the natural unit charge Stoney discovered in the 1870s before anybody knew there was a particle. He called the charge unit "electron" then when his friend J.J.Thomson discovered there was actually a particle with the unit charge on it (1897) he used Stoney's name to name the particle. That amount of charge is our fundamental constant for charge. It is great that there are quark charges of 1/3 and 2/3 e!!! Murray Gel-man who invented quarks did not ask to change e to 1/3 e. It's fine. e stays e, the charge on the electron. and we can have fractions of it.

When Planck defined Planck units in 1899 in effect he used h-bar. He got the units you get using h-bar. The values Planck gave for the basic units in that 1899 paper are amazingly close to the ones we use today. Exactly how and why I can't explain even though I have read the relevant parts of his 1899 paper! Somehow h-bar is at the historical root and not h. Some people think h-bar is "more fundamental". Maybe Planck thought that then. It is perhaps useless to discuss which is more fundamental! The thing to remember is that if you say PLANCK units those are the historical ones which he defined and which have gradually come into use over the past century. We cannot change them. You or I can only make up our OWN units and try to get physicists to be interested in them.

Anyway. Planck units use h-bar, for whatever reason. Also the value of h-bar does not depend on space-time geometry because h-bar is physically meaningful and can be measured. You measure h-bar. You don't need to go around measuring h and dividing by 2 pi. Another thing: locally "pi is pi". It is a mathematically defined number that works locally. Indeed there is a lot of evidence that spacetime has negative curvature so that for VERY LARGE circles C/r could be bigger than 2 pi. But at your scale and mine and at the scale of atoms pi is not worried by this. Non-Eucl. geometry has an idea of local flatness which is compatible with large-scale curvature and our old friend pi works in local flat neighborhoods.

Hope this helps.

"Quantum physics states that it is impossible to divide a unit of measurement (length, mass, time, temperature) into segments smaller than the Planck constant, while obeying the known laws of physics."

Given that the Planck temperature is 1.4x10³²K, this seems just a bit contradictory. Maybe someone who knows this stuff better can explain how this applies to temperature? -- JohnOwens 08:34 Mar 24, 2003 (UTC)

Now that I think about it, ditto for the mass. -- JohnOwens 08:46 Mar 24, 2003 (UTC)

One important property of Planck units is that at Planck temperature the kinetic energy of "typical" particles (or heavier than the Planck mass?) is such that their de Broglie wavelength is smaller that their Schwarzschild radius (= critical radius of black holes). This was when the Universe was younger than 1 Planck time (see Timeline of the Big Bang).

A limit wavelength photon can be defined from the Planck length unit. This wavelength photon has the energy density to produce a pair of black holes such that each black hole would have a photon capture radius (3Gm/c squared) equal to the photon wavelength divided by two pi. This limit wavelength is defined as (3/2) exponent 1/2 times (2 pi) times ( Planck length). The limit wavelength is (3pi hG/c cubed) exponent 1/2. The square root of the product of this wavelength and the length (2 pi) squared times (c times one second) meters is 2 pi (3pi hG/c) exponent 1/4. This is a photon wavelength that has energy equal to the mass energy of one electron plus one positron.The electron Compton wavelength is 4 pi (3pi hG/c) exponent 1/4. The electron mass will then be (h/4pi c) times (c/3pi hG)exponent 1/4. This indicates a Planck length value 1.6159455 x 10 exponent -35 meters. The value of the gravitational constant is required to be 6.6717456 x 10 exponent -11 if no small corrections apply. See Talk:Time dilation. Don J. Stevens 4/10/04

Is it appropriate to call the Boltzmann Constant a fundamental one? I thought that its value has no bearing on the behaviour of the universe. Still, may be that it is not worth making the article read less cleanly with a reword and best to leave it as it is. EddEdmondson 10:27, 18 Jul 2004 (UTC)

So where is the permittivity of vacuum used in determining the units? --213.73.165.109 11:59, 21 Aug 2004 (UTC)

We should mention Gaussian units here, which would get rid of the electron charge as "fundamental unit", instead replacing it with a charge sufficient to induce the Planck force on two particles of Planck mass whose distance is the Planck length. IIRC, the ratio between those two charges is the square root of the fine structure constant. In fact, I believe scaling by powers of 2, pi, or that constant does not really effect the naturalness of a unit system. For example, when trying to define a natural acceleration, given a natural time and natural length, both the definition

"that acceleration which will reach unit velocity in unit time"

and

"that acceleration which will make a resting point reach unit distance from its origin in unit time"

seem fairly natural to me, and they differ by a factor of two. Prumpf 10:28, 6 Sep 2004 (UTC)

I must disagree, in addition to others, that the Elementary Charge, e, is the fundamental natural unit of charge in the Planck scheme of things. The Planck charge is the charge that makes the Coulomb force constant, k = 1/(4*pi*epsilon0) equal to one just as the Planck Mass is the mass that makes the gravitational constant G equal to one. The historical reference to Stoney is non-sequitur. What Natural Units are about are the units that are fundamental to the field equations (that get rid of the constants in the field equations) without reference to any particular particle or "thing" that those field equations may operate upon.

The Planck Current as currently displayed is wrong because it is based on a faulty notion of the Planck Charge (which Planck never defined) being the Elementary Charge.

In addition, the natural units for plane angle (radian) and solid angle (steradian) are nice and natural, but they are not really physical measure but are mathematical concepts in the same way as is the natural logarithm base. They don't belong on a Planck units page.

r b-j (talk)

The article is entitled Natural Units, and there is an explicit caveat immediately above that the angle and solid angle are natually defined, but are not part of the Planck scheme. Angle and Solid Angle come into Physics at several places, being, for example, part of the SI system of physical units, as you will know.

I can see the logic in your argument about the Planck Charge, although there are several university webpages (using Google) that use Elementary charge as the Planck Charge.

Ian Cairns 13:34, 11 Sep 2004 (UTC)

Ian, would you list a few of those several university webpages that use Elementary charge as the Planck charge? i have tried to repeat your experiment and have not gotten the same results. there are websites that copy wikipedia that say Qp=e and there is www.planck.com that says Qp=e, but i have not found many other sites nor publication references that say that. r b-j 05:26, 14 Sep 2004 (UTC)

Apologies for the unconscionable delay in replying - due to pressure of day work. I have tried to locate those webpages that formed the basis for my creation of entries on the Planck page. I have been unable to relocate these pages. I can assure you that this was beyond what I could have 'made up', and therefore represented what had been present on the web at an earlier date. Clearly, in the absence of any justification, I can not stand in the way of your current editing. Good luck! Ian Cairns 23:27, 3 Oct 2004 (UTC)

don't sweat it on my account. it looks like you seen that besides changing a few things, i moved it back to "Planck units". i want to do a more general philosphical article about Natural Units in which Planck and Atomic units and others are particular examples (but i think that "rationalized Planck units, where 4*pi*G and epsilon0 are normalized to one are the Natural Units, the "units that God uses" and the ones E.T. will use when we finally get to talk to them :-) as in http://dbserv.ihep.su/~pubs/tconf99/ps/tomil.pdf or http://www.jgiesen.de/astro/NaturalUnits/stoney.html . as i wrote below, i also want to write a bit referencing Duff in http://xxx.lanl.gov/pdf/physics/0110060, and use Natural Units to illustrate "The operationally indistinguishable world of Mr. Tompkins" as to why we could not tell the difference if dimensionful physical constants, such as c, change while the dimensionless constants, such as alpha, remain constant (there is no way we could measure the change). Anyway when i finally get around to that, i will revert the link back to Natural units and undo the redirect to Planck units. also, i have to opine that i agree with Lumidek above about Boltzman's constant. i don't view temperature as a fundamental physical quantity the same that i view length, mass, time, and charge. r b-j 00:52, 4 Oct 2004 (UTC)

I also think that Rbj's approach to defining the elementary charge (and thereby the natural unit of current) is more "natural" than simply using e. I would be willing to bet a buck that the extraterrestrials don't use e. However, I don't know whether Rbj's definition is in common use, and what Planck thought. Maybe it would be best to add a section to the effect of "another possible elementary charge (and resulting unit of current) suggests itself on the following grounds..." After all, the article is called "Natural units" and not "Planck units", so that discussion is clearly on-topic here. Rbj, you want to write something? AxelBoldt 23:24, 11 Sep 2004 (UTC)

Rbj's definition (which is equivalent to the definition I gave before that, so we really only have two candidates) is common knowledge. I've heard the term Gaussian units used for it, but there seems to be some amount of confusion about it. To quote units.dat, version 1.35 (sorry, I don't have a better source handy)

# Gaussian system: electromagnetic units derived from statampere.
#
# Note that the Gaussian units are often used in such a way that Coulomb's law
# has the form F= q1 * q2 / r^2.  The constant 1|4*pi*epsilon0 is incorporated
# into the units.  From this, we can get the relation force=charge^2/dist^2.
# This means that the simplification esu^2 = dyne cm^2 can be used to simplify
# units in the Gaussian system, with the curious result that capacitance can be
# measured in cm, resistance in sec/cm, and inductance in sec^2/cm.  These
# units are given the names statfarad, statohm and stathenry below.

In other words, charge is already a derived quantity, having the dimension of sqrt(force) * distance. Similarly, Boltzmann constant (and simple intuition) seems to suggest that temperature is a derived quantity, not being anything but a macroscopic averaging of effects of the fundamental forces. The permittivity of vacuum isn't necessary when Gaussian units are used. Lastly, the electron charge has been discussed to death, and isn't necessary either.

That still leaves the h or ℏ question (which would scale some units by 2π), plus various possibilities of deciding which of two alternative laws is more natural and deserves to be stated without a factor of 2 creeping in. I've given an example for that above. So, I don't think the statement that natural units eliminate all arbitrariness from the unit system really can be made. Prumpf 01:04, 12 Sep 2004 (UTC)

Prumpf, i would think it's pretty clear that hbar is more fundamental than h. just go to Schrödinger equation and you see hbar, not h. truly natural units would normalize hbar. the cgs idea of choosing charge to normalize the Coulomb force constant, k=1/(4*pi*epsilon0), is fine, but it would be better, from the POV of Maxwell's Eqs., to normalize epsilon0 instead. also i have real dimensional issues with the concept of "capacitance in cm". electric charge *really* is another dimensional quantity and is not sqrt(force)*length. not in my opinion anyway. it is not as appropriate to equate conceptually charge to sqrt(force)*length as it is to dimensionally equate force to the momentum/time.

just to get the semantics back, i believe we should be consistent with the [NIST site (http://www.physics.nist.gov/cuu/index.html)]. "Elementary charge" is the charge of a proton (or the negative of the charge of an electron) whether it may be thought of as the "natural unit of charge" or not. my objection is using that for the "Planck Charge" (which you won't see on NIST) and deriving Planck Current from that definition of charge (also not on NIST). the only Planck Units you see on NIST is Planck Time, Planck Length, and Planck Mass, and it would be my suggestion that we leave it at that. in addition NIST (and Planck's original paper) uses c, hbar, and G and i would suggest we leave it at that. we should note the difference between Natural Units and Atomic units. for Atomic units, setting the unit charge to "e" and the unit mass to Me might be appropriate because sub-atomic particles are intrinsic to the field. but not so with Natural Units.

BUT - i would suggest that the term "Natural Units" be scrutinized more and not conceptually equated to Planck Units. Planck had the right idea but I think Planck missed it a little (from the POV of E.T.) when he normalized G to one instead of normalizing 4*pi*G. and Planck did not define a natural unit of charge (although Stoney did with the Elementary Charge). I *did* post a little [article (http://groups.google.com/groups?selm=BB9D3555.40C2%25rbj%40surfglobal.net)] to sci.physics.research about philosophically what the most natural physical units should be and i had a few email conversations with some real heavyweights in physics (Okun, Veneziano, Duff, Baez, Lodder) about it, and while they didn't shoot me down, it was a sorta "ho-hum, this ain't worth changing our convention". but i still maintain that the Most Natural Physical Units are those that send the (dimensionful) conversion factors (a.k.a. "fundamental constants") in the pedagogical most fundamental field equations to 1. that means c=1, hbar=1, 4*pi*G=1, and epsilon0=1. you could find that article on google groups but i have added to it and i would post it somewhere here if you want, but i dunno if that would be appropriate or where the best place to do it is. (i put it on my talk page.) it is pure ASCII and i'm afraid that the wiki math rendering might goof it up a little and i haven't yet taken time to make it nice for wiki. where might a good test page (not the sandbox) be to do that so that you can see it, yet it is not yet made part of the canon? (i put it on my talk page for anyone to see and comment. r b-j 03:39, 13 Sep 2004 (UTC))

So to repeat, I think that wiki should just say what Planck Units are and what they were meant to be, but be more defensible in the long term about what Natural Units are and they may come out a little bit different.

r b-j 04:20, 12 Sep 2004 (UTC)

Just to let you guys know that I think I am done editing Planck Units. Eventually, I would like to edit Natural Units to provide comparisons between different systems of which Planck is but one (Stoney, Atomic units, etc.). Similar to http://dbserv.ihep.su/~pubs/tconf99/ps/tomil.pdf . But this is about all that I can think of saying about Planck units and I hope this contribution survives. Some of the thoughts are my own "layman's interpretation" but I *did* draw from authoritative sources (Michael Duff, Frank Wilchek) and I don't believe I misintrepreted these guys. I really think that Duff's refutation of Gamow's Mr. Tompkins is an important concept that goes with Planck Units and that's why I included it. I wanted this article to be good for high schoolers and college undergrads. Feel free to improve this. r b-j 20:21, 6 Oct 2004 (UTC)

Dimensions

I think that the table at the end with quantities and dimensions is a bit strange. The idea behind natural units (not all physicists agree with this) is that fundamentally there are no units or dimensions.

If you put h-bar = c = 1, then Time = Length = 1/Mass

If you put c = G = 1 then Time = Length = Mass

Both systems are 1 dimensional unit systems. If you put all the constants equal to 1 you have a zero dimensional system unit system (i.e. no units or dimensions at all). Lengths, squares of lengths, masses, they are all the same quantities.

In no way does this lead to conflicts. Using dimensional analyses, e.g. you can derive that the period of a pendulum should be SquareRoot[L/g] times a constant of order unity. You can still do that in a zero dimensional system. You then define a physical length, time etc. that are obtained by rescaling (using h-bar, c and G) from the dimensionless planck scale quantities. You then demand that the desired relation does not involve infinities in the (independent) limits c->Infinity, h-bar-->0 and planck length --> 0. This is formally the same as dimensional analyses with meters seconds and grams.

Count Iblis 16:42, 11 Dec 2004 (UTC)

What is the rational for "changing dimensions to those of SI base units, changing symbol for temperature"?

it is the case for SI that the Ampere is defined first, and from that the Coulomb is defined as an Ampere-second. however, in cgs, the unit of charge or Statcoulomb is defined first. any system of units need to have base units and it could be somewhat arbitrary what units are chosen as the base units (heck, instead of a base unit of time, there could be a base unit of velocity and the derived unit of time comes from that and the unit length), but there is no reason to appeal to SI as the standard convention.

electric charge is conceptually a more fundamental physical quantity and current is most simply conceptually drawn from that. charge is this "stuff" that exists in nature and current is the rate of change of that stuff w.r.t. time. Gene, i'm reverting these last changes. i don't see them helping at all and the symbology put in only confuses. let's talk about these non-cosmetic changes before changing them. that's what i did before first hacking away at this article. r b-j 00:01, 24 Apr 2005 (UTC)

The formulas given, with those 4π factors, are the formulas corresponding to those for SI units, and not for a nonrationalized cgs system.

You can just as validly get a base unit of Planck current as you can get a base unit of "Planck charge" from those five fundamental formulas. That Planck current can just as validly be chosen as a base unit in the Planck units as an ampere is chosen as a base unit in SI, or the Planck charge can just as easily be chosen as a base unit just as the coulomb was in some obsolete MKSC systems.

In other words, there DOES NOT EXIST A UNIQUE SYSTEM OF PLANCK UNITS. There are several different systems which are called "natural units".

there has been some historical variance of the definition of "Planck charge" since Planck did not define it in his original paper. some take the Planck charge as the elementary charge and you will find that published in some places. but, i believe, after some discussion on sci.physics.research and some old emails with Michael Duff and John Baez (and some others i forget) that using "e" for the Planck charge is not in keeping with the philosophy of the definition of Planck units. the Planck units are those that cause the scaling constants in the fundamental field equations to go away and are not based upon any prototype, object, particle, or "thing". now other than the Planck charge, there is no ambiguity of definition of the base Planck units. they are what they had originally been defined to be.

now i don't like the un-rationalized Planck units as good as the rationalized ones. i think the more natural fundamental physical units would be those that normalize c, h-bar, epsilon_0, and the gravitational counterpart to epsilon_0: 1/(4 pi G). those are nice natural units but they aren't Planck units. i don't get to redefine them to my liking.

i agree there are many definitions of "natural units", Christoph Schiller has another interesting opinion (http://www.arxiv.org/abs/physics/0309118) of what the most natural physical units are. but, excepting Planck charge, there is really only one definition of Planck units and currently, every physicist that i've corresponded with would define the planck charge in the same unrationalized way as in cgs. the only other usage of the term has been equating it to the elementary charge.

The Θ is pretty conventional for tempurature in dimensional analysis. Where else is K used for this purpose?

i left it in your way. i'm not averse to changes, but only to those that make things worser. :-)

Those "dimensions" should be removed entirely from that opening table, and should only appear after the arbitary choice of base units has been made, and it should be made perfectly clear that that choice is arbitrary.

it's only arbitrary from a antropocentric POV. i think, conceptually, the physical quantity of charge comes before current.

In fact, the dimensional analysis does appear there, duplicating that original listing. That third column should be removed entirely from that early table; it properly appears in the later section (which still uses charge as one of the dimensions).

However, that latter section uses entirely different symbols for the quantities; not very good ones either, IMHO. Those probably should not be italic as they appear in that final listing; maybe you could enclose them in square brackets such as [L], which is one pretty conventional way of representing these dimensions.

I'll help you out by taking out that third column. Gene Nygaard 00:35, 24 Apr 2005 (UTC)

i don't think we should take it out. just because you can express reality without dimensions using natural units, doesn't mean that the concept of dimension isn't there. i might agree surrounding everything with brackets makes the notation more conventional. r b-j 01:12, 24 Apr 2005 (UTC)

09-June-05 revert

To answer the question asked while removing text around <math>E = E_p \frac{m}{m_p}<math> from article version 09-June-05 "revert. could 85.72.227.5 say what his/her addition means and why it adds something that wasn't there before?" Yes, I can. This equation wasn't in the article before. It's just one example of many possibilities to generate equations where the natural constants are expressed by Planck units that correspond to the target unit of the equation (in the example mentioned it's E). These inherent possibilities have the same "right" to be mentioned like the inherent possibilities of removing conversion factors as described at the beginning of the article (which is a bit difficult to understand for less experienced readers as it does not mention that the simplification described involves a change in dimensions). 85.72.227.5

okay, there are manifold equations that we could add that weren't in the article before. we need to make sure that when adding them, the addition is subtantive. so two issues:

first, notation:

<math>E = E_p \frac{m}{m_p}<math> i think should be written

if i understand what you meant to say. the symbol <math> m_p \ <math> is often understood to be the mass of the proton.

secondly, in terms of Planck units,

<math> E = m \ <math>.

that equation has been written. if you want to have the same meaning in any consistent set of units, then that would be

(which is equivalent to your equation) and i wonder what that adds. not trying to pick on you. just trying to keep the content of the article from creeping up in size without really adding content.

also, could you get a wikipedia ID or login? i don't care if it's only a pseudonym but i don't like talking to IP addresses. r b-j 23:03, 12 Jun 2005 (UTC)

OK re notation.

<math> E = m \ <math> involves a change in dimension vs. current dimension of E and therefore it isn't that simple as it looks like. This can easily be seen because E also is

<math> E = \frac{1}{t} <math> and

if treated this way.

Agree that

is equivalent to the equation I mentioned as an example. However, the way I expressed it shows that the resulting target unit is obtained by modification of the corresponding Planck unit. The modification factor in the example I mentioned is

This way of expressing equations I think is important if Planck units are not only seen as a concept but as physical "realities" that significantly contribute to the cause of the target units we see.

Therefore this way of expression I think has the right to be mentioned in the article. And, of course, the aspect of concept vs. "reality" also should be discussed. Happy to contribute. Oddy alias IP 85.72.227.5.

fine, Oddy. i do not (nor anyone else) own this article. i am not the keeper of the article. i suspect that "right to be mentioned" is a little non sequitur. if you put it back in, i will not get in a revert war with you (but someone else might revert it, i dunno). it seems to me that your interest is in having a good article and i'm happy to have you contribute.

back to specifics. just like

<math> E = m \ <math> in Planck units

means the same thing as

<math>\frac{E}{E_P} = \frac{m}{m_P} <math> in any arbitrary but consistent set of units

so it is that

<math> E = \frac{1}{t} <math> and

<math> E = \frac{1}{l} <math> in Planck units

means the same thing as

<math> \frac{E}{E_P} = \frac{t_P}{t} <math> and

<math> \frac{E}{E_P} = \frac{l_P}{l} <math> in any units.

in fact, for instance, Coulomb's Law

<math> F = \frac{q_1 q_2}{r^2} <math> in Planck units

means the same thing as

<math> F/F_P = \frac{(q_1/q_P) (q_2/q_P)}{(r/l_P)^2 } <math> in arbitrary, consistent units.

and if you combine all of those Planck units normalizing the variable quantities, then you get

<math> F = \frac{F_P l_P^2}{q_P^2} \frac{q_1 q_2}{r^2} <math> in arbitrary, consistent units which is

<math> F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} <math>

all this is fine and good and true, but i am still wondering what is added. what is the salience in expressing every physical equation like that with the fundamental constants removed but then with every quantity divided by their corresponding Planck unit? what does that do for us? what does it tell us? i am still listening. r b-j 02:33, 19 Jun 2005 (UTC)

Thanks for your comments, Robert. The example of Coulomb's law is a very good one and your equation

comes close to what I am after. But I would like to modify it just a bit to show better what I am trying to communicate:

Even better than the simple example of Einstein's equation we see that the modification factor can be more complex. But consistently it shows that we get fractions of units related to their Planck units. In this example the modification factor is composed by the relation of sqrt r to sqrt Planck length (which tells us that an underlying mechanism involving something of the size of the Planck length may play a role) and the relation of two charges to sqrt of the Planck charge (which tells us that Planck charge itself may play a role in the mechanism). This is the reason why I think that Planck units tell us much more than just being a concept.

Try it with another example, Newton's law of gravity (expressing masses by their corresponding wavelengths).

Appreciate your acceptance of trying to get an improved article. However, before putting the stuff in I would appreciate if we could get a consent about because I understand that you have also a key interest to keep the article to be an optimum. Oddy.

sorry for getting back so late on this, Oddy. perhaps i'm wrong, but i think the pertinent point you're trying to make is: "which tells us that an underlying mechanism involving something of the size of the Planck length may play a role". i think you are wanting to express some of these physical laws in such a way that emphasizes some fundamental role that Planck units have in nature. i also believe that Planck units (or the rationalized Planck units i have mentioned above in the other segment) do have a fundamental role. but what that fundamental role or even if there is such a fundamental role is still a little controversial among the real physicists. they've been telling me (on sci.physics.research) that my ideas about this fundamental role is more Platonic than it is hard-core physics. but i agree that as long as quantities are expressed in Planck units, the constants in these equations go away, and that sure seems to me to be something that Nature is trying to tell us. expressed in general units then we get physical law that looks like:

<math> E/E_P = \omega t_P \ <math>

instead of

<math> F = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2} <math>

<math> E = \hbar \omega \ <math> .

and i agree that this is salient, but i still believe that point is already made in the article. i hope it's not disconcerting that i ask if you could explain again or in a different way what it is you are trying to add that is something more or different than what i've been saying here? thanks. r b-j 05:20, 23 Jun 2005 (UTC)

Robert, I absolutely agree to what you stated. Maybe some more considerations help to make even more clear what the message should be. The statement "which tells us that an underlying mechanism involving something of the size of the Planck length may play a role" is less the pertinent point itself rather than an example of the pertinent point. I think the pertinent point is that Planck units like Planck length, -time, -mass, -charge, -impulse, -force, -frequency etc. seem to be the result of some unknown but nevertheless really existing ultra-micro-structures being not only the cause of the numbers and sizes of the Planck units (and therefore the natural constants as well) as they are but also the cause of the phenomena we observe. Taking as an example your above expression of Newton's law (that describes most of the gravitational phenomena quite well) we see from expressing the equation via Planck units that the Planck force and the Planck length might play a key role. This includes the mass/Planck mass relation because this can be expressed as corresponding (wave)lengths. I.e. we look to Planck force being modified by "geometry" where the Planck length seems to be the real basis of all geometry.

The interesting question then is: what is it the geometry applies to. We said, the planck force in the example mentioned. But I mentioned, too, that the Plack force might just be the result of so far unknown structures.

So, what builds the structures? Needs to be investigated which is not subject to WIKI. Also, therefore mainstream physics will not tell much about, of course.

I'm still thinking how those aspects can be phrased in the article to be in line with WIKI rules. Hope I can come back to you with a proposal soon.

Finally, you said that "that point is already made in the article". Pls help me to understand that a bit more. To me it seems that there are two different points:

- eliminate natural constants totally (e.g. E=m) which includes change in dimensions

- express natural constants by Planck units while keeping conventional dimensions (the approach that I believe I made).

Thanks a lot, Oddy.

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Talk:Planck units

Planck units and fundamental constants

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Dimensions

What is the rational for "changing dimensions to those of SI base units, changing symbol for temperature"?

09-June-05 revert

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