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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 $G\$ and the Coulomb $1/(4\pi \epsilon _{0})\$ 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 $4\pi \$ and i am convinced that it is more natural if $\epsilon _{0}\$ and $\mu _{0}\$ and $Z_{0}\$ are more fundamental and should all be normalized to one as well as $c\$. the same arguement could be raised regarding gravitational radiation. the speed of propagation of gravitational radiation has been normalized to $c\$, but the characteristic impedance of propagation is, again, $4\pi \$, because they normalized $G\$ instead of $4\pi G\$. 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 $1/(4\pi \epsilon _{0})\$ verses $\epsilon _{0}\$, 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 $G\$, $c\$, $\epsilon _{0}\$, and $\hbar \$. 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 $G\$ or $4\pi G\$ that is normalized or $1/(4\pi \epsilon _{0})\$ verses $\epsilon _{0}\$. i'm in favor of rationalized Planck units that nomalize $4\pi G\$ and $\epsilon _{0}\$ (as well as $\hbar \$ and $c\$). 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.

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 where he concisely points out exactly what dimensionful universal quantities are normalized by the choice of units.

Planck units: $\hbar =c=G=1\ \ e^{2}=\alpha \$

Stoney units: $c=e=G=1\ \ \hbar =1/\alpha \$

"Schrodinger" units: $\hbar =e=G=1\ \ c=1/\alpha \$

"Dirac" units: $c=e=m_{e}=1\ \ \hbar =1/\alpha \$

"Bohr" units: $\hbar =e=m_{e}=1\ \ c=1/\alpha \$

(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: $\hbar =c=G=e=1\$

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 $1/(4\pi \epsilon _{0})\$) 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:

$F={\frac {Q_{1}Q_{2}}{r^{2}}}$

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

$F=\alpha {\frac {Q_{1}Q_{2}}{r^{2}}}$

and that's fine, but you'll be carrying that $4\pi \alpha \$ 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 $4\pi \alpha \$ 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: $\hbar =k=e=c=4\pi \epsilon _{0}=1\$

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 $G\$, 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

$\hbar =c=4\pi G=\epsilon _{0}=1\ \ \ e={\sqrt {4\pi \alpha }}\$

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 $4\pi \$ 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: $\hbar =k=e=c=4\pi \epsilon _{0}=1\$

This, of course has the nice consequence of setting $\alpha =1\$. 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 $\hbar =c=e=1\$, which I do, then I'm going to be stuck with $\alpha =1/(4\pi \epsilon _{0})\$. I guess I could live with that. I wouldn't be carrying $\alpha \$ 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: $\hbar =c=k=G=e=1\ \alpha =1/(4\pi \epsilon _{0})\$

Jimp 17Jun05

Jimp, i should have made it clear that the $\alpha \$ 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 $k\$ 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 $\hbar =k=e=c=4\pi \epsilon _{0}=1\$ that does not force $\alpha \$ 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 $\epsilon _{0}\$ and $e\$, but you can't, well, i think you should just accept the inevitable wisdom of the "r b-j units": $\hbar =c=4\pi G=\epsilon _{0}=1\ \ \ e={\sqrt {4\pi \alpha }}\$ . 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 $\epsilon _{0}=1\$ 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 $k=1\$. 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 $m_{e}=1\$ 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

$E=k{\frac {Q}{r^{2}}}$

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

$E=k_{r}{\frac {Q}{4\pi r^{2}}}$

and it's the rationalized constant $k_{r}\$ 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 $10^{25}l_{P}\$, but it is, or why biological cells are about $10^{5}\$ bigger than an atom, but they are, or why we are about $10^{5}\$ 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 $10^{35}l_{P}\$, our clocks would tick about once every $10^{44}t_{P}\$, and, by definition, we would always perceive the speed of light to be $c={\frac {1l_{P}}{1t_{P}}}\$ which is the same as how we do now, no matter how some "god-like" manipulator changes it.

now if some dimensionless value like $\alpha \$ changed, that's different. we would perceive the difference. but to attribute that change to a change in $c\$, that case is not defensible. you could argue that the change in $\alpha \$ 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 ${\sqrt {4\pi }}\$, 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)

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"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.

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"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).

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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

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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)

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

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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)

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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)

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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]. "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] 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 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 $E=E_{p}{\frac {m}{m_{p}}}$ 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:

$E=E_{p}{\frac {m}{m_{p}}}$ i think should be written

$E=E_{P}{\frac {m}{m_{P}}}$

if i understand what you meant to say. the symbol $m_{p}\$ is often understood to be the mass of the proton.

secondly, in terms of Planck units,

$E=m\$.

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

${\frac {E}{E_{P}}}={\frac {m}{m_{P}}}$

(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.

$E=m\$ 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

$E={\frac {1}{t}}$ and

$E={\frac {1}{l}}$

if treated this way.

Agree that

${\frac {E}{E_{P}}}={\frac {m}{m_{P}}}$

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

${\frac {m}{m_{P}}}$

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

$E=m\$ in Planck units

means the same thing as

${\frac {E}{E_{P}}}={\frac {m}{m_{P}}}$ in any arbitrary but consistent set of units

so it is that

$E={\frac {1}{t}}$ and

$E={\frac {1}{l}}$ in Planck units

means the same thing as

${\frac {E}{E_{P}}}={\frac {t_{P}}{t}}$ and

${\frac {E}{E_{P}}}={\frac {l_{P}}{l}}$ in any units.

in fact, for instance, Coulomb's Law

$F={\frac {q_{1}q_{2}}{r^{2}}}$ in Planck units

means the same thing as

$F/F_{P}={\frac {(q_{1}/q_{P})(q_{2}/q_{P})}{(r/l_{P})^{2}}}$ in arbitrary, consistent units.

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

$F={\frac {F_{P}l_{P}^{2}}{q_{P}^{2}}}{\frac {q_{1}q_{2}}{r^{2}}}$ in arbitrary, consistent units which is

$F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}$

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

$F={\frac {F_{P}l_{P}^{2}}{q_{P}^{2}}}{\frac {q_{1}q_{2}}{r^{2}}}$

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:

$F=F_{P}{\frac {l_{P}^{2}}{r^{2}}}{\frac {q_{1}q_{2}}{q_{P}^{2}}}$

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:

$F/F_{P}={\frac {(q_{1}/q_{P})(q_{2}/q_{P})}{(r/l_{P})^{2}}}$

or

$F/F_{P}={\frac {(m_{1}/m_{P})(m_{2}/m_{P})}{(r/l_{P})^{2}}}$

or

$E/E_{P}=m/m_{P}\$

or

$E/E_{P}=\omega t_{P}\$

instead of

$F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}$

or

$F=G{\frac {m_{1}m_{2}}{r^{2}}}$

or

$E=mc^{2}\$

or

$E=\hbar \omega \$ .

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.

you said: "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."

i suspect that is true, too. otherwise i don't understand why Nature would bother to take the electromagnetic flux emanating or diverging from some point and bother to scale it with some constant before it can be the force acting on a charged particle. that's why i see the rationalized Planck units (those that normalize $4\pi G\$ and $\epsilon _{0}\$) as truly fundamental units in which all of measurements and perception of reality ulimately is scaled against. it's not yet real physics. but they're talking about it in some contexts. there is sci.physics.discrete which is a newsgroup on discrete space-time theories of physics. but those guys do not see the Planck Time or Planck Length as plausible discrete units for this discrete space-time. i dunno why. r b-j 15:17, 23 Jun 2005 (UTC)

i realize that i did not address your question at the end. in my opinion, saying that

$E=m\$ in Planck units

or

$F={\frac {q_{1}q_{2}}{r^{2}}}$ in Planck units

or

$F={\frac {m_{1}m_{2}}{r^{2}}}$ in Planck units

means the same thing as

$E/E_{P}=m/m_{P}\$

or

$F/F_{P}={\frac {(q_{1}/q_{P})(q_{2}/q_{P})}{(r/l_{P})^{2}}}$

or

$F/F_{P}={\frac {(m_{1}/m_{P})(m_{2}/m_{P})}{(r/l_{P})^{2}}}$

manipulating these equations get you the same as your equations, no?

also, someone added (and i expanded) some lines that are sorta inverse mappings that define those 5 fundamental constants in terms of combinations of Planck units. you can plug those expressions into the conventional equations of physical law and get something that looks like your equations, no? r b-j 02:03, 24 Jun 2005 (UTC)

Agree to your first response. The answer to the question why "those guys do not see the Planck Time or Planck Length as plausible discrete units for this discrete space-time" certainly is manyfold but the key point appears to me that they do not yet realise that the Planck units seem to be a result of the underlying structures mentioned earlier which I think are THE fundamental structures. This may explain why they do not consider Planck units as fundamental as they should be considered in my opinion. That Planck units could be misunderstood as being not discrete (and therefore not "accepted" by "discretionists") is obvious: they are upper resp. lower limits, depending whether c is in the numerator or the denominator of the equations defining them from the natural constants. Approaching those limits is quasi-continuous until getting close to the limits. Then the approaching process I think gets more and more discrete. In other terms, taking Planck length as an example, I think there is 1 Planck length, 2, 3, 4 etc. to define a distance. Climbing up the numbers we pretty soon get to big numbers that look like a continuum.

Getting to your second response, first "no?": Of course, yes. However, it might be helpful for a less experienced reader of the article to outline a bit the manipulations to get from e.g. $E=m\$ to $E/E_{P}=m/m_{P}\$

Re second "no?": Of course, yes, as I used exactly that approach to get to the examples I mentioned. Oddy.

Having thought about the way to explain the "manipulation" for less experienced readers I would like to propose a little extension of the section at the beginning of the article where it states:

"Natural units have the advantage of simplifying many equations in physics by removing conversion factors. For this reason, they are popular in quantum gravity research."

Extended text:

"Natural units have the advantage of simplifying many equations in physics by removing conversion factors. For this reason, they are popular in quantum gravity research.

The removing process is as follows taking Einstein's famous mass-energy equation E = m c^2 as an example:

First c^2 gets expressed by Planck units to provide

$E={\frac {E_{P}}{m_{P}}}m$

Because in equations based on Planck units the normalisation factor

${\frac {E_{P}}{m_{P}}}$

becomes 1, the resulting equation for Energy becomes

$E=m$

In the following examples that process is applied to some other equations:"

Proceed with current article text (but remove redundency on Einstein's equation, later).

Oddy, 26-June-05

Significant Figures

Your Planck units of length, mass, etc. have too many significant figures. The gravitational constant itself is only known within .01%, four significant figures. Using as many as 6 significant figures on measurements that include G is simply absurd and meaningless. -RobertDonald 25 Oct 2005

(Robert, try using four tildes to sign and timestamp your edits)

G is listed to 5 digits even though the last one is less than the std error. when you square root, you get another approx ¹/₂ digit. the NIST values for: Planck Time Planck Length Planck Mass all are listed to 6 digits. we just copied their numbers. if it's good enough for NIST, i think it's good enough for WP. but you're right, G messes up accuracy. that's why the Planck Charge has more digits. r b-j 01:47, 26 October 2005 (UTC)

Planck Units only a concept?

Would like to pick up the discussion we had in June. Sorry for being that late. Based on some consent we found those days I think the following part of the article

"The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is."

might benefit from some additional perspective. Even if true it discourages to look into possibilities of underlying structures we communicated about in June. Therefore I propose to phrase something like:

"The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is. Accordingly Planck units usually are considered as a concept only and are just used as a tool to facilitate certain types of physical equations. However, it cannot be excluded and some aspects of the Planck units point to the possibility that the units are not only a concept but are the result of underlying structures not yet known due to their sizes and the difficulties to measure such sizes. It might be rewarding to look closer into that aspect.

The electromagnetic force ..."

What do you think?

Oddy, Nov. 10, 2005

Oddy, you should get a wikipedia account so your edits can be connected to your name and not some IP address.

i am not sure what it is that is added by the words you propose to add (i took the liberty to italicize them above). The point of saying "The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is." is to make the point that it isn't clear that "Gravity is an extremely weak force in comparison to other fundamental forces." indeed, from the POV of Planck Units, gravity and E&M are not directly comparable and are ostensibly equal in strength in terms of gravity acting on the Planck Mass and E&M acting of the Planck Charge. the reason why, for subatomic particles, that gravity is so weak (compared to E&M or the strong or weak nuclear forces), is that the charge of these particles are roughly the Planck Charge but the masses of these particles are far, far less than the Planck Mass.

Planck Units aren't merely meaningless concepts since there is a whole discipline of physics regarding the "Planck scale" which is where we were immediately after the Big Bang. e.g. a Planck Mass squeezed into a sphere or cube the size of the Planck Length becomes a black hole. that's a solution to a physics problem, not just a concept or an empty definition. r b-j 06:27, 11 November 2005 (UTC)

Robert, perceived "the strength of gravity ..." differently. Thought it was about saying in other words that Planck units are what they are and there is no value in attempting to find out why they are as they are. Hence I interpreted this as "only conceptual value". No problem to discuss the aspect of concept and the discipline you mentioned at a more appropriate part of the article. Think readers might be interested in learning about.

Squeezing the Planck mass into a sphere sized a Planck length produces a black hole. But squeezing the square of a Planck mass into that sphere you get a set of natural constants. No? --Oddy 17:33, 13 November 2005 (UTC)

i don't even know what you mean by"But squeezing the square of a Planck mass into that sphere you get a set of natural constants." what is the "square of a Planck mass"? Oddy, we need to keep original research out of the article. i will admit that, by including all of these equations, with and without the dimensionful universal constants, that i was expanding on what i thought was the first osetensible consequence of what happens when you use Planck Units. the Invariant Scaling section is a sorta translation of what Duff (and others) were saying, but using the language of Planck units more explicitly (for the sake of us engineers, etc.). i was not trying to inject pet theories into it, even though i have one or two. r b-j 19:35, 13 November 2005 (UTC)

Squeezing ${\frac {\hbar c}{G}}$ (= square of Planck mass) into ${\frac {\hbar G}{c^{3}}}$ (a 2-dimensional "sphere" = square of Planck length) "produces", i.e. remains to be on the level of, natural constants: hbar, c and G.

Similarly you may "squeeze" e.g. the Planck charges into such a "sphere". Playing with the formulae of your article, is that original research?

Shouldn't we read in the article a bit more about the discipline of physics related to the "Planck Scale" you mentioned? Seems to be important for the topic. --Oddy 10:23, 20 November 2005 (UTC)

forgive me for interleaving comments, Oddy. if you don't like it, you can revert this.

Playing around with the equations provides for example that the square of the Planck mass multiplied by the gravitational constant equals the square of the Planck charge multiplied by the Coulomb force constant.

i pretty sure that is exactly true. $G\$ is to mass as ${\frac {1}{4\pi \epsilon _{0}}}\$ is to electric charge.

How does this relate to the statement in the article: "The strength of gravity is simply what it is and the strength of the electromagnetic force simply is what it is. The electromagnetic force operates on a different physical quantity (electric charge) than gravity (mass) so it cannot be compared directly to gravity."? Appears that a comparison is possible? --Oddy 20:41, 1 December 2005 (UTC)

i think that is true, but i don't know exactly what statement you want to add that really adds to the concept. because, by definition, a pair of Planck Masses will exert the same force on each other as a pair of Planck Charges spaced at equal distances, and since they're both inverse-square, that will be true at any common spacing. so it is, from this Planck units POV, meaningless to say that "the strength of gravity is so, so much weaker than the other fundamental forces." it appears to be so weak in the context of fundamental particles, because if such a pair of particles have charge, the amount of charge is about a unit charge (in the ballpark, anyway), but their masses are so, so much less than the unit mass. anyway, so propose a statement that you would like to add, Oddy. or just add it, i am not the "keeper of the article". but if it appears untrue or unnecessarily redundant or tautological, i might edit it. r b-j 21:32, 1 December 2005 (UTC)

Robert, interleaving comments are ok for me. So far I don't know either what statement exactly we should add to the article. I think we need to discuss that further. What strikes me is that there seems to be an equivalence between mass and charge. Above equations also can read as: $m_{P}^{2}=q_{P}^{2}{\frac {k_{c}}{G}}$.

if, $k_{c}={\frac {1}{4\pi \epsilon _{0}}}$, then that is true, but i am not sure what is added by explicitly including it.

From earlier playing around I got to the following equation for gravity: $F=F_{P}{\frac {l_{P}}{\lambda _{1}}}{\frac {l_{P}}{\lambda _{2}}}{\frac {l_{P}^{2}}{r^{2}}}$ where $\lambda _{1}and\lambda _{2}$ are the "wavelengths" of mass 1 and mass 2. If you set the "Wavelengths" as Planck length you get an equation that in terms of "strength" of force is similar to the Coulomb's law: $F=F_{P}{\frac {l_{P}^{2}}{r^{2}}}$.

hmmmm. "wavelengths of mass 1 and mass 2"? (i know... mass is energy is frequency is reciprocal of wavelength, but i don't get the point.)

In other words, this points to an aspect that the vast majority of difference between electromagnetic forces and gravitational forces might result from gravitational forces operating on a "big" thing, i.e. proton sized, whereas electromagnetic forces might operate on something that is Planck-length-sized (maybe electrons have a "nucleus" of that size?????).

this really looks like original research or, at least, a sorta pet theory if it came from someone other than you, Oddy.

The remaining differences may result from differences in electric charge and Planck charge as expressed via Fine Structure Constant in the article. --Oddy 09:31, 3 December 2005 (UTC)

anyway, this ain't the place to test a theory. if i or anyone else wrote something here that was not written somewhere else, either it should follow conservatively from what is common knowledge in the field or it is maybe original research and then shouldn't be in the article. i will admit that i never saw a single article or paper list all of those field equations without their dimensionful physical constants in there, but listing them here is a conservative extension of simply the definition of Planck units. the "invariable scaling of nature" section is something that Duff, et. al. had published, but i restated the concept using the concept of Natural units and a thought experiment that even neanderthal engineers, like myself, could readily understand. i truly believe i had not added original research, and if some other editor thinks i had, they can remove it and we can have a discussion about how orthodox those words were or not.

anyway, Oddy, you have to think about how orthodox some of these ideas of yours are. and other people also get to say so. r b-j 06:30, 4 December 2005 (UTC)

Robert, the intent of above was not to include it into the article but to provide some perspective on statements that are in there. Based on those perspectives I think that e.g. the presence of Wilczek's statement "...the strength of gravity simply is what it is, a primary quantity, while the proton's mass is the tiny number ..." should be reconsidered. It discourages readers to look into the fascinating field of "why is it as it is". Instead I hope we find a way for statements that encourages readers to look into such questions.

if the "why is it as it is" question is about the tiny, tiny mass of the proton (as well as other fundamental particles) i don't think it discourages pondering that at all. what Wilczek is sorta discouraging is pondering why G or the strength of gravity is so small, because it really isn't. without the context of objects with some mass and some charge, the comparison of field strengths of different interactions is not meaningful. it is really not small or large.

Also I vigorously support to mention as much of the "Planck equations" as possible and the view of showing "extensions of simply the definitions of Planck units". I do not necessarily understand why these extensions need to be treated conservatively. As they are (mathematical) facts and no theories or research I do not see a reason to hide them to the readers if deemed potentially helpful for them. Think of the reader's needs for a comprehensive picture!

what particular "Planck equations" do you mean? like how are these expressions for the Base Planck units derived?

In that context I would like to repeat my earlier question: "Shouldn't we read in the article a bit more about the discipline of physics related to the "Planck Scale" you mentioned? Seems to be important for the topic." Do you see a chance that you insert something about that discipline into the article? --Oddy 21:31, 7 December 2005 (UTC)

not by me. i don't know enough about high-energy physics to do anything like that competently. i certainly would welcome it if some real physiker wrote something like that. r b-j 05:49, 8 December 2005 (UTC)

Fundamental?

I'm having trouble following the above discussion, which I think is about the same question I want to ask. What is the theoretical basis for assigning such importance to the planck units? I'm not talking about using them as a better system of measurement, I understand that, but what makes anyone think that "physics breaks down" at the planck scale of time and space? Combining G, h and c gives a very small length and a very small time, but it gives a pretty big mass, relatively, so why does physics break down at the planck length, but not the planck mass? If there is a well-known, accepted reason that these units are considered a real boundary, I think it belongs in the article. --Monguin61 05:03, 11 December 2005 (UTC)

i know this is not your issue ("a better system of measurement"), but i still believe the primary salience of Planck units is a standard of quantitative description of physical values that is based on nothing. not based on any property of any substance, object, particle, or "thing". in this system, there is no variable c, or h, or G or epsilon0, because they're all just 1 (well epsilon0 = 1/(4*pi), but there i think Planck units could be better). when you expression masses and times and lengths and electric quantities in terms of Planck units, these quantities are shorn of all of their dimensional dependence and that helps physicists to ask the right questions. (i.e. see the Duff paper disputing the variable speed of light hypotheses.)

as far as physics breaking down at Planck scales of length and time, we need some real physicists to chime in here. below are links to a paper of a guy who thinks he has a slightly better idea of the most natural units based on absolute maximum physical quantities possible in the universe. the speed of light is one that we know of, but this guys claims to have worked out that there is a maximum force (about F_p/4), and other limits (which are his basis for "natural units"). maybe this might be helpful, but i cannot atest to the veracity of the physics here, but it might be right(??) websie chapter on universal limits appendices r b-j 06:40, 11 December 2005 (UTC)

When reading the link I found a statement which I believe is incomplete. It says

"The exploration of the force and power limits shows that they are achieved only at horizons; the limits are not reached in any other situation."

There is another situation where they can be achieved as well: Everywhere and at every time. This is because force and power are vectors. If the "diameter" of such a vector is just a Planck length, a huge amount of such vectors, each being the Planck force, could apply to big particles (compared to Planck length) like a proton from every direction and, if applying isotropically, the resulting force that we are able to measure would be zero. And if we disturb the isotropicity by applying "usual" forces to such a proton we would experience those vectors opposing "our" forces with exactly their amount. These vectors must be present everywhere because their bulding blocks are everywhere, too: the natural constants.

Also one of the paradoxons mentioned in the link can easily explained by the equation I mentioned before: "If any interaction is stronger than gravity, how can the maximum force be determined by gravity alone, which is the weakest interaction?"

Expressing Gravitational force by playing around with Planck units produces for example the equation:

$F=F_{P}{\frac {l_{P}}{\lambda _{1}}}{\frac {l_{P}}{\lambda _{2}}}{\frac {l_{P}^{2}}{r^{2}}}$

This describes gravity based on the Planck force and also explains why the resulting force is so small nevertheless. --Oddy 12:11, 11 December 2005 (UTC)

Personal opinions

Lucretius speaking here: I don't agree RBJ that your changes have improved matters. My concern here is that this invariant scaling section looks like a personal opinion, as evidenced by your rhetorical question at the end. I've now removed the rhetorical question (Gamow is unavailable to answer it) but I haven't yet made any other changes. I think even Duff was rather more objective than you have been since he at least includes in his paper (which you link to) the opinions of those who rejected his paper. I also have concerns about the length of this section. It really does lack conciseness. I'm sorry but this section appears to be the Gospel according to RBJ and I still think it is in need of considerable revision if Wiki's claim to being an impartial encyclopaedia is to mean anything. Lucretius 06:58, 31 December 2005 (UTC)

you go to sci.physics.research and see how much of a personal opinion it is. also talk a look at Talk:Variable_speed_of_light#A_changing_C_is_meaningful where i am discussing with "Scott" (he hadn't registered as an editor and created this article as an anon IP) about what the consensus of the physics community is and why (in the opinion of this electrical engineer) they have that consensus. it is not just my personal opinion, but i could tell that folks like Michael Duff and John Baez were getting tired of people not getting this and physicists like Paul Davies confusing the issue even more. this is why i thought putting this in this article was salient. when the quantities of the universe are measure or described in terms of Planck units there is no speed of light (or those other normalized constants). if someone thinks there was a cosmological (or a sudden) change in the speed of light and they think they measured such a phenomenon, what changed was the number of Planck lengths in their meter stick or the number of Planck times in the second of their clock or maybe both, and those (dimensionless) quantities are the salient ones that have changed. that is the whole point of that section. it is not simply my opinion and certainly not my original research. but it is my paraphrasing of the language used by Duff and other physicists that i have discussed with this on the moderated newsgroup sci.physics.research. r b-j 18:03, 31 December 2005 (UTC)

Lucretius again - I've deleted a large amount of text that I put here on the discussion page. I did so because it was ill-informed, because it was just waste of space, and because nobody replied. I hope this is OK - you can check the history page if you are curious about my failure to grasp the issues thus far.Lucretius 03:40, 2 January 2006 (UTC)

I think I am having problems with this issue because it is hard to know where the argument is coming from, Rbj. The papers you link to do not feature the argument you put forward - you express the argument in terms of Planck scale (which is appropriate to the article page) whereas those papers hardly touch on Planck units at all. Can you find a more appropriate link? I mean where did the argument in Planck terms come from? I really would like to understand the argument well enough to contribute to your article, if I may. I believe I can contribute something about the papers you linked to, (I've now read them several times) but as I said they're not strictly relevant.Lucretius 05:00, 2 January 2006 (UTC)

i've already provided two links. they are strictly relevant (but there is a paraphrasing on my part). your rewrite is far less concise. the point is simple. if our measuring standard is against the Planck units, the speed of light or the graviational constant or Planck's constant or the Coulomb electrostatic constant or the Boltzmann constant do not change. if, for some reason someone thinks they have, what really changed is the dimensionless ratio of the number of Planck lengths in a meter or the number of Planck times in a second (which is contrary to the assumtion of using Planck units as the standard of measure). Lucretius, please post to sci.physics.research and ask those guys and banter it about there before changing something like this.

This revert is of course your right. But did you actually read my revised version? This was my second rewrite and it was not the same as my previous rewrite, where I did try to make alterations to the argument. In this second rewrite, I merely tightened up the language but it was YOUR argument I phrased. I included in the revised version the link below, which is to a university sponsored web page that also puts forward your argument in quite simple and entertaining terms. I did not remove your links. I did remove some rhetorical devices you use, such as repetition, which indicate that you have an emotional investment in the article. I also removed redundant phrasing. The present intro, for example, is twice as long as mine without adding anything significant to the meaning. I won't bother to touch this article in future but, in its present form, someone is certain to rewrite it for you, and the next person might not try to honour your intentions, which is what I made a very conscientious effort to do.

I notice that you are using your real name whereas I of course am using an alias. This gives me an unfair advantage, particularly if you think I am using 'banter'. It is hard sometimes to criticize a piece of writing without also appearing to criticize the writer and it may be that I haven't always got the balance right. How does one stop the ball without tackling the man who is running with it? But I do try not to throw any sneaky punches. If anything I have said thus far causes you personal discomfort, you have my permission to delete it.

I should also add the reason why I originally misunderstood your intentions. There are two reasons:

1) the links to Duff et al are links to controversial papers (Duff for instance argues that no physical constants are truly fundamental, which is extreme even by the standards of his two colleagues. It's also extreme within the context of Planck units, which many believe are indeed fundamental). 2) your treatment of the subject appears controversialist owing to rhetorical devices.

It took me a while to get through these appearances and to realize that your article is not actually controversial but simply a statement of a commonly held position.

Anyway, I've enjoyed this little debate even though I don't much like the final outcome.

CheersLucretius 23:27, 2 January 2006 (UTC)

just to clarify (at least from my understanding), Duff doesn't say that no physical constants are truly fundamental, only that the dimensionful ones are not fundamental. all physical theories, the Standard model, GR, strings, whatever, can be expressed in their entirety without any dimensionful scaling constants. yet, according to John Baez, there remain some 26 fundamental numbers (dimensionless) that are needed. i don't think Duff means to imply that these physical constants are not fundamental to our current physics. also Veneziano does agree with Duff on that basic concept. as i read it, from sci.physics.research, there really is not much debate about it, despite the proponents of VSL or variable G or whatever. r b-j 06:14, 3 January 2006 (UTC)

Here is a link I have which seems better. It doesn't refer to Planck units but it does provide an uncontroversial overview of your general argument. Maybe you could rebuild the article around this:

[1]

[http//www.phys.unsw.edu.au\einsteinlight/jw/module6_constant.htm]

Lucretius 05:29, 2 January 2006 (UTC)

I've just saved a rewrite of the invariant scaling article, Rbj. It preserves the integrity of your meaning but expresses it more simply and concisely. My aim was to help you develop this into a better article and it was not to force my opinions on you. I hope you'll accept it as such. Lucretius 07:46, 2 January 2006 (UTC)

Pointless equations

I removed 5 equations because they are pointless and therefore lower the quality of the whole page. Eg:

$c={\frac {l_{P}}{t_{P}}}$

We could just as well substitute my Compton length and time for those of the Planck mass and the result would still be c. What does this prove? I apologize if this observation offends the contributor who inserted the equation.Lucretius 08:50, 31 December 2005 (UTC)

the original contributor was an anonymous IP and was done last February [2]. he did it for the 3 "more fundamental" universal constants, c, $\hbar \$, G. i added the latter two $\epsilon _{0}\$ and k. i am not invested in this, but i will say that it does has a small amount of meaning. expressed in terms of Planck units, there are no scaling factors (oh, there is the $4\pi \$ for $\epsilon _{0}\$, but that is because they convention, springing from cgs, did not choose to normalize $\epsilon _{0}\$, which i believe is a mistake, but the article isn't "r b-j's definition of natural units". this is not true (for all 3 or 5 constants) for any other system of units. as bantered about above, expressing one of these sorta fundamental equations in terms of Planck units (but with quantities measured in any consistent system of units would be, for example:

$F/F_{P}={\frac {(q_{1}/q_{P})(q_{2}/q_{P})}{(r/l_{P})^{2}}}$

and that can be rearranged to say:

$F={\frac {F_{P}l_{P}^{2}}{q_{P}^{2}}}{\frac {q_{1}q_{2}}{r^{2}}}$

$F={\frac {m_{P}l_{P}^{3}}{q_{P}^{2}t_{P}^{2}}}{\frac {q_{1}q_{2}}{r^{2}}}$

$F={\frac {1}{4\pi \epsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}$

and that is where these "pointless" equations come from and only when it's Planck units are all of those scaling factors gone. it's not sophisticated physics, but it does say something of note, which is why i chose to complete the idea of that anonymous IP rather than delete it. r b-j 17:41, 31 December 2005 (UTC)

Thanks RBJ for explanation. As you imply above, the significance of the 5 equations was much less than the space they took up. Thanks also for not restoring them. Lucretius 00:33, 1 January 2006 (UTC)

Can someone help me decode the meaning in the last edit of the article?

This in one sense contradicts George Gamow in Mr. Tompkins who suggests that if a dimensionful universal constant such as c changed, we would easily notice the difference;...

(new edit follows)

however, as noted, the disagreement is better thought of as the ambiguity in the phrase "changing a physical constant", when one does not specify whether one does so keeping all other dimensionless constants the same, or does so keeping all other dimensionful constants the same.

this is the sentence i have the most difficulty decoding.

The latter is a somewhat confusing possibility since most of our unit definitions are related to the outcomes of physical experiments which themselves depend on the constants, the only exception being the kilogram.

i don't see the kilogram as much different. the experiment is a scale where you put a weight of something in one side and the kilogram prototype in the other and compare. it is true that other experiments could be better, such as defining the kg in such a way to fix Planck's constant to a fixed value (as they did with the meter and c - this is something they are actually considering to do at NIST or whatever standards body).

Gamow does not address this subtlety; the thought experiments he conducts in his popular works assume the latter.

i would like the meaning of this to be more spelled out, also.

thanks, r b-j 07:27, 9 January 2006 (UTC)

Sure. It's a subtle point, but someone raised it!

The question is, if you change the speed of light, what else do you change?

Let's make things simple, and rewind to an earlier era when all of our units were defined in terms of physical objects.

OK, Gamov imagined (say) changing c, and leaving all the other dimensionful constants the same. For example, the gravitational constant G is still the same number, h is still the same number, listed elsewhere on the wiki. He did this for a popular book so you could notice e.g. relativistic time dilation driving in your car.

However, doing this makes things weird. In particular, it changes some dimensionless constants. e.g., the fine structure constant. Among other things, the FSC tells you (roughly) how strongly light interacts with matter. So Gamov's world is not just our world + relativistic effects coming in at much smaller velocities. It is actually a radically different world. Everything would be messed up. But Gamov doesn't describe that aspect of things.

That Duff et al. paper takes issue with doing that. "Changing a constant", they note, is vague in an important sense. What do you keep constant when you change c? G and h, like Gamow did? Or things like what you get when you combine them with other constants to make dimensionless numbers?

One would think Gamow wanted to "keep everything the same -- e.g., the interaction between light and matter -- but change the speed of light." That would mean keeping the dimensionless ratios the same.

If you did that, then you wouldn't mess up the interaction between light and matter. In fact you would never notice the difference at all -- you wouldn't even suddenly discover that running fast caused time dilation! Everything would "scale." This is described earlier in the section. Hence the disagreement is due to an ambiguity in the nature of the term.

OK, now things get even more complicated. The meter is defined in terms of the speed of light. If you changed the constant c even the way Gamov did, you would change the definition of the meter. Actually, things get hugely complicated if you change c the way Gamov did and reference your units to the constants, for example if you were driving in a car, suddenly your speed would be redefined to something else! Hence that little parenthetical remark about everything going to hell for poor old Gamov because our unit definitions are all referenced to the constants except the kilo.

Does that make sense? Do please rewrite, I tend to be very longwinded and have long sentences.

PS: all of this is very super tricky. In the Duff paper the three authors disagree on this, and they are all very smart, e.g. Gabriele Veneziano. I'm finishing my doctorate and had to pause and think very slowly even to figure out their paper.

Sdedeo (tips) 11:25, 9 January 2006 (UTC)

Lucretius wrote this: I agree with Sdedeo that the Duff and trilogy papers are 'super tricky' (from the viewpoint of anyone who is not fully across the subject), which is why I've said here before that they are not the most suitable reference material, particularly for the sort of readers Wiki is likely to attract. I've also said that the article, as it now appears, tends to invite indiscriminate editing, because it looks like a draft. I really think you need to work on it more Rbj. However, I agree with you that Sdedeo's addition does not improve the clarity of the argument and the article is better off without it.

Sdedeo, you should realize that Rbj already understands the basic issues that you have outlined (it's one of his favourite topics). I guess your doctoral thesis is on an entirely unrelated subject. Lucretius 00:37, 10 January 2006 (UTC)

Hey, it's the wiki, be bold! If you're going to get into the details in that section, you need to get it right, though. Sdedeo (tips) 01:16, 10 January 2006 (UTC)

i think that i got it right. BTW, about 2 or 3 years ago, i was in email conversation with all three, Duff, Okun, and Veneziano, and after discovering that other Duff paper i have been back in contact with Duff and bounced this paraphrase off of him and he did not dismiss it. also, in the Trialogue paper, Veneziano essentially agrees with Duff in the overall issue: "I also agree with Mike that all that matters are pure numbers."

Duff did caution me (in an email) not to emphasize Planck units ($c=\hbar =G=4\pi \epsilon _{0}=1,e^{2}=\alpha$) over other natural unit systems, e.g.: Stoney units ($c=e=G=1,\hbar =1/\alpha$), "Schödinger units" ($\hbar =e=G=1,c=1/\alpha$), "Dirac units" ($c=e=m_{e}=1,\hbar =1/\alpha$), and "Bohr units" ($\hbar =e=m_{e}=1,c=1/\alpha$). i fully admit that i have a personal preference for rationalized Planck units ($c=\hbar =4\pi G=\epsilon _{0}=1,e^{2}=4\pi \alpha$) but these are essentially Planck units. i like Planck units because they are based only on the measurable properties (measurable in terms of anthropometric units) of the vacuum and not based on the properties of any anthropocentric prototype or choice of substance or particle or "thing".

anyway, my problem is with sentences like: "...however, as noted, the disagreement is better thought of as the ambiguity in the phrase "changing a physical constant", when one does not specify whether one does so keeping all other dimensionless constants the same, or does so keeping all other dimensionful constants the same." which are nearly impossible to parse. now when you say "The question is, if you change the speed of light, what else do you change?", i think i start to understand what you mean, but you're not dispelling the point. i would say this, if some "god-like" being changes the speed of light, nothing would be perceptibly different if $c,\hbar ,\epsilon _{0},e$ were changed in such a way to keep α the same and if all particle masses relative to the Planck mass remained the same (and all other dimensionless quantities). so i still do not get your point.

now, if you were to say instead, The question is, if you change α, what else do you change? then i would think that you're asking, if α changes, then some factor of it, like c or h or e or ε₀ or a combination of them has changed. which one? and my (and Duff's) answer to that is simply it depends on what unit system you use. and, unlike Duff, i really think that there is a natural preference for Planck units (because these are the units of the vacuum, or nothing) and that would imply that it is e that is changing. but Duff disagrees and i accept his authority for the most part. he says that an electroscope calibrated in terms of e is just as "natural" or valid to measure charge with as one that is calibrated in terms of q_P.

the point eventually boils down to this: you can sweep up all of the physics textbooks and papers in the literature and reword the text and rewrite the math so that $c=\hbar =G=4\pi \epsilon _{0}=1$ is true everywhere. then there is no speed of light or Planck's constant or gravitational constant anywhere to change or to notice a change. but there remain α, this measure of the relative strength of the E&M field. if α were to change, it really doesn't matter if it is e that changes or c or h, the end operational effect is the same.

so Sdedeo, how might you suggest we reword the sentences to most clearly and concisely say what it is you want to say? r b-j 03:08, 10 January 2006 (UTC)

BTW, Sdedeo and Lucretius and anyone else listening in, there is a serious effort to get rid of the kilogram prototype you refer to Sdedeo. Redefinition of the kilogram: a decision whose time has come. Just as they have redefined the meter to set c to an exact value, this redefinition would have the effect of setting h to an exact value and would replace the kilo prototype with a watt-balance. They have three proposed redefinitions, the one i like best is:

The kilogram is the mass of a body at rest whose equivalent energy corresponds to a frequency of exactly [(299792458)²/6626069311] × 10⁴³ Hz.

now with c and h defined, all there is left is to fix G to a constant value, but the current SI definition of a second, in terms of Cesium radiation is a very stable standard and, in terms of that standard, our measurement of G is relatively sloppy, that this would not make practical sense. but if they did, it would be equivalent to measuring everything in terms of Planck units. our meter, kilogram, and second would just be defined to be fixed multiples of their respective Planck units. i think that's another way to think about the "inoperability" of this "varying c" or "varying G" debate. r b-j 03:41, 10 January 2006 (UTC)

Hm. These questions of what is "really changing", c or α I think are more philosophical than scientific. I just think it's important to make clear that there are two distinct notions for "changing the speed of light." Change c and keep alpha etc. constant, or change c and keep e, h, etc., etc. constant. I started to draft a new version, but got tired! Will come back to the article. Sdedeo (tips) 03:53, 10 January 2006 (UTC)

Sorry Sdedeo, i must fully disagree with you about "questions of what is "really changing", c or α I think are more philosophical than scientific. The prospect of α changing is operationally meaningful. It makes a difference in our lives, how we perceive and measure things. It makes no difference what unit definitions you use to measure stuff, if α changes, things will be different. Now whether it is c or h or e changing, is just a matter of what units you use and, as Duff says: The laws of physics "do not give a fig which units are chosen. ... The failure to tell the difference between changing units and changing physics is more than just semantics. It brings to mind the old lady who, when asked by the TV interviewer whether she believed in global warming, responded: “If you ask me, it’s all this changing from Fahrenheit to Centigrade that’s causing it”." You should go to sci.physics.research and ask those guys what is physics about this and what is philosophical. r b-j 04:20, 10 January 2006 (UTC)

r-b-j, I find your comments here needlessly aggressive and confrontational. Furthermore, there is a clear difference between changing a unit and changing a dimensionful constant, as I've explained above, and two separate senses can be given to the idea of changing a dimensionful constant, both of which are separate from the sense of changing a unit.

Further, whether you want to view a "VSL" theory such as those proposed by Joao Magueijo as a "changing speed of light" or a "changing alpha" seems to me to be a matter of taste, which is why I've referred to it as "more philosophical than scientific." You are free to disagree. What is important for the article is that we represent the views of others correctly. Right now, the article only represents the "zero constants" view of Duff (which you seem to prefer), and does not give appropriate attention to the dissenting views of the other two authors on that paper.

Sdedeo (tips) 04:56, 10 January 2006 (UTC)

Lucretius wrote this: Sdedeo, you might read the debate I had with Rbj on this page under the heading 'Personal Opinions'. If nothing else, it might save you time arguing this point again. Or you might choose to continue it in an expanded form. However, I have already said I would not bother to touch the article again and I have to stand by my word or I'll look like someone who never says what he means. Best of luck to you and my respects to Rbj. Lucretius 05:11, 10 January 2006 (UTC)

i am not trying to be confrontational. i'm just trying to hold the line on an apparently dubious notion that, unfortunately finds its way into the New York Times as well as other places. i know that Magueijo and John Moffat and Paul Davies get a lot of popular press with their promugation of VSL, but as best as i can tell on many blogs and a couple of newgroups like sci.physics.research, the measurability and meaningfulness of the VSL or varying-G or varying any dimensionful universal "constant" is just not given much credence. the argument goes many ways (most of which do not use Planck units) but essentially boils down to that all of the descriptions and equations of physics and all of the constants of nature either are, or can be expressed with no dimensionful quantities or dimensionful scaling constants. in this representation, there simply is no c or h or G. if you think there is a measured change in c or h or G, there is always a more salient dimensionless "constant" of nature that is changing. i think they presently believe there are about 26 of these constants of nature. Magueijo and Moffat and Davies can write books and get all of the popular exposure they want and this fact is not diminished. Duff is probably the most strident opponent of ascribing any meaningfulness to the VSL notion but he is certainly not alone. John Baez, Ted Bunn, Jan Lodder would say the same thing.

now the VSL or varying-G or whatever theories or hypothesis deserve mention (and space) in WP. but until they become really established physics, there should be some qualification included. r b-j 07:11, 10 January 2006 (UTC)

BTW, are you in or from Vermont, Sdedeo? i see a lot of edits with your name there. just curious. r b-j 07:11, 10 January 2006 (UTC)

The point I'm making here is that the views of other scientists -- including the co-authors on Duff's trialogue paper -- need to be represented in this article. I don't think we should get into a debate about what you and I think about the issue, and we certaintly should not be debating what is "more salient". You seem to be much more engaged in this debate than I, so you are perhaps the person who could do it best. I don't think VSL or varying-G is going to become mainstream any time soon (for the simple reason that the experimental evidence is strongly against.)

I lived in Vermont for a little bit -- I taught there before going to graduate school! Sdedeo (tips) 20:25, 10 January 2006 (UTC)

cool, you may have seen at my user page that i'm in Burlington. (where/when were you in VT?)

i dunno exactly how to validly represent any position that variation in dimensionful constants can be measured. about "the simple reason that the experimental evidence is strongly against" VSL also does not really make sense to me. it's more about whether or not there is experimental evidence of whether α (or some other dimensionless parameter) varies or not. but we do not measure the speed of light. we might measure it against a like dimensioned unit, perhaps constructed from a meter stick and a clock, but then this dimensionless number that comes out is not just c. so i do not even understand how there can be any experimental evidence strongly against (or for) VSL. r b-j 23:31, 10 January 2006 (UTC)

I was near Brattleboro, down south. Loved the state, really beautiful.

I think we're agreed on the idea that we should represent other views, e.g., those of Duff's collaborators, and also that we should clarify the errors in Gamow's presentation. So let me just add some thoughts of my own.

I think (not to repeat myself) that there is a sense to changing the speed of light. For example, doing so (let's say instantaneously) would potentially change the causal relationship between two points in spacetime (the original idea of Joao's VSL, AFAIK.) Two points in spacetime that were causally disconnected would become connected. This all makes sense in a world without h, or even G in the flat space case, and so there would be no way to discuss things in terms of dimensionless quantities.

VSL as I understand it makes a prediction about the causal relationships of spacetime in the early universe. Now whether or not consequences of those predictions can be measured in the lab is another question. Sdedeo (tips) 23:50, 10 January 2006 (UTC)

well, this still begs the question about VSL. if what you say about it is accurate if a different c made an operationally different effect in spacetime in the early universe, would that not be a measurable difference? we have these two world outcomes: one in which c was different long ago than it is now and made some different astronomical observation than we would make in the other outcome if c was not operationally different. the universe (and our telescopes) is the lab. however it is that we measured what c was long ago, to make this difference in the causal relationships of spacetime in the early universe, it is still measured against something of like dimension. that ratio is the salient quantity. r b-j 05:28, 17 January 2006 (UTC)

Lucretius wrote this: I won't be editing this article but I just want to remind you there is a very good link here:

[3]

It's simple and quite entertaining and it explains the basic argument very well. Lucretius 23:02, 17 January 2006 (UTC)

link doesn't work. backslash suspect. r b-j 23:30, 17 January 2006 (UTC)

That's odd - it works this end. It's to an Australian uni website but it should open even for an American. Just before you click on the link, say the magic word G'day and it should open that end also. Lucretius 23:48, 17 January 2006 (UTC)

三Take that, Balthazar!

i still get:

Not Found

The requested URL /einsteinlight/jw/module6_constant.htm| was not found on this server.
------------------------------------------------------------------------
Apache Server at www.phys.unsw.edu.au Port 80

Sorry, there was some garbage hanging on after the "htm". It should work now. P0M 08:15, 18 January 2006 (UTC)

Why no Planck force link?

I fail to understand, Rbj, why you think the link to Planck force was irrelevant, particularly since you went out of your way to edit that article so as to give primary significance to Planck quantities.Lucretius 03:40, 15 January 2006 (UTC)

as i said in the Edit summary, it is already linked two different places, just like nearly all of the other Planck units. why should the Planck force appear in the See also section and not the Planck mass? or Planck length? r b-j 04:34, 15 January 2006 (UTC)

My apologies, Rbj. Lucretius 18:09, 15 January 2006 (UTC)

Simplification, and basic and derived Planck units

Interesting to read all your above discussion.

In the article it reads now: "Natural units have the advantage of simplifying many equations in physics by removing conversion factors. For this reason, they are popular in quantum gravity research."

Propose you add a line how this removal of conversion factors works to enable less experienced readers to better understand how the subsequent tabulation was generated. --Oddy 01:14, 24 January 2006 (UTC)

Ooops, forgot to ask why the key objects of the article, the tabulations of basic and derived Planck units, are displayed so far down in the article? I think they should be as far on the top as possible. --Oddy 01:19, 24 January 2006 (UTC)

Discussion page

I vote this nerdiest discussion page on wikipedia! -nerd who has been humbled —Preceding unsigned comment added by 69.234.250.240 (talk • contribs) on 03:43, 19 April 2006

edits of 5/5/06.

okay about anonymous IP User:132.181.160.42 (University of Canterbury, Christchurh NZ) and anonymous IP User:202.36.179.65 (Christchurch College of Education), i strongly suspect that this is the same editor (why not get an account and username?). not all of your edits make the article better.

some changes back: Planck units are not only the base Planck units, just as SI units are not only the SI base units. Planck units are not the only "natural units". there are other systems of natural units (Stoney, atomic, etc.) that normalize different natural quantities. i added a sentence about why Planck units might be "more natural".

the idea of E.T. is not just that E.T. could use or know of natural units but that extra-terrestrial intelligence might be expected (by us or a 3rd party E.T.) to use the same system of units. this addresses the remote possibilty of one-way communication with E.T., if we receive a message or send one (that somehow the other can decode) and then to make references to distances, sizes of things, etc. how do we communicate this to E.T.?

"The dimensionless fine-structure constant can be thought of as taking on the numerical value that it does because of the amount of charge, measured in Planck units, that nature has assigned ..." this is a qualification and has to do with the fact that it could also, just as legitimately, be thought of the other way around. maybe the fine-structure constant is the fundamental value and the amount of charge in electrons, etc. take on the value they do because of that.

other changes are hopefully self-explanatory. we can talk about it. Rbj 06:42, 5 May 2006 (UTC)

some more comments on those edits of 5/5/06

It's certainly true that Planck units are not the only "natural units"; indeed the whole concept of natural units is a somewhat fuzzy one. They presumably should be based on aspects of physics that are uniform throughout the whole universe (like the radius of a hydrogen atom in its ground state) instead of entities that are only found in a specific location (the length of a specific king's foot, or the length of a specific platinum rod), but what about this:

the distance that light emitted by a cesium 133 atom transitioning between the two hyperfine levels of its ground state will travel as it vibrates exactly 9,192,631,770 / 299,792,458 times?

This distance - the current definition of a meter - can be replicated throughout the universe, at least wherever there are enough protons, neutrons and electrons to make an atom of cesium 133. So, in some sense it's natural. However, it's absurdly complicated, and nobody would consider it a sensible "natural unit". How about this:

the distance that light emitted by a cesium 133 atom transitioning between the two hyperfine levels of its ground state will travel as it vibrates exactly 1 time?

or this:

the distance that light emitted by a hydrogen atom transitioning between the two hyperfine levels of its ground state will travel as it vibrates exactly 1 time?

Now it's starting to seem more "natural". You see there's a fuzzy borderline... I can produce units of length that range continuously in how "natural" they seem, from the Planck length to the length of Louis XIV's right foot.

It's not true that the Planck units are "unique in that they are not based on properties of any prototype, object, or particle but are based only on properties of free space". I can make up tons of systems of units like that. To take just my favorite, I prefer the units where 8 π G = 1 instead of G = 1. If you look at Einstein's equations in the article you'll see why. I also prefer units where Maxwell's equations lack the factor of 4π, and pretty much all theoretical particle physicists agree with me on that one - if you look at quantum field theory books, you'll never see a 4π in Maxwell's equations.

I hope my point is clear here: not that my tastes are correct, but that units are a matter of convenience and there will always be disagreements in taste as to which units are "best" or "most natural". Given this, it's silly for an encyclopedia to try to settle the issue, or for the encyclopedists (us) to argue about it. Maybe it's fun, but it's like trying to settle which 1980s rock band was best.

Given all this, I will change the comment that an article "shows that" hbar should not be used, to saying it "argues that" hbar should not be used. Personally I think this is poppycock: hbar is what shows up in all the basic equations I use every day, not h. But my point is that we should keep a neutral point of view here.

John Baez 15:55, 12 May 2006 (UTC)

replies

hey John, i'm really glad that you poked your head here. i can't tell what change you made on the line with Wilczek's name on it. as for the link Blaze Labs Research, i think it should be deleted (because it's poppycock) but i have edited this page a lot and i have grown weary of arguing with people about it. it was added only yesterday. if no one else deletes it by next week, i'll probably do so.

regarding Planck units not being "unique in that they are not based on properties of any prototype, object, or particle but are based only on properties of free space" and that you can make up tons of systems of units like that, with the exception of factors that might be 2 or 4 or 2π or 4π or 8π whatever, what "constants" or "conversion factors" or property of free space would you use? the elementary charge is a property of a prototype, object, or particle. the Bohr radius is a property of a prototype, object, or particle. the electron mass or some other particle mass is a property of a prototype, object, or particle. i can't think of other dimensionful properties of free space other than those that Planck units are based on. and i can't think of another system that does not have a property of some oject, substance, or particle that it has chosen as "special" and bases the unit system on it.

please feel free to edit any crap out of any article or to edit anything that you believe is appropriate into the article. while you're here, please take a look at Bogdanov affair and Gravitomagnetism (i think the principle name should be Gravitoelectromagnetism but was out voted). r b-j 21:57, 12 May 2006 (UTC)

I haven't actually read that page saying that h is better than hbar, so I can't say it's poppycock, but I would not be in the least shocked to hear that it were so. Generally speaking only people who aren't professional physicists prefer h to hbar. Doing so is the same as preferring wavelength to wavelength/2π, or cycles per second to the other widely used notion of frequency - it sounds great at first, but when you start doing calculations, you quickly realize it amounts to preferring the functions sin(t/2π) and cos(t/2π) to sin(t) and cos(t): every time you differentiate them, a factor of 2$\pi$ shows up, which gets very tiresome!

After wisdom dawns, one realizes that preferring h to hbar amounts to preferring a circle whose circumference is 1 to a circle whose radius is 1. You get the sine and cosine functions when you look at the horizontal or vertical position of a dot moving around a unit circle at constant speed. These functions show up whenever you study waves, which is what Planck's constant is all about. Setting h equal to 1 instead of hbar = 1 amounts to working with a circle of unit circumference instead of unit radius. A factor of 2π has to appear somewhere, but if you compare the equation of the unit circle to the equation of a circle whose circumference is 1, and start thinking about how trig would change if we took this smaller circle as basic, it becomes clear why the standard approach is better.

Basically my philosophy is that factors of 2π, 4π, 8π and so on should show up not in basic differential equations, but in their solutions. For example, we get 2π when we ask what is the period of the solution of

$d^{2}f(t)/dt^{2}=-f(t)$

since a dot moving around the circle at unit speed takes 2π to go around. Similarly, we get a 4π in Coulomb's law if we solve a version of Maxwell's equations without any π's in it to get the electric field of a point charge. Ditto for gravity and Einstein's equation, which is why I don't like the version of Planck units with G = 1; I like the version with 8πG = 1.

As for other systems of units based on the properties of "free space", the easiest ones come from making other decisions about this π-related junk. Indeed the standard Planck units come from making what I consider a suboptimal decision along these lines, as I just explained!

I could make up even weirder systems, but we'd have to start with a long argument about what counts as "free space" versus "particles", and I'm not up for that. I'm pretty happy with the page as it stands.

I may look at those other webpages you mention, but only when I feel like becoming annoyed.  :-)

John Baez 20:08, 13 May 2006 (UTC)

---

Regarding h & h-bar

First of all, let me introduce myself, Saviour Borg, graduated in both mechanical and electrical engineering courses 15 years ago. I was university lecturer for 5 years, now private lecturer and run Blaze Labs, by no means am a genious, but neither would I post poppycock material on my favourite web source!

I do not agree with you saying that the difference between h and h-bar amounts to working with a circle of unit circumference instead of unit radius, for the simple reason that h is not a dimension of length, but of angular momentum. Some of you seem to base their choice on what makes their calculations easier, but in reality there is no such choice.

I invite you to look at what you can get by putting the values of planck units based on h, in the space-time system of units (an advance zero redundancy system which inter-relates all present SI units into just two dimensions).

http://www.blazelabs.com/f-u-allconstants.asp

See what you get for Planck's resistance using this system, you simply get Von Klitzing constant- the value for quantum resistance!. Now see what we've got for Wiki's presently published Planck's resistance? You get Zo/4pi!! and that's what I would call poppycock! Zo should be related to quantum resistance and hence to Planck's resistance by a factor of 2Alpha and not by a strange 4pi! Same applies for all other units. With h-bar, some of them will be different from our known values by sqrt(2pi), some by 2pi, some by 4pi^2..its a whole mess...all for someone to feel comfortable not to have to write 2pi in some of his equations. The reason for such a mess is simply because that 2pi factor, doesn't belong to h, and in my opinion h-bar would have better never been defined. If you say professional physicists prefer the h-bar then I certainly would not like to be called a professional, but I am afraid this is just a personal thought, as I see planck units correctly stated in terms of h, on respectable scientific sources. Those who are not sure about which units to choose, have in fact listed two sets of values, one based on h and another set based on h-bar, see Wolframs science:

http://scienceworld.wolfram.com/physics/PlanckLength.html http://scienceworld.wolfram.com/physics/PlanckTime.html

You cannot just ignore information which you cannot prove its wrong, or worse, that proves you are wrong, and this is what makes Wiki different (in a positive sense) than others - it's a GROWING source of information - just let it be so. Thanks for leaving my link (till now) and follow my suggestion - show two sets of values. The real professionals will then make their own choice!

Regards Ing.Saviour Borg (Blaze Labs Research 17:11, 15 May 2006 (UTC))

---

greetings Ing. Saviour Borg. you might want to be aware that many of us have formal education in the sciences (inc. physics) and engineering with degrees. i got mine about 28 years ago. you might also want to be aware of who the real heavyweights are (i'm not one of them, but i have tried to represent what they have published faithfully here). most of those heavyweights (like John Baez) have WP bio pages (not just a userpage) about them that you can read here. also, you need to be aware of that WP is not a place to publish original research. the place to do that is to float your ideas on the USENET newsgroup sci.physics.research and see if you can get someone to sponsor or endorse publication in arXiv. given that, if i were to compare credentials between Ing. Saviour Borg and John Baez, there just simply would not be much comparison.

we all have pet theories or pet "natural unit" systems. i personally feel that it should be $\hbar ,c,4\pi G,\epsilon _{0}\$ that is normalized (Planck units normalize $G,4\pi \epsilon _{0}\$ instead ). some people want to normalize the mass or charge of some favorite particle or the radius or some favorite atom. all these are "natural" since they are based on some property of nature and are "universal". i believe that a salient property of Planck units (or a variant like "reduced" Planck units) that differentiates from Stoney or atomic units is that Planck units normalize dimensionful quantities of no arbitrarily chosen objects or particles. instead of arguing of whether it is more natural to normalize the mass or any other property of the electron or proton or neutron or the H atom or a cylinder of platinum/iridium in Paris or some monarch's foot, no particular object is chosen as the special object or prototype.

for instance, you think that normalizing the von Klitzing constant makes more "natural" sense than normalizing the characteristic impedance of free space. your definition requires introducing the a particle called an "electron", normalizing the characteristic impedance of free space requires no introduction of anything other than the vacuum of space itself. it may seem to you that this is more natural, but it seems to me to be more contrived.

Planck units were originally intended to eliminate these constants (literally conversion factors) in physical equations which is why people like Baez say it would be better to normalize $8\pi G\$ and many agree with him. but, historically, it is not Planck units. differential equations, such as Schrodinger's equation use $\hbar \$ instead of $h\$ because, as far as calculus is concerned, measuring angles in radians is more natural than measuring angles in "turns".

Christoph Schiller has argued another set of "most natural" units at [4] and [5]. he has good points, too, but the article is about "Planck units" not "Schiller units" nor "Stoney units" nor "atomic units" nor "Borg units".

perhaps your ideas will catch fire in the physics community and someone will create a WP page about it. but it's not Planck units.

scienceworld might list Planck units with $h\$ and $\hbar \$, but i would use a site like NIST as more of an authoritive reference. r b-j 22:45, 15 May 2006 (UTC)

---

Dear Rbj, thanks for your feedback. I do appreciate the fact that most in here do have formal education in sciences, I would be surprised if the contrary was true. I've also had a glance at J.Baez curriculum Vitae and you are right on that as well. However let me tell you that from my (limited) experience I found that with higher 'mainstream education' comes a greater risk of 'mainstream paradigms' which some may handle better than others. It is this that makes one researcher better than an other (I am not referring to Baez here, just talking in general). You said "but the article is about "Planck units" not "Schiller units" nor "Stoney units" nor "atomic units" nor "Borg units"", and I fully agree with you. The question is, which numerical values did Max publish as his Planck units? As far as I know his original units were based on h and not on h-bar, I remember I had an old print in German showing the first approximate values Planck came out with, and these were not the ones on Wiki (actually far off). So, unless you can show the contrary, the values for Planck units on Wiki, have to be historically correct, otherwise they wouldn't be "Planck units". As to NIST, I like to refer to their values as well, I also have them listed on my web links page, however it was found more than once that the values shown on their site contradicts their own values from one published set to the next (I really mean contradict not change), in one instance they were in fact forced to withdraw there published set of values. I do not want to go off topic, so if this is news for you, try to gather the past NIST records for the gravitational constant G, and look carefully at the uncertainty values in each. Thanks for suggesting the Newsnet newsgroup.

(Blaze Labs Research 07:22, 16 May 2006 (UTC))

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the image of Planck's original paper is the link above the link to your Blaze Labs. my reference to NIST is as an authoritive reference to what the physics community says are Planck units and the definitions therein use $\hbar \$. as for changes in G, i know that the 2002 CODATA gave a value with standard uncertainty of 1/10th the previous 199x CODATA and that affected the Planck unit values (expressed in SI) a little. also Planck's constant is depicted with a higher uncertainty in 2002 (which might seem odd except that i have read that they might revise G to a value of greater uncertainty than present). doesn't matter, CODATA (as shown by NIST) pretty much defines what the terms Planck length, Planck time, Planck mass, and Planck temperature mean in terms of physical constants. the definition for Planck charge came from usage in some publications i found on the arXiv. i made a reference to the Duff paper as a verifiable source. some persons have (incorrectly IMO) called the elementary charge the "Planck charge" (and that misses the point of defining Planck units without a prototype, substance, or particle chosen somewhat arbitrarily by some humans). all other units are derived from the base units in exactly the same way that SI derived units are from SI base units (with the exception that SI defines ampere first and then derives coulomb).

other than a contradicting symbol for the permittivity of free space (they sometimes use $\varepsilon _{0}\$, but more often use $\epsilon _{0}\$), as far as i can tell, the CODATA values are self-consistent. r b-j 19:33, 16 May 2006 (UTC)

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to our anonymous IP Christchurch NZ editor: how about talking about substantive changes here on this talk page before making them? or, at least, afterward. that's what this talk page is for. r b-j 19:33, 16 May 2006 (UTC)

---

Saviour Borg wrote:

"I do not agree with you saying that the difference between h and h-bar amounts to working with a circle of unit circumference instead of unit radius, for the simple reason that h is not a dimension of length, but of angular momentum."

My comments had nothing to do with units of length, so I'm afraid you just confirmed my opinions. The unit circle in the complex plane has circumference 2π without any "units of length" - its circumference is not 2π feet, or 2π meters, just 2π. That's because the coordinates on the complex plane are dimensionless. Choosing h as more fundamental than hbar amounts to preferring a circle in the complex plane that has circumference 1, as I explained quite carefully above. It makes everything a mess.

However, it is just a matter of taste. The only really important fact is that modified Planck units based on h rather than hbar should not be the topic of this encyclopedia article. John Baez 22:59, 23 May 2006 (UTC)

Redundancy

There is a redunancy in Planck units (actually even two redunancies).

First, Coulomb constant $1/(4\pi \epsilon _{0})\$ is not fundamental. It is equal to square of the speed of light (with 10^-7 factor or so).

Second, the Boltzmann constant k is not a fundamental constant (and was never considered so) but just a proportionality factor between two units of energy (kelvin anf joule). Temperature is routinely cited in other units of energy like eV.

So, there are only three fundamental constants.

Sincerely, Enormousdude 18:46, 5 May 2006 (UTC)

you're not telling us anything we don't know. guess what? the other three you say are fundamental aren't. they, too, are human constructs and take on the numerical values they do only because of the units of length, time, and mass, that humans have somewhat arbitrarily decided to use.

nonetheless, just like the unit temperature can be defined to make k be whatever positive value you want, so also can the unit charge be defined so that ε₀ can be whatever positive value you want (but not with an independent definition of both c and μ₀. so one is free to set c = 1 and ε₀ = (4 π)^-1 as long as we can let μ₀ float to whatever it comes out to be. if i were king of the universe, "natural units" would be those that set c, $\hbar$, 4πG, ε₀ (and therefore μ₀) to 1. i suppose either k or k/2 also.

there is no redundancy. if you include temperature, there are 5 degrees of freedom and 5 constraints. results in one solution set. Rbj 22:26, 5 May 2006 (UTC)

"Nature sets a practical limit to things. "

Just a few silly points : 1) If we have Planck space, and Planck time, then perhaps Planck "spacetime" is not too bad an idea. We also have Planck energy - what about Planck "energy density"? There, perhaps, should be a notion of 'temporal' energy density "Planck energy" per "Planck time". Essentially, if space-time, matter and, essentially, everything is 'quantised' in the sense of Planck, then some extra Planck unit MIGHT be worthwhile. 2) Has anyone ever managed to manipulate matter at the Planck scale in space, or to time events to Planck scale in time. If the notion of Planck energy density makes sense - has anyone ever come close to it (NO, the answer is one one of the wiki-pages). Is it theoretically/practically possible to contain enough energy within a small enough space so as to interact with the universe at these scales? (Answer, probably not - but Planck energy located within a Planck space-time event seems like it should be possible. The energy density would be massive, but the energy is reasonable, perhaps?).

I think point (1) has some validity. Perhaps the units may appear to be too much verbiage? Point (2) is clearly mad.

Naturallimits 19:11, 23 May 2007 (UTC)