Talk:Planck length

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1.616199(97)×10−48 metres[edit]

Am I the only one who has a problem with the claim that the Planck Length may be reduced to 1.616199(97)×10−35 metres? Planck length itself is defined in terms of physical constants - there is no uncertainty as to its value. The article quoted doesn't imply that Planck length itself may be redefined. It only mentions that the quantum graininess was originally expected to manifest itself at around Planck scale, but now there is evidence it may be of the order of 10-48 or smaller. Observing quantum graininess doesn't change a quantity defined by physical constants. And even if it would, the article most certainly doesn't imply that quantum graininess is a precise power of ten factor smaller than Planck length (as demonstrated by keeping the significant digits exactly the same). From my understanding, whoever added this part completely missed the boat, though I am reluctant to change it directly myself in case I am the one who's missing something. — Preceding unsigned comment added by (talk) 09:48, 27 August 2014 (UTC)


2010-04 thread[edit]

Black Holes, with masses less than ~1.1e-8 kg, would have Schwarzschild Radii less than the Planck Length. So, if you cannot have Black Hole Entropies less than ~1, perhaps you cannot have Black Holes with masses less than 1.1e-8 kg ?? (talk) 11:34, 15 April 2010 (UTC)

The Planck Length is (essentially) equal to the wavelength of a Photon, which was energetic enough, that its wavelength was equal to its Schwarzschild Radius (Lambda = R_SC). A Photon, w/ a wavelength of (of order) 10^-35 meters, would create such "crisp" curvature in spacetime, that it would "buckle" or "nipple" spacetime into a singularity. (talk) 02:19, 23 April 2010 (UTC)

Inconsistency in the length template and Value section values[edit]

The value in meters for Planck Length seems to be correct in the Value section of the article, but the length template shows wrong value. I tried fixing it, but apparently there is some bug in the template. Can anyone fix it? --George (talk) 10:39, 12 March 2010 (UTC)

Statements moved to talk page[edit]

Moved these statements here since they seemed wishy-washy. Please move them back if you can go into detail about which physicists make these statements and why.

His paper says nothing about its being "the smallest meaningful length in quantum mechanics" although some contemporary physicists talk like that. In 1899 quantum mechanics had not been invented yet. It might or might not be helpful to say "two points separated by less than the Planck length are indistinguishable from each other". This is an issue for today's physicists irrelevant to the original definition of the Planck length a hundred years ago.

It might or might not turn out to be useful to think of it as "the smallest meaningful division of time." One hears speculation about that, but the jury is still out. —The preceding unsigned comment was added by (talkcontribs) on 15:51, 25 February 2002.

Nature article[edit]

Here is an article from Nature that seems to raise doubts about the Planck Length:

—The preceding unsigned comment was added by (talkcontribs) on 06:46, 24 June 2004.


What does that (12)-thing do there? It seems to be totally out of place. Crakkpot 15:11, 10 March 2007 (UTC)

If I recall correctly, a number in parentheses in a figure tells you what the standard deviation is in the measurement (where it's pretty likely to be within one standard deviation, very likely to be within two deviations, etc). So, it's telling you how accurate the value given is. The deviation value is in terms of the last place in the original number, so 1.61624(12) means 1.61624 with a standard deviation of 0.00012. --Christopher Thomas 20:28, 10 March 2007 (UTC)
The numbers in parentheses are the uncertainty of a measurement or result of a calculation of two or more measurements. So, for instance, 1.650(25) is the same as saying 1.650, plus or minus 0.025. Uncertainty and standard deviation are two completely different things. Standard deviation is a statistical measure of the variation within a sample. Uncertainty represents the accuracy of a measurement. Mtiffany71 (talk) 20:13, 19 April 2008 (UTC)
I think user Crakkpot has located an error in Wikipedia! But what kind of an error is 12? Unfree (talk) 20:48, 19 October 2009 (UTC)

Uncertainty in Momentum[edit]

Uncertainty in momentum is not a momentum, but a delta momentum, in the case of Heisenberg's equation the delta momentum is a range of possible momentums. So I think it should read something like "precision of position of an object to the plank length would mean that it would be impossible to distinguish if the object was a something moving like an electron, or having the capacities of a black hole." This is also meaningless because black holes do not necessarily have momentum.

== Compton Length== question: Is this meant to be the same as Compton Wavelength? Also, if one knew the sum total of all energy in the universe, would the corresponding wavelength be the Planck length?

Yes, same as compton wavelength. I don't know what you mean. If you mean the corresponding compton wavelength for all the energy in the world. I'm pretty sure that the answer would be no. The mass that has a compton wavelength equal to the planck length is equal to the planck mass. And the sum total of the energy in the universe is much larger than the energy in the planck mass.McKay


The article does not distinguish, but I presume it is not whether or not the baseball is at rest or moving that matters, but that the speed can only be estimated within ±51 mph--JimWae 04:50, 2004 Nov 25 (UTC)

Yes essentially. The uncertainty of velocity in this case would be 51 mph. I don't think it's a +- 51, but that the range is 51, so its like +=25 McKay 00:49, 28 Nov 2004 (UTC)
Does this phenomenon appply to footballs as well as baseballs? Indeed, how about any other type of ball? Arcturus 16:36, 30 Mar 2005 (UTC)
Yes, the phenomenon works fine with any object, but I'll bet the masses are different. The article on uncertainty principle covers the ground nicely. Note my recent change to this article though. If you've further questions about the uncertainty principle, feel free to ask (here or my talk page works fine).McKay 23:26, 30 Mar 2005 (UTC)
So perhaps object would be a better word to use than baseball? I'll change it unless anyone disagrees. Thanks, Arcturus 16:34, 31 Mar 2005 (UTC)
Object doesn't work, because the uncertainty in this case is in the momentum. Since we can probably safely assume the mass of the baseball is unchanged, the uncertainty is in the velocity (the typical case). The momentum is the uncertainty, so you can't just say "object" but you could say an object of 34kilos (or whatever the size of a baseball is, I forget), like a baseball if you want to.
OK let's stick with baseball. However, not being a specialist in these matters I found it difficult to understand the concept as it is currently written. Could you elaborate within the article on the point about the mass? Arcturus 16:52, 4 Apr 2005 (UTC)
Mabey it should say "something with the same mass as a baseball" so people know it doesn't work with all objects.Daniel 19:05, 11 Apr 2005 (UTC)
A baseball with a mass of 34 kg? I don't know whether that was a parody of Americans not understanding the metric system or a genuine mistake. JIP | Talk 04:25, 11 April 2006 (UTC)

It is not the speed of the basaeball that is uncertain, but its velocity. One can be certain of a baseball's speed yet still not know what its velocity is. That is, uncertainy in velocity can come from uncertainty in speed, uncertainty in direction, or a combination.Flarity

You would be correct in saying that it is the velocity that is uncertain, but if the velocity is that uncertain, can you really know the speed? What I'm saying, is that if you certainly know it's speed, you do know something about its velocity, so can there actually be that imprecise about velocity? Its easier to visualize the variation on a constant, rather than a vector. McKay 20:24, 30 October 2006 (UTC)
It would be less US-centric to use a type of ball used more in the rest of the free world such as a cricket ball. (talk) 02:21, 26 March 2014 (UTC)

Schwarzschild radius and Compton length are not equal[edit]

"The Planck mass is a mass whose Schwarzschild radius and its Compton length are equal distances. This distance, called the Planck length, is equal to:"

The above statement is wrong.

m = mC / lC

m is the mass

mC is the constant of proportionality

lC is the compton wavelength

Mass is inversely proportional to the Compton wavelength.

The constant of proportionality, mC, is about 2.2102188e-42 kg.m

This shows that the Compton wavelength of the Planck mass is equal to the Planck Length times 2.pi

Confirmed. We should probably update all of the Planck unit pages accordingly. They, and compton wavelength, state that the Schwarzschild radius is equal to both the Compton length and the Planck length, whereas it's twice the Planck length and (1/pi) the compton wavelength.
The error most likely originally arose because some texts (including the one I'd first seen Planck units in) _define_ the Planck length in this manner, while Planck units defines it as the length that, with the Planck mass, makes G = 1. --Christopher Thomas 06:59, 25 Jun 2005 (UTC)

Reference frames and black hole information[edit]

I have two problems with the explanation given in this article. First, doesn't the issue of whether something is less than the Planck length depend on the reference frame? Suppose there is a ship traveling at .9c relative to me, and they are trying to measure a distance that, to them, is 1.2 Planck lengths. Wouldn't I measure it to be less than a Planck length?

Also, how would being absorbed by a black hole mean that the photon can't give information about the particle's position? Wouldn't the black hole carry information from the photon, such as mass and momentum?Flarity 21:27, 28 October 2006 (UTC)

What is it the length of?[edit]

Most lengths are defined as the length of some physical item. I see that the Planck length is 10^-20 x the diameter of a proton... but why? I do understand that the length falls out of other constants, it doesn't lead to the other constants, but not how the length was defined to be what it is.Garrie 05:05, 30 August 2007 (UTC)

It's not the length of anything in particular. In any theory that has G, h and c as constants, the Planck length, or small multiples of it, is likely to turn up just because of dimensional analysis — it's the only way to get a length from those constants. There's no reason to believe that it's a quantum of length or a minimum meaningful distance or anything like that, unless some theory of quantum gravity predicts that it is. There's actually some reason to believe that area is more fundamental than length — Loop quantum gravity has a quantum of area, the string theory Lagrangian is proportional to the surface area of the world sheet, and the Bekenstein entropy bound is roughly one bit per Planck area. -- BenRG 21:13, 30 August 2007 (UTC)
So "It is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate" is nonsense. Quantum effects dominate at much higher scales. --Rumping 00:04, 11 September 2007 (UTC)
That's talking about quantum effects on spacetime specifically. But, yeah, it's nonsense to claim that spacetime is dominated by quantum effects at the Planck length when the truth is that nobody has the faintest idea what happens at the Planck length. I rewrote that paragraph. -- BenRG 14:41, 11 September 2007 (UTC)

Imperial values in info box[edit]

Is there some reason why these figures are not in normalised standard form? CrispMuncher (talk) 14:45, 3 February 2009 (UTC)

I've just noticed that the same holds for the SI figures as well. Since I can't see any rational reason for this I'm going to go ahead and change them now. CrispMuncher (talk) 17:28, 4 February 2009 (UTC)
I see the problem now. It is the defined behaviour of the units of length template to use engineering steps. This seems strange especially for the imperial values, and arguably it is not relevant here since the unit is not really used in practical applications. However, I won't touch it for now without any comments. I am tempted to subst in the template and manually edit it but won't do that for now. CrispMuncher (talk) 17:36, 4 February 2009 (UTC)

Within the info box "Natural units" has the value 11.706 /s. Isn't this the sqrt of the inverse of the fine structure constant? How do you get that number from the Planck length? (talk) 01:54, 26 February 2009 (UTC) Krakers 20:53, 25 February 2009.

True Meaning[edit]

Just to clarify, is the article saying that anything that can possibly be noticeable length wise must be at least a size equal or greater than the Planck length or it can't be observed? And if this is what it is saying, does that mean that with the advance of technology there could at some point be a way to observe something smaller than Planck length, or that it will always be impossible to observe such a thing? Livingston 16:14, 22 July 2009 (UTC)

What it's saying is that anything with a wavelength short enough to be smaller than the Planck length would have enough energy to have an event horizon larger than the Planck length (it would end up being a miniature black hole). So, the Planck length is the smallest length that anything can have (either its wavelength or its event horizon size is forced to be equal to or larger than this length). --Christopher Thomas (talk) 19:49, 22 July 2009 (UTC)::
That doesn't prove that nothing in existance can be smaller than planck length, it just states that it's mathematically inconvenient to consider such things. Who's to say that these ultra small wavelengths can't exist, and that they don't cause miniature black holes all around us? Obviously there are units smaller than Planck length, otherwise what is planck length "made of" (for lack of a better term)? Is it completely in and of itself? That seems teleological to me.
Planck length represents the quanta of space, as do Planck time for time. See, space-time is discrete (like any virtual reality system) and not a smooth continuum as some believe. Unfortunately, many great physicists got/get stuck here. (talk) 22:56, 26 April 2010 (UTC)
(adjusted indentation above). Isn't it the original/actual size of the universe? (talk) 07:19, 12 September 2010 (UTC)

Planck length geometry[edit]

It seems to me that geometry at the Planck length cannot be Euclidean. Since a fractional value of a Planck length is nonsense, then there would be no way of measuring the hypotenuse of a right triangle with arms 1 Planck length long. How would one measure the circumference of a circle with a radius of 1 Planck length (note the impossibility of a diameter equal to one Planck length--"diameter" implies two radii--each 1/2 Planck-length long)? What kind of geometry WOULD apply at the Planck length level? Is there a point at which geometrical measures in Planck-length units greater than 1 WOULD consistently yield Euclidean values in all cases (i.e., no fractional values smaller than a Planck length)? If the geometry is indeed non-Euclidean, what kind of geometry would make sense at this level? Is it possible that this geometry might suggest physical properties of interest?

Marringtontoo (talk) 06:06, 8 August 2009 (UTC)

From :

Arguments showing why h-bar (Dirac's constant ) should NOT be used to derive Planck units Unfortunately, a lot of scientific literature state Planck units expressed in terms of (=h/(2p)) known as Dirac's constant, or the reduced Planck's constant. THIS IS INCORRECT. The 2p factor in fact leads to totally different (and wrong) numeric values for Planck units, than the original values set out by Planck himself. The 2p factor is a gratuitous addition, coming from the failure to address the Hydrogen atom's stable orbits as defined by the orbital path length being an exact multiple of the orbital matter (standing wave) wavelength. The statement that the orbital electron's angular momentum is quantised as in: m.v.R = n.(h/2p) = n. for integer values of n, is just a mis-statement of 2p.R = n.h/(mv) .... which when substituting for h=E/f, v=f.l, and m=E/(f.l)2... we get: 2p.R = n.l ..... which means that the 2p factor has nothing to do with h as such, and that the orbital path is just an integer number of wavelengths as described by Louis De Broglie! (see diagram above). Dirac's was thus defined due to lack of understanding of the wave structure of matter, and its use should be discouraged. Some physicists still prefer to use h-bar, not for any scientific reason, but mostly for the sake of simplicity in their calculations. —Preceding unsigned comment added by (talk) 03:04, 25 October 2009 (UTC) ~~ Magmatrix

If I understand correctly, the classical (non-quantum) way of looking at it is just to say that your measurement uncertainty of any length is always at least the Planck length. So, you'd measure the hypotenuse to be 1.5 Planck lengths long, but plus or minus at least 0.5 Planck lengths. Trying to triangulate more precise positions by making many measurements stops working, due to this uncertainty.
Nobody's quite sure what the quantum gravity picture ends up looking like. The loop quantum gravity people propose that spacetime ends up being a lattice of nodes of roughly Planck length (and Planck time) size, if I understand correctly. Whether the resulting geometry is Euclidean or non-Euclidean depends on how these nodes connect to each other. --Christopher Thomas (talk) 06:19, 8 August 2009 (UTC)
User Marringtontoo says, "note the impossibility of a diameter equal to one Planck length--'diameter' implies two radii--each 1/2 Planck-length long". This seems to be a trick of semantics. Does the idea of "circle" imply "center"? Does it imply "two semicircles"? Perhaps the idea of a diameter only seems to imply the idea of two radii because that's the way you think of it. Unfree (talk) 20:31, 19 October 2009 (UTC)
Space can fail to be Euclidean for various reasons. It might be curved but still support notions of continuous angle and length, as with the hyperbolic geometry of Lobachevsky (et al). Or it might be flat but with only limited notions of angle, length, and area and no notions of right angle, rectangle, square, or circle, as with Euler's affine geometry. Or it might support right angles but not be able to subdivide them, so you could have squares and rectangles but not triangles or circles and rotation would be in discrete multiples of a right angle, basically the geometry of free abelian groups, aka Zn. Lots of possibilities to speculate about down there. Perhaps the wars of the next millennium will be fought over choice of geometries at the Planck length instead of how to pray to whom. --Vaughan Pratt (talk) 05:55, 2 November 2009 (UTC)
I came here wondering something similar to this. Imagine you have two photons, having been emitted from the same point, and traveling along lines that diverge by only one angular degree. Say at Planck time T they are L Planck length units from each other. Then at Planck time T+1 they must be some non-integer Planck length units apart. But no, you're saying they remain (most likely) the same distance apart for a while, but as they travel the probability gradually increases that they are now L+1 Planck length units apart. Is that it?
In other words, it is a little bit like the anti-aliasing that takes place in digital photography, with pixels along a diagonal edge. (talk) 21:31, 28 September 2011 (UTC)
Get a grip man. Just because it can't be measured does not mean it does not exist. (talk) 02:24, 26 March 2014 (UTC)
So you're saying two photons could be a non-integer number of Planck units apart, but we can never hope to measure that? (talk) 18:45, 12 June 2014 (UTC)

Quantum effects[edit]

I'm casually curious about what "quantum effects" are, but the term redirects me to "quantum Hall effect", which doesn't help. Unfree (talk) 20:10, 19 October 2009 (UTC)

Odd sentence in the history section[edit]

The last sentence of the history section reads "Note that at such a distance scale, the uncertainty principle materially impairs the ability to make any useful statements about what is actually happening." What is this supposed to mean? Could someone either explain its meaning and perhaps also its relevance to a section ostensibly about history or delete it? --Vaughan Pratt (talk) 05:21, 2 November 2009 (UTC)

Deleted (along with the rest of the section). -- BenRG (talk) 14:17, 2 November 2009 (UTC)

Plain Language[edit]

Can this article get a section where less technical language is used? --JSleeper (talk) 02:14, 7 July 2010 (UTC)

I have tagged it as too technical, and hopefully somebody who understands the article can (at the very least) make a non-technical opening paragraph. Crisco 1492 (talk) 02:07, 8 January 2011 (UTC)

Significance of the Planck Length / Rest mass / Gravitational field energy[edit]

Fr = mc² / αx²

Fr = force times distance = energy ≈ energy in the gravitational field of a particle between infinity and its bohr radius. Escape_velocity#Calculating_an_escape_velocity)
F = Gm²/r² = force due to gravity between 2 particles of mass m at a distance of r
r = Bohr radius for a particle of mass m (orbiting a nucleus of infinite mass and charge = 1)

mc² = energy in the rest mass of a particle
m = mass of particle
c = speed of light

αx² = ratio of energy in rest mass to energy in gravitational field above the Bohr radius
α = (dimensionless) Fine-structure constant = 1/137.035999 = 0.0072973525 = e²/4πεℏc
x = r/Lp = (dimensionless) number of Planck lengths in the Bohr radius of a particle with mass m
r = Bohr radius of particle of mass m = (m/mₑ) * 5.2917720859 × 10−11 meters = (m/mₑ) * 0.529 Angstroms
mₑ = mass of electron = 9.109 × 10−31 kg
Lp = Planck length = √(ℏG/c³) = √(mαcrG/c³) = √(mαcrFr²/c³m²) = 1.616252 × 10−35 meters
= mvr = mαcr = angular momentum of particle in ground state of bohr atom
G = Gravitational_constant = Fr² / m²

particle with a Bohr radius of 1 Planck length

m = xₑMe = 0.298 grams = 13,692 Planck masses.
xₑ = 3.274 × 1026 = number of Planck lengths in the Bohr radius of an electron
Me = mass of electron
Planck mass = 2.17644×10−8 kg
αx² = α
Amazingly, at this size, the energy in the gravitational field is 137 (1/α) times the energy in the rest mass.
Such an intense gravitational field would exhibit significant Gravitomagnetic effects.
Its Schwarzschild radius is 2Gm/c² = m * 1.48 × 10−27 meters/kg = 4.41 × 10-31 meters = 27,313 planck lengths

Bohr model

mv²/r = e²/4πεr² (Bohr_model#Electron_energy_levels)
mv²/r = mr(v/r)² = Centrifugal force
e²/4πεr² = Electrostatic force between 2 equal charges at a distance of r
mvr = mαcr = = h/2π = e²/4πεαc = angular momentum of particle in ground state of Bohr atom
v² = α²c² = e²/4πεrm = e²v/4πεℏ
r = ℏ/mv = 4πεℏ²/e²m
v = αc = e²/4πεℏ = velocity of particle in ground state of Bohr model (of atom with nucleus of infinite mass and charge = 1)
v is independent of the mass of the particle
Bohr magneton = μB = ℏγ = ℏe/2m = Spin magnetic moment of electron (See Gyromagnetic_ratio)

Other radii

Reduced_Compton_wavelength (of particle of mass m) = λ/2π = ℏ/mc = rα
λ = Compton wavelength
Classical electron radius = rα²
Van der Waals radius of hydrogen = 1.2 Angstroms = 2.268r


Volume of Sphere = (4/3)πr³
Surface area of Sphere = 4πr²
Angular momentum of Sphere = (2/5)mvr = (2/5)mr²(v/r) = I(v/r) (See List of moments of inertia)
radius of sphere with angular momentum ℏ and angular velocity 2πcR = √(5)r = 2.236r
2πcR = Rydberg Angular frequency = 2πmα²c²/4πℏ = 2πmα²c²/4πmαcr = αc/2rb
cR = Rydberg frequency = Rf = mα²c²/4πℏ
Net outward force acting on all parts of a rotating sphere = (2/3)mr(v/r)² = (2/3)mv²/r
Centripetal force = mr(v/r)² = mv²/r
Net inward force acting on all parts of a charged sphere due to an equal and opposite central charge = 3(q²/4πεr²)
q²/4πεr² = Electrostatic force between 2 charged particles at a distance of r

Just granpa (talk) 12:18, 20 November 2010 (UTC)

Too Technical[edit]

Although it is mentioned above that a Planck length is roughly the size of a flea's egg, there is nothing in the article itself that is clear enough for a general reader to understand the Planck length as more than just a really small measurement. Hence why it is tagged as too technical. Crisco 1492 (talk) 12:24, 7 January 2011 (UTC) Hi, I came to Planck length for a link marked Planck volume on a page giving orders of magnitude of volume. Without getting too technical, I am not seeing anything obvious here about a Planck volume. In the commonsense world, a volume is just a length cubed. Is that the case here? Is a Planck volume just a Planck length cubed? I could imagine (just as speculation) all sorts of possibilities for knowing a volume more precisely than a length, but only in. 2 of the 3 (or more;) dimensions. A non-technical introduction would be useful. And maybe Planck Volume should be on a page of its own. (talk) 14:28, 11 June 2012 (UTC) G1CMZ And that bit about being the size of a fleas egg sounds so wrong. A fleas egg.presumably has structure (little fleas, food, if its at all like a ,chicken). But there is no room for such structure inside of a Planck length. (talk) 14:39, 11 June 2012 (UTC) G1CMZ

It is a technical topic and there is little point to make it looks non-technical. Consider the fact that one has to "bootstrap" their knowledge on QM first to properly understand what it means, put that into account. -- (talk) 10:33, 9 November 2013 (UTC)

Additions of 18 Feb 2011[edit]

This strikes me as a lot of unsourced pseudoscience. Certainly isn't well written and may be factually inaccurate. I am new to making large changes like this, but I really think the longer it stays up the more likely it is to perpetuate misinformation. Ashaver (talk) 20:28, 19 March 2011 (UTC)

A different kind of ultimate limit (7/2012)[edit]

In my humble opinion, the current design of the page says more about Wikipedia guidelines than it does about the Planck length. The page now essentially contains an equation and an annotated bibliography. The history of the page is sort of a "flight to safety": in the relentless pursuit of committee-enforced verifiability, all attempts at interpretation - or even justification of the definition - have been sacrificed. The result is nice and safe, and meets the Wikipedia guidelines. But the result is uninteresting to experts and not very useful for non-experts. — Preceding unsigned comment added by (talk) 23:49, 6 July 2012 (UTC)

I have changed the section from "Physical significance" to "Theoretical significance". It seems that you think even "significance" is too much, feel free to edit.
The lead section is the most problematic, the lack of physical application means that its quantity is not important. The lead should express its theoretical definition and meaning first. For instance, the smallest measurable length and the shortest length are very different, the former is a technical result from QM, it is technical that the word "measurable" differs from the common interpretation, the latter is a philosophical ideal, probably what we mean by unit or infinitesimal. Planck length also serves as an argument for ultrafinitism and "computable universe" for the claim that the universe is discrete. AFAIK, Planck length is a theoretical length that we fail to measure length beyond this length. It gives no answer on the ultimate nature of space or universe. -- (talk) 10:24, 9 November 2013 (UTC)


I was surprised not to find the following (rough) visualization of the scale. Keeping in mind that arithmetic is not original research (e.g. dividing the radius of the sun by that of the earth and saying the former is "roughly 110 times bigger" or "about 100 times bigger" is arithmetic - not original research) here is the visualization that is a remarkable coincidence and allows us mere human beings to visualize, roughly, the Planck scale.

1) Per the article, the Observable_universe has a diameter of some 91.4 billion light years which in meters is

8.64692296 × 10^26 meters

or roughly 10^27 meters.

The smallest thing the human eye can see (for this, one can find references) is about 1/10 of a millimeter, or 10^(-4) meters (excellent eyes can have a "resolution" of 0.04mm, or 2.5 times smaller, per ScienceFocus.come - but that's for the best eyes, Naked_eye gives " 0.1 to 0.3 mm" and perhaps 0.05 seeable - either away, to within 1 (or even half) of an order of magnitude, it's 10^(-4)meters

Ratio is about 10^27/10^(-4) or 10^31

2) Now Planck length is given in our article as 1.616199(97)×10^(−35) again less than a half an order of magnitude away from, more simply, 10^(-35)

The ratio from a 0.1mm particle to this is, coincidentally, none other than: (10^(-4)) / (10^(-35)) which is again 10^31

Disclaimer: I'm *not* suggesting we put all this arithmetic in the article..this is just the background.

But this little arithmetic calculation means we can state:

"If a particle about 0.1mm in size, roughly the smallest the human eye can see, were magnified in size to be as large as the observable universe, then inside that universe, the Planck length would be roughly the size of the smallest object the naked human eye can see" (is accurate to within (actually significantly less than) an order of magnitude) and we can add the clarifier, "in other words, the diameter of the observable universe is to within less than an order of magnitude, larger than a 0.1 millimeter object, roughly at or near the limits of the unaided human eye, by about the same factor as that 0.1mm object is larger than the Planck length" Harel (talk) 03:09, 9 July 2013 (UTC)

One can add, a little less precise but still fairly accurately, that since the ratio of the diameter of the observable universe to the radius of the Milky Way galaxy is close to 10^6 (the former a bit under 100 billion LY, the latter a bit more than 100 thousand LY) and since the diameter of a Hydrogen_atom is given as 1.1 angstroms or very close to 1 angstrom 910^(-10) meters which is 10^6 times smaller than that 0.1mm sized dot in question, we can expand this visualization to say that:
If the diameter of the observable universe is representing that barely-visible 0.1 millimeter dot or particle, then our Milky Way galaxy by its diameter would represent a Hydrogen atom, and the Planck length would in this "universe" be represented by an actual 0.1mm dot" ; or the three part proportion
(Observable universe diameter) : (Milky Way diameter) : (0.1 mm barely visible dot)
representing (better than up to an order of magnitude, fairly good approximation actually) the three part proportion:
(that same barely visible with naked eye, 0.1mm dot) : (diameter of Hydrogen atom) : (the Planck length)
(I may be away from internet access for a couple of days so may only try to add later, but will check back later) Cheers, Harel (talk) 00:36, 10 July 2013 (UTC)

Use of "the" before "Planck length"[edit]

There appears to be some disagreement over whether the phrase "Planck length" should always be given the article "the", or whether the article can be left out in some cases. Looking over various web pages that mention the phrase, it appears the use of "the" is pretty close to universal.

  1. -- all (7) uses include "the"
  2. -- two uses with "the", one use with "within a Planck length"
  3. -- all (2) uses include "the"
  4. -- all (4) uses include "the"
  5. -- 1 use of "the", 2 uses of "a", 1 use of "one", and 1 use of "This".

As such, I've reverted the removals of "the". I'm glad to reconsider if further evidence is provided. (talk) 20:53, 31 October 2013 (UTC)

I've already discussed with you on Talk:scientific consensus that "the" is a definite article in English. What you've showed here are examples, but I can't see what argument they serve as evidence. -- (talk) 15:33, 5 November 2013 (UTC)
They show usage in reliable sources, which is what we should be following. I did a quick check at google books and the unit is used with the definite article. Garamond Lethet
16:40, 5 November 2013 (UTC)
Reliable sources of what? Explain yourself. -- (talk) 16:18, 8 November 2013 (UTC)
Also, a simple Google search on "Planck length" excluding "the Planck length" returns about 45,800 results. I think it is appropriate to cleanup excessive use of "the" according to WP:CLARITY and readability. To justify the need on definite article, you should show us reliable sources on how there is/are other "Planck length"s which causes possible confusion (or multiple interpretation..) among physicists. -- (talk) 07:27, 9 November 2013 (UTC)
Every hear of Bronx? Even though disambiguation isn't an issue, we still call it The Bronx. We follow common usage here, and based on Google "the planck length" is overwhelmingly more common. Garamond Lethet
07:40, 9 November 2013 (UTC)
Your issue had been discussed many times, see WP:DEFINITE. If you are right, then maybe we should also change the title from Planck length to The Planck length. Moreover, you have misunderstood the edit that it doesn't abolish "the" but only the excessive use of it, it is reasonable to use "the Planck length" for the first time to indicate its unfamiliarity. -- (talk) 08:57, 9 November 2013 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Can you point me to a textbook or well-known paper that follows the style you prefer? Garamond Lethet
22:24, 9 November 2013 (UTC)

Which style you don't prefer? To revert the edit you abolish the use of "Planck length", I really would like to hear why. -- (talk) 18:15, 14 November 2013 (UTC)
Sure. "The" is used consistently in reliable sources. I've looked at the results from google books, I've looked at the results from google scholar, and most sources use "the planck length". I'm going to assume that you have a particular reliable source in mind that doesn't follow this convention. What is that source, and why do you think we should give it precedence? Garamond Lethet
20:27, 14 November 2013 (UTC)
Are you playing dumb or you insist that the 4,6000 results above (as you've quoted and seen) do not exist? -- (talk) 21:06, 14 November 2013 (UTC)
Of course they exist. I've read several of them. You haven't. That gives me a bit of an advantage here.
When used in a table, as a header, or as a parenthetical expression, the article is usually eliminated. So your hits are returning a lot of pages like this one, where the phrase is not used in a sentence, this one where it used as a song title, and this one, which tells you how many miles are in the planck length. If you're not a scientist, I can understand why you might think google hit counts would give you some indication of how scientists use the term. That's an understandable mistake, but it's still a mistake. To make a convincing argument, you're going to need to cite material actually written by scientists. That will be a Google Scholar and, to a lesser extent, Google Books. After looking at a couple dozen heavily-cited papers from the 1980s through 2012, what I'm seeing is, most of the time, physicists write "the planck length" unless it occurs in a title, header, or parenthetical expression. Alternatively, you can ask a physicist, which I can do tonight over dinner. I'll let you know what she says. Garamond Lethet
22:00, 14 November 2013 (UTC)
Here's the the (paraphrased) response I received: When say something is meters long, we are using the meter as the unit of measurement. Likewise, when we say something is Planck lengths, we need to specify "length" (as there are several different units with Planck's name), and in doing so we are using the Planck length. Does that help? Garamond Lethet
00:43, 15 November 2013 (UTC)
Nice, I love to see some actual argument instead of RS of nothing, so we can discuss. Frankly, you can see that Google Scholar's result is 3,410 over 11,900.
But that's not important, because they may subject to the cases you've pointed out. The physicist you've asked is completely right and explained everything completely clear and full well, thank you for that.
However, now we need to go back to the actual edit, which I suspect that we overlooked, since I can't see the relation between the edit and all of the discussion so far. If you happen to read 63.251's complaints a lot, you may overlook it, but it is ok, this mistake is understandable.
Here you can see that none of the case is relevant to discussion. That is, for instance, I do not remove the "the" she mentioned
Planck length is the length scale at...
As you can see, all of the "the" which is removed is on the beginning of name, see WP:THE. That is,
(The) Planck length is the length scale at...
And that one is kept as it should,
There is currently no proven physical significance of the Planck length
so the edit has already differentiated where to specify "length" and what to do with it. (That's what I meant by "I didn't abolish "the"" before, I can't explain myself clearly enough without her effort.) We both stayed correct and the edit is legitimate, unnecessary reverts have caused us lots of trouble. -- (talk) 23:21, 19 November 2013 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── Note above, "physicists write "the planck length" unless it occurs in a title, header, or parenthetical expression". The places you removed it from are none of these. And Garamond Lethe's source did not dispute this (as I understand the response) (Garamond, please clarify if needed). Again (see below), WP:THE does not apply -- we are not talking about article titles. Also, while I sympathize with your frustration, please avoid personalizing the discussion, as you did with your various comments about my reverts. (talk) 23:37, 19 November 2013 (UTC)

I'm sorry, perhaps I was being emotional. I should have understood that unnecessary reverts actually wasted everyone time, not just my personal time. So, I corrected the line to "unnecessary reverts have caused us lots of trouble" instead of indicating whose fault, meaning the discussion doesn't worth the time and we better be thoughtful on reverts next time, I hope that should fix it or tell me if you want to remove it.
Back on content,
physicists write "the planck length" unless it occurs in a title, header, or parenthetical expression
I think there is no RS to support this claim, and it has to be false. Counterexamples are plenty and notable, as you can follow the link above. The first few one is obvious, say this one from "Annals of Physics, 1985", "Physical significance of Planck length", "The significance of Planck length in a quantum gravity", "It is shown that Planck length is"..etc.
It is not incorrect that one uses "the Planck length" all the time, but that would be excessively long and noisy, it is trivial to dig up more example outside Planck length that follow similar vein too. I would love to know why you want to keep that. -- (talk) 00:37, 20 November 2013 (UTC)
Looking at your first link, most of the examples on that page do use "the", just not directly before "Planck length": "the eleven-dimensional Planck length", "exceedthe Planck length"[sic], "the 5-dimensional Planck length". The only examples that lack "the" are three papers by T Padmanabhan (who appears to have an idiosyncratic preference in this area, considering the other sources) and one example of "Planck's length" (which wouldn't have "the" in any case). Your 2nd link is to one of Padmanabhan's 3 papers. (talk) 01:28, 20 November 2013 (UTC)
Continuing to the next page, I see further instances of "the eleven-dimensional Planck length", and "Planck's length", and instances of "the fundamental Planck length", "the 27 dimensional Planck length" and a parenthetical, "(∼ Planck length?)". There are two instance that seems to support your view, the papers by K Nozari, and G Modanese, and one instance I agree with: "measuring time in Planck length units". I don't think any of the disputed uses of "the" are of the form "Planck length Xs", but if so, I apologize, and I'm happy for those ones to have "the" removed. Overall, those two pages rather strongly argue against your claim that omitting "the" is better for clarity or succinctness. (talk) 01:28, 20 November 2013 (UTC)
Both are obviously correct, but the claim that "the Planck length is required" is a strong claim and it is incorrect. This is what you've stated until recently.
A few things should be put into consideration on Wikipedia, when you search papers from Google scholars, the authors already expected you to know what Planck length is, most papers focus on application (or derivation) of Planck length and take "Planck length" as a subject, which is highly likely specific, thus "the Planck length".
Here, we focus on definition and description. As you can see from the article, we often take Planck length as an object, "Planck length is.." and this is called a generic noun.
Imo, generic noun is the most fluent and precise candidate because we are describing its generic means. On the other hand, both generic and specific noun doesn't serve much difference as an object, they both refer to "Planck length".
The reason I point you to WP:THE is that, it serves as consensus that we've decided that "the" is not part of its name (this is what Garamond challenged before), hence the discussion can move on to grammatical preference(WP:MoS) and readability, it would be specific noun vs generic noun.
Btw, I just pick up a link "Physics and Reality" by Albert Einstein on Planck constant, there is a line "Planck's constant h relates the frequency H,/h to the energy values H,.", it is a generic noun. -- (talk) 05:19, 20 November 2013 (UTC)
First of all, thank you for expanding on your rationale. I appreciate it. I don't think the term "generic noun" is usual in English (at least, I was not able to find much in the way of definitions or descriptions of that term). You did prompt me to see what Wikipedia had to say about English articles, and I found this: Zero article in English. Does that match your explanation? (talk) 18:40, 20 November 2013 (UTC)
Yes, and Wikipedia has not done anything about it yet. Generic noun is *everywhere* in English. "Apple is red.", "Sky is blue."...etc. instead of "The apple is red.", they differ slightly in semantics, "the apple" means a specific apple is red. Well, you also overlooked my quote from Albert Einstein. Do you still think that such grammar is idiosyncratic? -- (talk) 07:01, 21 November 2013 (UTC)
"Apple is red" and "Sky is blue" are non-standard English, according to my ears. I would write them as: "Apples are red", which falls under "generic plural noun" from Zero article in English, and "The sky is blue", since "sky" can be neither a mass nor a plural noun (at least, not with the usual meaning paired with "is blue"). The quote from Einstein uses the noun phrase: "Planck's constant", not "Planck length" -- that has no bearing on the question of when "Planck length" should take an article. (talk) 17:41, 21 November 2013 (UTC)
Are you looking for lecture or are you sure that you aren't wikihounding me? How can generic noun be non-standard? The overly zero-marking style of language is non-standard, for example, the lack of tenses, but not all zero-(something) you see on that article is non-standard.
"The sky is blue"
Sure, you can use that and never find an inadequacy, because there is only one sky above us, so "the sky" is expressive enough to express what we mean, but it can be exploited in sci-fi.
Apple is different, there are many apples. So,
How about "The apple is red." vs "An apple is red." vs "Apple is red.", the difference is immediate obvious, "The apple is red." specifies a definite apple. "An apple is red" specifies an indefinite but still single apple. "Apple is red." does not specify, both identity and quantity, it is a generic concept/type/set/class, are these countable? I think not.
For example, "I like apple." is exactly what we mean. "Do you like an apple?" "Do you like the apple?" "Do you like apples?" are all too specific. -- (talk) 15:47, 22 November 2013 (UTC)
I'm sorry, but "I like apple" is still non-standard English. "Apple" is not a mass noun. Neither is "length". That's the problem. I and Garamond have repeatedly pointed this out to you, with many many examples -- including explaining why the examples you have provided are not actually on point. If you don't believe me, I encourage you to request the attention of other editors, and see what they say. (talk) 17:56, 22 November 2013 (UTC)
That's again some big claim. Is abstract noun non-standard? You can't interpret "apple" as an abstract entity(concept)? Your ignorance/absence of abstract noun is non-standard. It also shows that you have not enough understanding to judge which is standard and which is not.
That's what happens to Planck length.
I and Garamond have repeatedly pointed this out to you
Interesting, your argument is vastly different in terms of content and quality. I actually agreed to all of Garamond's point.
including explaining why the examples you have provided are not actually on point
As I responded earlier, none of Garamond's argument addressed the edit (Planck length as an object(grammar)). You deliberately overlooked the examples I've given by claiming that "T. Padmanabhan is idiosyncrasy" "Your grammatical preference is idiosyncrasy." "This is non-standard". -- (talk) 20:27, 22 November 2013 (UTC)

Er, WP:DEFINITE refers to article titles, not the use of "the" in article text, at least, as I read it. If I misunderstood, please point me to the particular text on that page that supports your claim. Regarding the Google results, I think User:Garamond Lethe did a very good job of laying that issue to rest., you seem to have a number of idiosyncratic grammar preferences -- while you are certainly welcome to them, working on improving the wording of articles might not be the best thing for you to focus on. (talk) 23:17, 11 November 2013 (UTC)

Is the use of "the" missing? Maybe you can read up WP:THE too as referred by WP:DEFINITE.
You also claim that "the" must precede "Planck length", you showed the use of "the Planck length", and you call it "evidence". I have shown you the use of "Planck length" and have yet to see how is it invalid. -- (talk) 18:15, 14 November 2013 (UTC), you seem to have a number of idiosyncratic grammar preferences -- while you are certainly welcome to them, working on improving the wording of articles might not be the best thing for you to focus on.
Is it even a valid argument? You seem to have a number of idiosyncratic irrelevant concerns -- while you are certainly welcome to them, you can talk to me on my talk page, working on improving the wording of articles might not be the place for you to focus on. -- (talk) 18:15, 14 November 2013 (UTC)
I'm sorry, but I can't even follow what you are trying to say here. Garamond Lethe has explained quite clearly why you are wrong about "the", and my suggestion to you wasn't an argument, merely a recommendation about how you might chose to spend your time. (talk) 00:27, 15 November 2013 (UTC)
Garamond Lethe has explained quite clearly why you are wrong about "the"
Good point and that's what you didn't do so far.
merely a recommendation about how you might chose to spend your time.
Thank you, it is very constructive. -- (talk) 23:21, 19 November 2013 (UTC)
And WP:THE redirects to Wikipedia:Naming conventions (definite or indefinite article at beginning of name) which, as it sounds like, concerns article titles, not wording within articles. This was already pointed out to you. (talk) 00:29, 15 November 2013 (UTC)

Bringing this to a close[edit]

There are two proposed edits that are amenable to more specific google searches: "square of [the] Planck length" and "Since [the] Planck length".

Google Google Scholar Google Books
square of Planck length 5390 22 1
square of the Planck length 455000 172 565
since Planck length 28400 6 1
since the Planck length 16800 82 75

It's curious that the vanilla ghits are 2:1 in the second case, but as the searches of more reliable material show a preference for "the" I'm comfortable keeping the argument as it is. I sympathize with arguments from grammatical correctness, but that's an argument to be made to journal editors, not here. Garamond Lethet
04:26, 25 November 2013 (UTC)


I added information about the collapse of the photon and the Heisenberg uncertainty principle at the Planck scale (in the proofs). The proofs is here. Alexander Klimets (talk) 16:50, 25 March 2014 (UTC)

Reference 3 does not exist[edit]

A lot of the more mathematical claims in this page are supported supposedly by reference 3, but searching for it on google just brings us back to this page. Technically, they make some claims that counter modern physics, include Lorentz invariance, but more importantly, the reference does not exist. The person making these edits is Alexander Klimets, and the reference is to Klimets A, so I think this is also original research. (talk) 13:18, 23 August 2014 (UTC)

Reference 3 exist. See [unsigned, posted by Alexander Klimets]
Reference 3 exists, but has two substantial problems.
1: It was published by Lambert Academic Publishing, which is basically a vanity press. It cannot therefore be considered a WP:reliable source.
2: References to the author's own work added to Wikipedia by the author are a clear WP:CONFLICT OF INTEREST. Klimets is trying to promote his work by adding it here. Combined with point 1, it is also effectively WP:ORIGINAL RESEARCH.
For these reasons, it is important that Alexander Klimets stop editing this article, or at the very least stop adding reference to his own work. Also, any material supported by reference 3 can be considered unsourced, challenged and removed. Oreo Priest talk 20:16, 23 August 2014 (UTC)
I agree to delete all and return to the original view. Alexander Klimets (talk) 21:49, 23 August 2014 (UTC)
I do not agree with the complete removal of the text. There is my article about the collapse of the photon at the Planck scale and three-dimensional space in the journal "FIZIKA B" (Zagreb, 2000) at (reference 4). It is a reliable source. Alexander Klimets (talk) 03:51, 27 August 2014 (UTC)
Sorry Alexander, but your view of the photon's collapse into a black hole is unfortunately not accurate because it requires a special reference frame. We know that one does not exist since the concept of an absolute space does not exist. You can always boost to a reference frame where the photon has an arbitrary amount of energy. Remove the proof as it is inaccurate and betrays a serious lack of understanding of the mechanisms at work here. See here for more relevant discussion: Michael Waddell (talk) 07:53, 27 August 2014 (UTC)
Hamilton-Jacobi equation is generally covariant (physical content of equations does not depend on the choice of coordinate system). Alexander Klimets (talk) 07:52, 1 November 2014 (UTC)
It is known that the spin of the photon - its internal quantum characteristics, unexplained in the framework of relativistic mechanics. Gravitational collapse of a photon is also a quantum phenomenon, and is outside the scope of relativistic mechanics.Alexander Klimets (talk) 08:49, 6 February 2015 (UTC)
It is not appropriate to promote your own research on Wikipedia. (talk) 15:25, 27 August 2014 (UTC)
The system of two photons is considered in reference 4 (above). Alexander Klimets (talk) 01:55, 30 August 2014 (UTC)
It is still probably not appropriate as it's not a secondary source. Please see WP:SCHOLARSHIP for details. Oreo Priest talk 10:26, 1 September 2014 (UTC)
On this subject there is my report on the 5th International Conference on Gravitation and Astrophysics of Asian-Pacific Countries. Moscow, October, 2001,(ICGA-2001). See: . My report is in the Programme of Scientific Session, October 2, Tuesday, Sections "Relativistic Astrophysics and Black Holes", item 6, title "Geons Are Real Candidates for the Role of Primary Miniholes and Their Implication for Planckian Physics", (A.P.Klimets). See: . Alexander Klimets (talk) 06:29, 6 February 2015 (UTC)
The fact that you also presented your work at a conference doesn't change any of the above points, sorry. Oreo Priest talk 20:29, 9 February 2015 (UTC)

Order unity?[edit]

I'm not a mathematician, and am confused by this part of the article:

"the Planck length is, in principle, within a factor of order unity, the shortest measurable length"

Is it saying that "order unity" means "the shortest measurable length"? If so, should "order unity" have its own page and should it be italicized or something? (talk) 08:04, 21 November 2014 (UTC)

I've linked it as "order unity". It means it's within a factor of 10 of the shortest measurable length. Oreo Priest talk 15:05, 22 November 2014 (UTC)

Length/volume confusion[edit]

The sentence at the end of the value section:

"At this scale, more Planck lengths would fit inside a grain of sand volumetrically than grains of sand would fit inside the observable Universe."

makes no sense whatsoever. Length is a single dimension and has zero volume. An infinite number of lengths can fit inside anything. There is no citation on the statement either. I am removing it.Linktex (talk) 16:07, 28 January 2015 (UTC)