Talk:Planck mass

Planck-sized black holes

 * The issue is that general relativity predicts that smaller black holes can exist within an event horizon of radius less than the Planck length, while quantum mechanics predicts that the mass would probably be outside the event horizon.

Sounds fascinating, but what does it mean?

It means that, at the high energy density limit, (maximum energy density), photon energy could produce gravitationally confined mass particles (black holes). If the electron is a gravitationally confined particle, it is expected to have a relationship to the Planck mass energy.

The electron mass is approximately equal to (h/ 4 pi c) times (c/ 3 pi hG) exponent 1/4. The mass energy of two electrons (2 m c squared) is approximately equal to the square root of the product of (2/3) exponent 1/2,(Planck mass energy) times the energy h/(2 pi) squared. When (if) this relationship is verified to be correct, rather than approximate, the gravitational constant value (G) must be very close to 6.6717456 x 10 exponent -11. This is slightly smaller than the current CODATA value (by the factor 0.9996323). DonJStevens (talk) 14:42, 19 December 2011 (UTC)

See Talk: Time dilation, See also Black hole electron.

Hmmm
"The Planck mass is the value for which the Schwarzschild radius and the Compton length are equal, and equal to the Planck length"

according to this sentence, and the sentence proceeding it, fleas are a planck length in diameter, and their Schwarzschild radius and Compton length are equal. Very strange indeed. I think the sentence should be like this:

"If an object with a mass equal to the Planck mass has a Schwarzschild radius and Compton length that are equal, its length is a Planck length"

However, I don't understand how such a sentence would fit in the structure of the article. We could add "On another note, if an object..." or "The Planck mass is such that if an object..."

Basically, could the author or someone else who feels competent change this sentence or delete it?ChadThomson 12:37, 20 September 2005 (UTC)

no, the sentence is quite right. You may read it as 'if you compress a flea to the size of the Planck length, it will become a black hole', or 'the energy required to resolve, by Heisenberg's uncertainty principle, a distance as small as the Planck length, will be sufficient to create a black hole within that length'. Maybe this article should be merged with Planck energy, since the distinction of mass and energy becomes really pointless at this scale. Baad 10:07, 31 October 2005 (UTC)


 * Note that the Planck Energy is already listed as a "derived natural unit" and it is stated in the energy article that it is equal to the Planck mass. I think they stand alone well enough, and if you merge them, you'd have to merge every natural unit.-- Rmrfstar 11:28, 31 October 2005 (UTC)

"naturally it is impossible to truly set either of these dimensionless numbers to zero." I believe the author intends to say "naturally it is impossible to truly set either of these dimensionless numbers to one."

There's no motivation or precedent for setting natural constants to zero (it's not even possible, in general). Setting constants "equal to" one is common practice. — Preceding unsigned comment added by 207.183.239.226 (talk • contribs) 2015-04-16T00:42:33

Schwarschild radius and Planck Length
I corrected what appeared to me to be an anomoly. As I understand it, the Planck length is half the Schwarzschild radius and it is equal to the Compton length divided by Pi. There are similar 'anomolies' on the Planck length page but I'll leave those until I see what reaction this change gets. Sorry if I stepped on any toes by this or if I've misunderstood some physical process in correcting the maths. Lucretius 04:54, 17 January 2006 (UTC)

I also made a small correction in the wording, it didn't seem right to talk about general relativity and use "simultaneous" in the same sentence. Jparrish88 (talk) 07:59, 8 May 2008 (UTC)

Back to the flea
I think the point is that to humans a Planck mass is small but not tiny, unlike Planck length or Planck time. Similarly Planck energy is fairly large but not huge, unlike Planck temperature or Planck density. There is nothing special about Planck mass (there are living things larger and smaller - I think including some kind of lesser flea) until you start looking at black holes. --Rumping 23:44, 11 November 2007 (UTC)


 * I have removed the statement that the body mass of some fleas is roughly 5000 Planck masses. The statement was unsourced, and the figure seems to be much too high; 5000 Planck masses is over 100mg, while sources that I have seen put the mass of a flea at 0.5mg or 0.25mg.


 * I have also removed the statement that the mass of a bacterium is roughly 0.0000001 Planck masses. The statement was sourced, but is practically meaningless since the mass of the largest bacteria exceeds the mass of the smallest by a factor of over 109.  In addition the statement, even if it is taken as true, does not serve its intended purpose of making the Planck mass conceivable to humans.


 * In place of those two statements, I have inserted the statement that the Planck mass is about the mass of a flea egg. A flea egg is oval, about 0.5mm long, and about 0.3mm wide .  If we take it as being a prolate spheroid with those dimensions and with the same density as water – a good approximation for a wide range of biological materials – then its mass comes out as 1.08 Planck masses.  Prim Ethics (talk) 00:53, 19 August 2010 (UTC)

Planck-mass black hole
The article states: "The Schwarzschild radius of a Planck mass black hole is the Planck length."

Is this actually correct?

The Schwarzchild radius is given by rs = 2GM/c2. Plugging in the numbers, rs = 2 x 6.67x10-11 x 2.176x10-8 / 8.99x1016, which works out as 3.23x10-35 metres, or around twice the Planck length of 1.62 × 10−35m. --Christopher White 1982 (talk) 22:59, 26 September 2008 (UTC)

Derivation
I have moved the following out of the article because it seems less clear than "$$m_P = \sqrt\tfrac{\hbar c}{G}$$ where c = speed of light in a vacuum and G = gravitational constant". --Rumping (talk) 11:39, 22 July 2009 (UTC)
 * There no original in this text. So, with additional references this text should be restored in the paper. 195.47.212.108 (talk) 06:54, 23 July 2009 (UTC)

The standard Newton gravitational law can be written as:
 * $$F_N = G\cdot \frac{m_x^2}{r^2}. \ $$

We can redifine gravitational constant in the form consistent with the Coulomb's law, written in the SI units:
 * $$G = \frac{1}{4\pi \kappa_0}, \ $$

where $$\kappa_0 - \ $$ is the "gravitational permittivity" of free space. Now we can rewrite the gravitational law in the form:
 * $$F_N = \frac{m_x^2}{2\kappa_0 hc}\cdot \frac{\hbar c}{r^2} = \gamma_x\cdot \frac{\hbar c}{r^2}, \ $$

where $$\gamma_x = \frac{m_x^2}{2\kappa_0 hc} \ $$ is dimensionless "gravitational fine structure constant". The standard Planck condition for this parameter
 * $$\gamma_P = \frac{m_P^2}{2\kappa_0 hc} = \frac{Gm_P^2a}{c\hbar} = 1 \ $$

defines the Planck mass. More natural is another approach to the gravitational fine structure constant, where it is equal to the electric fine structure constant ($$\alpha \ $$):
 * $$\gamma_{P\alpha} = \frac{m_{P\alpha}^2}{2\kappa_0 hc} = \frac{Gm_{P\alpha}^2a}{c\hbar} = \alpha = \frac{e^2}{2hc\epsilon_0}, \ $$

from which the "renormalized Planck mass" can be derived:
 * $$m_{P\alpha} = \sqrt{\alpha}\cdot m_P. \ $$

Here we have the same value for the electric Planck charge equal to the electron charge. Johnstone Stoney (1881) first proposed this mass.

Rubbish
The whole article contains more wrong sentences than correct ones. It should be removed. (August 2009) —Preceding unsigned comment added by 129.187.87.10 (talk) 12:55, 10 August 2009 (UTC)


 * If you have concerns with any specific statements, please state those concerns. --Christopher Thomas (talk) 17:32, 10 August 2009 (UTC)

Say it in words, not only in formulas
http://en.wikipedia.org/wiki/Planck_mass#Units_dimension_approach tells me in formulas what Planck mass ist but why don't you try to say it in words also? Again, what is a Planck mass? Why has the Plank mass the mass it has? --92.74.31.46 (talk) 13:07, 3 September 2009 (UTC)
 * In simple words the Planck mass is only the "maximum scale" for physical value "MASS", and nothing more. There are no any elementary particles connected with this value.195.47.212.108 (talk) 10:32, 4 September 2009 (UTC)

Would it be preferable to move the flea egg comparison to the top of the article, near the equation proper? I don't know about other readers who dislike math, but personally I cannot even try to comprehend the formula. In my opinion, having the flea egg comparison near the top would let readers who are not good at math understand how much a Planck mass is, give or take. Crisco 1492 (talk) 22:02, 22 December 2010 (UTC)

Name
The Planck mass gets its name because it is one of the Planck units, not because it is defined in relation to Planck's constant. --Humanist Geek (talk) 20:57, 11 November 2010 (UTC)

Not clear
It's not clear from the article whether the PLanck mass and reduced Planck mass utilize the same notation for different values. By way of contrast, the Planck constant has two forms, both of which are denoted differently: h and h-bar. — Preceding unsigned comment added by 70.247.160.87 (talk) 05:55, 3 April 2013 (UTC)

Schwarzschild radius and wavelengths appear to be incorrect.
The Schwarzschild radius, as I have just calculated, appears to be not 1 Planck length, but 2. I repeated the calculation many times, to no avail. Finally, I checked up with Wolfram and many forums, and many people appear to have gotten the same answer as me. The value of the Schwarzschild radius is 2 Planck lengths. Is there a reason for this apparent mistake?

Also, I haven't bothered calculating, but is it the Compton or the de Broglie wavelength we speak of here as equal to the Schwarzschild radius? As I can mentally picture it, the de Broglie would be infinite because the object is not moving. Can we have a check up on this? ReallyFat B. (talk) 18:03, 5 May 2014 (UTC)

Error with value of Planck mass?
I am surprise to spot it in first formula: 2.17651(13)×10−8 kg, (or 21.7651 µg) - if 2.17651 is in 10-8 order kg then it should be 217.651 in 10-6 order kg or µg (microgramm). Am I right?

It can be 10-7 kg from the start through. KOT-TOK (talk) 21:47, 30 July 2014 (UTC)


 * I think not: it is possible that you have made a mistake in calculation. The formula SQRT(hbar*c/G) yields a value of 21.765 micrograms, which would be 2.1765e-8 kilograms. There are other ways to check: using the Planck Length as a starting point, you can divide c by it to find a frequency. Then use the Planck relation, multiplying by hbar, to find a value for energy. This value divided by c^2 is also equal to 2.1765e-8 kilograms. Perhaps you made an error in calculation? — Preceding unsigned comment added by ReallyFat B. (talk • contribs) 22:04, 30 July 2014 (UTC)

The value given may be the 2010 CODATA value, but reference [1] points to the (slightly different) 2014 CODATA value. I think it should be changed to reflect the updated value.Kdpw (talk) 11:42, 17 August 2016 (UTC)
 * ✅ I changed the value to the 2016 value. I also changed the citation label in the source code, so as to avoid confusion. Isambard Kingdom (talk) 13:13, 17 August 2016 (UTC)

Main article could simply use standard character for h-bar
ℏ — see H with stroke — Preceding unsigned comment added by 50.79.227.209 (talk) 15:18, 30 April 2015 (UTC)

Dimensional analysis section is pretty dopey
Sure, given c, h-bar and G you can figure out the Planck mass from dimensional analysis alone, but it sidesteps the question of /why/ you'd pick those three constants in the first place. In particular, if someone asked me to find the "Planck mass" from scratch, and told me it was the smallest mass capable of holding an elementary charge, I'd probably at least expect there to be a variable with units of charge in there somewhere (like the electron charge). The fact that it's not there is surprising and unexplained. The whole thing is begging the question. 143.167.76.27 (talk) 14:48, 30 May 2016 (UTC)

Math needs checking
How can the Planck mass be "approximately 0.02 milligrams" and also be "4.341×10−9 kg"? Michael McGinnis (talk) 22:18, 9 November 2018 (UTC)