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).

User: DonJStevens

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)

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)

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 r_s = 2GM/c². Plugging in the numbers , r_s = 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}^{2}a}{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 }^{2}a}{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.

References

1. Sivaram C. WHAT IS SPECIAL ABOUT THE PLANCK MASS? [PDF]
2. Johnstone Stoney, Phil. Trans. Roy. Soc. 11, (1881) —Preceding unsigned comment added by 195.47.212.108 (talk) 06:50, 23 July 2009 (UTC)

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)