Why Is the Planck Mass So Large Compared to Other Planck Units?

  • Thread starter Thread starter Sheyr
  • Start date Start date
  • Tags Tags
    Mass
AI Thread Summary
The Planck mass is significantly larger than other Planck units, such as length and time, which are extremely small compared to elementary particles. This discrepancy can be explained by the relationship between the Compton wavelength and the Schwarzschild radius, leading to the equation m = √(ch/2G), where G's small value increases the mass. The large Planck mass highlights the "hierarchy problem," questioning why gravity is weaker than quantum forces. The Randall-Sundrum model suggests that gravity operates in a higher-dimensional space, resulting in fewer detectable gravitons compared to quantum particles. This discussion illustrates the complex interplay between fundamental forces and dimensions in physics.
Sheyr
Messages
32
Reaction score
0
While the other basic Planck’s units i.e. length and time are extremely small in comparison to elementary particles (length is about 10^-35m and time is about 10^-44s) the Planck’s mass is about 10^-8 kg!

As we can see the Planck’s length is about 10^20 times smaller than are the dimensions of electron but the Planck’s mass is about 10^23 times bigger than the electrons’ mass. How can this weird phenomenon be explained?

Sheyr
 
Physics news on Phys.org
The Planck mass is the mass whose Compton wave length, \frac{h}{mc} equals its Schwarzschild radius \frac{2Gm}{c^2}. Here c is the speed of light, h is Planck's constant, and G is Newton's constant (the coupling strength of gravity).

When you equate these two quantities you get m = \sqrt{\frac{ch}{2G}}. C is a big number, h a small one, but G in the denominator is very small (gravity is weak), so dividing by it increases the value.

So the reason the Planck mass is large is the same as the statement of the "hierarchy problem"; why is gravity so much weaker than the quantum forces represented by Compton? The Randall-Sundrum model gives one possible explanation: quantum forces are carried by open strings confined to a "brane" (our observable spacetime), while gravity is carried by closed strings that can move off the brane into a larger dimensional space called the "bulk", so we see less gravitons than we do quanta of standard model forces because some of the gravitons are outside our visible universe.
 
Last edited:
Thanks. I do understand although I don’t get the point, I think….
Following your post – if the Planck mass gives the Planck length, so the electron’s mass should give the electron's length which should be about 10^-58m.
Am I right?
 
Just ONCE, I wanted to see a post titled Status Update that was not a blatant, annoying spam post by a new member. So here it is. Today was a good day here in Northern Wisconsin. Fall colors are here, no mosquitos, no deer flies, and mild temperature, so my morning run was unusually nice. Only two meetings today, and both went well. The deer that was road killed just down the road two weeks ago is now fully decomposed, so no more smell. Somebody has a spike buck skull for their...
Thread 'RIP George F. Smoot III (1945-2025)'
https://en.wikipedia.org/wiki/George_Smoot https://physics.berkeley.edu/people/faculty/george-smoot-iii https://apc.u-paris.fr/fr/memory-george-fitzgerald-smoot-iii https://elements.lbl.gov/news/honoring-the-legacy-of-george-smoot/ https://www.nobelprize.org/prizes/physics/2006/smoot/facts/ https://www.aps.org/publications/apsnews/200611/nobel.cfm https://inspirehep.net/authors/988263 Structure in the COBE Differential Microwave Radiometer First-Year Maps (Astrophysical Journal...

Similar threads

Back
Top