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

[Sheyr]

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

 

[selfAdjoint]

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.

 

[Sheyr]

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?