Planck mass

The formula for the Planck mass can be derived by dimensional analysis.

The Planck mass is a small unit of mass used in physics.

The mass scale is at most the Planck mass.

"They counted it out for us in Planck masses.

In principle, a black hole can have any mass significantly above the Planck mass.

Why is the electron mass such a tiny fraction of the Planck mass?

This smallest mass for a black hole is thus approximately the Planck mass.

This is not quite the Planck mass: It is a factor of larger.

As mentioned above, Planck force has a unique association with the Planck mass.

Note that Newton's constant G can be rewritten in terms of the Planck mass.

This is normally seen as an indication that Planck mass is the lower limit on the mass of a black hole.

This was reformulated by Kowalski-Glikman (2001) in terms of an observer independent Planck mass.

Thus, the Planck mass is:

For ordinary electromagnetism, the mass bound is not very useful because it is about same size as the Planck mass.

In standard general relativity, Newton's constant, or equivalently, the Planck mass is always constant.

Various models predict the creation of black holes, ranging from a Planck mass to hundreds of thousands of solar masses.

On the other hand, the previous "derivation" of the Planck mass should have had a proportional sign in the initial expression rather than an equal sign.

The lower classical quantum limit for mass for this equation is equivalent to the Planck mass, .

Note that in terms of the Planck mass, we set , whereas the last term keeps all the SI unit factors.

However, in some scenarios involving extra dimensions of space, the Planck mass can be as low as the TeV range.

Any primordial black hole of sufficiently low mass will evaporate to near the Planck mass within the lifetime of the Universe.

Planck particles are sometimes used as an exercise to define the Planck mass and Planck length.

The Planck mass can be derived approximately by setting it as the mass whose Compton wavelength and Schwarzschild radius are equal.

So, in Kaluza-Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space.

This is so because a charged elementary particle has approximately one Planck charge, but a mass many orders of magnitude smaller than the Planck mass.