[Kryptid (OP)]

When reading the "micro black hole" article on Wikipedia (https://en.wikipedia.org/wiki/Micro_black_hole) I came upon the following quotation:

In principle, a black hole can have any mass equal to or above about 2.2×10−8 kg or 22 micrograms (the Planck mass).[2] To make a black hole, one must concentrate mass or energy sufficiently that the escape velocity from the region in which it is concentrated exceeds the speed of light. This condition gives the Schwarzschild radius, R = 2GM/c2, where G is the gravitational constant, c is the speed of light, and M the mass of the black hole. On the other hand, the Compton wavelength, λ = h/Mc, where h is the Planck constant, represents a limit on the minimum size of the region in which a mass M at rest can be localized. For sufficiently small M, the reduced Compton wavelength (λ = ħ/Mc, where ħ is the reduced Planck constant) exceeds half the Schwarzschild radius, and no black hole description exists. This smallest mass for a black hole is thus approximately the Planck mass.

Does this reasoning hold water? I have often heard conflicting descriptions of the Planck units. Some have said that the units have no physical significance, whereas others have claimed that they represent physical extremes that cannot be surpassed (that the Planck mass is, for example, the maximum mass of a subatomic particle or that the Planck length is the minimum possible length for an object).

[Paul25]

I don't think the Planck units are a limit but rather just the smallest units that have a meaning to us.

[yor_on]

I think it should. Planck scale was an invention by Max Planck and if I remember right, he didn't give it that much importance, instead considering it a clever mathematical 'trick'. I'll see if I can find a reference for that later.  " The Planck scale was invented as a set of universal units, so it was a shock when those limits also turned out to be the limits where the known laws of physics applied. For example, a distance smaller than the Planck length just doesn’t make sense—the physics breaks down."

https://en.wikipedia.org/wiki/Natural_units
https://www.huffpost.com/entry/what-is-the-planck-scale-and-why-do-physicists-use_b_59ee45cee4b031d8582f5767

And the 'uncertainty of distance' is explained here  https://www.forbes.com/sites/startswithabang/2019/06/26/what-is-the-smallest-possible-distance-in-the-universe/

so yes Kryptid, to me there are just too many 'coincidences' fitting it, for it to be just something 'invented'. And as far as I get it physics breaks down under it.

[Bored chemist]

"Is the Planck mass the minimum mass for a black hole?"
Well, if it was, and my maths is right, the people who were claiming that the LHC and such might make black holes are severely wrong.

[yor_on]

As for the mathematical trick. "

At the end of the 19th century, it was known that hot matter gave off radiation (light) called blackbody radiation. That radiation was emitted at all frequencies, and higher frequencies contained higher energies. As a result, at high enough frequencies the emission of even a tiny amount of light would require more energy than was available in the body. This problem is called the ultraviolet catastrophe.

Planck (inadvertently) solved the problem of the ultraviolet catastrophe by proposing an intensity curve which fit experimental blackbody radiation data very well. He then sought a set of assumptions that would lead to the functional form of the curve he had fit to the data. His assumption was that light at a given frequency could only be emitted by atomic matter in integer multiples of a certain small amount

E=nhf

where n is an integer, h=6.626×10⁻³⁴J⋅s is called Planck's constant, and f is the frequency of the light in hertz.

The reason this is sometimes referred to as a "mathematical trick" is that Planck proposed the assumption as a mathematical convenience to fit with his curve--not because it was backed by a physical explanation. That physical explanation was provided five years later by Einstein in his Nobel prize winning paper on the photoelectric effect. Some textbooks may imply that Planck was the first to notice the ultraviolet catastrophe being a problem. In fact, it had been known to be a problem for several years before he formulated his quantum hypothesis. "      https://socratic.org/questions/what-was-the-plank-s-mathematical-trick-to-formulate-the-quantum-hypothesis

And that Planck constant is what leads you to a Plank scale  " The Planck constant, or Planck's constant, denoted h is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. " 

" In physics we often do something called dimensional analysis. If we have a bunch of parameters we know might be relevant to the phenomenon we want to study, we can try combining these parameters to produce all different kinds of derived parameters. Planck length is essentially just taking Planck constant, the gravitational constant and the speed of light and combining them in such a way that the resulting quantity has dimensions of length. This length scale is supposed to be the one at which the two phenomena represented by the ingredient parameters - gravitation and quantum mechanics - start both playing some role.

Planck might or might not have invented Planck length himself. Dimensional analysis as I described above is such a common tool for physicists that anyone who just knew about the three constants could immediately do it and thus the "inventor" of Planck length is probably not known. " https://www.reddit.com/r/askscience/comments/6crsdd/how_did_max_planck_calculate_a_planck_length/

https://en.wikipedia.org/wiki/Planck_units

This one is pretty comprehensive. https://www.cosmos.esa.int/web/planck/max-planck
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forgot a link