# What if a molecule turned into a black hole? [closed]

Could it turn into the size of a quark? Could there be a quark-sized black hole?

## closed as off-topic by JDługosz, Anketam, Hohmannfan, Alexander von Wernherr, ZxyrraFeb 16 '17 at 6:50

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• Considering Micro black holes evaporate so fast if such a thing as this existed it would become Hawking radiation before it could be detected. – Anketam Feb 16 '17 at 2:54
• Welcome to World Building! This question however might be better asked on the physics stack exchange. – AngelPray Feb 16 '17 at 3:02

## 2 Answers

No, a molecule could not turn into a black hole the size of a quark and indeed, a quark-sized black hole is an ill-defined concept.

A quark in the Standard Model is defined as a fundamental point particle with no volume whatsoever.

The size of a black hole is a function of its mass, its angular momentum and its electric charge, but generally one disregards angular momentum and electric charge which means using its Schwartzchild radius.

One can take the mass of any given molecule and use that to calculate its Schwartzchild radius which would be non-zero, and therefore it would not turn into the size of a quark. The formula for the Schwartzchild radius of a given mass is:

r = 2GM/c^2

where G is the gravitational constant, M is the object mass and c is the speed of light.

Also, as noted in the comments by Anketam, due to Hawking radiation, such a tiny black hole would evaporate almost immediately. There is also another even more fundamental problem (explained in the same link) which is that such a small black hole might not even be theoretically possible:

In principle, a black hole can have any mass equal to or above the Planck mass (about 22 micrograms). 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/c^2, 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, lambda =h/Mc, where h is Planck's 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 lambda =hbar/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. . . .

All this assumes that the theory of general relativity remains valid at these small distances. If it does not, then other, presently unknown, effects will limit the minimum size of a black hole. Elementary particles are equipped with a quantum-mechanical, intrinsic angular momentum (spin). The correct conservation law for the total (orbital plus spin) angular momentum of matter in curved spacetime requires that spacetime is equipped with torsion. The simplest and most natural theory of gravity with torsion is the Einstein-Cartan theory. Torsion modifies the Dirac equation in the presence of the gravitational field and causes fermion particles to be spatially extended. The spatial extension of fermions limits the minimum mass of a black hole to be on the order of 10^16 kg, showing that mini black holes may not exist.

A molecule that had even 22 micrograms of mass would be extremely large. By comparison, a human DNA molecule (which is huge as molecules go) weighs about 3.59*10^-6 micrograms (in other words, it is about 6 million times smaller than the minimum mass for a theoretically well defined black hole).

Of course, it is entirely possible that the definitional assumption that the fundamental particles of the Standard Model of Particle Physics are not actually point particles in reality, but are instead, extremely small. The Standard Model of Particle Physics starts to get outside of its domain of applicability once you get to distances less than the Planck length of about 1.6*10^-35 meters.

The average mass of a quark in an ordinary atom is roughly 0.33% of the mass of a proton or neutron (most of the mass of an atom comes from the energy of the gluons that hold the quarks together in a proton or neutron mediating the strong force and not from the quarks themselves), and typically there are many protons and neutrons in a molecule, as well as a number of electrons equal to the number of protons that add a negligible amount to the mass of an atom (an average quark in a molecule is about seven times as massive as an electron, and there are usually three quarks in each proton to one electron).

Efforts to consider alternatives to the Standard Model often assume that a quark has a radius equal to its Schwartzchild radius, which would be a hundred to many thousands of times smaller than the Schwartzchild radius of a molecule, depending upon the molecule in question.

It has been suggested that in the early universe conditions were suitable for the creation of microscopic black holes. Debate goes on but these have probably evaporated through quantum tunneling.

Black holes do not just 'form'. A molecule does not have sufficient mass to collapse below it's Schwartzchild radius.

The size of a quark (although the concept is a bit flawed) is about 1e15 greater than the minimum theoretical size of a black hole which is about the Planck length.