John Carlos Baez @johncarlosbaez@mathstodon.xyz
Public

This chart shows all objects in the Universe, arranged by mass (vertical) and radius (horizontal).

The edge of the upper left corner is the "Schwarzschild radius" - anything along this edge becomes a black hole, so we don't expect stuff above and to the left of that.

The edge of the lower left corner is the "Compton wavelength" - anything here has a size so small that measuring its position that accurately would require enough energy to create a new one.

These two corners intersect in a white dot. This would be a black hole so small that it's heavily affected by quantum mechanics. By definition its mass would be the Planck mass, and its radius the Planck length. Nobody has seen such a thing.

The black region to the left of that dot, labeled "QG", contains imaginary objects that are more compressed than black holes, yet also ruled out by the uncertainty principle. So they're doubly impossible - unless Quantum Gravity, which we don't understand, changes the rules.

The pink strips of slope 3 are lines of constant density. For example "QGP" is the density of quark-gluon plasma, "BBN" is the density of the universe when Big Bang nucleosynthesis was going on, and so on.

The Earth is only slightly more dense than a flea.

The black dot labeled "Hubble radius" is the whole observable universe.

I like this chart a lot. It's from here:

C. H. Lineweaver and V. M. Patel, “All objects and some questions”, American Journal of Physics 91 (2023), 819-825. Free at pubs.aip.org/aapt/ajp/article-

A higher-resolution version is on Wikicommons:

commons.wikimedia.org/wiki/Fil

See the alt text for more!

Masses, sizes, and relative densities of objects in our Universe. The diagonal white dashed lines are lines of equal density. Gravity and quantum uncertainty prevent objects of a given mass from being smaller than their corresponding Schwarzschild radius or Compton wavelength. Schwarzschild black holes lie on the black m / r = 1 diagonal line which is the lower boundary of the “forbidden by gravity” region. The masses and Compton wavelengths of the top quark (t), Higgs boson (H), proton (p), electron (e), and neutrinos are plotted along the Compton (mr = 1) diagonal line. Among these, the top quark has the smallest Compton wavelength, because it has the largest mass: 173 GeV c^2. The smallest possible object is a Planck-mass black hole indicated by the white dot labeled “instanton”. The smallest observable (not yet evaporated) primordial black hole (PBH) that could have survived until today has approximately the same size as a proton. The large low-mass black dot in the SMBH (supermassive black hole) range is the 4 x 10^6 solar mass black hole at the center of our galaxy, while the more massive large black dot is the black hole Ton 618. The dashed horizontal line emphasizes the orthogonal symmetry of black holes (m / r = 1) and particles (mr = 1). Our Universe is represented by the “Hubble radius” and has a mass and size that places it on the black hole line.
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