Peering up from the bottom of my own personal black hole of ignorance, I was moved to wonder at the question of if two objects of any kind can be in the same Planck volume. (The case where the distance between the centers of the objects is less than the Planck length.)
That leads me to the usual expanding sheaf of questions, like: Are there any objects identified which have a diameter less than a Plank length? Are there theoretic objects which might have such a characteristic? I am not limiting the definition of such objects to observed particles. I know all the things I know the names of are larger than that size. (How big is a Quark, anyway?) But the multitude of timorous beasties out there in the particle zoo is mostly unknown to me. If a graviton were to exist, how big would it be?
For this thread, however I would be quite pleased to limit speculations to the first question, and some asides as to the other ones.
So, how crowded can the neighborhood get, if it’s Planck’s neighborhood?
No, that is not my question. My question is what is the smallest distance between two objects? Can it be less than the size of either of the objects. Or, more specifically can two things be in the exact location? My choice of planck length was due to the fact that I thought that was the closest thing to same location that I could specify.
At the scales we are talking about, “Size” is an ambiguous and unhelpful concept. For mathematical purposes, elementary particles are normally treated as point particles, although some particle theories such as string theory posit a physical dimension.
The lightest (and, presumably, the “smallest”) quark is the “Up” quark, with a bare mass of 1.5–3.3 MeV/c[sup]2[/sup]. Compare this to the rest mass of the electron. The invariant mass of an electron is approximately 9.109×10[sup]-31[/sup] kilogram, or 5.489×10[sup]-4[/sup] atomic mass unit. On the basis of Einstein’s principle of mass–energy equivalence, this mass corresponds to a rest energy of 0.511 MeV. The ratio between the mass of a proton and that of an electron is about 1836. The Up quark is, therefore, anywhere from three to seven times the mass of an electron.
The Top quark, the most massive known, has a mass of 172.9±1.5 GeV/c[sup]2[/sup], which is about the same mass as an atom of tungsten (or approximately equal to that of a gold nucleus (~171 GeV/c[sup]2[/sup])).
Due to a phenomenon known as color confinement, quarksare never directly observed or found in isolation; they can only be found within hadrons. Most of a hadron’s mass comes from the gluons that bind the constituent quarks together, rather than from the quarks themselves. While gluons are inherently massless, they possess energy—more specifically, quantum chromodynamics binding energy (QCBE)—and it is this that contributes so greatly to the overall mass of the hadron (see mass in special relativity). For example, a proton has a mass of approximately 938 MeV/c[sup]2[/sup], of which the rest mass of its three valence quarks only contributes about 11 MeV/c[sup]2[/sup]; much of the remainder can be attributed to the gluons’ QCBE.
The apparent “size” of subatomic particles is due to (among other considerations) the Pauli exclusion principle. This limits how closely two Fermions (electrons, protons and neutrons, e.g.) may approach each other. The scale of this distance is many orders of magnitude more than the Planck Length.
The Pauli exclusion principle does not apply to Bosons, which may occupy the same point in space at the same time.
I’d reverse that: The closest thing there is to a measure of size for a fundamental particle would be its Compton wavelength, and that’s inversely proportional to its mass. So we should be looking for the most massive fundamental particle. Which is probably the magnetic monopole, or possibly some SUSY or something.
