# How many objects can be located in a particular Planck volume?
**URL:** https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563
**Category:** Factual Questions
**Created:** [August 21, 2011, 8:08pm UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563 "2011-08-21T20:08:06Z")
**Posts on this page:** 9
**Page:** 1
### Author:  [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)
#### Post date: [August 21, 2011, 8:08pm UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/1 "2011-08-21T20:08:06Z")
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?
Tris
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [August 21, 2011, 9:26pm UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/2 "2011-08-21T21:26:02Z")
Long before you get to that scale, it becomes largely meaningless to speak of “objects” or “fitting into a space”.
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### Author:  [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)
#### Post date: [August 22, 2011, 1:17am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/3 "2011-08-22T01:17:09Z")
> [@Chronos](#):
>
> Long before you get to that scale, it becomes largely meaningless to speak of “objects” or “fitting into a space”.
OK, so what scale am I looking for to make my question meaningful?
Tris
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### Author:  [@Askance](https://boards.straightdope.com/u/Askance)
#### Post date: [August 22, 2011, 1:47am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/4 "2011-08-22T01:47:16Z")
So your question becomes “what is the smallest object”, I guess. If you follow string theory then it’s a string, otherwise a quark.
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### Author:  [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)
#### Post date: [August 22, 2011, 2:33am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/5 "2011-08-22T02:33:34Z")
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.
Tris
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### Author:  [@DHMO](https://boards.straightdope.com/u/DHMO)
#### Post date: [August 22, 2011, 3:32am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/6 "2011-08-22T03:32:40Z")
> [@Triskadecamus](#):
>
> 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?
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](http://en.wikipedia.org/wiki/Point_particle), although some particle theories such as [string theory](http://en.wikipedia.org/wiki/String_theory) posit a physical dimension.
The lightest (and, presumably, the “smallest”) quark is the “[Up](http://en.wikipedia.org/wiki/Up_quark)” quark, with a [bare mass](http://en.wikipedia.org/wiki/Quark#Mass) of 1.5–3.3 [MeV/_c_[sup]2[/sup]](http://en.wikipedia.org/wiki/Electronvolt#As_a_unit_of_mass). Compare this to the rest mass of the [electron](http://en.wikipedia.org/wiki/Electron). The [invariant mass](http://en.wikipedia.org/wiki/Invariant_mass) of an electron is approximately [9.109×10[sup]-31[/sup]](http://en.wikipedia.org/wiki/Orders_of_magnitude_(mass)#10-25_kg_or_less) kilogram, or 5.489×10[sup]-4[/sup] [atomic mass unit](http://en.wikipedia.org/wiki/Atomic_mass_unit). On the basis of [Einstein](http://en.wikipedia.org/wiki/Albert_Einstein)’s principle of [mass–energy equivalence](http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence), this mass corresponds to a rest energy of [0.511 MeV](http://en.wikipedia.org/wiki/Orders_of_magnitude_(energy)#1E-15). The ratio between the mass of a [proton](http://en.wikipedia.org/wiki/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](http://en.wikipedia.org/wiki/Top_quark), the most massive known, has a [mass](http://en.wikipedia.org/wiki/Quark#Mass) of 172.9±1.5 [GeV/_c_[sup]2[/sup]](http://en.wikipedia.org/wiki/Electronvolt#As_a_unit_of_mass), which is about the same mass as an [atom](http://en.wikipedia.org/wiki/Atom) of [tungsten](http://en.wikipedia.org/wiki/Tungsten) (or approximately equal to that of a gold nucleus (~171 GeV/c[sup]2[/sup])).
Due to a phenomenon known as _[color confinement](http://en.wikipedia.org/wiki/Color_confinement)_, [quarks](http://en.wikipedia.org/wiki/Quark)are never directly observed or found in isolation; they can only be found within [hadrons](http://en.wikipedia.org/wiki/Hadron). Most of a hadron’s mass comes from the [gluons](http://en.wikipedia.org/wiki/Gluon) 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](http://en.wikipedia.org/wiki/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](http://en.wikipedia.org/wiki/Mass_in_special_relativity)). For example, a proton has a mass of approximately 938 [MeV/c[sup]2[/sup]](http://en.wikipedia.org/wiki/Electron_volt#As_a_unit_of_mass), 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](http://en.wikipedia.org/wiki/Pauli_exclusion_principle). This limits how closely two [Fermions](http://en.wikipedia.org/wiki/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](http://en.wikipedia.org/wiki/Planck_length).
The Pauli exclusion principle does not apply to [Bosons](http://en.wikipedia.org/wiki/Boson), which may occupy the same point in space at the same time.
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### Author:  [@Chronos](https://boards.straightdope.com/u/Chronos)
#### Post date: [August 22, 2011, 5:24am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/7 "2011-08-22T05:24:08Z")
> [@](#):
>
> The lightest (and, presumably, the “smallest”) quark…
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.
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### Author:  [@DHMO](https://boards.straightdope.com/u/DHMO)
#### Post date: [August 22, 2011, 6:02am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/8 "2011-08-22T06:02:41Z")
> [@Chronos](#):
>
> 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.
Good point. You are correct.
🙂
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### Author:  [@Triskadecamus](https://boards.straightdope.com/u/Triskadecamus)
#### Post date: [August 24, 2011, 12:33am UTC](https://boards.straightdope.com/t/how-many-objects-can-be-located-in-a-particular-planck-volume/593563/9 "2011-08-24T00:33:48Z")
I will be reading for a while.
Thanks.
Tris