Are there any physical limitations to how small something can be? Not how small we can detect but how small something can actually be before it ceases to exist.
Not quite sure what you’re asking here. A single molecule is the smallest amount of a compound that can be said to exist - if you subdivide this into its atoms, properties change fundamentally.
Ditto for subdividing the atoms of an element.
Yes, there are limits: Planck length
Define “something” …
A substance only gets as small as a single molecule (10[sup]-9[/sup] - 10[sup]-12[/sup]m, although some are bigger) before it becomes atoms
An element only gets as small as a single atom (10[sup]-9[/sup] - 10[sup]-12[/sup]m) before it becomes sub-atomic particles
Sub-atomic particles like protons and neutrons (10[sup]-12[/sup] - 10[sup]-15[/sup]m) before it breaks into quarks
A quark or lepton (like an electron) gets as small as (0 - 10[sup]-15[/sup]m). This is the limit of our understanding.
The smallest distance that makes any sense is the Planck length 1.616199(97)×10[sup]−35[/sup]m
Si
Xema understood the question differently than I did. Subdividing below a certain point will indeed change it into something else, but it will still exist. “Planck length” is the size at which it simply cannot be subdivided any more. There’s no such thing as a half of a planck length. You can talk about it, but things at that size cannot exist.
Thanks, si_blakely. To translate your post in very rough terms, a Planck length compares to the size of an electron the way an electron compares to the earth.
Thank you for that link, I have always had this minor obsession that on a very small scale entire galaxies might be passing through our atoms without even being aware of their existence. It is kind of nice to know I don’t have to worry about that anymore.
What about a limit to things being larger, could their be an atomic structure too large for us to detect, say a billion light years across?
Wait, how do you determine the size of an atom? I thought the electron orbitals were defined in probabilities. So does saying an atom is between a picometer and a nanometer mean that the electrons have a 90% chance of being within that distance of the nucleus? 95%? 99%?
I don’t think we can rule out universes existing below the Planck length, or that our universe exists within a subatomic particle of another one. I do think we don’t have to worry about it though. Unless (or until) our understanding of physics changes drastically, we’ll never be able to perceive them anyway.
Note that the Planck length is not necessarily special. It’s what you get what you put relevant physical constants together in the right proportions to get a length out. Such a construction very often reveals something interesting about a physical system, but not always. The Planck length does appear in fledgling quantum gravity theories, but it’s all quite speculative at this point.
Electrons are theoretically described as pointlike (zero size), and there is no experimental evidence that they have any size. So one can’t compare anything to the size of an electron because we’ve never measured it. All we have are upper limits that are driven by the available experimental precision.
You are exactly right. The size is an arbitrary definition. This wiki page lists some of the definitions used.
Pretty goddamn small, but not too small because if it got any smaller it would be tiny.
As noted, the Planck length is very short. What is more paradoxical is that double that length is of considerable size, in fact it is notable that something is “thicker than two short Plancks” …
(it’s evidence of either the marvelous synchronicity of the universe, or its essential perversity that this fundamental constant wasn’t discovered by someone named, say, “Snodgrass”)
Imagine if it had been someone named “Dick”.
Great cite. People (like me, and even Green, in his Quantum Universe) start off or help impress upon you the relevant scales in atomic physics by using the “an atom is to this as a basketball is to that.”
Messed me up when “visualizing” necessarily non-discrete physical dimensions.
However, those are functional definitions of the effective range of effect of atoms or other charged particles. These distances are, of course, positive and finite, as they give rise to the “real” volumes of materials on the macroscopic scale. They are not, however, actual measurements of the size of the particle (which as you note may be a singularity) but rather the radius or volume at which its electrodynamic interactions occur.
Although the answer of a Planck length would seem to be the most applicable, it is important to note (as Pasta does) that there is no particular physical significance to that particular distance. It does fall out of quantum mechanics as a derived constant, but we cannot actually observe or measure any action at that scale (by definition, as it is the limit at which the indeterminacy principle even allows a measurement to be made) so there is no fundamental reason in currently established theory that space is quanitized at that level. We can say that the minimum distance is likely no larger than a Planck length, but it may be arbitrarily smaller, and only a working theory that rationalizes quantum mechanics (as we currently understand it) with the behavior on smooth Reimann manifolds used to describe the mechanics of general relativity (which a working theory of quantum gravity would have to offer) will reallly allow us to define a lower limit.
Stranger
Money quote. Thanks.