Unusual question about (particle) physics

This may be a dumb question, I’m not sure, but I’m asking sincerely.

As I understand it, in each atom, regardless of what kind of atom it is, the nucleus is a certain fixed distance from its electron shell and this does not change. (right?)

So, what if there were matter containing atoms all of whose constituents were closer together? (or farther apart I guess, but I’m asking about closer.)

Is it possible to speculate about the qualities of such matter? Would it be apparent (visible or detectable) to an observer made out of “regular” atoms? (live or machine.) Would it be able to interact with matter made of regular atoms?

Is it possible that what is called “dark matter” could be made up of these more compressed types of atoms?

Just wondering. Thanks!

By Rutherford and Bohr’s atomic models, yes. By the current probabilistic model, no. You’re thinking in terms of “electrons are tiny balls flying circular orbits around a bigger ball which is the nucleus”. Rutherford proposed the “electrons aren’t stuck to the nucleus but flying around it” model, Bohr added fixed circular orbits. The previous model, Thomson’s, had the individual electrons stuck to a positively-charged, indivisible “blob”.

But the electrons are neither balls nor waves but depends on what you’re doing they can be simulated mathematically as if they’re one or the other, the orbitals (which is not the same as an orbit; thinking in terms of “balls”, orbitals are "the area within which a certain electron can be found within a given probability, they’re volumes not lines) are not round.

Also, the sizes of the orbitals vary from element to element and energy state to energy state, and depending on the environment (the orbitals of a C which is part of methane aren’t the same as for a C which is part of formic acid).

An atom with structure identical to that of [sup]1[/sup]H which has its electron relatively close to its nucleus (remember, I’m forgetting about the wave part but remembering the probability part) is still a hydrogen atom, it’s still normal matter.

Good question, though.

Well, I’m just thinking about how people say that the distance from the Earth to the Sun is comparable in some way to the distance between the nucleus and electron(s). I did not know that the orbitals of a given atom changed when combined in differring atoms; ignorance fought!

For simplicity, consider the specific case of the hydrogen atom. Despite the name, orbitals aren’t circular (or elliptical), and electrons don’t orbit the nucleus like planets orbit a star; they have wave-functions that describe the probability distribution of their location. In the classical hydrogen atom, the orbitals are given by spherical harmonics, which have more complicated shapes as the quantum number increases. You can define an atomic radius as the mean radius of that wave-function or spherical harmonic, though; take it with a grain of salt if you’re trying to do any atomic physics or chemistry with it, but it’s a convenient back-of-the-envelope number that makes sense. The value you heard mentioned was probably the Bohr radius, which is an approximation to that value that’s still the right order of magnitde.

One problem is that there aren’t any free parameters to modify to get atoms that are closer together. In the classical case of the hydrogen atom, for example, the only potential is the one from the electromagnetic force; the energy eigenstates pop out of the equation based on that, and there’s no place for other orbitals to arise. Why would this matter be like ordinary matter but more compressed?

Atomic radius decreases with electron mass, so one possibility is trying to make atoms with muons and tauons, which are more massive and therefore give smaller atomic radii. This is really not something I know much about, but my guess would be that it would act like a heavier isotope of an ordinary atom; there’s not much difference between the three generations besides their mass. One issue, though, is that heavier leptons are not stable. (Electrons, on the other hand, are light enough that there’s nothing for them to decay into.) Could you get stable atoms that way?

Why wouldn’t these compressed atoms, whatever their origin, be detectable like normal atoms?

Again, they’re talking non-probabilistic models. The human mind has problems with the idea of “matter is pretty empty once you go small enough”; trying to add that plus “electrons aren’t balls (of what, anyway?) and btw neither are nuclei” plus “everything is changing all the time” plus “it’s not dead it’s not alive it’s not being born it’s not dying” plus “the measurement changes the entity measured” produces some serious headaches. Most of my classmates and quite a few of my teachers treated Quantum Physics like they treated the Holy Trinity: “you’re supposed to accept it, nobody expects you to understand it”.

There’s one whole family of orbitals, the S orbitals (which include the two lowest-energy orbitals in any atom) where the peak of the probability distribution is right exactly on top of the nucleus, in that exact position. Now, it’s unlikely that the electron will actually be found within the nucleus, just because it’s such a very small volume… but it’s more likely to be found there than in any other volume of the same size.

Let me make this very, very clear: The atom is not “mostly empty space”. There is no empty space at all within an atom; it is all 100% full. What it is full of is mostly fields, especially (in the case of an atom) the electromagnetic field, but that doesn’t matter: The electromagnetic field of an atom is just as real, and just as much a “thing”, as the protons, neutrons, and electrons. Heck, for that matter, the protons, neutrons, and electrons are themselves just manifestations of fields.

You first need to decide3what laws of physics you are going to change to make the atoms smaller.

Very cool. Thanks.

This is the key.
The atom’s size comes from the laws of physics - the relative charge, weak force, etc. determine what the “orbit” space is. That can’t change, any more than we can have an earth orbiting a sun at half the distance, but still taking a year to orbit. (The earthw ould either orbit in much elss than a year, o fly off in an elliptical orbit, or the sun is much smaller and hence less luminous, etc. etc. etc.) The specific size is determined by the inputs, they are the rules that govern behaviour.

Our current universe is a result of a certain combination of “sweet spots”. Change any fundamental constant, and things likely will be very different.

(I.e. Ice expands for a while below zero, unlike many other compounds, because attractive forces between polarized water molecules. Would this continue to happen if you change some cosntants? How significantly different would our world be if ice did not float, if cold caused water to freeze all the way down instea of the surface?)

(And that’s a very minor change!)

The lower orbitals of the electrons are fixed by our understanding of physics, but we do have the scenario of atoms where the electrons are “further away” than normal. This happens when the electron absorbs the energy from a photon or something and is temporarily bounced up a level. It quickly returns back to its normal level though, emitting energy. The only difference in the characteristics of matter in this state that I know of relate to the release of energy as it comes back to the base state.

This is what I thought the OP was asking - is it possible that there could be more than one set of constants (maybe this means two superimposed universes) - one set comprises the stuff we can readily interact with; the other set comprises ‘dark matter’ that maybe doesn’t interact with our stuff, because of the differences in the configuration of the constants.

IANAP and doubtless my understanding of these things is oversimplified. The reason dark matter is dark is that it doesn’t interact with photons. The reason ordinary matter interacts with photons is that electrons move to higher (that is more energetic) shells, absorbing a photon to make up for energy needed and resulting in absorption spectrums or to lower orbits emitting a photon in the process and resulting in emission spectrums. So dark matter would have to be of a different kind that has no mechanism for changing energy levels. Or at least none mediated by photons.

This is all very erudite and highly edifying. Thank you all so much; there are several things of which I was unaware that have much furthered my understanding.

I was hoping to possibly corroborate something I have often experienced in my exploration of interstitial spaces. Ah, well, in the words of Poe:

“'Til secrecy shall knowledge be,
In the environs of heaven.”