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I know that someone has asked how chemistry would be in four dimensions but I was wondering what would chemistry be like in two dimensions? From what I understand, in two dimensions, particles, instead of being either fermions or bosons, would be anyons. Anyons can only exist in two spatial dimensions and, unlike fermions and bosons, do not have to have spin that is either half integer or integer. Would the existence of anyons in two spatial dimensions have an impact on chemistry and whether there would be chemicals in two spatial dimensions?

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  • $\begingroup$ Anyons are quasiparticles, not actual particles. And fermions and bosons can exist in two dimensions - what makes you think they couldn't? $\endgroup$ – HDE 226868 Oct 14 '15 at 14:57
  • $\begingroup$ Well, subparticles as small as electrons are considered spherical (3D) in shape. I guess you must flatten them somehow? $\endgroup$ – Mikey Oct 14 '15 at 18:14
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    $\begingroup$ @Mikey They're treated as point-like particles in modern quantum/particle physics. The idea of a classical electron radius is obsolete and inaccurate, so there's no problem here. $\endgroup$ – HDE 226868 Oct 14 '15 at 21:53
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    $\begingroup$ @HDE 226868: Anyons are quasiparticles because true space is 3-dimensional. If it were 2-dimensional, true anyons could exist. However, it is true that fermions and bosons can exist in two dimensions too. $\endgroup$ – BartekChom Oct 15 '15 at 7:42
  • $\begingroup$ What makes....? Logical error of contropositive. The noted quasiparticles exist in 2 dimensions, therefore other kinds of particles don't. $\endgroup$ – JDługosz Oct 15 '15 at 14:51
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You can build complex organisms

Leptons (electrons, muons, etc.) are point-particles and I think quarks can safely be considered as points in space too. I think it's safe to consider that they can exist in 2D. Consequently, you still are able to achieve complicated chemistry since you can build flat atoms and with them you can build flat molecules, then flat proteins and give your proteins some complex behaviours like "hooking" one to the another. Removing a dimension does not make mechanics impossible.

I don't think you should care about flat orbits

Particles do not obey our common sense of "location", the very notion of orbit is irrelevant in quantum mechanics. Basically they are somewhere and then somewhere else, they don't move from one place to the other, they just somehow change their location in space-time accordingly to the probability of being there or there. It gives us the very famous "tunnel effect" with allow electrons to "move through" impenetrable walls. The only thing which should still apply is the Pauli exclusion principle and the Fundamental forces.

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  • $\begingroup$ The flatness, or 2d nature, affects the kinds of waves that are possible. So the standing wave is not a circle, but the orbital is, like our s orbitals are spheres. $\endgroup$ – JDługosz Oct 15 '15 at 14:55
  • $\begingroup$ This is true, I'm not a specialist about wave functions. I just wanted to clarify the fact that the notion of orbits are very different in quantum physics and in "real" world. Plus, I think that digging in how it's work in 2D is too broad though and deserve a whole series of questions. $\endgroup$ – Ephasme Oct 15 '15 at 15:14
  • $\begingroup$ Fwiw, I have a story in the works that takes place in a flatland. It's been "in the works" since 2008 actually. $\endgroup$ – JDługosz Oct 15 '15 at 16:22
  • $\begingroup$ "Leptons (electrons, muons, etc.) are point-particles and I think quarks can safely be considered as points in space too. I think it's safe to consider that they can exist in 2D." -- that is not really relevant, in "true" 2D universe the 2-volume, or area, is what matters. (3-)volume is zero by definition. $\endgroup$ – Radovan Garabík Oct 15 '15 at 17:18
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    $\begingroup$ What's the point of your comment ? @RadovanGarabík $\endgroup$ – Ephasme Oct 15 '15 at 17:28
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Although answers have been provided, I think it is very important to note that not all chemistry would be possible, and the formation of proteins would be impossible.

Atoms bind based on electric forces, and the structure and stability of familiar molecules is greatly dependent on 3 dimensions. For example, hydrocarbons are chains that require 3 dimensions. The hydrogen atoms form rings around the carbon atoms that are chained to each other along a different dimension.

In 2 dimensional space, the mechanics for this structure do not exist. The bonds between the atoms would not support "moving" the carbons further apart to make room for more hydrogen (that would break the bond) or forcing the hydrogen atoms together into a single plane, which would make it unstable (they would repel each other since the valence of carbon maintains the bond with the electron, the exposed protons repel). You cannot just "flatten" the structure and expect it to remain stable, especially for more complex molecules like proteins.

So while basic molecules may exist, and even complex ones, they would not likely be similar to anything we experience in 3 dimensional space. However, that does allow some creativity in your writing, since you can justify when the rules of 3 dimensional space "do" or "do not" apply, if you like.

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I don't know much chemistry but assuming that atoms can exist in two dimensions, i.e. electrons orbit flat, then surely you can make molecules. The problem of course is that any non-2d connections in molecular structures are impossible, which is a lot of limitation.

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Per this physics stackexchange answer, QCD works pretty much the same in 2D, so hooray! You get stable atomic nuclei!

The lower dimensionality, however, means that there is less space (both actual physical "volume" and state space) for nucleons to pack into energy shells, so you have fewer stable nuclei--the periodic table is truncated at the bottom. Additionally, the reduction in space for electrons means that you fill up orbitals faster, and the periodic table is squished horizontally.

Fortunately, however, life doesn't use most of our periodic table very much, so there's probably plenty of structural complexity left for your 2D life to use.

Introducing anyonic electrons weirds things. No longer can you depend on Fermi statistics to define the energy shell structure. You would probably get significantly more variation in the chemical properties of your limited set of stable elements... but they would be much harder to predict, and the periodic table would no longer be particularly periodic.

You also have the issue that 2D electric fields only decay proportional to $\frac{1}{r}$, which means that isolated charges have no escape velocity, and it is impossible to fully ionize an isolated atom. It's a good thing opposite charges neutralize! This has some fun consequences in that 2D atoms can absorb arbitrarily high-energy photons; while there may be energy band gaps that allow transparency to some lower energies, all matter should end up opaque to high-energy light. That makes UV shielding by a planetary atmosphere conveniently easy, if you want this chemistry to support lifeforms.

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