2-dimensional analogies are often used to motivate physical concepts in our 3+1 dimensional world. But a world with 2 space and 1 time dimensions would look *very* different from our world Some crucial differences:🧵 1/10 - ThreadSky

martinmbauer.bsky.social • 82 days ago

2-dimensional analogies are often used to motivate physical concepts in our 3+1 dimensional world. But a world with 2 space and 1 time dimensions would look *very* different from our world

Some crucial differences:🧵 1/10

Comments

johnbrown1325.bsky.social•82 days ago

Really interesting, thanks!

vsorichetti.bsky.social•81 days ago

As everyone who's read Flatland will know :)

martinmbauer.bsky.social•82 days ago

1. Planetary motions: In 2 dimensions Newton's law of gravity is replaced by F = G m M /r. The 1/r dependence results in unstable orbits and solar systems like ours wouldn't have formed in a 2D universe 2/10

jacopobertolotti.com•82 days ago

That's my animation! 😃

martinmbauer.bsky.social•82 days ago

Sorry, Jacopo! It's an old twitter thread and I forgot where I got it from. Your animations are a gold mine. I regularly find them on wikipedia, so I'm not surprised this one is from you, too :)

jacopobertolotti.com•82 days ago

I released it in the #PublicDomain, so you can use it without worrying, but I maintain my right to be happy when people use my animations 😉

wmorong.bsky.social•82 days ago

I'm not sure what the consequences would be in practice, but in 2d all conducting materials would be unstable to Anderson localization with infinitesimal disorder as well (see, e.g., https://www.nature.com/articles/s41467-020-18652-w)

wmorong.bsky.social•82 days ago

Ok, one more from the condensed matter world: the Mermin-Wagner theorem prevents spontaneous breaking of continuous symmetries in 2d (and below). In practice, that means no ordered materials of certain types in a flat universe, like magnets and superconductors.

austen.uk•82 days ago

What does unstable mean here? You just mean the orbits don’t close? The main consequence would probably be the invention of physics being slowed by the difficulty of understanding such motion… even worse if we lived in a binary system

martinmbauer.bsky.social•82 days ago

2. Biology: A not very appetising fact about a 2D world is that a digestive system as we know it in 3D cannot exist. If there were 2D creatures they would need to eat and excrete through the same opening 3/10

(sketch by
@joabaldwin.com )

digoryk.bsky.social•82 days ago

It's also possible that they could open up a new vessel for each bit of food being digested, like cells do.

So the opening of the mouth would be covered by a membrane that engulfs the food and pinches off to form a case around the food, and a new membrane to cover the mouth

martinmbauer.bsky.social•82 days ago

3. Chemistry: Even if we allow for such weird lifeforms, chemistry would look very different in 2D as well. Solving the Schrödinger equation in 3D predicts the atomic shell model with subshells of 2, 6, 10, 14, ... electrons. In 2D this sequence is instead 2,4,4,4,...

4/10

martinmbauer.bsky.social•82 days ago

Chemical bonds could therefore be more *universal*, because all heavy elements would have the same subshell structure. But the number of crystal structures would also be strongly limited.

5/10

https://jstor.org/stable/40024865

martinmbauer.bsky.social•82 days ago

4. Electrodynamics is very different in 2D: It requires infinite energy to take an electron from a 2D atom,
the 2D magnetic field has only 1 component and the photon can be massive

6/10

https://slac.stanford.edu/pubs/slacpubs/3750/slac-pub-3764.pdf

martinmbauer.bsky.social•82 days ago

4. Particle physics: In 3D we are used to fermions and bosons. If you swap 2 fermions the wavefunction picks up a sign, while it is invariant under the exchange of 2 bosons.

The 2D world is much richer. 7/10

jessecm.bsky.social•82 days ago

two-way digestive tracts are the way jellyfish, corals, sea anemones, etc digestive systems work... sponges and tapeworms don't have guts (although the former often have unidirectional water flow, and the latter would probably be sad without one-way digestive tracts to hang out in)

fccstudy.bsky.social•82 days ago

Flatland!

https://gutenberg.org/ebooks/97

frasersanders.bsky.social•81 days ago

Where is this picture from? It looks cool!

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