Spacetime Of Flatland

I'm trying to really get the intuition of spacetime.

This video explains how Minkoswki was the first to think that maybe our universe does not consist of a 3d space which evolves in time, but rather a 4d non-euclidean mathematical space, Minkowski spacetime.

Not even to say this made no sense for me.
Head hurts when I think of non-euclidean spaces and 4,or more, dimensions.

So, I made some more caotic researches, watched other videos and I bumped into this explanation which resulted more intuitive and understandable.

This video, showed how spacetime whould have looked for a 2d event, as time passes. It blew my mind.

As soon as I finished this video I remembered about this book I read "FlatLand", which is about some 2d creatures who live in a 2d world, and so, I started wondering what would have spacetime looked like for this 2d space world, hoping it would help to clarify the concept, or to make it more "accesible".

In any way, I've just a small background in special relativity and some videos, and some spare readings behind my back, so I don't know if I can really dig into this with my current knowledge.

In the end, I'm just curious if anyone else have used this kind of help to initially understand this concept and if it can be a good way to start.

Can spacetime be thought for a flat world? How much would resemble the idea behind our 4d spacetime? What would light look like there? and, Could I ideally graph spacetime from a 2d big-bang to a certain time?
I don't expect these questions to be answered, I'm just asking if is lecit and useful to discuss about something like that and maybe to open a discussion.

• Hi Gabriele. I think this is too vague to be usefully answered here. Jan 12, 2018 at 16:13
• @JohnRennie ah...ok. Do you suggest to post somewhere else or just give up? Jan 12, 2018 at 16:15
• You could try the chat room, though it's a little quiet at the moment. Jan 12, 2018 at 16:17
• @JohnRennie I'm thinking of a way to make the post having a more precise goal without losing the core idea. Hope to manage it in a little, otherwise I will delete it Jan 12, 2018 at 16:29
• Lower dimension simificstoons are used all the time. In fact, most of Special Rrlativity is studied in 2 dimensions, one spatial and one temporal. Jan 12, 2018 at 17:54

I am VERY far from expert in GR so take this with a few tones of salt, but I hope that people more versed in the topic will build up on this. Since this is a set of related questions perhaps we can tackle them one at a time?

Can spacetime be thought for a flat world?

In principle You can try to solve GR in any number of dimensions, and lower-dimensional models are sometimes useful either pedagogically or to learn something new. Even looking around SO You can easily find questions about 1+1 and 2+1 spacetimes, where first number stands for space dimensions and the second for time dimensions. But...

How much would resemble the idea behind our 4d spacetime?

The 'idea' is the same, since You use the same equations. The problem however is that the results in spaces other than our 3+1 are, sometimes very unintuitively, dissimilar, especially if You start to include any matter or energy. IRC 2+1 doesn't even support matter fields? At the very least, it doesnt allow gravitational radiation: 2+1 on wikipedia

What would light look like there?

I guess it would be identical to ours, but this is a point which would require someone much more experienced than me.

Could I ideally graph spacetime from a 2d big-bang to a certain time?

Why not? You have one less dimension to compactify than in our 3+1, so it's even easier.

Some links as a primer for more literature research:
https://arxiv.org/pdf/0706.3055.pdf
http://www.isr.umd.edu/Labs/CSSL/simonlab/pubs/GottEtAlGenRelGrav1986.pdf
https://arxiv.org/abs/gr-qc/9503024
https://arxiv.org/pdf/gr-qc/9503024.pdf