# Shapes of Space-Time

Ok let’s get the legwork done first.

A common way to visualize our current space-time is as a 3D grid. The lines of this grid are perfectly parallel until a significant amount of matter causes them to bend inward toward the center of mass, thus causing gravity. In this case (since it appears to describe the world we live in) we know how time, light, acceleration, gravity, etc all behave in this arrangement of space-time.

My question is how a different arrangement of space-time might affect things. Of course that’s a rather general statement so let’s narrow the focus a bit.

• This specific space-time is a 3D spiral instead of a grid.
• All constants that would not be affected by this change are exactly the same as in our 3 dimensions.
• Each of the 3 new dimensions are spirals, so the new X, Y, and Z “lines” of space-time are now each spirals.

Would this arrangement of space-time change the “flow” of time? For instance, near a gravity well in our universe, time moves forward and down toward the center of mass. Around black holes, time does this but also dilates to the point that time might not even pass at all within the singularity itself, due to the fact that escape velocity now exceeds the speed of light. Would this naturally spiraling space-time cause alterations in the flow of time like this, in a completely different way, at all?

Any insights on how this might change the flow of time, as well as how it might change the behavior of things like light, gravity, the expansion of the universe, etc… as well as how such a dimension might look and generally operate are also appreciated. Also if you just happen to know how other “shapes of space-time” (angled, looping, knotted, or what have you) might affect these things that would be cool to know too, otherwise I may have to make this a series.

Edit 1: To clarify what I mean by each dimension is a spiral, think of an xyz coordinate graph. Instead of the x, y, and z being straight lines, each of them are intersecting spirals. So if we view our space-time as a grid of intersecting xyz lines where all of x is parallel, all of y is parallel, all of z is parallel, and they are all at right angles to each other, this new space-time is laid out the same, but instead of straight lines the xyz lines are now spirals. As far as the scale goes, I guess this would be on the macro side. However, the inspiration behind this question came from reading about how, in string theory, spatial dimensions could be curled up or compacted. This got me wondering how a universe might behave if space-time were twisted into different shapes, much how gravity does currently.

• What do you mean with "each dimension is a spiral"?
– L.Dutch
Aug 23, 2022 at 2:44
• Frame-dragging seems to have popped-up a lot on physics.se recently - are you wondering about that? It would necessitate spin. Lots of it. Unless it wouldn't - could you clarify? Are you talking on a subatomic scale or a macro-one? Aug 23, 2022 at 2:46
• FWIW: My understanding is that time flows in the direction it does because entropy can only operate in one direction (unlike almost every other physical system). It's not obvious (to me) that entropy would cease to be a factor simply because spacetime is shaped differently, so I would expect time to still flow forward.
– Tom
Aug 23, 2022 at 4:15
• I've always personally believed that the default shape of space-time is that of a lemon.
– Alot
Aug 23, 2022 at 7:35
• Which might just explain all the Gin and Tonics. @Alot Aug 23, 2022 at 8:14

Before delving into the maths I don't quite understand what you want to achieve with your alternate space time? If you have an answer to that we may be able to give you ideas on how to modify it to achieve that result.

For space time you need to distinguish between local and global effects.

Locally in a small neighborhood our space time looks like a 3 dimensional rectangular grid. If there are no major masses nearby the grid is exactly rectangular and the grid lines are parallel. Major masses make the grid lines somewhat bend.

This is completely independent of what the global topology looks like. A regular piece of paper is flat, the analogy of a 2 dimensional grid with no masses. You can put the paper on the table and it will have 4 edges (or, if you want, be infinite in two directions). You can also glue together 2 opposing edges to form a cylinder. The paper now has only two edges (or is infinite in one direction). Mathematically you could even glue together the two remaining edges. You would then have a torus with no edges but with finite total area. You can't do that with paper in real life 3-d but you could do that with a 2-d regular flat paper in a 4 dimensional space.

Now putting the dimensions of a 3 dimensional space time into spiral shape doesn't change anything locally. In a small neighborhood it is still approximately flat. It also doesn't change anything globally in the topology, each dimension is still in infinite line. So all this does is putting your space time into some higher dimensionmal space in a complicated way, it doesn't change anything for the beings inside the space time.

• Good answer. I’m mostly just trying to figure out what effects it would have. Like if space-time was naturally bent instead of straight, then there might always be a slight pull in the direction of the bend, which would also effect light and, to a small degree, time.
– Nick
Aug 23, 2022 at 13:15
• No piece of paper is entirely perfectly flat at the microscopic level Everything is a fractal. Aug 23, 2022 at 13:47
• @JustinThymetheSecond verbal semantics. He was using a piece of paper as an analogy, quite common when explaining dimensions.
– JNC4
Aug 25, 2022 at 9:19
• @JNC4 The point was the 'fractal' part. There is no such thing as a 'perfectly straight line' or a 'perfectly flat plane'. Unless, perhaps, at the quantum Planck level. But then you have the indeterminacy principle. A flat plane or a straight line only exists for an indescribably brief moment Aug 25, 2022 at 13:36