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Has anybody explored GR equations with multiple, say 2, timelike dimensions? We're making some "obvious" assumptions about how physics should work and one of th

by akomtu 5y ago

Has anybody explored GR equations with multiple, say 2, timelike dimensions? We're making some "obvious" assumptions about how physics should work and one of the central assumptions is the single straight line of time. I feel like this assumption is similar to the Ptolematic model with Earth in the center. GR works equally well with all topologies of spacetime and we're just assuming that it's 3+1. The Kaluza-Klein theory adds a small 4th dimension and derives most of the EM equations out of GR. So I wonder if we just need to make a better guess what the timelike dimensions look like.

throwaway81523 5y ago
> Has anybody explored GR equations with multiple, say 2, timelike dimensions? Entire topic is too big for my brain, but I think the cool kids these days consider classical theories of any sort to be uninteresting, that the universe is really an infinite dimensional quantum state, and that GR and everything else emerges from that. https://arxiv.org/abs/1801.08132 https://arxiv.org/abs/1801.08132
- beecafe 5y ago
  You're right about the classical theory part. But the infinite dimensional is just one representation that is mathematically convenient - for example, you could consider a 2D image of 10x10 as a vector from a 100 dim space, each scalar being a pixel, or as one from a 2^100 space, with a vector of all zeros except at it's "index" in the list of all 10x10 images (this repr also allows you to express superposition within it by turning on multiple indices). Or as an element of a much lower dimensional subspace embedded in those spaces, like ML uses. In general infinite dimensional should just be taken to mean that using the inductive bias endowed by a specific representation isn't necessary for whatever we want to use the theory for. It's also how you (imo, crudely) represent functions as first-class objects in math.
layer8 5y ago
> Has anybody explored <idea> The answer to those questions is always “yes”, unless you’ve spent years of research to come up with <idea>. https://en.wikipedia.org/wiki/Multiple_time_dimensions https://en.wikipedia.org/wiki/Multiple_time_dimensions
4ad 5y ago
Of course that people have explored physics in spaces with multiple time dimensions. They aren't stable, orbits can't form, atoms can't form, etc. As far as I know 1+3 (three time dimensions and one space dimension) is stable, but can only contain tachyons, but that's not my area of expertise.
- akomtu 5y ago
  I've read that paper. It only considered the case with flat and long dimensions. The second time dimension could form a tiny circle, just like the 4th space dimension.

by akomtu 5y ago

throwaway81523 5y ago

> Has anybody explored GR equations with multiple, say 2, timelike dimensions? Entire topic is too big for my brain, but I think the cool kids these days consider classical theories of any sort to be uninteresting, that the universe is really an infinite dimensional quantum state, and that GR and everything else emerges from that. https://arxiv.org/abs/1801.08132 https://arxiv.org/abs/1801.08132

beecafe 5y ago
You're right about the classical theory part. But the infinite dimensional is just one representation that is mathematically convenient - for example, you could consider a 2D image of 10x10 as a vector from a 100 dim space, each scalar being a pixel, or as one from a 2^100 space, with a vector of all zeros except at it's "index" in the list of all 10x10 images (this repr also allows you to express superposition within it by turning on multiple indices). Or as an element of a much lower dimensional subspace embedded in those spaces, like ML uses. In general infinite dimensional should just be taken to mean that using the inductive bias endowed by a specific representation isn't necessary for whatever we want to use the theory for. It's also how you (imo, crudely) represent functions as first-class objects in math.

layer8 5y ago

> Has anybody explored <idea> The answer to those questions is always “yes”, unless you’ve spent years of research to come up with <idea>. https://en.wikipedia.org/wiki/Multiple_time_dimensions https://en.wikipedia.org/wiki/Multiple_time_dimensions

4ad 5y ago

Of course that people have explored physics in spaces with multiple time dimensions. They aren't stable, orbits can't form, atoms can't form, etc. As far as I know 1+3 (three time dimensions and one space dimension) is stable, but can only contain tachyons, but that's not my area of expertise.

akomtu 5y ago
I've read that paper. It only considered the case with flat and long dimensions. The second time dimension could form a tiny circle, just like the 4th space dimension.