4 ms·

Some points you may find interesting: * If you're like me and are clueless about the terms "hyperbolic", "too simple" etc. used in the plot, take a lot at this

by Jun8 3y ago

Some points you may find interesting: * If you're like me and are clueless about the terms "hyperbolic", "too simple" etc. used in the plot, take a lot at this SE answer that explains it (relatively) simply (https://physics.stackexchange.com/a/110880 https://physics.stackexchange.com/a/110880) * In his books the hard-SF writer Greg Egan has explored worlds with more than one timelike dimensions, see the discussion on HN ( https://news.ycombinator.com/item?id=36431620 https://news.ycombinator.com/item?id=36431620) and this comment on SE (https://physics.stackexchange.com/a/14106 https://physics.stackexchange.com/a/14106) * For very short distances space-time dimensions get reduced from four to two, see this post by Sabine Hossenfelder(http://backreaction.blogspot.com/2013/05/dimensional-reduction.html http://backreaction.blogspot.com/2013/05/dimensional-reducti...)

codethief 3y ago
> * For very short distances the so-called spectral dimension is theorized to get reduced from four to two in certain approaches to quantum gravity, see this post by Sabine Hossenfelder([…]) FTFY. Hossenfelder's blog post says: > The notion of dimension that is relevant for the effect of dimensional reduction is not the Hausdorff dimension, but instead the “spectral dimension.” The spectral dimension can be found by first getting rid of the Lorentzian signature and going to Euclidean space. And then to watch a random walker who starts at one point, and measure the probability for him to return to that point. The smaller the average return probability, the higher the probability he’ll get lost, and the higher the number of dimensions. One can define the spectral dimension from the average return probability. (The Hausdorff dimension is what we typically mean when we say "spatial dimension.") Moreover, all the papers cited are "approaches to quantum gravity", as she says, i.e. attempts at finding a theory of quantum gravity that works. No one has found one yet, though.

by Jun8 3y ago

codethief 3y ago

> * For very short distances the so-called spectral dimension is theorized to get reduced from four to two in certain approaches to quantum gravity, see this post by Sabine Hossenfelder([…]) FTFY. Hossenfelder's blog post says: > The notion of dimension that is relevant for the effect of dimensional reduction is not the Hausdorff dimension, but instead the “spectral dimension.” The spectral dimension can be found by first getting rid of the Lorentzian signature and going to Euclidean space. And then to watch a random walker who starts at one point, and measure the probability for him to return to that point. The smaller the average return probability, the higher the probability he’ll get lost, and the higher the number of dimensions. One can define the spectral dimension from the average return probability. (The Hausdorff dimension is what we typically mean when we say "spatial dimension.") Moreover, all the papers cited are "approaches to quantum gravity", as she says, i.e. attempts at finding a theory of quantum gravity that works. No one has found one yet, though.