[HN Gopher] On the dimensionality of spacetime (1997) [pdf]
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On the dimensionality of spacetime (1997) [pdf]
Author : niklasbuschmann
Score : 95 points
Date : 2024-01-21 16:59 UTC (6 hours ago)
(HTM) web link (space.mit.edu)
(TXT) w3m dump (space.mit.edu)
| dvh wrote:
| Imagine what kind of computers could you make if you could
| radiate heat into more than one dimension. Or maybe you would get
| greedy and use up all available dimensions for interconnects and
| use one remaining dimension for heat dissipation anyway.
| simonh wrote:
| Can't we already radiate heat into 3 dimensions?
| radarsat1 wrote:
| I think what he means is that chips are 2D, so heat is
| radiated orthogonal to the plane of the circuit -- up or
| down.
| paulddraper wrote:
| Yes. See: radiators
| thfuran wrote:
| A hypercube's surface area to volume ratio grows without bound
| with dimension, so radiating heat ought to be easier with more
| dimensions even if you build a fairly blobby (I'm sure that's
| the technical term) core, though an n-sphere's peaks at n=7, so
| you don't want to get _too_ blobby in higher dimensions.
| calamari4065 wrote:
| Wouldn't a 4th dimension allow connection between any two
| points in a 3D space? I _think_ that 's how that works but I'm
| no mathemagician.
| mminer237 wrote:
| Essentially, but you still have to travel the distance in a
| parallel dimension. Think about layers on a circuit board or
| road overpasses. You can connect two things separated by
| something by going "up" in the third dimension, but you still
| have to actually go the distance after avoiding the collision
| (and then go down).
| ikari_pl wrote:
| so in current design you travel the distance in the time
| dimension
| falsandtru wrote:
| It is possible by deforming it in the fourth dimension, like
| folding paper. However, the shapes that can be created by
| folding are considered limited.
| falsandtru wrote:
| A CPU, a planar object, does so by extending its fins in the
| three-dimensional direction, but not without limit. Similarly,
| even if the fourth dimension can be used, it cannot be used
| without limit. Also, just as there are no two-dimensional
| objects without thickness in three-dimensional space, there are
| no three-dimensional objects without thickness in four-
| dimensional space, and all three-dimensional objects are
| considered to have size in the fourth-dimensional direction in
| four-dimensional space.
| qwerty456127 wrote:
| I didn't read the paper yet, but the title reminds me of Robert
| Bartini who had a theory of time being 3-dimensional as well as
| space is.
| djmips wrote:
| Tegmark's paper does seem related in that it is arguing that
| proposals like Bartini's might produce a universe that is
| 'dead'. It seems that Tegmark's paper is suggesting that only 4
| dimensional (3+1) universe produces a world with 'observers'.
| The math is beyond my ken.
|
| This appears to be the Bartini paper (1965)
| https://www.researchgate.net/publication/26408302_Relations_...
| Theizestooke wrote:
| Bartini the aircraft designer? I'd like to read more about
| that, but most of the Bartini-related stuff is about airplanes.
| qwerty456127 wrote:
| AFAIK he was also a mystic of a kind and what we would call a
| "fringe scienctist" in today language. Which makes a curious
| case when such a character actually builds serious
| sophisticated working products like cutting-edge airplane
| designs. The latter leading to a clue that his theories may
| be worth exploring (they still can be wrong, but there is a
| chance of finding some interesting food for thought there).
| Another example of an inventor of similar kind coming into my
| mind obviously is Nikola Tesla.
| emchammer wrote:
| The chart on the second page of the article used to be located on
| a Wikipedia page called "Privileged character of 3+1 spacetime".
| I think it's curious that it seems to be mirrored over a diagonal
| axis.
| georgeg23 wrote:
| Not too surprising given time and space are pretty symmetric
| (or anti-symmetric).
| sigmoid10 wrote:
| That's expected when you realize that time and space are not
| different things but just two aspects of the same, pseudo-
| Riemannisn structure that describes our universe. The only
| thing separating them is a sign which in turn is based purely
| on convention.
| abhayhegde wrote:
| The link to Wikipedia page for the curious [0].
|
| [0]:
| https://en.wikipedia.org/wiki/Spacetime#Privileged_character...
| balaise-rustine wrote:
| Isn't 2+1 dimensions gravity a thing ? https://arxiv.org/abs/hep-
| th/9204099v3
| AlecBG wrote:
| I think you end up with no degrees of freedom in 2+1 and below
| pa7x1 wrote:
| Yes, and even 1+1 gravity theories, like JT-gravity (https://en
| .wikipedia.org/wiki/Jackiw%E2%80%93Teitelboim_grav...).
|
| But 2+1 Einstein's gravity is locally trivial (i.e. there are
| no local degrees of freedom) and is purely topological (i.e.
| holes and global structure of spacetime is what matters).
| KierPrev wrote:
| Couldn't be other than Max Tegmark
| anonymousiam wrote:
| It seems that this paper assumes all the dimensions are flat. I
| believe that most current theories assume the higher dimensions
| are folded.
|
| https://en.wikipedia.org/wiki/Extra_dimensions
| i_k_k wrote:
| See the footnote on page 1:
|
| "Hereafter, we let n and m refer to the number of non-
| compactified space and time dimensions, or more generally to
| the effective spacetime dimensionality that is relevant to the
| low-energy physics we will be discussing later."
| trhway wrote:
| For example, in 2 dimensions embedded in our 3 the force
| potential decreasing with square distance would have given a
| hint to the 2-dim occupants that they are embedded in 3. We
| don't see the decreasing with cube, so we don't seems to be
| embedded in full-flat 4+. (even more - the force falls off
| linear with distance in galactics, i.e. "dark force"/MOND,
| which seems to be another indication of some holograghy-like
| "folding" 3->2 (the other being is the black hole holography))
| thechao wrote:
| My personal take is that 3+1 is _not_ privileged; but that the
| physics that takes place in the other combinations is either so
| uninteresting it doesn 't meaningfully interact, or that the
| number of Feynman paths through the non-3+1 cases all (mostly?)
| cancel out.
| LASR wrote:
| Nice analysis. But the point about stability - in other
| configurations of the universe, the subset of those that do
| evolve intelligence in some fashion is going to have different
| physics from our own.
|
| Stable intelligences might be another condition to explore in
| such an analysis.
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