Jason D. Padgett, a student at Tommaso Dorigo’s blog, who has to my knowledge previously been ignored, left an interesting comment, an edited version of which I shall post here.

Hello again, thanks for the comment. Some were not as kind … The equation I am referring to comes from the Planck constant and the pure geometry of space time. What I did initially was to try to draw … the structure of space time keeping in mind Planck’s constant. In other words … every time you move through space you must move exactly one or whole multiples of one Planck constant.

Don’t take this literally to mean spacetime, but think of it as a local model for spacetime, in which there is a proper notion of local Planck scale. Carrying on:

Planck constants also vibrate at the speed of light. What causes the Planck constants to vibrate is uncertainty … Anyway, once you have a grid drawn with Planck lengths and you start them vibrating (from uncertainty) you will see that at specific points the Plancks will collide with each other at the speed of light …

OK, so this is kind of fun, but is it telling us something interesting? Next we have:

When you draw this diagram the only shape that space time can take is a 2 dimensional hexagon or 3 dimensional cube …

Heisenberg’s hexagons from fractals! Now that’s cool. I’m hoping to take a closer look at his work.

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## Anonymous said,

August 16, 2007 @ 1:00 am

Jason D. Padgett said:

“… from the Planck constant and the pure geometry of space time … try to draw … the structure of space time keeping in mind Planck’s constant.

In other words … every time you move through space you must move exactly one or whole multiples of one Planck constant. …

the only shape that space time can take is a 2 dimensional hexagon or 3 dimensional cube . …”.

I agree with Jason D. Padgett that spacetime is fundamentally a lattice, each bit of which is Planck-constant size.

My view is that

hbar is the uncertainty product of the Planck Energy and the Planck Time: hbar =

= Mplanck^2 G / c = c^2 Mplanck^2 G / c^3 =

= ( c^2 Mplanck ) ( Mplanck^2 G / c^3 ) =

= Eplanck Tplanck

so that,

if you use Energy-Time uncertainty,

then

hbar is the uncertainty probability for Gravitons to create a new bit of SpaceTime.

However, I do not agree that “… he only shape that space time can take is a 2 dimensional hexagon or 3 dimensional cube …”.

For example,

a high-energy 8-dim lattice spacetime can come from E8 lattice structure,

and

down at the low energies of our experiments, a 4-dimensional HyperDiamond Feynman Checkerboard is realistic.

My relevant web pages are at

http://www.valdostamuseum.org/hamsmith/simph.html

http://www.valdostamuseum.org/hamsmith/ClifTensorGeom.html

http://www.valdostamuseum.org/hamsmith/USGRFckb.html

Tony Smith

## Kea said,

August 16, 2007 @ 1:15 am

Hi Tony. Well, until he shows us the details of his work it isn’t clear what he means by hexagons and cubes, but I know what

Imean by hexagons and cubes, which is something sufficiently abstract to allow E8 lattices and all sorts of other goodies!## L. Riofrio said,

August 17, 2007 @ 4:40 pm

As bees know, the most efficient way of packing spaces is by hexagons. 6-sided cubes have correspondences to hexagos too. There might be something to this. Lattice idea deserves to be explored.

## a quantum diaries survivor said,

August 17, 2007 @ 8:41 pm

Hi Kea,

funny – I never considered seriously the ideas of Jason, mainly because I do not understand the stuff enough. But I am happy you picked it up… Only, if Jason becomes the next Einstein, I will be jealous because you will be the discoverer of his talent, not me 🙂

Cheers,

T.

## Kea said,

August 17, 2007 @ 9:58 pm

Hi Tommaso! I don’t think that’s likely.