What Is Spacetime, Really?

Post by chr1 » Sat, Dec 05, 2015, 9:03 AM UTC

drdeca wrote: post #97

I'm having trouble finding any other references to a notion of a dimension of a graph which is based on howthe number of vertices which can be reached through a path of a given length increases with the length. I'm finding things like, a dimension of a graph as the minimum dimension of euclidean space where the vertices can be placed and have each edge have length 1, and another thing which seems closer which is base…

His definition of the dimension is quite similar to the definition of the dimension of a fractal.

His definition also works better than euclidean dimension, e.g. for a grid on cylinder euclidean dimension will be 3 and his definition will give 2. I think a modification of the definition above to allow minimum dimension of non-euclidean space will be same as Wolframs definition for the cases when dimension of the graph is not fractional number.

Post by euyyn » Mon, Dec 07, 2015, 4:34 PM UTC

yetihehe wrote: post #105

euyyn wrote: post #96

Earlier quoted context omitted.

> The uncertainty principle hints that something discrete may lie at the bottom. Not necessarily. The uncertainty principle is a direct consequence of some quantities being "the Fourier transform" of each other. You can't play a pure tone unless it extends infinitely in time, and vice versa: You can't play an infinitesimally short sound unless you ring all frequencies. That's all. And actually, if something discrete…

There IS known max energy, it's called Planck scale ( https://en.wikipedia.org/wiki/Planck_scale ).

The only "max" about that is in the name Max Planck :)

Re: What Is Spacetime, Really?

Re: What Is Spacetime, Really?