B Are dimensions a fundamental property of the universe or do they emerge due to other laws?

Doesn't CDT (Causal dynamical triangulation) a background approach to quantum gravity appear to have a good semi-classical description - in that at large scales, it re-creates the familiar 4-dimensional spacetime, but it shows a dynamical reduction of spacetime to two dimensions at the Plank scale and a fractal structure of slices of constant time?

And the discovery that in the limit of short distances, spacetime becomes effectively two-dimensional may indicate the presence of a dynamically generated ultraviolet cutoff: "...quantum gravity may be "self-renormalizing" at the Planck scale, by virtue of a mechanism of dynamical dimensional reduction."

 

My view is that the evolution of the universe is dependant on change. Change is dependant on the ability/facility to exchange information between 2 coordinates in 3 - D space and time. So without the existence of this facility to exchange information, there would be nothing.

 

While its obvious that standard model physics need dimensionality as a framework to start with some of us will not settle until dimensionality is better understood as well.

Imho, there are sound hopes to expect that dimensionality of spacetime should eventually be understandable im terms of spontaneous decoupling of internal vs external information between interaction observers. Ie spacetime may be seen as the interconnecting structure between subsystems, and this structure is then by construction the result of a negotiation game - spacetime is simply what everyone that disagrees can agree about.

/Fredrik

 

What do you mean by "dimension" of space and time? Do you mean the size? Or the fact that they are measured in dimensional units (meter, second)? Or the topological dimension (3 for space and 1 for time)?

 

The emergent nature of dimensionality in LQG is quite elegant. In LQG what is fundamental is the number of other points in space-time that a point is space-time can be connected to. The fact that these connections can be sorted out into what amounts to a 4-D space-time with locality at a classical scale is emergent.

In principle, you could show that space-time is emergent by showing that a tiny share of space-time connections are non-local. Arguably, the need to include a small number of sub-luminal and super-luminal paths (at reduced weights with distance from "c") in photon path integrals is suggestive evidence of these kinds of pervasive, but slight non-local connections which would point to the emergent picture.

 

atyy has recently introduced the following papers which might be relevant here. Going to bed now. Will have a look at them tom.

http://arxiv.org/abs/1605.05694
Spontaneous Dimensional Reduction in Quantum Gravity
S. Carlip
(Submitted on 18 May 2016)
Hints from a number of different approaches to quantum gravity point to a phenomenon of "spontaneous dimensional reduction" to two spacetime dimensions near the Planck scale. I examine the physical meaning of the term "dimension" in this context, summarize the evidence for dimensional reduction, and discuss possible physical explanations.

http://arxiv.org/abs/1605.05979
On the UV dimensions of Loop Quantum Gravity
Michele Ronco
(Submitted on 19 May 2016)
Planck-scale dynamical dimensional reduction is attracting more and more interest in the quantum- gravity literature since it seems to be a model independent effect. However different studies base their results on different concepts of spacetime dimensionality. Most of them rely on the spectral dimension, others refer to the Hausdorff dimension and, very recently, it has been introduced also the thermal dimension. We here show that all these distinct definitions of dimension give the same outcome in the case of Loop Quantum Gravity. This is achieved by deriving a modified dispersion relation from the hypersurface-deformation algebra with quantum corrections. Moreover we also observe that the number of UV dimensions can be used to constrain the ambiguities in the choice of these Loop-Quantum-Gravity modifications of the Dirac spacetime algebra. In particular, we find that the the simplest polymerization of connections i.e. K→sin(δK)δK, which is much used in the literature, cannot reproduce the shared expectation of dUV=2.

 

I like this paper by Witten,

https://www.sns.ias.edu/ckfinder/userfiles/files/Reflections(3).pdf

However, string theory doesn't seem to give an explanation of why we have one time direction; also, it seems to allow for two spatial dimensions on top of the often quoted nine; we simply don't know how to 'decompactify' such a theory to three.