Noob to PF, Quantum Foam question triangles?

[netefficacy]

Hi I am a noob on here, first post. Not a physicist by any stretch, but am researching the quantum mind and a while ago came across a paper that proposed that the quantum foam (if that is the correct term, maybe spacetime?) was geometrically just a bunch of triangles. If anyone can post a link to that proposal or paper I would appreciate it. In the spirit of giving to get, here is a link to Plato on triangles:

http://www.ellopos.net/elpenor/physis/plato-timaeus/default.asp:

And every sort of body possesses solidity, and every solid must necessarily be contained in planes; and every plane rectilinear figure is composed of triangles; and all triangles are originally of two kinds, both of which are made up of one right and two acute angles; one of them has at either end of the base the half of a divided right angle, having equal sides, while in the other the right angle is divided into unequal parts, having unequal sides. These, then, proceeding by a combination of probability with demonstration, we assume to be the original elements of fire and the other bodies; but the principles which are prior to these God only knows, and he of men who is the friend God.

δυνατὰ should read mightily/loudly not "fairer" so take the translation for what its worth.

 

[Simon Bridge]

Welcome to PF.
Entering into anything to do with QM without a grounding in the subject leaves you open to a lot of pseudoscience that like to use QM ideas in a waffly way. Strongly urge that your research include a primer course on Wave Mechanics at the very least.

It should be observed that everything can be described as a construct of triangles, so it is not a deep observation. Do you have a link to that paper?

Meantime - quantum mind ... presumably you have seen Shadows of the Mind (Penrose 1994) and Consciousness: Creeping up on the Hard Problem (Grey 2004).

Basically, Quantum Mind is a highly speculative area of ... well, speculation.

 

[netefficacy]

Hi Simon,

Thank you for the thoughtful reply. I googled some more and found this: http://physics.aps.org/story/v14/st13

that refers to what I read a while ago. There is a paper but I am not registered yet to download.

I understand that QM is highly speculative and my interest relates to a thought experiment mostly. At the same time, as a practical matter, I am interested in this area (physics of consciousness) since I am an attorney and this area is beginning to develop rapidly. See, e.g., neurolaw and fMRI research.

Thanks for the welcome, the recommended books, and the Wave Mechanics study suggestion.

Take care,
Scott

 

[atyy]

I googled some more and found this: http://physics.aps.org/story/v14/st13

that refers to what I read a while ago. There is a paper but I am not registered yet to download.

http://arxiv.org/abs/hep-th/0404156
http://arxiv.org/abs/0711.0273
"We would like to emphasize that the presence of discrete simplicial building blocks does not introduce any fundamental discreteness of spacetime in the theory. The simplices are the analogues in dynamical gravity of the fixed hypercubic lattice cells used to define QCD nonperturbatively. The geodesic length parameter a characterizing their edge lengths serves merely as a short-distance cut-off which is taken to zero in the continuum limit."

 

[Simon Bridge]

What he said - and just a caution: "QM" is a term of the art and stands for the entire field of Quantum Mechanics - though it is often used to refer to Wave Mechanics.

Quantum Mind theorists look like they are still mapping out the scope of the theory. Empirical evidence seems pretty restricted to demonstrating various quantum effects in organisms and in various brain structures. There is yet no special reason to believe that these processes have anything to do with consciousness and free will.

You also may want to take a look at some other models for consciousness for contrast.

 

[Markus Hanke]

I believe what you are looking for is the model known as "Causal Dynamical Triangulation". A basic introduction can be found here :

http://en.wikipedia.org/wiki/Causal_dynamical_triangulation

The fundamental idea is that on a basic level the quantum vacuum is made up of so-called 4-simplexes, which are ordered in such a way as to make a causally connected, globally smooth and continuous space-time manifold. It's an interesting approach which I am personally very enthusiastic about.

 

[netefficacy]

I believe what you are looking for is the model known as "Causal Dynamical Triangulation".

Thank you thank you! CDT is exactly what I was trying to locate. Another poster mentioned that I should get up to speed on Wave Mechanics. It sounds like you are familiar with CDT, can you recommend a basic curriculum of math/physics in order to get to CDT? I am proficient at things, so learning is not an issue.

On CDT, a first question that I have is when the vertices of the "triangles" are at t and t+1, and a third vertex is at t, how does a new "triangle" with 3 vertices of t+1 come into being? I will explore.

 

[netefficacy]

"We would like to emphasize that the presence of discrete simplicial building blocks does not introduce any fundamental discreteness of spacetime in the theory. The simplices are the analogues in dynamical gravity of the fixed hypercubic lattice cells used to define QCD nonperturbatively. The geodesic length parameter a characterizing their edge lengths serves merely as a short-distance cut-off which is taken to zero in the continuum limit."

Thanks for the clarification. This reminds me (as a non-scientist) of the dichotomy paradox (one of Zeno's). Involving halving distances.

http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

 

[netefficacy]

What he said - and just a caution: "QM" is a term of the art and stands for the entire field of Quantum Mechanics - though it is often used to refer to Wave Mechanics.

Quantum Mind theorists look like they are still mapping out the scope of the theory. Empirical evidence seems pretty restricted to demonstrating various quantum effects in organisms and in various brain structures. There is yet no special reason to believe that these processes have anything to do with consciousness and free will.

You also may want to take a look at some other models for consciousness for contrast.

What is the difference between QM and microphysics? I saw that term recently. Free will is at the core of what I am looking into from a legal perspective.

 

[Markus Hanke]

Thank you thank you! CDT is exactly what I was trying to locate. Another poster mentioned that I should get up to speed on Wave Mechanics. It sounds like you are familiar with CDT, can you recommend a basic curriculum of math/physics in order to get to CDT? I am proficient at things, so learning is not an issue.

On CDT, a first question that I have is when the vertices of the "triangles" are at t and t+1, and a third vertex is at t, how does a new "triangle" with 3 vertices of t+1 come into being? I will explore.

Picture spacetime to be made of 3-dimensional spatial "slices". Each slice represents a time t. The basic building blocks, the 4-simplexes, have 10 edges and 5 vertexes; 4 of these vertexes will lie within the 3-dimensional time-slice and are therefore spatial in nature. The fifth vertex on the other hand will connect with a new simplex at time t+1; this one, and the corresponding edges, are time-like in nature. The trick is to arrange the time-like edges in such a way that they are all aligned in the same "direction", meaning all points in space-time are causally connected so that cause precedes effect in all cases. What you get is a time arrow pointing in only one direction ( the future ).
One interesting feature here is that, at very small scales of the order of magnitude of the Planck length, spacetime can be approximated to be 2-dimensional to a good degree, however, it then has a fractal geometry.
The maths behind this model is actually very complex; you will need good knowledge of differential geometry, Regge calculus and the path integral formulation of quantum physics. The basic idea, in simple terms, is to formulate a path integral that sums over all possible ways to arrange the 4-simplexes ( = all possible space-time geometries ). You then impose constraints from first principles, chiefly the demand that time-like edges align in the same direction, and see what happens.
I am unfortunately not aware of any textbooks dealing specifically with CDT; I would recommend the following papers, but you would need to be familiar with the maths already in order to follow these :

http://arxiv.org/PS_cache/hep-th/pdf/0509/0509010v3.pdf
http://arxiv.org/PS_cache/hep-th/pdf/0505/0505154v2.pdf

 

[jtbell]

can you recommend a basic curriculum of math/physics in order to get to CDT?

It would help to tell us where you are starting from. How much math and physics have you studied already, in the sense of being able to work out exercises etc.?

 

[netefficacy]

It would help to tell us where you are starting from. How much math and physics have you studied already, in the sense of being able to work out exercises etc.?

Not much high level formal coursework. College Calculus, high school physics. Self-taught though in stats and differential equations and QM and chemistry via web/MIT Open Courseware etc.