TOEs and the Quantization of Space and Time

Almost 20 years ago I read Paul Davies book "The Mind of God" in which he postulates that theoretical physicists were (and presumably still are) close to formulating a so-called TOE (theory of everything).  One thing he said is that it was obvious that the final theory would need some "magic" numbers for our particular "instantiation" of reality.  God chose these particular numbers so that our universe could exist and support life.

Personally I don't think we are anywhere near formulating a final TOE.  And when we do I believe there will not be many if any such magic numbers.  Things like the maximum speed (C) will just be a consequence of the basic building blocks of the universe.  Not that I think the universe is made of blocks (see below).

I first starting contemplating the basic nature of the Universe when I first read about quantum mechanics about 35 years ago.  It seemed natural that not only matter/energy was quantized but also space and time should be too though I do not know if anyone else thought so at the time.  (Actually I believe that the only "real" numbers are integers but I'll leave that for another post.)

The problem with quantizing space (discussion of time has to wait for now) is that it did not make a lot of sense to think of space made up of tiny little cubes for many reasons.  First, it would mean we would have some sort of absolute Cartesian coordinate system to which the cubes were oriented which just seems stupid.  Also we know that space can be curved which would mean that the cubes become misshapen which is unappealing.

A few years later when studying graph theory it occurred to me that if the space was made up of a huge graph (here I am talking about the edges/vertices type of graph) then with the appropriate topology space would appear to be three-dimensional.

For example, if each vertex of "space" had two edges then we would get a 1-dimensional universe.  (You could call this a straight line but it really makes no sense to think of this universe as being curved or straight.)  With more complex graph topologies you could create a "space" of 2, 3 or more dimensions.  This would explain space but what of things (matter/energy) that exist in space.  It always seemed pretty obvious that matter/energy are not independent of space/time but are some sort of property of it.  The obvious conclusion was that matter/energy is simply some sort of attribute of the graph vertices and/or edges.

It later occurred to me that we don't have to assign attributes to the elements of the graph.  It would be simpler to consider matter/energy to be some sort of localised twisting or distortion of the graph itself.  I remember at the time that physicists were looking for a few "fundamental" particles but experiments were uncovering more and more particles that all appeared to be indivisible.  Perhaps this was just that the graph could become twisted in more and more complicated ways meaning that theoretically there are an indefinite number of "fundamental" particles (though to create more and more exotic ones would probably be "harder" in some way - eg, require more and more energy).

Game of Life

Also at the time (~1980) I was intrigued by a computer "simulation" called the "Game of Life" which basically simulates the creation and death of "cells" using some very basic rules.  Since starting this post I have dicovered that it is generally called Conway's Game of Life - see http://en.wikipedia.org/wiki/Conway's_Game_of_Life

In brief, the game consists of a 2 dimensional grid of cells that have either of 2 states: alive or empty (dead), alive cells will die if they are surrounded by too many or too few other live cells.  New live cells are created when an empty cell is surrounded by the correct number of live cells.

The game creates interesting dynamic patterns one of which is called a "glider", which slowly (on each tick or quantum of the game's "clock") moves across the grid.  This lead me to think that particles that travel at or close to the maximum speed in space (neutrinoes etc) might be similarly produced by continual twisting of the fabric of space.  Like gliders they can only exist while they are moving.  And as in the Game of Life there are not just neutrinoes (gliders) but more complicated shapes, that also can only exist while they are moving, called photons.

The maximum speed that these particles can move is determined by the quantization of space and time and is denoted by the letter C.  This is often called the speed of light (in a vacuum) though I believe that neutrinoes and photons do not travel at quite the maximum speed (just as gliders do not move at the theoretical maximum speed in the Game of Life).

The Speed of Light and Neutrinos

Coincidentally, a few days after I wrote the above (but before I published it) there was news all over the papers saying that an experiment had shown that neutrinos travel faster than light.  This was apparently shocking to many physicists but I did not find it surprising.  The papers were saying that, if true, this would mean that Einstein was wrong, time-travel is possible, and all sorts of other nonsense.

Of course, if true (and I believe it probably is) it only means that photons travel at very slightly less than the maximum speed limit or C.  I believe neutrinos also travel at less than C but slightly faster than photons, because they have a simpler structure than photons, just as gliders in the "Game of Life"  travel faster than other objects like the LWSS.

I will probably have more to say on this later.

Humans have 4 Colour Receptors

The rainbow made by a prism is has 7 colours (red, orange, yellow, green, blue, indigo and violet).  Though they seem to somehow merge together these colours appear to be distinct to most people (except for maybe the last 3), ignoring colour-blind people.

Thinking about this I concluded that human eyes must have 4 different colour receptors.  Each receptor must receive a small range of frequencies in the electromagnetic spectrum and it seemed likely the ranges overlapped (since there are no invisble gaps in a rainbow).  Looking at how the receptors' frequency ranges might overlap it occurred to me that, in general, given N receptors you can detect (2N - 1) different colours (though for certain configurations you might get less).  My conclusion was that humans have 4 different types of colour receptors since we see 7 (= 2 x 4 - 1) different colours.

I remember specifically asking my science teacher (Mr Connell?) around about 1975 "why the rainbow has 7 colours", not so much to find out the answer but to find out if it was generally known what I had concluded.  His answer was vaguely along the lines of it was to do with physiology and we were studying physics not biology.  I actually did a bit of research but I could find no information about this (the Internet did not exist at the time).

It wasn't until several years later (doing Psychology I at Sydney University) that I found out that the eye has rod and cone cells to detect light.  There are 3 different types of cone cells used for the detection of different colours, while rod cells are used for "night vision".

I am still waiting to hear of research that shows that rod cells also play a part in colour reception (probably in the blue-indigo-violet region).  Then there would be the 4 colour receptors I had theorized.

Introduction

Recently I rediscovered an old 1974 diary that I had been given as a teenager.  Though I never used it as a diary I had written down a lot of ideas in it and over subsequent years had added to it until it was overflowing.  Most of these ideas were about science, technology and the future (though there were also a few ideas for science fiction stories).

Some of the ideas were stupid, some were fairly accurate predictions of the (then) future.  Some are still interesting so I have decided to document them in a blog for posterity as I re-read them.  Note most of the ideas are from the mid-1970's to mid-1980's as noted (but may be refined or embellished before publication).  Some may be more recent.

Also note that I am not claiming ownership of any of these ideas, since many of them have been discovered or proposed independently by other people since then.