Monday, 21 February 2011

10 spacial dimensions: what does that mean?

In my previous post I explained why we think there are multiple dimensions. In this post I want to clarify exactly what I mean by "dimensions" and to try to give you a way of visualising what that means in practical terms. The word "practical" is hardly appropriate when we are referring to states of being - of existence - that are literally out of this world, but bear with me.

Esoteric science and spiritual definitions of dimensions include "vibrations" or "planes of existence". For example in the the theosophical and taoist traditions, there are seven named planes: the Physical, Astral, Causal, Akashic, Mental, Messianic and Buddhaic planes. Those who subscribe to a belief in Pleiadian extra terrestrials have a 12 "dimensional" definition of consciousness (more info about this at the foot of this post).

I want to make it clear that the dimensions referred-to in string theory are not (necessarily) the same. In this blog, when I refer to the word "dimension" I am using it as defined by the science of mathematics, unless stated otherwise.

In mathematics the dimensions of a point are the minimum number of co-ordinates necessary to define the position of that point. For now, forget the idea of space-time and try to imagine a dimensionless domain in which there exists a single point. That point has no height, width, depth or any other dimension that can define its position. This is the "zeroth" dimension.

Now define another point, anywhere, and join it to the first by a line. We now have a one-dimensional object that has length but zero width. Another way of thinking about this 1D line is that it consists of an infinite number of points stacked side-by-side in the direction of the first dimension.

Now stack an infinite number of 1D lines side-by-side, parallel to one another. The shortest distance between any two of these lines would be at right angles to the line, measured in the direction of the second dimension. You can imagine that all these 1D lines when placed side by side, define a flat surface or a 2D plane. It has length and breadth but zero height.

Now stack an infinite number of 2D planes on top of one another. The shortest distance between any two of these planes would be at right angles to the plane, measured in the direction of the third dimension. You can imagine that all these planes when placed one on top of another, define a three dimensional domain, like the one that we live in which we call "space".

It is a requirement of each new dimension that it must be at right-angles to all of the other dimensions. In mathematics we use an expression to describe the idea of all the dimensions being at right angles to one another. We say they are "mutually orthogonal".

A diagonal line on the 2D plan can't be a new, third dimension in its own right because any point on that line can be defined entirely using 2D coordinates. Tilt that diagonal line upwards, above the 2D plane and you still haven't defined a new dimension because the line isn't at right angles to the plane. Only when the line is orthogonal to the plane is it possible to move along it - in the third dimension without changing your co-ordinates in the first or second dimensions.

I'm using imagery to help you visualise higher dimensions one at a time, but now we have arrived at our familiar 3D space how can we visualise the 4th spacial dimension? I'll let physicist Carl Sagan do that for you in the following videos.

Part 1

Part 2

We can't easily conceptualise what a 4th spacial dimension might look like, but if you've followed my reasoning so far, you will appreciate that the 4th dimension consists of an infinite number of 3D spaces stacked parallel to one another at right angles. Perhaps these might be thought of as parallel worlds?

Continuing the idea, the 5th dimension is an infinite number of parallel 4D realms stacked together orthogonally, the 6th dimension is an infinite number of parallel 5D realms stacked together orthogonally and so-on until we reach the 10th spacial dimension which is an infinite number of parallel 9D realms stacked orthogonally.

The stacking order of the dimensions is important because each higher dimension consists of an infinite number of realms of the next dimension down.

Supposing some or all of the extra dimensions of string theory are below the first dimension? In other words, could they be a subset of 3D space? This would mean that our 3D space might actually be the 8th, 9th and 10th dimensions. The following video describes the model developed by mathematicians Theodor Kaluza and Oskar Klein in which a 4th spacial dimension is described as "curled-up" within 3D space. To my way of thinking, if they are contained within our space then they are lower dimensions.

The Extra Spatial Dimensions of String Theory

We can only speculate about what the individual characteristics of each additional dimension are and how it adds meaning to the ones below. I subscribe to Rob Bryanton's visualisation as described in his book "Imagining the 10th Dimension". His video (shown below) has certainly reached the imagination of the public having scored nearly 1.5 million hits on YouTube.

Rob Bryanton: Imagining the 10th Dimension
Part 1

Part 2

If you are confused by the fact that M-Theory states there are 11 dimensions and Rob is describing a 10-dimensional model, then realise that 10 dimensions are sufficient to describe reality and to unify gravity and quantum mechanics and that the 11th dimension is the one that explains why there are many possible 10D models. Rob has produced a vlog to discuss this in more detail - "Aren't there really 11 dimensions?"

The order of the dimensions is not important to my view of reality - specifically the role consciousness plays in the universe - but exactly where time fits-in is one of those questions that has caused me a great deal of wonderment. In my next post "Is Time a Dimension?" I will discuss this in more detail.

From the perspective of THIS universe, I am "The REAL" Jeff Hall

More reading

Imagining other dimensions

David Roberts 12 Dimensions of Consciousness (Esoteric)

Sunday, 20 February 2011

Why we think there are multiple dimensions

As promised in my introductory blog post, I now want to explain where this idea of multiple dimensions originated. I need to talk about mathematics and physics. At this stage, I don't want to go into detail about the implications and ramifications of multiple dimensions but merely to describe the scientific basis for the claim that there are several more dimensions than the ones we are immediately aware of.

Prepare yourself for an introduction to the leading edge of advanced mathematics! I promise I'll make it as easy to understand as I can, but don't worry if you don't follow everything. There are a couple of videos at the bottom of this post that may be of some help. The important thing is that you get to the end of this post with a realisation that all of this is for real. It's not a flight of fancy. Here goes....

Einstein's general theory of relativity beautifully describes the physics of the universe on a large scale. It is also referred-to as the theory of gravity. It describes the motions of an apple falling from a tree, the rotation of a planet around a star, a star round a galaxy and even the motion of a galaxy itself. The mathematics of geometry are used in its formulation. However, it breaks down on the small scale. For example, it can't describe the motion of an electron within an atom.

For that, we need to turn to a different theory: that of quantum mechanics. A "quantum" is the name given to the smallest unit of any physical entity that is involved in an interaction. Quantum mechanics uses (amongst other things) the mathematics of probability to describe the behaviour of sub-atomic particles and is widely regarded as the most validated branch of science. In particle accelerators such as the European Large Hadron Collider and the US Tocomac at MIT, it predicts the outcome of atom-smashing experiments to an incredible degree of accuracy.

Just as general relativity can't explain quantum interactions, quantum mechanics can't explain interactions at the cosmic scale. The two branches of scientific theory are at odds with one another and yet we know from experiments and observations that the different worlds they describe are actually part of the same universe: the one we live in.. There must therefore be a bigger, overriding theory that unifies them at all scales.

This was one of the major scientific quests of the 20th century and Einstein went to his grave without a satisfactory answer. This all changed in 1985 when theoretical physicist John Hagelin developed a revolutionary idea that finally appeared to solve the conundrum. The "Grand Unified Field Theory" as it was called (GUFT), used the vibration and rotation of one-dimensional superstrings to model the behaviour of sub-atomic particles and the four fundamental forces of physics: the nuclear strong force, the nuclear weak force, electromagnetism amd gravity. "String Theory" was thus born.

Within a few years another four, apparently different, competing 10-dimensional GUFT's were developed. Clearly the universe couldn't exist in all 5 states - or could it? In the early 1990's one of modern physics' most revered theoreticians, Professor Edward Witten put to rest the growing doubts about string theory by unifying the five unified theories into a single theory which he called "Membrane Theory".

He did this by adding yet another dimension to the model making it 11-dimensional. Each 10 dimensional GUFT could now be thought of as a different aspect of the higher dimensional model. Think of it like a 3D cube that that can cast a number of different 2D shadows on a flat surface. Each shadow is a different representation of the cube in the lower (2D) dimension. Witten subsequently became sceptical about membranes and the theory is now referred-to as just "M-Theory".

An argument soon broke out amongst those closest to string theory about how to - or even whether to - interpret M-Theory in practical terms. I will discuss the concepts and meaning of dimensions in detail in my next post but, for now, suffice it to say that another SEVEN dimensions beyond the familiar three spatial dimensions plus the dimension of time has deeply profound philosophical and religious implications when taken literally.

Internationally famous physicist, Richard Feynman is reputed to have retorted "Just shut up and calculate" when asked to speculate about the implications of a multi-dimensional universe. The 11D GUFT model was very good at mathematically verifying the results of particle collision experiments and as far as he was concerned that's as far as it goes!

Needless to say, this whole blog is predicated on the assertion that it is right and valid to interpret M-Theory in words. The implications are massive in terms of where we humans fit into the true picture of reality. When I was employed as a professional mathematician by the Coal Board in the UK, we created models of economic and logistical systems that fitted all the data that we knew. We then purposely interpreted the models to tell us things about those systems for which we had no hard facts. Sometimes the revelations were unexpected but they invariably proved correct in the longer term as more data became available.
I therefore have an answer for those who doubt the validity of interpreting M-Thory: "Shut up and stop being afraid of the child you have given birth to."

Before I end this post it would only be fair to point out that we don't know for sure that there are multiple physical dimensions outside of space-time. M-Theory is just a theory and there are other interpretaions that have been put forward that don't include multiple dimensions. Having said that, the Large Hadron Collider at CERN is, as I write conducting experiments to try to test the theory, and according to a recent on-line news story the first tangible evidence may be discovered very soon.

My next post will be called "10 spacial dimensions: what does that mean?"
From the perspective of THIS universe, I am "The REAL" Jeff Hall :)

Further Information:

The Elegant Universe - Einstein's Relativity

Here is a 7 minute clip about Einstien's theory of relativity

Discovery of The Unified Field

And the great man himeself, John Hagelin talks about the unified field. Today he has moved on a long way and in fact is one of the major influences for the subject of this blog.