Chapter 1 — An introduction to dimensions

Previous — Introduction

What is energy?

If you have ever got hold of strong magnets and pushed the two like-poles together you may have wondered what was going on. We know that this is the repelling magnet force but there’s a strange quality about it. What is it that lies between the poles that prevents the magnets moving together?

Energy is related to movement and movement is related to time. Without movement there is no time.

What is thought?

Have you eve wondered what is consciousness and thought? How is it that science can explain matter and to a certain extent energy but consciousness and thought remains unexplainable?

In Seattle, Washington in the USA is one of the largest buildings in the world. It is used by Boing to manufacture a range of its airplanes. It is so big that it has its own climate. Now, imagine an ant in the corner of that building. What it sees is very small part of the building, so it can only speculate about the rest of the building, and the purpose of the building is totally beyond its comprehension.

We are like ants. We live in a corner of a galaxy that contains billions of stars and is one of possibly trillions of galaxies in the universe. As to the rest of the universe we really have very little idea, and as to the reason for its existence, that is totally beyond our comprehension.

We are aware of three spacial dimensions and of half of the dimension of time, in that we can see back into the past but not into the future.

Imagine fish in a pond. Every so often it rains and the pond gets disturbed. The fish don’t know about rain. Their universe is constrained to the pond and they are unable to conceive of events outside. We are like these fish. We get perturbed when events happen in the universe even though they are outside of perception.

In this book I will explain consciousness in terms of multiple dimensions and how these dimensions interact with our lives.

Understanding dimensions

We all understand the three dimensions that we call the spatial dimensions: width, length and height. Although a physical object requires all three dimensions to exist, they are interchangeable in that length may become height and in a sphere, for instance, the labels are quite arbitrary. Although we represent these three dimensions on flat surfaces as two dimensions in reality something that lacks one of these dimensions cannot exist.

Scientists talk of time as being the forth dimension. I’ll explain why later on and also we shall explore the fifth and sixth dimensions but first let us examine the concept of dimensions.

A quantum — a point with no dimensions

When we break down matter into smaller and smaller units, we get to an infinitesimal size: 1.6160 x 10–35 metres. The exact value is imprecise due to quantum uncertainties, which we will explore later on. This number is called Planck’s constant, named after Max Planck the German physicist and one of the pioneers of quantum theory. Although we can express this as a size, when we get down to these very small units we are not dealing with matter (which has a size) but energy (which doesn’t). As such Planck’s constant can be referred to as a Quantum, the smallest possible unit. The word comes from the Latin ‘quantus’ which means ‘how much’. Because a quantum is the building block from which we construct dimensions, it is dimensionless. If we were to express a quantum in terms of time it would be around 5.39121 × 10–44 seconds.

A Quantum (plural: quanta) can also be considered as a mathematical point. An entity with no dimensions but from which we can construct a line.

One dimension — the line.

A line has only one dimension, length and can be formed from a series of points. Each point has no dimension, it is essentially a quantum.

If you can imagine a one-dimensional insect, it could travel from one end of the line and back. This is its universe. It is finite and bounded because it has ends. The ant can go to each end of its universe but not further.

Because there is only one dimension, any point on the line can be defined with one number.

We can travel from point to point without going through the intervening points by traveling into the next dimension. Our one-dimensional insect would see you disappear from one place and reappear elsewhere on the line.

Two dimensions, the plane.

A plane (two dimensions) can be formed from a series of one-dimensional lines.

If you can imagine a two-dimensional insect, it could travel to the edges of its universe. It is finite and bounded by its edges.

Because there are two dimensions, any point on the plane requires two numbers to be defined.

As with one dimension, we can travel from point to point without going through the intervening points by traveling in the next dimension. If you can imagine a flat piece of paper we can place a pencil on one point and draw a line, in which case we travel over all the intervening points, or we can make a mark, raise the pencil off the paper (that is take it into the third dimension) and then bring it down somewhere else to make another mark without traveling over the intervening points.

Three dimensions — an object.

An object (three dimensions) can be formed from a series of two-dimensional planes. This is like stacking a ream of paper to form a solid block.

A three-dimensional insect could travel to the edges of its universe in the same way as the two-dimensional insect can. This is like a fish in a fish tank. Its universe has finite boundaries.

Because there are three dimensions, any point within the object requires three numbers to be defined.

It is theoretically possible to travel from point to point without traveling through the intervening points by traveling back in time.

If at 12:05 we could go back in time to 12:00 then we would have travelled through the forth dimension and gone from point to point without traveling through the intervening points by traveling through time. In practice human beings haven’t developed the technology to do this.

Four dimensions — the time space continuum

The time-space continuum (four dimensions) is formed from a series of three-dimensional objects.

Because there are four dimensions, three spacial dimensions and one time dimension, we require four numbers to define a point in space-time. We live in a four dimensional universe. For instance if you are going to meet someone you need to give the place, for example the corner of x and y streets on the fourth floor, but you also need to say when (e.g. at 2pm).

It’s worth noting that in reality a line or a plane can’t exist in our universe because they lack all the dimensions. A flat plane with no depth dimension would have no substance, as would a line. However, a three dimensional object could not exist unless it existed for a certain length of time. It requires the forth dimension.

Similarly, time can’t exist without matter. For there to be time there has to be movement of some 3-dimensional object.

Unbounded dimensions

All these universes that we have considered have been bounded, that is, they have ends. Consider now if we curve our one-dimensional universe through the second dimension to form a circle.

This universe is finite but is unbounded. A one-dimensional insect can travel the length of its universe and get back to where it started but will not know how. The universe is curved in the second dimension.

Similarly with a two-dimensional plane that is curved in the third dimension to form a sphere. A two-dimensional insect can return to where it started but will not know how.

Our three-dimensional universe is curved in the forth dimension (time). This forms the time-space continuum. If we travelled far enough we would theoretically return to where we started from.

Energy and time

We can consider that our three dimensional space is ‘sliced’ into time slices each of one quantum where each time-slice is minutely different from the previous one. This is similar to a film strip where each frame is like a snapshot of a minute amount of time and is slightly different to the previous one. At every moment of time there is a very slight change from one snapshot to the next.

This series of snapshots shows a ball being bounced. We see the ball going down on the left, hitting the bottom and bouncing back up on the right. However, there is nothing in each snapshot from which one could determine whether the ball is going up, down or is stationary. We can only know the movement of the ball because of the way the snapshots change from frame to frame.

The ball in the photograph has movement, (what scientists call kinetic energy). The movement is a product of time. Each frame is subtly different from the previous one and this is movement. It exists outside of the three dimensional frame but is shown as a result of the forth dimension. There is another kind of energy, however, known as potential energy. Potential energy does not necessarily have a movement, although there is the potential for movement. If we raise a ball off the ground it gains potential energy as it will release this energy as kinetic energy when it falls.

Even if we take a simple snapshot of a lamp sitting on a desk, there is nothing in that snapshot that tells us about the gravitational pull on the lamp. We know that if we were to suddenly remove the desk the lamp would drop to the floor but there is nothing in this picture, or in subsequent ones where nothing has changed, that indicates this. This potential energy is stored as part of the mass of the object. This is obvious in the case of gravity where heavier objects have more potential energy. It’s less obvious, but just as true, in the case of a compressed spring which has more mass than in the non-compressed state.

We can model potential energy in four dimensions by resolving the potential. That is, if I removed the table and the lamp falls I can then tell how much energy will be released. However, in order to really understand potential energy we need to look at the fifth dimension.

Next — Chapter 2






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