Fair warning before you read further, this is going to be complex. However I hope you will hang in there as the results are interesting on more than the Physics front. There are social implications to this investigation.

What got me started on this research was a description in a science fiction story that used an explanation of how two dimensional beings would see a three dimensional object and it got me thinking about multiple dimensions in a completely different way than I had before. Further thought resulted in some interesting discoveries. So, let me see if I can lay out my reasoning from beginning to conclusion.

This is all about dimensions. In many fields besides Physics what we normally call the X, Y, and Z axis in Cartesian Coordinates represent the three dimensions of physical space. Each of these axes represents one of the three dimensions of the space we live in. These coordinates are said to be orthodonal. This is an important characteristic of dimensions. True individual dimensions are orthogonal to all the other dimensions. What this means is that if I have objects at specific positions in the X-Y plane and I move them in the Z direction, those objects X and Y positions do not change. This means that forces in one dimension do not effect the motion in the other dimensions. This will be true if there are only 3 dimensions or if there are many more than three. We only know how to apply forces to objects in the three dimensions we can see, but there are, potentially, many other dimensions that we can’t see, but that still effect us. For instance, time is often considered to be a dimension. We move through time, but somewhat differently than we move through space. Since we don’t seem to comprehend how to apply forces in this dimension, we move through time at what appears to be a constant speed. The important thing is that if time is a dimension, then it is orthogonal to all three spacial dimensions.

Now, lets reduce our three dimensions to just two. Now we can put any other dimension against these two and still be able to visualize how it would look. So, for starters, lets just say there is a fourth spacial dimension that we can’t perceive directly, and we want to know how we might interact with that dimension. To start with, one of the things you notice about the two dimensional world is that objects outside a closed circle can not get inside the circle. It looks completely secure. But if you can move in the third dimension, you can see that what appeared to be a wall in two dimensions is now no such thing in three space and crossing over to the inside is simple. So, if we generalize this idea to a safe built in three space, from our point of view the safe can not be entered (without the combination) but to a four dimensional being (or if we were to be able to move ourselves to a different spot in that fourth dimension, all the points in three space would be equally accessible in four space. Not only would the safe be easy to enter, but every organ in your body would be accessible without cutting the skin. Surgery in four dimensions would be trivial.

Now, lets take our two dimensional space and wrap it onto the surface of a sphere. Now we have a globe where all the particles of the two dimensional universe lie on the surface of the sphere. Now the third orthogonal spacial coordinate is the radius of the globe. To those living in this two dimensional space it basically looks flat, but from the three dimensional perspective it is curved. Using this as our model for four dimensional space, our 3D space would appear to be flat, even though in four dimensions it is curved. So, for the two space dweller, only able to apply force in the two spacial directions, can’t apply force directly to the third dimension, but can create a force in that direction by traveling at high speed. Then the centrifugal forces would move the object off the globe, away from the center, and in that way they could move to a different location on that axis (and could enter the vault) In the three space world, if we pick time as the fourth dimension then special relativity is completely explained by this curvature in the fourth dimension. When you speed up you generate more force in the plus time direction. We don’t notice this because at conventional speeds the force is small and the changes too small to measure. However, we can measure these changes against the additional curvature created by gravity. Clocks in orbit run at measurably different speeds. If you were to be able to actually reach the speed of light all of time would pass in an instant. At reasonable speeds, like 85% of C, it appears to the stationary observer that time in the moving frame has slowed down, but from the traveling vehicle it looks like the rest of the universe has speeded up. In fact the craft is traveling faster through time than the stationary portions of the universe. When it arrives at its three dimensional destination, much more time has elapsed in the universe than on the craft, as the craft has not only traveled through space but also through time.

Another consequence of curved space is the value of Pi may not be a constant. Consider our two dimensional space on the glove. In very small spaces on the globe the curvature would not alter the value of Pi to a measurable amount from values that would hold if the space were flat, but consider the circle drawn on the equator of the globe it would, indeed, be the locus of all points equal distant from the pole of the globe, but Pi for this circle would be 2, the diameter of this circle being half the length of the circumference of the circle. If three dimensional space were curved in the fourth dimension like we did with the 2D model, then small circles, maybe as big as our solar system, would still appear to have Pi equal to 3.14159. The fact that we can compute Pi to a high degree of precision (a large number of digits past the decimal point) doesn’t mean we can measure it that precisely. So, at galactic distances it is possible that Pi gets smaller for extremely large R. What would this mean for how the galaxies look to us through a telescope? It would mean that the distance around the galaxy as you move away from the center gets shorter than would be computed using the value of Pi that we use to compute the circumference. Thus stars in those orbits would appear to move around the center faster than the gravity field of the galaxy would produce. This suggests that there is something producing more gravity than is generated by the visible matter of the galaxy. It is these motion discrepancies that are actually observed and are attributed to “Dark Matter”. The curvature of space time is all that is needed to resolve this perceived problem. A matter of point of view. The explanation needs no dark matter to make it work.

A recent article about octonions suggests that even the elementary particles can be completely described using eight dimensions. The dimensions that describe these particles that compose our universe are all quantum sized dimensions with lengths smaller than the plank length. Of course there are just as many points along those coordinates as there are in any other coordinate, so all the particles in the universe could exist within these dimensional limits, only having the freedom to move larger distances in the four space we perceive and live in (we are, after all, made up of these particles.

So, if we need eight dimensions to describe all the particles and three spacial and on temporal dimension for them to occupy, then the complete universe can be described in 12 dimensions. If we could move in the 13th dimension we would see the universe as a fixed object, but why stop at thirteen dimensions. Why can’t there be an infinite number of dimensions. This conclusion would answer several questions. When you use field theory to derive the equations of quantum mechanics, everything looks fine on the positive energy side of the equations. However on the negative energy side the basically explode. The equations only work if there is an infinite amount of negative energy. With an infinite number of dimensions infinite energy becomes more acceptable. More than that, and infinite number of dimensions gives enough room for an infinite number of 12 dimensional spaces. One conclusion that can be made here is that although a single 12 dimensional space is in fact a static object. It only means that everything that happens in that universe is pre-determined. This would mean that all our actions are pre-determined and free will is an illusion. But, if the principles of quantum mechanics are to be believed, and the observer can actually effect the observed, then with infinite universes to choose from, when we have the opportunity to make a choice, to collapse the probabilities into a particular outcome, if the dimensions we currently occupy don’t have that as the next event to happen, consciousness is already looking at the dimensions of another universe that does exercise that choice.

From a social perspective, the consequences of these two possibilities are extremely different. If there is only one instance of the 12 dimensional universe, then the position of every particle in the universe at every point in time is determined by the shape of the twelve dimensional construct, since time is an element of the universe, someone looking from a higher dimension would perceive a static object containing all the points in time and space. Thus everything that will ever happen has been determined by the shape of the twelve space comprising the universe. Everything is predetermined and can not be changed. Everything you will do or say in your life is outside your control. If that is true, then you have no responsibility for anything you do, say, or even think. It is already set in a higher dimension. Under these circumstances free will is not just an illusion, it is a flat out lie! If, on the other hand, there are an infinite number of twelve dimensional universes and the quantum mechanics of consciousness provide the means of switching between dimensions based upon the choices we make then free will appears to be possible, even an integral part of how consciousness perceives the universe. If you think any deeper on this issue, you might come to the conclusion that even free will may be a truth or a lie depending on your point of view.

The bit conclusion I take from all of this is that everything is a matter of point of view. The fact that an object gets longer and more massive when observed to travel close to the speed of light is a matter of parallax, which is another way of saying point of view. The fact that we see objects move and time progress may all be because we can only see four of the twelve dimensions that describe our universe. Each dimension is an orthogonal point of view. We can only perceive the three spacial and one time dimension, so what might be revealed by looking in the other dimensions is currently hidden from our view, like the man standing behind the hill is hidden from our view. I suspect the reason for this is that this is the only interesting way to look at the universe.

If you Google “The Law of Attraction” you will find an interesting self help theory that basically says you find in the world what you look for in the world. If you expect people to be mean and nasty, you will experience mean and nasty people. Another point of view will yield a different outcome. My partner expresses this theory when she says “Be careful what you put out to the universe.” This theory is another way of saying that point of view is important. More important than we usually give it credit.

Point of view is everything! An unconstrained point of view can see everything! Now I just need to find a point of view that lets me see everyone as rational reasonable people.