Understanding 4 dimensional space
By Engineer Saviour – Blaze Labs
Recall ages ago, when most people believed that the earth was flat. Some thought that they would “fall off the edge” of the earth if they went out too far. Little did they know, that if they kept on going, they could possibly end up where they started, having experienced the entire trip as being in a straight line! No matter how far the subject travels (by boat, train, or plane), he will never come to a boundary: there is no “edge” to fall off from!! It is because the earth exists on the surface of a sphere that these properties hold true. Let us now take this a step further.
Launched from the earth is a rocket ship that is travelling out into space. Its mission is to continue outward in a straight line in its current direction until it reaches the “outer edge” of the universe. When will the rocket ship reach the outer edge of space? In the previous example we find a similar situation: the concern of “falling off the edge” of a flat earth – an earth that in reality has no “edge” to fall off from. Now, if our universe reality is not 3D we will find out that the ship will never encounter an outer edge. Not only that, but it could also possibly end up where it started, having experienced the entire trip as being in a straight line! No matter how far the rocket ship travels through space, it will come across no boundary of any kind. These properties would hold true if the universe existed on the surface of a hypersphere in the same way that the earth exists on the surface of a sphere.
The hypershpere is the 4D analogue to a circle in 2D or of a sphere in 3D. How would we picture a hypersphere? The key to approaching something of the fourth dimension is by means of the tool of analogy: we rely upon corresponding lower-dimensional structures we have studied as the means by which their 4-dimensional analogue is constructed. A solid circle is a 2-dimensional object. When cut into 1 dimensional slices, you will see a line, that varies in length between the size of a single dot to its full length. A solid sphere, as shown above in the flatland animation, is a 3-dimensional object. When cut into slices, we find that a solid sphere is in essence an array of solid circles that increase and then decrease in diameter. Having obtained the knowledge we have so far, we now possess the ability to bring these lower-dimensional structures “up a notch” through analogy to envision a 4D hypersphere.
We cannot directly visualize a hypersphere for the very reason that it is a 4-dimensional object and goes beyond our senses. What we can visualize, however, is a hypersphere in the form of 3-dimensional slices (as is displayed to the left). A hypersphere is in essence an array of 3 dimensional solid spheres that increase and then decrease in size. This would represent our basic conception of the hypersphere, and is shown in the animated picture here.
As I have said, in 4D space, our ‘time’ is integrated in a space dimension, and then action at a distance (gravity being the purest example), becomes much clearer to us. Just imagine, in the classic 2D example shown above, that the 2D person is somehow able to impart a force on the circle he sees on the plane. What would the consequences be? He would eventually move the whole sphere and would also change the position of the future circles in the plane. He would also move all points on the circle, as if all points are ‘entangled’, and the transmission of this force from the point of action to any other point on the circle does not depend on the time it takes for the sphere slice to pass through. So, to the question, is gravity a push, a pull or both, or does gravity act on a body, or is gravity generated by the mass of a body, there is no answer if the problem is analysed only in 3D space, as the interaction between two bodies is just an effect we see due to the interaction on a single body existing in a higher dimension. The interaction between the two different dimensions takes place in the ‘mirror plane’ where the time dimension does not exist, but is rather a perception of the observer. That also means that issues like ‘the finite speed of gravity’ clearly make no sense.
If you try to extend this to our existence and to the existence of all matter, you will find that all actions (including gravity) are at work at a higher dimension and we are here in 3D space observing the effects that are being played at this higher dimension. The 4D I am referring to, is quite different from Einstein’s 4D Space time, in that it is a 4D space and no time. The time coordinate comes in as a false perception of the 4th space dimension, which we are unable to imagine, analogous to the flatland man who cannot understand height and depth. In this figure, you can see what a 4D sphere looks like when differenciated in 3D space. When one differentiates this 4D dimension with respect to an infinitely small mirror thickness (Plancks length being the best candidate), then you get the universe we observe, with Plancks time being the time taken for each 3D slice to pass through the ‘thickness’ of the mirror, and such universe is equivalent to Einstein’s Space-time.
So, what is the speed of light? The speed of light can now make more sense, it is the thickness of the mirror divided by the time it takes for the next slice. It is the maximum speed of differenciating the 4D reality from a 3D spatial point of view. In our context, the value would be equal to Planck’s length/Planck’s time which is equal to c, the speed of light. That’s why Einstein’s theory of relativity although correct, CAN NEVER give us all the answers to our questions, because it is NOT COMPLETE. As Rudolf Steiner stated: “Anything dead tends to remain within the three ordinary dimensions, while anything living constantly transcends them”. Applying the same rule to everything, we may modify this statement as “Anything stationary exists in the ordinary 3D, whilst anything moving is being constantly differentiated in each 3D plan,e and hence exists in the fourth dimension”. This statement is thus defining the 4D space as space in motion with respect to itself. Click here for an excellent site discussing Space in motion.
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