As humans, we are inextricably caught between the large and the small. We are much too small to capture the wonder and size of the cosmos. Oh sure, we have developed powerful telescopes that we can use with clever techniques to get keyhole sized views of the universe in the distant past. Because the speed of light is a finite number (although large to us), everything that we see that is distant is old. Our current vision extends back about 12.5 – 13.5 billion years, and at that edge of perception we see many strange and wonderful things. Galaxy Clusters. Pulsars and Quasars. Energetic jets (vortices?) that stream from unknown sources in opposite directions at speeds approaching a meaningful percentage of the speed of light.
But since the speed of light is finite, we will never know what these wonders look like at the present time, and we can only speculate what they have become and where they are now. If we assume that they are rushing away from us at the rates implied by the red shift of their light as we perceive it, then the universe is actually twenty five to fifty percent larger than we can see. And we’re looking at it through a keyhole, a spyglass, a soda straw that is miles long and that can only view a very small portion of the sky at one time, due to the physics of light and its magnification. And oh, BTW, at these distances we’re mostly looking at the visible and the near visible spectrum, because, of course, we haven’t learned enough about manipulating the other frequencies of energy to be able to effectively magnify very much of the full spectrum. We’ll never even get an overview of the humble galaxy in which we live, one cosmological flyspeck among hundreds of millions of others, because of the enormity of its scale in relation to us and our limited abilities.
And on the other hand, we are just too large to comprehend the ‘things’ and the forces that comprise the ‘stuff’ from which we are made. Again, due to physics, our ability to perceive the subatomic world is limited and governed by the tools that we have developed and our ability to derive meaning from events conducted at perceptible levels.
To understand the structures inherent in the very small, we use giant ‘atom smashers’ (don’t you just love that term?) to smash subatomic particles together at enormous speeds and energies so that we can observe the quantum mechanical debris that come shooting out from those collisions. This gives us insight, of a sort. One could argue that the energetic packets that come out and exist for less that a millionth of a millionth of a second are not truly stable, countable particles, but no matter.
The thing is; we can never be sure, we can’t know because we will never actually see an atom, it’s electron clouds or much less, it’s nucleus, because they are too small. We can only imply their structures through the observed debris from those collisions and the way that they interact with the things that we can see. We’re just too damn big.
And so it is that the things that we perceive and understand best are those objects and actions that scale well to our size; those things that we can most easily watch and study. And that is the reason, most logically so, that we have supposed that we live only in the Linear Dimension.
In our new formulation, we express the linear dimension as distance per time, or l/t. This is, of course the normal description for velocity, and by the reckoning expressed in this book, is the minimum measurement that can be actually ‘known’. Distances can be calculated by knowing the velocity over time, and locations can be determined in a similar fashion.
Acceleration is the derivative of velocity over time, l/t2 which represents its change in magnitude over some given increment of the clock.
In the Linear Dimension, every action has an equal but opposite reaction (thanks Newton!).
The Linear Dimension comes with this specific set of rules for the interrelationship between velocity, mass and acceleration, and because of our limited perspective, we believe that these are the dominant rules of the universe.
They are not.
These rules are important to us in our everyday lives and our understanding of the space that surrounds us, but as we’ll see, each dimension has its own rules, and its own relations between objects and space.
In the Linear Dimension, position, velocity and acceleration are all separate entities. One can have a position with no velocity (theoretically of course; we’ve discussed this at some length and zero velocity is only achievable on a small scale, relative sense); a velocity without an acceleration or perceivable position, and an acceleration without velocity, since gravity is expressed in the General Theory as a characteristic of the curvature of space.
Furthermore, as the esteemed Dr. Einstein has pointed out, the laws of physics for an enclosed system that has velocity are the same as those exhibited by a system ‘at rest’, which we talked about at some length back in the chapter about Relativity and its paradoxes. But the point here is that in the Linear Dimension, one’s velocity, one’s speed, does not affect how matter interacts and behaves. You could weigh yourself on a Bullet train going thousands of miles an hour (if one could), and if the ride was smooth, you would weigh the same as on your own bathroom scales. (The other dimensions are not like this, as we shall soon see.)
As we discussed in the chapter regarding Einstein’s elevator, in the Linear Dimension, the direction of the force (gravity) created by acceleration is always opposite to the line of that action for that acceleration, opposite and applying uniformly to the system that is being accelerated.
Is there some sort of inertial frame of reference that follows an object and allows the object to react and create an internal force, even in the total absence of a nearby gravitational field? Since we live within a rather substantial gravitational field [strong enough to keep a major planetoid like Pluto in orbit way out in ‘deep’ space (imagine trying to do that with a rope)], we may never know the answer to that question.
But the fact remains, that as defined by our situation, acceleration in the Linear Dimension creates a flat field in the closed system, one that is opposite to the direction of the change in velocity.
Oh, and one other thing, in the Linear Dimension, as well as in the others, when you change direction, which is merely acceleration in another direction, the same basic field effect occurs (that is; creating gravity) whether one is speeding up or slowing down. Very curious when you think about it.
And one more. Systems that operate on the Linear Dimension exhibit ‘point gravity’, that is; the source of gravity and, more importantly for this discussion, the center of inertia (or gravity), is at the mass-center of that object, its ‘center of gravity’ which is a point in the very-est middle. This is not the case for the other dimensions, as we’ll see.