I remember the moment very clearly. It was in the fall, in the Great Lakes region of Ohio. The leaves were starting to turn, making the wooded area surrounding our porch into a mad palate of varied colors and hues. Fall is a particularly beautiful season in the upper Midwest, and this one was no exception. Greens of all shades, reds, yellows, oranges, pinks, ambers, magentas and browns, all intermingled and were dispersed as can only be done in a northern semi-temperate climax forest.
Like many days in that season and area, it was gray and rainy. Not the pouring thunderous rain of the summer, but a misting, gentle rain that soaks the fallen leaves and nurtures the late season mushrooms and other fungi. It was a tepid, dripping, almost tinkling sort of rain that keeps you under shelter while making you want to stay outside and listen.
I was taking a stay-cation as they say these days, although it was many years before that term was created. My wife and I were working on our house, and I was doing some small projects, although I can’t remember specifically what they were. We were always doing something.
She was out running errands and I was taking a break. I’d been pondering some of the great theories of physics while working (it’s what I do, OK?), especially Relativity and Quantum Mechanics as ensconced in the Standard Model, with a little bit of String Theory thrown in just for flavoring. While each of these is founded on some strong and valid premises, they all seem to get lost in their expressions.
Each seemed to have reached a dead end in terms of its ability to provide a basis for a unified theory to describe all matter and physics. Why was that?
I thought about the shortcomings of the Standard Model, where all of the forces are considered to be point-like in origin, and how that skews the results. I thought about Relativity and its inability to describe the nature of the very small. I thought about String Theory, and its many indescribable dimensions, that when combined in an alchemist’s concoction produces many correct answers. And suddenly I realized:
They are all based on static geometry.
What if you reject static geometry?
What if you reject the assumption that time and distance are separate quantities and assume that the lowest fundamental measurement that can be the basis for the construction of a geometry must include both time and space to be considered as the basis for a dimension?
Velocity must be the basis for an authentic workable geometry.
It still seems very unusual and quite coincidental that when I conceived of this those many years ago, I still ended up with three distinct dimensions. As it turns out, when you consider velocity as your primary, lowest level measurement, there really are three and only three distinct ‘dimensions’ each with its own properties and distinctive features. But I’m getting a little ahead of myself.
Think about this:
There are exactly three basic types of velocity dimensions that are separate and unique.
The first dimension is the most obvious: Linear velocity. It is this type of motion that is generally referred to when one is discussing the common conception of the speed of light or some other sort of trajectory that is characterized by having no rotational component. A forward or arrow sort of motion, in this sense, is pure linear velocity, along a straight line. Dimensionally, this term can be represented as: l/t but as we’ve just defined above, this will actually be a velocity dimension defined as Vl . This is stated mathematically below, and given as a sort of translation equation between the old and new geometry.
Vl = l/t
The second dimension is Rotational velocity, but we’re going to define it here a little more concisely than in normal usage. For this dimensional status we’re going to define rotation as that sort of motion having no linear component whatsoever, that is: pure spin. Rotation in this sense is somewhat like the rotation of the Earth, whose diameter is, to a great extent, a constant, unlike its orbit around the Sun, which can and does vary. It is like the rotation of a top. The spinning of a wheel. It is this precise type of velocity that an object can have that we are attempting to capture here. For the purposes of this book and beyond this point, this velocity will be noted as Vω, and shall be defined as ω/t, omega (rotations) per time. The mathematical relationship is shown below:
Vω = ω/t
The third type of motion would, at first, seem to only be a combination of the other two, but for reasons that will be discussed later on, this is not the case.
For the purposes of this paper, we’ll call this Spiral motion, that is; motion in which both the length of the radius and the arc speed can be time variables, but they are codependent and each provide only a portion of one coherent velocity. This type of motion-dimension can be used to describe velocities as widely varying as: the Quantum Mechanical path of an electron in its cloud, the orbit around the Sun by the Earth and the pattern of the Milky Way galaxy. For this velocity, we’ll use the notation shown below:
V lω = l ω/t
Three distinct motions. Each can exist, and more importantly, can be defined, without referencing the other. Interestingly enough, each one has its own unique characteristics in relation to space in general, which we’ll discuss at some length in the following chapters.
And when I realized this, those years ago, it gave me chills, and actually the thought still does sometimes. It was like the moment in “Indiana Jones and the Lost Ark” where Indy and Sallah were looking for the site of the Ark in the Map Room of the Lost City with the staff that had the proper length (as opposed to the one that the evil Nazis were using which was one foot too long) and the sunlight came in and the jewel on the head of the staff focused the sun’s rays on a particular structure (the Well of the Souls, BTW) and Indy and his companion stared at each other with a look of delighted surprise in their faces and said in harmony; “They’re digging in the wrong spot!”
Yes, we’ve been digging in the wrong spot. By using a geometry that does not reflect the way that the universe is quantized, the way that its properties are organized, we have built our physics upon a foundation that cannot support the structure needed to explain things properly. And instead of realizing this, we continue to cobble together endless patches in the form of exceptions and arbitrary rules onto the edifices that we have built in the hope that this shoddy remodeling will complete the framework and will allow us to glimpse the inner workings of the universe that we inhabit. They will not. We’ve been digging in the wrong spot.
This is a new set of dimensions, related to the old ones through logical definitions, that can easily, handily and effectively define the physical world that surrounds us, and it’s really not any new information, it’s just a different way of looking at and talking about things.
But since it is the language that you use that frames the discussion and gives one the ability (or not) to provide an accurate description, a velocity based system would seem to be one that would offer a great improvement over those that have been utilized in the past, and one that has the possibility to provide new insights into the inner workings of matter.
All those years. All those complicated, complicated mathematics. All of this effort expended regarding position, rather than velocity. These three dimensions, in combination, can be used to describe the velocity of any known ‘thing’, be it proton, photon or Neutron star. Of course, the forces will influence these velocities (or maybe vice-versa), but if one knows the precise velocity of an object one can use it to describe space.
And since it is a continuous solution, rather than a segmented approximation as derived from point based theories, there is hope for some exact solutions.