Abstract: Scale Theory proposes that scale is an extra dimension and that scale can be curved just as space-time can be curved. And while acknowledging that certain phenomena dominate at different masses and speeds, the proposal is that at scale extremes (the very large and the very small), the properties of space are fundamentally different. The theory proposes that Dark Matter and Dark Energy are a result of the warping of scale at these scale extremes.

*“I realise that in this undertaking I place myself in a certain opposition to views widely held concerning the mathematical infinite and to opinions frequently defended on the nature of numbers.”** – **Georg Cantor on Transfinite Numbers*

*“Because scale-time has a geometry, maybe it is the actual shape of scale-time itself that is giving rise to dark matter and dark energy.”** -Sal Lucido*

**Is Scale a Dimension?**

When you move in the three spatial dimensions, such as when traveling from Phoenix to Hawaii or from Earth to a Black Hole, you are able to experience different things. In Phoenix you can golf in the desert, and in Hawaii you can surf in the ocean. And on Earth you experience one G of gravity, while at a Black Hole you experience infinite gravity. Why? Because you are in a different place – dimensionally. The same seems to be true when you shift between scales from the very large to the very small. At large scales you experience Einstein’s Relativity. At very small scales you experience Quantum Mechanics. Mathematically speaking, Relativity is incompatibility with Quantum Theory because we have not yet discovered *the theory of everything*. I believe the solution might be found if we consider scale itself as a dimension.

My theory is that scale is a dimension.

And if scale is a dimension, this could explain some of the observed physical phenomena we are currently unable to understand such as Dark Energy and Dark Matter. Just as three dimensional space separates Phoenix from Hawaii and Earth from a Black Hole, the very small may be separated from the very large. These may be completely different places – dimensionally.

**What is Scale?**

With model trains, scale is the ratio of the model to the real-life train. For example, O Scale is 1:48 Scale where 1 inch on the model equals 48 inches in real life. Thus, a 48′ freight car would be 12″ on your model railroad. HO Scale, my preferred size, is 1:87 and N Scale, the smallest popular scale, is 1:160.

The scale my theory refers to is similar to this idea, but instead of train scales, we are talking about the different scales or levels at which physical events take place. For example, chemical reactions take place at the molecular level, while the level at which we encounter planetary orbits is at ‘solar system’ scales. Each of these levels or scales requires a different type of analysis for modeling physical phenomena. And although you can measure scales in terms of the three familiar spatial dimensions, length, width and height, my proposal is that scale itself is a dimension. And because scale is a dimension, you are able to experience different phenomena at different scales. And although we know that certain phenomena dominate at different masses and speeds, I’m proposing that…

At scale extremes, the properties of space are fundamentally different.

And this can happen only if scale itself is a dimension. So this is why at very very small scales we encounter the strangeness of quantum effects while at larger scales we encounter the mathematically incompatible effects of General Relativity and at very very large scales, at the edge of the known universe, we see the Big Bang or a singularity.

**Curved Scale-Time
**

So if scale is a dimension, what is different at the scale extremes? I propose that at the scale extremes, the very very small and the very very large, scale-time is curved. And if scale-time is curved, we may perceive something equivalent to a gravitational force. And while we might attribute this gravitational force to particles called Dark Matter, or a pull at the edge of our universe called Dark Energy, I propose that…

Dark Matter and Dark Energy are a result of the warping of scale-time at these scale extremes.

It would follow that at the two scale extremes, scale-time is curved so severely that they present an impasse or boundary, much like the boundary of a black hole.

And, given this theory proposes quantum effects of the very small are a result of warped scale-time, this may be why, according to Stephen Hawking, the event horizon of a black hole (warped space-time) has quantum-like characteristics.

**How to Visualize this?**

Here is a way to visualize this. Before Columbus sailed the ocean blue the earth was thought to be flat. In essence, the known universe was imagined to be roughly two-dimensional. Then of course we discovered that in fact the earth was spherical and our imagination expanded to the notion that the known universe was three-dimensional. This shift can be visualized as someone looking down on the earth and concluding it is a flat disc. Then when we rotate our view around, the extra (previously hidden) dimension is revealed. Next it took Einstein to explain how the fourth dimension of time fits into the picture and now we imagine space-time as a fabric. And since it is a dimension, we can rotate around and see its true shape. Space-time is bendable.

So now all you have to do is take this idea one step further and imagine that scale is a dimension and rotate yourself around so that you can see this dimension. Look to the left where we experience the very very small and now look the right where we view the very very large. And now imagine that to the left scale-time is curved or warped giving rise to quantum effects, and in the middle scale-time flattens out, allowing for classical effects. Then, to the right near the edge of our universe, where we observe the Big Bang, scale-time is again curved or warped. By the way, the thing that is attractive to me about this theory is that it is elegant and symmetrical. This single idea seems to explain both Dark Energy and Dark Matter.

Scale-time is bent at both extremes of the scale dimension. At the one end we primarily perceive quantum effects and at the other we see the Big Bang.

**Definition of Terms**

For purposes of describing the idea of Scale Theory, terms need to be defined.

**Scale Theory:**A theory that scale is an extra dimension.**Scale-Time:**A proposed mathematical model that combines scale and time into a single interwoven continuum.

**Scale Boundary:**Scale-time is bent at the very large and very small ends, similar to how space-time is bent at a Black Hole. The imaginary, but never reached endpoint of these bends will be called Scale Boundaries.**Scale Horizon:**Analogous to the Event Horizon at the edge of a Black Hole.**Large Scale Boundary:**The boundary at the very very large scale extreme.**Small Scale Boundary:**The boundary at the very very small scale extreme.**Scale Gravity:**Gravitational effects resulting from warped scale-time.

**Dark Matter**

Dark Matter is a mystery because there seems to be no matter in empty space that would account for the observed gravitational effects. The current belief is that we will find some particles that account for this gravitational effect – much as we found the Higgs boson – using the LHC. I propose that there may be a different reason we see what is perceived to be matter throughout the universe. I propose that because empty space has scale, and since scale-time is bent at the small scale boundary, there is a gravitational effect (scale gravity) produced throughout the universe. And furthermore, the scaffolding structure of Dark Matter is a reflection of ripples at the scale boundaries. Where these ripples peak, there is more scale, and therefore more scale gravitational effect.

**Dark Energy**

Dark Energy would also be explained. The bend of scale-time at the large scale boundary would also produced gravitational effects (scale gravity), essentially pulling the universe apart.

Note – the small scale boundary is found everywhere, throughout the universe and the large scale boundary is not located within the universe but visible in every direction you look. Coincidentally, the same can be said for Dark Matter (everywhere) and Dark Energy (surrounding our universe).

**Higgs Particle in the Wrong Place
**

The LHC recently made a measurement of the mass of the Higgs boson. The good news is that the mass was not found to be at 140 GeV. This “heavy Higgs” would buttress the multiverse hypothesis, essentially ending our ability to discover more particles and ending our chances of understanding how the universe works. On the other hand, the Higgs boson was not found to be at 115 GeV, which is where Supersymmetry calculations place it. In fact it was measured to be right in the middle at 125 GeV. This means neither theory is confirmed nor ruled out. Ain’t nature a bitch.

But, strangely enough, I believe Scale Theory may solve this problem. If at the small scale boundary scale-time is warped, then particles near this boundary should appear to have a greater mass, just as a human is heavier on earth as compared to the moon. So essentially, heavy bosons, such as the Higgs particle, gain weight due to scale gravity (essentially what we call Dark Matter).

**A More-General Theory of Relativity?**

I believe we may be able to model this mathematically by adding a fourth dimension and applying the same techniques as those used for describing space-time? This may give us a ‘more’ general theory of relativity – including the scale dimension. Essentially we will find that the quantum/classical boundary is due to the warping of scale-time.

**What’s Warping Scale-Time?**

If scale-time is warped at the large and small scale boundaries, what is warping it there? I don’t know but a good guess would be that these are the boundaries of our universe. And if we reside within a Black Hole (as proposed in the holographic principle), then the event horizon of our Black Hole is warping scale-time. If we reside within a brane (as suggested with a multiverse construct) then the brane boundaries are warping scale-time. So just as mass warps space-time, these types of boundaries (whatever they may be) are warping scale-time, giving rise to scale gravity.

**Predictions **

So given the theory that scale is a dimension and that scale-time can be curved, what are some predictions resulting from the theory?

- All of the higher energy particles (>125 GeV) predicted by Supersymmetry should be overweight, as was the Higgs boson.
- There will not be a Dark Matter particle found given the phenomenon is scale gravity not mass induced gravity.
- The speed of light may be found to be ‘set’ by the curvature of scale-time.
- Cosmological Inflation may be due to a change of the curvature of scale-time as the universe expanded after the Big Bang. (Side Note: Did the Big Bang actually happen or are we observing what looks like a singularity because scale-time is warped at the large scale boundary?)
- We should get better understanding of the CMB (cosmological microwave background radiation).
- This may explain why there are quantum effects at the event horizon of Black Holes (Hawking Radiation).
- Entanglement or “spooky action at a distance” may be explained given scale-time is bent at the small scale boundary, which essentially collapses the three other spacial dimensions.
- Transfinite numbers, as proposed by mathematician, Georg Cantor, may be proven to be infinite numbers with a hidden scale dimension. This may also explain irrational numbers.
- Maybe we would get closer to a Theory of Everything.
- We should find that the quantum/classical boundary is due to the warping of scale-time at the small scale boundary.
- I may be sent to a mental hospital given the nonsensical nature of this entire idea.

**Questions **

Of course every theory has its problems and unanswered questions. This is a list of mine:

- Why would curved scale-time create a gravitational effect?
- The small scale boundary is everywhere which means there should be some Dark Matter effects (scale gravity) everywhere. Is Dark Matter everywhere?
- I think I might be wrong in assuming that the Higgs boson is smaller in scale than the other lower energy particles already discovered. The energy measurement doesn’t tell us how big the particle is. Is the Higgs closer to the small scale boundary than the other particles already measured?
- I could also be wrong in assuming scale-time is a construct. The reason I assume this is because of scale gravity. However, maybe scale gravity is the result of scale space-time being warped at the scale boundaries. My proposed nested reference frames (further on in this paper) may shed light on the correct model to be used. The bottom line is that scale is a dimension and is warped at the scale extremes, giving rise to dark effects. And if the math works out better using scale space-time as a model over scale-time – then I would substitute scale space-time for scale-time in this whole paper but still propose the same fundamental idea – warped scale.
- If scale-time is curved, what is its shape? I’m assuming it’s warped so much at the two scale extremes that boundaries are created, but it may be curved in some other way.
- Wouldn’t time slow down as we approach the scale boundaries? How would this manifest itself?
- What are the effects of compounded time dilation due to warped scale-time at the small scale boundary, and warped space-time near a black hole?
- Similarly, what are the effects of compounded time dilation due to warped scale-time at the small scale boundary and time dilation near light speed travel?
- Would we treat the scale boundaries as a limit, just as light speed is a limit, and develop a transformation (similar to the Lorentz Transformation) to develop a more general theory of relativity?
- Does this explain why the properties of nature seem to be emergent as opposed to fundamental? As we shift to different scales, as a scale time changes, properties of nature that didn’t exist at a smaller scale, emerge as we shift to a larger scale.
- How does the arrow of time and entropy fit into this theory?
- Are other properties of time, space and matter such as temperature also dimensions that are subject to curving?

**Mathematical Approach **

General Relativity explains gravity by postulating that mass changes the geometry of the space-time, by curving it. The Lorentzian metric in differential geometry is used to mathematically model this concept. A Lorentzian metric is a way of measuring distances and straight (or curved) angles in ambients called manifolds.

General Relativity says that our universe is modeled by (N4,g) , where N4 is space-time and k is a manifold of dimension 4 – where 3 dimensions corresponds to the space and 1 dimension corresponds to the time.

We would most likely use this type of math to model scale theory, however I am uncertain about the approach. You could simply use a 5 manifold ambient where three manifolds represent space, one represents scale and one represents time.

However, I intuitively feel that a better approach would be to nest reference frames. So space-time would continue to be modeled using the 4 manifold ambient Lorentzian metric. Next we would insert this entire frame within a separate Lorentzian metric that represents the scale frame. Then we would define scale space as straight (not warped) away from the scale boundaries, essentially reducing it to the currently used General Relativity frame. However, as you near the scale boundaries, the scale frame begins to warp, which in turn warps the space-time frame, nested within the scale frame. In this paper I describe scale-time as being warped but as I ponder the model mathematically, I would have to try both a scale-time and scale-space approach. Either way,** **(Whether scale-time is warped, or scale space-time is warped) the idea remains the same…

scale itself is a dimension and warped scale at the extremes fundamentally changes the properties of space-time, inducing dark effects.

This compound warping near the scale boundaries would result in:

– space-time itself warping at the scale boundaries.

– Objects, resident within space-time being affected (e.g. changes to mass, length and relative time).

Of course all of this is guesswork on my part and I am not a mathematician but at least this is a starting point for how we might build the scale theory model.

Regardless, I would need to work with a mathematician fluent in differential geometry to determine the best approach. And if nested reference frames is the correct approach, we would need to work out the applicable equations.