Emilie Du Chatelet, an 18^th century mathematician and philosopher, did not agree that Newton’s gravitational equation told the whole story: how gravity worked, not just that it seemed as a force between objects. [Seduced By Logic: And The Newtonian Revolution—Chapter 2: Creating The Theory of Gravity: The Newtonian Controversy (2012 by Robyn Arianrhod)].

I have attempted to explain my understanding of gravitation in a relational point of view (POV) based on relationship boundary curvature (curvature of the interface of a two-fluid expanding system, an approximately two-dimensional droplet). This explanation requires the flow of something around massive objects. But if the flow is space, like the flow in my expanding droplet comes from a source of inner fluid, where does the space come from, and how is it created?

I know, the more mysterious dimension is time. But, if you think about it, what does a chance of something happening in time mean? Well, It may mean: what is the percent statistical chance of sampling the event with some detector. A detector in my relational story is a specific perspective (POV) that we give to our experimental sampling. It can also be identified as an experimental setup in a designed and controlled experiment.

In my relational view of the world (relational philosophy) there needs to be some change boundary across which energy/information flows.

To find the statistical change in a time event, we would need to believe that there is a fluid or continuous moment-to-moment distribution in time. But what would that look like?

If time is but sampled at a point, then it, itself, does not change. It is the space that changes, or across which form/functions/events are distributed. But we take the idea of space as a matter of fact. What if it isn’t?

A quote by Einstein (Theory of General Relativity) is “Matter tells space how to curve, space tells matter how to move.” To which John Archibald Wheeler (Gravitation) [who coined the phrase for the strong anthropic principle: “We are the universe becoming aware of itself.”] adds, “Mass tells space-time how to curve, and space-time tells mass how to move.” But how does all this come about? Is it possible for us to get a handle on physical behaviors looking more carefully into what space is?

I always thought it strange that time and space looked so different. But maybe, because everyone else cared about defining time, I, also, wondered about space.

And that wonderment is important. Without the creation of space, there would be no redshifts between two systems, because there would be no increase of space between objects moving apart. There would be no space into which my expanding droplet can move. And there would be no expansion of the universe between massive bodies. So we need to somehow explain how space is created at a singularity source, so it can be seen to “flow” around and past massive objects.

Let’s go back to the singularity that might have served as the point source of our universe. We believe the singularity at that point was coherent. It couldn’t have been anything but coherent. In mathematics, a point can represent a scalar, a zero-dimensional location of energy intensity or information. But for our relational philosophy, that energy/information does not exist. It has no dimensions, which means it does not contain a change/relationship boundary. It represents only one value and so there will not be flow until a change occurs. Nothing exists without flow, change, and relationship. And so it should not be a surprise that trying to discover what happened before the singularity is pointless (excuse the pun. Except what we think of as a singularity source must exist because of something I will soon explain).

Before the source singularity that supposedly led to the creation/expansion of our universe, everything—energy or information-wise—was implicit (See David Bohm’s Wholeness And The Implicate Order, reissue edition 2002). An expanding boundary could only be formed if there was a change in coherency. That change meant there was some sort of boundary forming, or, at least, a degree of freedom in which to move. That degree of freedom formed not only a change/relationship boundary (of some level of focus) but also a unique POV, since a relationship must necessarily involve at least two mutual perspectives. (A meniscus in a mercury thermometer has a concave-upward POV and a concave-downward one).

Now that I’ve established my definition of change in the universe and its formation of boundaries creating points of views, how do I account for changes automatically existing in a coherent field out of our source flow singularity?

I believe that’s covered with the idea of entropy. As the intensity of the coherent system expands in space, it loses its point/scalar energy potential. But why does it do that? I believe that the following is true and leads to the understanding of entropy and change:

There is no such thing as zero in the universe. For a system expanding, if there were a zero, remember I said it would spell nonexistence at an isolated singularity and, therefore, the zero point would form the limit of a set of error values, and not be included in our universe, or the expanding field.

The same might be true of one, two, and three-dimensional objects. Because there is always error in the expanding field, these dimensions are only limits of boundary configurations and do not exist in and of themselves (a much better characterization is a fractal dimension derived from a dimensionless number involving all contributing parameters: density, mass, viscosity, size, flow rate, for example (like the Capillary Number in fluid mechanics derived from the Navier–Stokes energy equation)).

Back to space.

We know that when there is error on an expanding boundary, it leads to another change on the boundary—no matter how small. In this way, new potential perspectives or points of view are formed along with new degrees of freedom.

So spatial distributions may be formed by infinitesimal errors which perturb the boundary while expanding it. But if these changes in degrees of freedom, no matter how small, resulted in changes of POVs then how can we call this space?

There seems to be an energy/information spectrum, a real/virtual spectrum in universal relationships. Those closer to forming toward the singularity, we consider real, those farther away (maybe in recent conscious thought) we consider virtual.

Experiments have been formed which image hydrogen atoms whose mass is low enough that a single atom appears to be in two places/locations at any time of sampling. (Though there are numbers that represent their state, I believe that if the dimensionless number derived from an energy equation (as was the Capillary Number) will show a number at which this locality vs. nonlocality function changes with fractal dimension).

So, for very small, primitive energy packets deriving from the singularity source, space is created through error. In computational fluid mechanics or computational mechanics of any energy flow field, if flowing radially, or spherically, there will be spaces/cells on the expanding boundary that will be unfilled with a constant energy emanating from the singularity source.

The error will fill these spaces thus creating the opportunity for troughs in a buckling wave to form in those locations. In stable systems, those troughs, created by error, will fill in. But in unstable systems the troughs will remain. On the expanding universal boundary, these troughs are a source of concave-upward locations of high curvature (perhaps, representing masses in a 3-D field) past which the original higher energy crest boundaries flow.

Now for the natural interpretation of gravitation due to mass. My experimentally destabilized expanding droplet boundary would flow to either side of these troughs, extending the boundary even farther. Again, error in the boundaries creates more unstable buckling into troughs and crests radially farther out from the initial troughs. Once the troughs/masses are formed they cannot easily be moved. The troughs closer into the singularity are of higher curvature than those farther away. Through these mechanics, the distance between the troughs stays relatively the same as space/fluid expands/flows outward around it.

So, gravity with this relational POV is a relational phenomenon (not surprising with the discovery of general relativity). Troughs, masses, by themselves, mechanically in their initial forms, move toward or away from each other very little. What causes this is not necessarily an attraction as given in Newton’s Gravitational Equation, but the flow of space around the trough actually keep the troughs from moving toward one another. The orbits exist just because the space in three dimensions is curved and there is another degree of freedom of movement, but the potential and distance between objects changes little, depending on the curvature of the trough/mass. (The closer in to the expanding field, the greater the curvature and greater the mass. The farther radially in the expanding field, the lesser the curvature and the smaller the mass.)

Because space has less curvature farther out, those smaller troughs can move, but as troughs have greater and greater curvature toward the center, they move little. (Attraction between smaller planets can cause them to relate by merging rather quickly as opposed to black hole galaxies that take much, much longer to merge).

I, myself, haven’t done the math on this, but Chandrasekhar [Hydromagnetic and Hydrodynamic Instabilities] gives a solution to a viscosity/density contrast problem that could explain the formation of very massive 3-D troughs of high curvature close to the singularity source (which in this case would be centered on the sun’s accretion disc).

The next step for my thought experiment about consciousness and how to understand it, given the above information, is, if humans are massive relationship systems on the expanding boundary, then, as part of that boundary, each of us are composed of both troughs and crests. My guess is that the nonlocal crests of conscious functioning need to, somehow, distribute themselves among the troughs of our mass. This gives us a glimpse into the formation of relationship/boundary systems and how the boundary itself, at least the complex boundaries within us, might invaginate, rather than expand as in my experimental model. That would make sense, if human consciousness had to possess a path-length or duration in order to become aware.

Now, we can look at complex relationships and how they might form a duration of experience from close to the singularity (absolute time?) and closer to us (subjective time?).

[At the mass of a hydrogen atom with one proton and one electron, space begins to flatten and on that relationship/change boundary the mass begins to cluster to either side of a centroid. More mass forces a three-dimensional trough surrounding a more stable centroid, or cg.

 So, maybe in our attempt to understand the initial conditions in our solar system required for life (and eventual consciousness) we need to look into what happened to propel relatively large stable masses farther away from the sun [See February 2017 Astronomy article, Explosive Origins, our solar system’s violent past].