We have used the word ‘topology’ because it more exactly conveys the meaning we require. The graph in (a) below, is a profile of a fluctuation event showing the change of intensity within the width of a cell of space, the x axis, which I have held constant to make the illustration simpler. If one regards the y+ axis as the energy intensity, it is apparent that the fluctuation in energy intensity could just as well be in the opposite direction away from the mean, the y– direction. The fluctuations of the energy intensity of space will vary infinitely within a range at very small scales. This and the influence of the contiguous event cells will result in an infinite variety of dimensions, shapes and topologies of the consequent event cells. In this infinite variety of fluctuations, it is inevitable that event cells that have a toroidal topology will occur.
Before continuing, I will clarify the difference between the meaning of the words ‘torus’ and ‘toroid’ and indicate why I have chosen to use the latter. The OED defines a ‘torus’ as a surface or solid conceived of as generated by the circular motion of a circle about an axis outside itself but lying in its plane; and a ‘toroid’ as an object having the shape of a torus. Thus, the word ‘torus’ denotes the shape and the word ‘toroid’ denotes an object with that shape. Since we are referring to event cells as objects which have the shape of a torus, I will refer to them as ‘toroids’.
A fluctuation event
A fluctuation event
(a) A single fluctuation in the intensity of space. All fluctuations are event cells that are intrinsic to space, which is ‘crumpled up’ into the shape of a toroid.
(b) A dynamic toroid with rotation around the long circumference— poloidal rotation —shown by the blue arrow, and the apparent direction of tension shown by the pink arrows.
In (b) I have represented the fluctuation as a toroid for the following reasons: if the energy intensity of space is decreasing there will be a tendency for the surrounding space to expand into that depression, with the result that space will locally curl into itself in much the same way as smoke does to form a smoke ring, in which case the smoke rotates around the circumferential axis of the ring. Conversely, if the energy intensity of space is increasing there will be a tendency for the fluctuation to expand, but the pressure of the surrounding event cells will force it back on itself with a similar result to before, but this time the toroid will rotate about its circumferential axis in the opposite direction.
When I say that the toroid will rotate about its circumferential axis, this should not be taken to mean that it rotates independently of the space with which it is intrinsic, the action will be more of a curling or wrapping-up about the longitudinal axis in the same way that a sheet of elastic material may be crumpled into many shapes but each shape is still intrinsic to the material.
Of course there will be other topologies and shapes but I have settled on the toroid because the process of its formation, as explained above, makes it more probable that a disproportionate number of fluctuations will be toroidal. In addition, if the fluctuations have a toroidal topology they have the propensity to interact with each other in a ‘leap-frogging’ action, as shown in the simulation here, which may result in them lasting longer with the result that they accumulate in significantly greater numbers than event cells with other topologies. On the other hand if, for example, all fluctuations were spherical, it is difficult to see how they might interact to form chains or some other form of extended structure. Although, of course, I am unable to assess an infinity of shapes, the multitude of other possible shapes that I am able to consider also seem to lack the propensity to link up.
Effects of the topology of the fluctuating cells
Alternative topologies of event cells
(a) Spheres have no way of ‘gripping’ each other, so they unable to form linkages.
If a significant proportion of the fluctuations are toroidal event cells and are able to interact as shown, it is possible that they will survive longer than unlinked event cells and they may survive long enough to provide the building blocks of matter to create more complex structures.
It is important to emphasise again that the toroidal event cells are intrinsic to space, they are fluctuations of space, and the cumulative effect is that they form a potential energy field with both local and universal features.
Although most of the fluctuations of the energy intensity of space may have different topologies and different dimensions, we have deemed it more likely that at least the event cells that survive long enough to accumulate will be toroidal. Since toroids are objects that require three dimensions in which to exist, it follows that any structure resulting from the linking of toroidal event cells will also be at least three dimensional, so the cumulative result of the linked toroidal event cells will be the three dimensions with which we are familiar.
Although I am reluctant to introduce new words into a field in which unique words are already prolific, rather than continually repeating ‘toroidal event cell’, it will be more convenient to refer to it as a ‘toroidino’. The ‘-ino’ suffix means ‘small one’, in Italian, in the same way that Wolfgang Pauli named the ‘neutrino’ to mean a small neutral particle.
Summarising progress so far: space is the fundamental something that comprises the universe and from the inherent fluctuations in the intensity of space very small event cells with toroidal topologies, toroidinos, emerge to form a potential energy field. Although most of the fluctuations may have different topologies, we have deemed this less probable.
In addition to the points made in the summary, we have assumed that event cells with toroidal topologies will be preferred for forming extended patterns, however, we will leave the investigation of that until the appropriate time. At this stage it is extremely important to remember that, although the size of the event cells has so far been held constant to make the explanation simpler, depending on the intensity of adjacent toroidinos, they will expand and contract, which means that the ratios of the rates of expansion and contraction and the eventual sizes of the events cells will be strongly influenced by their environments. These observations lead to one of the most important aspects of this investigation and I will return to it after clearing up the question as to why fluctuations must be small.
Why must the fluctuating toroidinos be small?
If the toroidinos were large we would almost certainly have been able to observe them or at least to detect the effects of them. Distortions in space such as changing intensity would cause differences in the passage of light through space for two reasons; first the changing energy intensity would mean changing energy density of space which would cause varying diffractions which, if the changes occurred at a large enough scale, would result in apparent changes in the position of stars in much the same way as fluctuations in the density of the earth’s atmosphere causes us to see the stars ‘twinkle’. Secondly, if space plays an active role in the passage of light, the fluctuating intensity would mean changing permeability and permittivity of space, resulting in the changing ability to transmit light. If the fluctuations were on a large enough scale it would again result in distortions that we would be able to see, perhaps as dimming and brightening of stars as opposed to their ‘twinkling’. Using the measuring instruments available today it is possible to detect changes in wave motion down to less than 10-16 centimetres. For example the sensitivity to distortion of a laser beam, such as the ones being used in the gravitational wave detectors, has been tested to 1 x 10-16 centimeters, that is one thousandth the diameter of an atomic nucleus. Scientists running these detectors have been conducting tests and looking for distortions in their instruments for more than a decade.
Since no one has detected the sort of distortions that fluctuations of the energy intensity of space would cause, it is reasonable to assume that, if the distortions are occurring, they are occurring at a scale too small for detection by these sophisticated instruments. Of course, it is also possible that the distortions are being detected but, because they are not of the profile for which the researchers are looking, they are discarded as “noise”.
For the present, let us accept that if this activity is occurring it is occurring at a very small scale. Generally, changes at very small scales occur at a greater rate than changes at larger scales for at least three reasons; first, the ‘inertia’ of larger events is greater, so they will require more energy to bring about change; secondly, the larger an event, for a given speed, the longer it will take to occur; thirdly, the larger an event the higher the probability that it will be comprised of smaller events.
Fluctuations are well connected
Because it is extremely important that we do not lose sight of the fact that the fluctuations in the energy intensity of space occur unremittingly, I emphasise again that toroidinos are fluctuating event cells. A toroidino begins when the energy intensity of space departs from the mean and ends whenever it returns to the mean. Although for the purposes of explanation we have been referring to these fluctuation events as though they are both physically and temporally separate, there are no bare toroidinos, either physically or temporally. All toroidinos are intrinsic to space and, therefore, connected to it in every direction as I have tried to show in the illustration below.
Toroidinos are intrinsic to space
Toroidino showing its intrinsicalness to space
All toroidinos are intrinsic to space and, therefore, connected to it in every direction as I have tried to show in the illustration above.
If the intensity of the energy in the toroidino falls to zero, there will be a consequent contraction of the toroidino to a point and the event ends. This would tend to create a region of ‘nothing’ which, as we have already concluded is not possible, so we have to discover a mechanism by which the contraction of the toroidino is replaced.
Through the following explanation it is important to remember that the events being discussed are occurring at the Planck scale, which mean the events are very small, last a very short time and occur very rapidly, about 1043 times a second. This means that as one event ends others will be beginning so that even as a toroidino is contracting, new events will be occurring and the contraction will allow these surrounding event cells to expand more rapidly to a larger size to take its place. We may liken this to the situation where you have immersed your hand in a container of a visible gas and then pull it out; your action will not create a hole that suddenly fills, the contiguous gas will expand into the space your hand had occupied as you remove your hand. In the case of the contracting toroidino, this expansion will be felt with diminishing intensity in ever-widening spheres, giving the impression of a general movement towards where the contraction has occurred. Therefore, since the cells are intrinsic to space, every contraction will cause the contiguous space to expand to fill the potential gap so that the space around each toroidino becomes curved. These contracting and consequent expanding actions occur at all scales from individual toroidinos up through small concentrations of toroidinos and regions of concentrations all the way to the cosmological scale.
It is difficult to communicate this concept because, although it should be clear that, because the cells are intrinsic to space there will be no boundary between the toroidino and the contiguous space, at the same time, due to the syntax and semantics of the language through common usage, when we talk about ‘individual toroidinos’ the implication is that they are separate entities. Awareness of this difficulty in communication accentuates the need to be careful in the use of language when conveying the complexity of the changes at the most fundamental scale, which is the scale we are concerned with. That is, every toroidino of space is intrinsic to space and to every contiguous toroidino as well as being affected by and affecting every change in the contiguous toroidinos. Although it does seem complicated, as long as we remember that we are dealing with one entity, space, it should be clear.
Again, the state of affairs is analogous to that in a container of gas if we regard the gas as space. Even the smallest disturbance anywhere in the gas, will be ‘felt’ by the contiguous gas. A graphic example of the impact of an event on a contiguous surface, in this case water, is shown below: the points of contact of the water strider’s legs spreading in the surface tension of the water in a pond to form wider indentations.
When a cell is expanding it will have the opposite effect to that of the contracting toroidino. We can imagine the expanding cell ‘pushing’ the contiguous space away from its centre, consequently spreading the effect of the expansion into the space that it is contiguous to and with which the toroidino is intrinsic.
A water strider on the surface of a pond
A graphic example of the impact of an event on the contiguous surface is shown above: the points of contact of the water strider’s legs spreading in the surface tension of the water in a pond to form wider indentations.
With respect to this contraction and expansion of the cells, we return to the analogy drawn with the atmospheric pressure. Cells with higher atmospheric pressure at their centres, that is the high pressure cells (H), are usually larger and tending to expand, with wider spaced isobars indicating a pressure gradient that is becoming more shallow; while cells with lower atmospheric pressure at their centres, low pressure cells (L), are usually smaller with a tendency to contract and a steeper pressure gradient, as indicated by more closely spaced isobars.
Although the toroidinos are very small, because they comprise everything in the universe, their characteristics and behaviour will determine the nature of space and the universal principle according to which the universe is organised. That is the stage of the investigation which we have reached, out next step is to investigate this universal principle.
- The fluctuations of the energy intensity of space will vary infinitely within a range at very small scales.
- In the infinite variety of fluctuations, it is inevitable that event cells that have a toroidal topology will occur.
- Since we refer to event cells as objects which have the shape of a torus, we refer to them as ‘toroids’.
- More fluctuations will be toroidal for the same reason that smoke curls into itself to form a smoke ring.
- If the fluctuations have a toroidal topology they will have the propensity of linking to form chains, which may result in them lasting longer in significantly greater numbers.
- Toroidal event cells are intrinsic to space and the cumulative effect is that they form a potential energy field with both local and universal features.
- Rather than continually repeating ‘toroidal event cell’, it will be more convenient to refer to it as a ‘toroidino’.
- Toroidinos must be tiny because, it they were large we would almost certainly have been able to observe them or at least to detect the effects of them.
- It is also possible that the effects are being detected but the data are being discarded as “noise”.
- When an event cell contracts, as it collapses the surrounding, rapidly occurring event cells will take its place.
- Because toroidinos comprise everything in the universe they determine the nature of space and the universal principle according to which the universe is organised. the ontological principle.