Chapter 2: A Point Of View

Footnote Article: The Universe: My Personal Perception

It is widely assumed that science provides an objective view of the universe. But any view of the universe can only be as it is separately perceived by each human consciousness from experiences invoked by inputs from the 5 senses. Consequently, any view of the universe must necessarily be sub­jective. [português] [PDF]

The universe, by definition, is a single object. As such, every part of it is, in some way, connected to all other parts. It seems to occupy three-dimensional space. The relative positions of its recognizable features change with time. It is thus, by definition, an event. Whatever may exist outside it cannot communicate with anything in­side it. If it could, then the thing outside would, by definition, be part of it, and therefore inside it. Consequently, the universe can be perceived only by conscious entities that are located within it. Notwithstanding, there could be aspects of the universe that must be fundamentally beyond the perception of such conscious entities.

I perceive myself to be such a conscious entity. I perceive the universe. However, my consciousness perceives that the depth and diversity of its physical perception, facilitated to it by the body within which it resides, is very restricted. And it is exclusively through the channel of this physical perception that I am able to per­ceive the universe. So, what has this power of physical perception of mine per­ceived of this physical universe of time and space within which I exist?

Perception of Space

My earliest experience of time and space was during long summer days spent as a young child in my grandparents' back garden. There was a big lawn, a greenhouse and a vegetable patch beyond. The garden was rectangular. I gained my infant sense of distance, direction, speed and even acceleration while moving from one favourite little niche to another as they basked in the summer sun speckled by the shadows of the fluttering beech and sycamore leaves. It was a small and relatively flat world that ended abruptly at the garden fence.

As I became a little older, I gained more of a sense of the world beyond. I remem­ber the "epic" shopping trips into the centre of Manchester on which I was taken with my mother and grandparents during the dark times of World War II. I was too young to be aware of the War. I had never known anything else. What impacted me was the enormity of this world beyond the back garden. Nevertheless, this bigger world worked by the same rules. The bus, although it went further and faster, moved in essentially the same way that I toddled. The laws of motion were con­served.

Soon, I reached the age at which I, like everybody else, acqu­ired the mental power of abstraction. I could, mentally, place things into categories and abstract properties or behaviours that were common to different things I saw and experienced in the world. I noticed, for instance, that the walls of the rooms in my grandparents' house were vertical. I saw that some were at right-angles to each other while others were parallel. The floor and ceiling were horizontal but at differ­ent levels. This practical observational experience facilitated my perception of the X, Y and Z axes of Euclidean geometry. Later, I gained the ability to perceive the idea of rotation also with regard to these 3 mutually-independent axes.

Flat Earth

Final Frontier by George Grie GNU License Years later, I was taught at school that people in ancient times thought that the world went on for an enormous distance as a kind of undulating flat plane. In other words, it was a vastly scaled up version of my grandparents' garden. It was a world that followed the rules of Euclidean geo­metry. It seems there was great specul­ation as to what was at the end or edge of this enormous Euclidean plane. Many believed that if a ship sailed over the edge, it would fall forever in an infinite abyss.

However, I was further taught that, thanks to the objective observations of science over the centuries, we all now know that the Earth is round like a ball. In other words, it is spherical. Of course, the objective view of science now tells us that even this is not the whole truth. The Earth is only approximately spherical. To get the "true" shape of the Earth it is necessary to apply elliptical corrections. But even this does not take account of certain gravitational dents (due to asymmetric mantle density), ground undulations and probably 1001 other factors as well.

Spherical View

I do not need to go up into orbit or even fly in an aircraft to see that the surface of the Earth is not a flat (Euclidean) plane. I have seen ships sail from Felixstowe harbour, watching as their hulls disappeared below the horizon while their masts and funnels were still visible. This clearly illustrated that the surface of the sea curved away from me. I have stood on an ocean cliff many times and in many places. There, on a clear day, I have seen the curvature of the ocean horizon. The straight edge of the superimposed blue rectangle in the following photograph clearly reveals that the ocean surface curves also from one side of my view to the other. The fact that I have seen that the ocean curves both away from me and from side to side shows that the curvature of the ocean horizon is spherical. The Earth is shaped like a ball.

I am therefore sceptical of the notion that there were not at least some observant thinking people, even from the most ancient of times, who could, from such a com­mon vista, deduce that the surface of the Earth was curved and not flat.

The observation that it is not flat, and the deduction that it must be spherical, gives the Earth a comforting property. It is a closed homogeneous surface. I can therefore wander around it forever in whichever directions, for however long, covering whatever distance. And I can do this without being in danger of ever falling off its "edge" into an infinite void. However, an important consequence of knowing that it is a very large sphere means that I now perceive the Earth differently from the only way I am able to see it.

The reason I can perceive the Earth as a sphere is that I have experience of spheres closer to my own size. For example, a football. My spatial perception can therefore scale up the notion of a football to a sphere the size of the Earth under the same geometric rules. However, as an Earth-bound non-astronaut, I can never experi­ence the Earth directly as a sphere from any point of observation I am able to occupy.

Polar Projection

To get some idea of how I could directly perceive the whole Earth from my lowly ground-based view-point, I have to imagine that I can see as far as I like across the surface of the Earth. I need to be able to look over the horizon. To achieve this, I shall conduct a thought-experiment. I shall imagine that light follows the curvature of the Earth, remaining always at essentially the same height above the surface. In other words, I shall imagine that a geodesic curve appears to me as a straight line. How will I then see the world?

The answer is that I see it as a flat disk, like the polar map shown on the right. Here, I am standing at the Earth's North Pole, looking outwards in all directions. I can see and recognise all the continents and oceans in their proper places. But they do not appear as they do on a spher­ical map. The nearer features are not very different. But South America and Australia appear seriously distorted. Antarctica ap­pears absolutely weird. Antarctica is, in reality, a compact island continent upon the spherical surface of the Earth. Contr­arily, in my Earth-bound view, it is nothing but a messy streak splayed out as a ring around the periphery.

I must, at this point, make a further stipulation. Light may travel from any place on any latitude, including the South Pole, to the North Pole. However, it may not con­tinue onwards to loop the Earth's surface completely. If it could, I would see a manifold comprising ever-fainter repetitions of the Earth's surface features in ever wider annuli, each annulus commencing with a view of the back of my own head splayed out around its entire circumference. The validity of this constraint will become apparent when I apply this idea to the whole universe later.

In this view, the South Pole, which is a single point, appears as a circle of over 80,000 km circumference. Assuming that the Earth's surface be uniformly lit, this distortion will cause objects further from my point of observation at the North Pole to appear dimmer. For example, the light falling on Antarctica is spread out all around the rim of my view. Only a small amount of light will therefore arrive from any direction. The luminosity of my view of the world must therefore appear as illustrated on the left. I see features that are close to me brightly. Features further and further away appear less and less bright. The South Pole itself will probably be black, so I won't see it at all.

This model of my Earth-bound view is not as far-fetched as it may appear. I could, instead of light, choose to view the Earth by means of some kind of over-the-horizon radar system using Low Frequency radio waves. These tend to follow the Earth's surface. These LF radio waves would take about 6·7 milliseconds to reach me from the South Pole. A consequence of this is that The South Pole would appear to me, not as it is "now", but as it was about 6·7 milliseconds ago. Things on the Equator will appear, not as they are "now", but as they were about 3·3 milliseconds ago. Things 1 metre in front of me would appear, not as they now are, but as they were just over 3 nanoseconds ago.

I will now add just one more constraint to my thought experiment. I shall suppose that light (or LF radio waves), instead of only taking 6·7 milliseconds, take about 13·7 billion years to get from the South Pole to me at the North Pole. I am con­scious of "me" as I am now. However, things only one metre in front of my face will appear to me, not as they now are, but as they were over 1,000 years ago. Things on the Equator will appear as they were 6·5 billion years ago. The South Pole will appear to me as it was 13·7 billion years ago. This is just a matter of scaling a perfectly scalable situation. The principle is the same.

Microwave Background

The theory among cosmologists, that has prevailed for some decades now, is that the universe began with a big explosion about 13·7 billion years ago. The concept is that the universe started (somehow) as an unimaginably vast amount of energy packed into what tended towards being an infinitely small point. This then expanded into the universe as it "is" today. From this theory, cosmologists predicted mathematically that there should exist an echo of the initial explosion, which should be in the form of electromagnetic radiation somewhere in the microwave spectrum.

In 1964 this radiation was discovered. The spectral profile of this radiation is shown by the graph on the right. Its peak intensity, at around 170 GHz, apparently fits comfortably with what the theory predicted. It was identified as the echo of the initial explosion that started the universe by the fact that it was measured to have equal intensity from every direc­tion in space. Since its discovery, better measurements have been obtained. Mod­ern satellite-borne instruments have map­ped this echo radiation over the entire celestial sphere.

Eventually, finer measurements revealed that the intensity of this radiation did vary ever so slightly with celestial direction. Below is a projection of the inner spherical surface of the background radiation sphere. The variation in colour indicates the subtle variation in intensity according to from which direction in space the radia­tion is being received.


Spherical Universe

This microwave background radiation (the echo of the Big Bang) is apparently the most distant phenomenon that can be detected. It originates from the maximum distance that it is possible to "see" into the universe. It comes from what appears to be the edge of the universe. This raises for me some interesting points of percep­tion.

The universe appears to me (a human observer) as a sphere. I am at the centre of this sphere. An apparent bounding shell of this sphere is the source of the micro­wave background radiation. All the stars and galaxies in the universe are contained in this shell. This suggests to me that I must be inside the Big Bang. From my terrestrial experience of space and time, I would have expected the Big Bang to ap­pear as a super-bright point of gamma radiation far out in space and hence way back in time: not a shell of dim microwave radiation surrounding everything. If it be an "echo", what "mirror" is reflecting this microwave radiation back towards me?

Then I realised the answer. I am not "seeing" the universe. Rather, I am not seeing the universe as it is. Instead, I am seeing an unfolding history of a part of the universe. It is the part of the universe that can be seen only from my unique position in space and time. I am seeing what is my own unique personal event-horizon. Of course, on the scale of the universe, the unique personal event-horizons of all human beings on Earth are indistinguishable from each other. But no two can ever be identical. The universe as a whole, as it is "now", is something neither I nor anybody else can ever see. For we who are bound by space and time, such does not exist.

So how can I build for myself a cogent perception of my personal event-horizon and the unseeable universe whose existence it implies. The only conceptual tool-kit I have to hand is the relationship between my perception of the Earth as a spherical planet and my surface-based view of it as a polar map described earlier.

Dimension Reduction

In the previous illustration above, I imagi­ned the visible universe (my event-horizon) as a hollow sphere containing stars and galaxies bounded by a shell of microwave background radiation. What if the 3 dim­ensional spherical event-horizon that I see is a polar map view of something that has 4 dimensions. The only way I can repres­ent such a thing is by reducing the number of dimensions. I shall therefore represent my 3-D spherical event-horizon by a 2-D slice of it. I thus end up with a disk whose diameter is the same as that of my spher­ical event-horizon. So imagine that the dia­gram on the right represents such a disk rather than the whole sphere.

I wish to add here that I do not feel intuitively comfortable with representation by dimension reduction. A two-dimensional plane is not really analogous to 3-dimen­sional space. So, when doing this, I must be permanently aware of conceptual pit­falls. I have the same reservations about representing time by a linear spatial dimension. Time is perceptually different from space and making it mathematically equivalent is, to me, dangerous. Nevertheless, I am lost for another option. I shall therefore continue cautiously with my dimension reduction as an aid to my percep­tion of the universe.

Event-Horizon

I therefore perceive my 3-dimensional spherical view of the universe as a polar map. My 2-dimensional slice of this visible polar map of the universe is a dimension-reduced version of the 3-dimensional polar map. In it, the "North Pole" of my event-horizon is the point in space and time from where I experience the universe. The outer coloured rim of microwave background radiation is equivalent to Antarctica, the very outer edge of which is the "South Pole". Light takes 13·7 billion years to reach me from this outer rim.

By analogy with my ground-based view of the Earth, I deduce that my 2-D disk is really the surface of a sphere, as depicted on the left. The disk's outer rim of micro­wave background radiation is therefore at the opposite pole. It is a point-sized super-brilliant "big bang". I have included in the diagram two arbitrary latitudes. One is where I see objects as they were 3·25 bil­lion years ago. The other is where I see objects as they were 8·94 billion years ago. Light from the "big bang" and all other objects that I am (theoretically) able to see "now" has travelled to me along the geodesics (lines of longitude) of my event-horizon as it fleetingly exists "now".

Even one nanosecond ago, my event-horizon was a slightly smaller sphere. Even one nanosecond hence, it shall be a slightly larger sphere. My event-horizon is a continually-expanding sphere. Nevertheless, at any instant, only a part of the universe is visible to me. Fundamentally, at any instant, only a part of the universe can be visible to me. This part universe comprises a continuous sequence of infinit­esimally small rings. Each ring corresponds to an instant in time stretching all the way back from "now" to the time of the "big bang". Each ring is where my event-horizon sphere intersects the real universe at each instant from "now" back to the time of the "big bang". So what does the real universe look like at any particular instant in the past?

Sphere Within a Sphere

According to this model, the universe must comprise the surface of a sphere that is twice the radius of my event-horizon sphere. On the right, my event-horizon sphere is shown contained within the uni­verse. My location ("Me") is a point on the spherical surface that represents the uni­verse at this instant. That same point is also at the North Pole of my event-horizon sphere, at which information from the uni­verse's past has, at this instant, just ar­rived. The North Pole of my event-horizon sphere is thus the exclusive point from which I am able to experience the uni­verse. The surfaces of the two smaller concentric spheres represent the universe as it was 3·25 and 8·94 billion years ago respectively.

At the centre of this enormous sphere, whose 2-dimensional surface represents the universe, is the universe as it was when it started. In other words, the point at the centre of this sphere is the Big Bang. This "point", however, is not itself an infinitely small sphere. The Big Bang is represented, in this reduced-dimension model, by the 2-dimensional surface of an infinitely small sphere. This is important. The infinitely small circle of latitude where the surface of this infinitely small sphere intersects with my event-horizon is my event-horizon's South Pole.

I imagine that the radiation of the super-brilliant Big Bang must have been of a species that is beyond scientific observation and theory. I shall call it super-gamma radiation. It must have circulated around the infinitely compact surface of the Big Bang micro-universe as radiation of a stupendous frequency and of planckoscopic wavelength. As the universe expanded, space (represented by the 2-D surface of my universe sphere above) also expanded. Consequently, the radiation pervading that space must have expanded correspondingly. This process has continued, with the result that today, the expansion of space has caused that radiation to increase its wavelength to about 1·9 mm and reduce its frequency to a corresponding 160·2 GHz [or wavelength 1·06 mm and frequency 283 GHz, depending on how it is cal­culated]. And this is why the Big Bang appears so dim when viewed today from the North Pole of my event-horizon.

I can only ever see (or otherwise detect) anything from information arriving along a geodesic of my event-horizon sphere. Con­sequently, the radiation arriving from the Big Bang can only have come along such a route. In fact, it is the one source of rad­iation that would come "equally" from all directions (lines of longitude) around my event-horizon sphere. The length of this radiation's journey must therefore have been ½ π r, where r is the diameter of my event-horizon sphere, which is the radius of the universe-now sphere. Consequently, the speed at which the radius of the universe-now sphere is expanding must be 2c/π, where c is the speed of light. Integrating with respect to time gives the radius of the universe-now sphere.

This offers one possible explanation as to how I got to where I am today ahead of the electromagnetic radiation that is only just arriving here from the Big Bang. I took a short-cut. I, or rather the point on the universe-now sphere that I occupy, travelled the direct radial route along the South to North axis of my event-horizon sphere. The radiation currently arriving from the Big Bang, on the other hand, took the long route. It travelled along a line of longitude on the surface of my event-horizon sphere. So I did not have to travel faster than light to get here ahead of the radiation. I only had to travel on average at just under 64% of the speed of light.

Event-Continuum

An interesting consequence of this model is that my own path through time, along the South-to-North axis of my event-horizon sphere, is fundamentally inaccessible to my experience. It is forbidden territory. I can never see, observe or experience "me" as I am now or as I was at any time in the past. My own past is just as inaccessible to my conscious experience as is my future. I can only experience the past of a small portion of what is not me. And how far back into the past depends on how far away the object of my experience is from me. Thus, what I am able to experience of the universe is fundamentally very restricted.

In this model, the universe-now sphere and my event-horizon sphere represent the universe and what I can experience of it at a single instant. Perhaps there is an indivisible unit of time. Some people refer to it as the Planck interval. However, at least on the macroscopic scale, there is no evidence to suppose that time is not a smooth continuum. In other words, an instant - as a real object - does not exist. Time passes smoothly. And it is always passing. The notion of taking a freeze-frame snap-shot of time is not a reality. It is simply an artificial construct of the imagin­ation.

To gain a true picture of reality, I must there­fore imagine my universe-now sphere and my event-horizon sphere as being in a continuous state of coordinated expansion. In the diagram on the right, I have tried to illustrate this by depicting a finite span of time, namely, my own lifetime. At my birth, the universe-now sphere has radius r, which is also the diameter of my event-horizon sphere. By the time of my death, the universe-now sphere has expanded to a radius of r+δr, which is also the new diameter of my event-horizon sphere. The universe-now sphere thus expands by a small amount δr dur­ing my brief lifetime, which is also the amount by which my event-horizon sphere expands. The coloured area represents the solid crescent that is the difference between my death and birth event-horizon spheres.

This solid crescent represents my event-continuum. It is the locus of my event-horizon sphere as I pass through time from my birth to my death. Thus it repre­sents the fundamental bounds of what I could possibly experience of the universe during my entire life. It is fundamentally impossible for me to experience anything in the universe that is outside the bounding surface of this solid crescent.

Time Appears Non-Linear

A striking observation I can draw from this representation is that the time-span, over which I can observe, contracts as I go back into the universe's history. At the time of the Big Bang, the solid crescent is infinitely thin. This means that, from my point of view, the Big Bang is frozen in time. This will essentially render it invisible. The microwave background radiation presumably originates from a very short time after the Big Bang. If I were to listen to it on my UHF scanner all my life, I would be really only sampling a few seconds worth of the original radiation. Hence, the 160·2 GHz signal I hear must really be super-gamma radiation of a stupendous frequency that tends towards infinity.

On the left, the inner red circle represents the sphere that represents the universe as it was 6·85 billion years before my birth. That's half-way back to the Big Bang. The first red dot on the blue radial line is where my birth event-horizon intersects that universe-now sphere. This red dot is on the circle of intersection (latitude) on my birth event-horizon sphere that corresponds to the time 6·85 billion years before my birth. Any object on this circle will appear as it was at that time. As time passes, such an object will move radially outwards from the Big Bang. At the time of my death, that radial (blue line) intersects my death event-horizon sphere. At this point, the universe-now sphere represents the universe only half my lifespan older than the universe sphere at the time of my birth.

At the time of my death, I therefore perceive that same object to be only half my lifetime older than it was at the time of my birth. The outer red circle represents the universe-now sphere that represents the universe as it really was 6·85 billion years before my death. But the object concerned is outside my death event-horizon. So it is fundamentally impossible for me ever to see it as it then was.

The upshot of all this is that time, as I perceive it along my event-horizon, is non-linear. It contracts according to a circular function. Space, on the other hand, appears to expand according to the spherical polar mapping function. So there is an apparent increasing contravergence in the scale of the relationship between space and time as I look further and further into history along my event-horizon.

All the foregoing presupposes that the rate at which the radius of the universe-now sphere, r, is increasing be constant. However, the effect of gravitational attraction between stars, galaxies and other objects in the universe tends to put a brake on the rate at which space can expand. Nevertheless, because all objects are neces­sarily getting further and further apart with time, the effectiveness of this gravity-brake gets ever-weaker. The rate at which the radius, r, of the universe-now sphere is increasing is therefore likely to be diminishing. The expansion of the universe is decelerating. This would tend to make my event-horizon sphere somewhat egg-shaped, making space and time and the relationship between them even more non-linear.

I have more confidence in the constancy of π than I do in the constancy of the velocity of light, c. Consequently, according to this model, since the value of c is locked to the rate of increase in r, the velocity of light, c cannot have been constant in the long term (i.e. over the 13·7 billion years of the universe's speculated existence).

Back to 3 Dimensions

I have used the event-horizon sphere within the universe-now sphere to represent the expanding universe. It is a continually expanding 3-dimensional object. To con­struct this representation, however, I had to reduce the 3-dimensional space that I experience in everyday life to the 2-dimensional surface area of my universe-now sphere. So the radial dimension of the sphere appears to be an extra dimension, which is non-spatial.

In my representation, this extra dimension behaves like time. But it is not time. It is merely a spatial representation of time. Time is not space. A scale drawn along a spatial dimension can be used to represent time in a quantitative sense. But it is not, and cannot represent, the concept of time. It cannot represent what time is. So the radial dimension of the universe sphere is not what it seems. In fact, it doesn't really exist. It is simply a way of representing the behaviour of time.

To create a more realistic representation of the universe, as I experience it, I need to convert the 2-dimensional surface area of my universe sphere back up to 3-dimensional space and carry with it the behaviour of the universe sphere's radial dimension. How can I do this? How can I get rid of a dimension? The answer is: by making the 3 space dimensions non-linear. However, their non-linearity cannot be arbitrary. It must reflect the behaviour or influence of the discarded radial dimension upon the 2-dimensional area of the universe sphere's surface.

Nested Non-Linearities

As previously discussed, time appears non-linear along my event-horizon and the passage of time also appears non-linear within the bounded event-continuum that represents how my event-horizon changes throughout the duration of my lifetime. This is the first non-linearity that greets my perception as I look out into the universe.

I have postulated a further non-linearity that superimposes itself upon the first one. This is that the 3 space dimensions themselves are rendered non-linear according to the way they are constrained by the size and rate of change of the radial dimension in my model. Consequently, the universe that I perceive, must be a complex compounding of these real and apparent non-linearities of space and time. So, as a con­scious entity, looking out into the universe through physical senses, I do not have a very good vantage point from which to attempt to understand the underlying reality of the universe.

What Am I Really Seeing?

I remember looking up one night into the clear tropical sky in northern Minas Gerais, Brazil. I was far from the madding street lights of any city or even a remote settlement. The stars leapt out before the backdrop of the ghostly white cloud of the Milky Way directly over my head. But what was I really seeing? Were these exotic objects, hundreds of thousands of light-years away, influencing my sense of sight from their majestic remoteness?

Not really. My sense of vision was receiving its input from electromagnetic fields that were oscillating directly within the retinas of my eyes - right at that moment. The observation that my corneas (the lenses of my eyes) focus my visual experience onto my retinas from just a short distance in front of them, suggests that the influence came from that particular direction.

But how far has this visual effect - this light - come? I don't really know. Nobody can measure how long it takes light to travel between two points. One can only measure how long it takes to make a round trip - there and back - between two points. Dividing this by 2 does not necessarily reveal how long the light took to travel one leg. This is especially so if, over cosmic distances, space and time are, both really and apparently, compositely non-linear.

Using the Döppler red-shift to calculate the distance of a cosmic object could there­fore give very erroneous results. Observed red-shift may not be due to the Döppler effect. It may be due to the expansion of space itself and the apparent contraction of time as seen through the observer's bounded event-continuum. Or it could be caused by something else.

My Perception of Time

Experience of my everyday world gives me a perception of time. This perception is the creature of the events that I see occurring within my everyday world. A human life is an event. An evening concert is an event. Each, however long or short it may be, has a beginning, a middle and an end. It is not surprising, therefore, that I am tempted to use this framework to try to gain a conceptual view of the universe.

But there is a problem with this. A human life or a concert are not really complete events. They are merely identifiable features of the one and only real event that is the universe. A human life is procreated. Something happened in order to bring it about as an identifiable phase in the dynamic continuum of life on this planet. It will most likely also be the part-procreator of another human life to follow. Similarly a concert had to have a procreator. Somebody had to organize it. Its musicians had to spend many years learning how to play their instruments to such high standards.

The universe, on the other hand, is by definition a complete event. Nothing caused it. If it had a cause, then whatever caused it is part of it. It will also cause nothing further. If it were to do so, then what it caused would be a continuation of it and thus be part of it. This necessitates that the perceived beginning of the universe be what mathematicians call a singularity. A singularity is where everything disapp­ears into nothing or appears out of nothing. Consequently, the universe's perceived demise must also necessarily be a singularity.

I have already said that I do not feel intuitively comfortable with dimension-reduction as a means of making dynamic models of space and time easier to represent geometrically on a flat piece of paper or computer screen. I feel the same way about singularities. Mathematicians can construct functions with singularities. But they don't jibe well with my experience of the real world. So the idea that the universe had an absolute abrupt beginning does not rest easy in my mind. The beginning of time is an incongruous notion for me.

Of course, the mathematics that theoretical cosmologists use, to objectively model the evolution of the universe from an initial point in time, seem well behaved. Notwithstanding, they cannot be sure that the operators and variables they are using are valid in such remote uncharted regions like the depths of the universe. All their mathematical techniques lie proven only within our small terrestrial domain. But suppose that variables they assume to be linear are not. Suppose that such variables cannot be related by known mathematical operators like + − × ÷ Grad, Div, Curl etc.. I think it is folly to go skating off into mathematical models that are geometrically un­imaginable. Extrapolating symbolically beyond what one can conceive is dangerous.

Fabric of The Universe

The universe is, by definition, a single object. The conception within my mind is that it is composed of a kind of force-field fabric. All features that exist within the uni­verse - waves, particles, atoms, molecules, planets, stars, galaxies etc. - can there­fore be nothing more than oscillating folds or convolutions within this universal fabric. I therefore perceive all things physical as either travelling or standing wave structures within this universal fabric.

Notwithstanding, the universal fabric seems not to be simply analogous to a piece of cloth or a latex membrane. There seems to be something quite different about it. It seems to be infinitely stretchable and twistable, and seems to flow like a fluid. It is as if this universal fabric is continuously extruding out of every information-source, in every direction, at the speed of light.

I use information-source as a generic term to include all travelling distur­bances within the universal fabric. These include electromagnetic waves, gravity waves and whatever other phenomenon may bring detectable information to an observer about an event that occurred within his past event-horizon.

I shall dare to take the liberty of extrapolating this idea and propose that therefore this universal fabric extrudes from every point in space at the speed of light. Consequently, from the point of view of every point in space, the universal fabric appears to be continuously extruding away from it in 3-dimensions.

If a standing-wave structure such as an atom falls to a lower-energy state, it causes a change in a local ruck in the universal fabric. Since the fabric is extruding continuously like a spherical conveyor belt in all directions at the speed of light, it carries the ruck with it. The ruck thus appears as an electromagnetic pulse diverging in all directions from the atom's location at the speed of light.

However, it is not the wave that is moving. The wave is something that gets left on the extruding fabric as it diverges outwards in all directions. The travelling wave is thus like the skin shed by a snake as it moves along on its journey. This is consistent with my reduced-dimension model where the space in the universe is represented by the surface area of the universe-now sphere. Light from a distant galactic source arriving at my eyes appears to me to have travelled along a geodesic (longitudinal line) of my spherical event-horizon. However, since the only reality in my model is the surface of the universe-now sphere, the real path of the light must have been along a geodesic of the universe-now sphere. The velocity of light in the real universe must therefore be 2c.

If the radius, r, is expanding at a velocity of 2c/π, then the surface of the universe-now sphere is expanding in circum­ference at a velocity of 4c, that is, 2c in each of the two op­posing directions. Any stationary "point in space" on the universe-now sphere will therefore expand as an ever-widening circle as the universe-now sphere expands with time. A ruck made in the fabric, by an atom "emitting" a wave, at one point in space and time will therefore natur­ally move outwards as an ever-expanding circle, whose radius increases at twice the speed of light.

However, this universal fabric is stranger still. An atom can also absorb energy from a travelling electromagnetic wave. The absorbed energy then causes the atom to shift to a higher energy state. But according to my universal fabric idea, it is not the wave that is impacting the atom. It is the atom that is hitting the wave. Or rather, it is part of an enormous spherical "ruck in space" that passes the point in space where the atom is located and thereby kicks the atom into a higher energy-state. This is what happens when the appropriate atoms in the retina of my eye observe the arrival of a light wave.

When light from a distant source arrives at my eye, my eye only captures energy from the small part of the expanding spherical wave-front that corresponds to the size of my eye. The rest of the enormous spherical wave passes by or gets absorbed somewhere else. The same occurs for other light sources from other directions in space. Together, the captured bits from all sources appear to converge towards my eye at the speed of light. They are all borne up on what appears to be the aspect of this universal fabric that is continuously converging towards the point in space where my eye is located. The remainders of the vast spherical wave-fronts from all these sources pass by my eye without effect. They are outside my past event-horizon and are therefore not part of my universe. I can have no sense of them or connection with them. To me, they do not exist.

However, the light I see does not appear as a shrinking circle of space on my universe-now sphere. It always appears to arrive from successive universe-now spheres of the past along the circumference of my past event-horizon sphere. Thus, from my point of view, along my event-horizon sphere, space is apparently being sucked-in to my point of observation at the velocity c from every direction. Con­sequently, as well as extruding the universal fabric in every direction, my point of observation appears to be independently sucking-in the universal fabric from every direction. Making the same extrapolation, may I propose that every point in space is also sucking in this universal fabric at the radial speed of light?

A Paradox of Perspective

Every point in space thus appears to be in continuous full-duplex communication with every other. And this is what unifies the universe. It is what makes it a universe. But it also raises a paradox. It means that the space represented by the surface area of the expanding universe-now sphere in my model, as well as ex­panding, is also contracting. As well as being spewed-out, it is also being sucked-in at every point.

This makes the Big Bang no more than a visual construction - a vanishing point of perspective - from which the expanding aspect of space-time is projected onto one's personal event-horizon. It follows that a second vanishing point - an Anti-Big Bang - must exist that corresponds to the contracting aspect of the projection of space-time onto one's personal event-horizon. They are analogous to the two vanishing points required to construct a projection of a 3-dimensional cube (physical reality) onto a flat paper or screen (one's personal event-horizon).

This duplexity suggests a dynamic steady state, or at least, a meta-steady state. It thereby sidelines the singularities at the beginning and end of time and space because vanishing points have no real existence. Of course, I cannot represent this within my reduced-dimension model. However, I can picture it quite cogently within a finite continuum of dynamic 3-dimensional non-linear space.

The apparent physical paradox of space at once being effectively both extruding from and sucked into every point seems overly complicated. It reminds me of the geocentric versus heliocentric controversy at the time of Nicolaus Copernicus. Of course, the movement of the planets appears much simpler if we regard the sun as the centre of the solar system rather than the earth. Notwithstanding, the position of the observer cannot change the mechanism. Pretending to be in the middle of the sun does not simplify the laws of physics: it merely alters the point of view of the observer. All positions of observation are equally valid, whatever the object being observed. It is just that things can appear much more complicated from some positions than from others.

A further paradox is that, under the above model, the velocity, c, at which light ap­pears to travel through space from a source to a sink, must be superimposed upon the rate at which space is apparently expanding. This also could increase or decrease with time or distance along any radial of an observer's event-horizon.

Perhaps, therefore, it is because of our disadvantageous position within the vast­ness of space and time that we can only come up with the equivalent of complicated "geocentric views" of the universe. If only we could observe from a different van­tage point (such as riding on a light beam), perhaps we could gain a simpler and more satisfactory view of what the universe is. For instance, perhaps we could apply a geometric transform to extruding and sucked-in space that can turn them into a single "stationary" frame of reference. Perhaps from such a vantage point the universe would appear a little more "heliocentric".

Time For a Re-Think

As a sentient observer, looking outwards through my physical senses, what do I really see? I see a person; a fellow human being. She is sitting at her desk working with her computer as I am working with mine. Her head is about 1½ metres away from mine. But I do not really see her as she is now. The laws of physics won't permit me to see her as she is now. They will only ever allow me to see her as she was 3 nanoseconds ago. I look out of the window. I see the city bounded by a mountain ridge about 15 kilometres away. But I am not seeing the mountain ridge as it is now. I can only see it as it was 50 microseconds ago.

How do I know how long it takes information to reach me from my colleague and from the mountains? I need to know the physical distances between my head and that of my colleague and the distance between my head and the mountain range at the edge of the city. Next, I need to know the velocity of light within these res­pective domains. I can judge by sight the physical distance between my head and the head of my colleague. If I want to be more accurate, I can use my 5-metre steel tape measure. I know the distance of the mountains from my map and also from the odometer in my car when I drive to the public park located on the near side of the mountains.

The time it takes light to travel to a remote mirror and back has been measured very accurately for precisely measured distances between the light-source/sink and the remote mirror. It is assumed - reasonably I think - that over such short ter­restrial distances, light takes half the time to travel one way that it takes to make the full round trip. I am confident that the velocity of light, so determined, is valid and accurate within the terrestrial domain in which it was measured. I can there­fore use it to determine how long it takes light to reach me from my colleague's head and from the mountains at the edge of the city.

Night falls. I see the moon. But I am not seeing it as it is now. I am only seeing it as it was about 1·3 seconds ago. Through a telescope, I can see the star Proxima Centauri. But I am seeing it as it was somewhat over 4 years ago. If I were to look through a large astronomical telescope, I could see the Galaxy of Andromeda. But I would only be seeing it as it was 2½ million years ago. Astronomers measure these distances using parallax methods. They use trigonometry to measure the distance of a star or galaxy by how its position changes against the backdrop of more distant objects as the earth moves from one point in its orbit to the diametrically opposite point. So the distance of the object is measured in multiples and fractions of the diameter of the Earth's orbit around the sun. Trigonometry is also the means of relating the diameter of the Earth's orbit around the sun (known as 1 astrono­mical unit) to physically measurable distances on the ground measured in metres.

So the distances of the Moon, the star Proxima Centauri and the galaxy of Andro­meda are calculated by trigonometry in terms of tangible units of distance. Not­withstanding, in order to put a figure on the time it takes light to arrive from them, I must assume that light travels at the same velocity out there as it does within the terrestrial laboratory where it was measured. This is a reasonable assumption, I think. But it is, nonetheless, an assumption. Consequently, how far back in time I am actually seeing these objects depends on the validity of this assumption.

For cosmological objects beyond a billion light-years, trigonometry is not suffici­ently accurate to give meaningful values. Another method is needed. For objects close enough for their distances to be measured using trigonometry, a phenomenon is observed whose magnitude corresponds to distance. It is known as red-shift. Red-shift is thought to have three causes: the electromagnetic Döppler effect, the grav­itational warping of space-time and the rate of expansion of space itself.

Assuming that the linearity of the red-shift phenomenon up to a billion light-years can be extrapolated, it can be used to measure the distances of objects beyond a billion light-years. The cosmological phenomenon with the greatest observed red-shift is the microwave background mentioned earlier. Its red-shift, z = 1089, corresponds to a distance of about 13·7 billion light-years.

Consequently, as I listen to the hiss of the microwave background on my scanner, I am hearing something that is 13·7 billion years old. If I look at the spherical intensity map of the cosmic microwave background, as shown on the right, I am seeing the universe as it was 13·7 billion years ago.

Earlier in this essay, I used a polar map of the Earth as a 2-dimensional analogy of my spherical event-horizon set within a universe-now sphere whose radial dimen­sion represented time. This showed how a super-brilliant vanishingly small Big Bang would, over the 13·7 billion years its light took to travel across the surface of my event-horizon sphere, end up appearing like the vast sparse sphere of the microwave background radiation. Notwithstanding, that whole model involved the represent­ation of time as a distance through a fictitious spatial dimension, namely, the radius of my universe-now sphere. However, the universe-now sphere and its radial dimension are mental constructs, which do not form a part of tangible real­ity. I want now to take a strictly pragmatic view of what I really see.

The premise of my pragmatic view must be that I can only ever see - or be affected by - that part of the universe which falls within my past event-horizon. So this is the only thing I can consider and examine. Everything outside of my past event-horizon is wholly irrelevant. It may as well not exist. So I will keep to what - one way or another and with the aid of artificial instrumentation if necessary - I can physically sense.

The most distant feature within my past event-horizon is the microwave back­ground radiation. Whether or not it be 13·7 billion light-years distant depends on the truth or falseness of the assumptions that the velocity of light be constant and that space and time be linear. Furthermore, whether or not I am really seeing its shape and form as it then was depends on whether or not the space-time, within my past event-horizon, has distorted its appearance. Nevertheless, I have no means of knowing whether these assumptions be true or false. Consequently, I have no choice but to assume that the content of my past event-horizon is - or rather, was - as I see it.

I see the microwave background as a vast, sparsely distributed, almost homogen­eous fluid. It looks like a nebulous nothingness of practically zero energy-density. And my pragmatic view must be to regard it as being - or rather, having been - as I see it. Consequently, this must have been the state of the universe when it was young. So, way back then, it does not look as if it were a super-hot singularity. It looks as if the universe started out as an immensely large cold sphere of space bathed in microwave radiation.

If red-shift indeed be a true guide to distance, it is evident that, with a red-shift ratio of 1089, the source of the microwave background is by far my furthest, and hence my youngest, observable phenomenon. Conversely, I, as the observer, am necessarily the oldest phenomenon in my past event-horizon. Every other observ­able feature within my past event-horizon is therefore younger than I am and older than the source of the microwave background. The next-youngest species of observable cosmic objects seem to have a red-shift ratio of about 11. However, the relationship between red-shift and distance seems to be very non-linear, being in reality fairly close to a sigmoid function. But this is because, space itself - as currently postulated by mainstream cosmology - is thought to be expanding.

But suppose that space isn't expanding. Suppose instead that our whole concept of space, as extents referable to three mutually perpendicular axes, is not as funda­mental as we may have been led to suppose from our formation and experience within our terrestrial womb. Suppose that the fundament of space is not distance but relative velocity, distance merely being the special case of zero relative velocity. Furthermore, suppose that time, instead of being a fourth dimension, is really an inseparable part of each of the three dimensions of velocity-space. Time is thus something which flows, radially inwards to the observer, at a constant rate from every direction, from the infinite extremity of his spherical past event-horizon.

This idea sits much more comfortably with my pragmatic observations. The basis of my conscious experience of life is that of being permanently ensconced at a fuzzy singularity in the middle of my universe, with information falling towards me, like flakes of snow, from every direction. Light and sound telling me about my colleague sitting next to me. Light telling me about the mountains on the horizon, the Moon, stars and galaxies. Microwaves telling me about the presence of the oldest phen­omenon in the Cosmos. But is this information falling towards me like an object does under gravity; or is something bringing it to me?

The sound waves, created by the clicking of the keys of my colleague's computer keyboard, are being propagated through a tangible fluid called air. By analogy, people assumed initially that therefore light must propagate through something they first thought of as a luminiferous æther. However, scientists have consistently failed to detect its existence.

Notwithstanding, space does have 2 fundamental properties, which science refers to as its electrical permittivity ε0 and its magnetic permeability μ0. The product of these two measured properties of free space has the dimensions of a reciprocal rate of change of area. This invokes, within my imagination, a vision of a volume that is collapsing at a constant radial velocity c = √{1/(ε0μ0)}. It appears to me, therefore, that the essence of space - what I shall from now on refer to as the æther - is some­thing that can only exist while in a state of flow, converging towards my point of consciousness at the velocity of light. When it reaches my point of consciousness, it can go no further. So it stops and, consequently, ceases to exist.

I am persuaded that it is this constant convergent flow of the æther, towards my point of consciousness, that gives me my sense of time. In fact, in my mind, I see the æther - the essence of space - as being synonymous with time. The flow of the æther is the flow of time.

Naturally, I realise that I am not the only conscious observer in the universe. My colleague, at the desk next to mine, is also a conscious observer. She therefore has her own past event-horizon, the centre of which is offset from the centre of my past event horizon by about 1½ metres. I therefore think it reasonable to assume that the æther - the essence of space and time - is also flowing convergently inwards towards her centre of consciousness. All observers experience the flow of time. Consequently, each must have his own private æthereal in-flow converging towards him from the extremity of the universe. But is it only conscious observers that have the privilege of a separate private æthereal in-flow? I think not.

My thought experiment here is that the vast majority of what I visualise as a spherical universe contains æther which is flowing radially towards a very small volume at its centre. This small volume is populated by what I call sink-holes. It is into these that the æther flows. Æther is a velocity-fluid. It only exists in a state of flow. So once it arrives at a sink-hole, it ceases to flow and therefore ceases to exist. As æther enters a sink-hole, it separates into its +ve and −ve compon­ents, producing a back-wash in the form of a standing-wave pattern. This is what we per­ceive as a primary particle. These form the composite standing-wave structures we call atoms and molecules.

In this alternative view of the universe, electromagnetic radiation does not travel outwards from its source as a spherical wave-front, expanding radially at the velocity of light. Instead, the source merely etches electromagnetic stresses into the æther as it passes by, on its radial journey towards its sink-hole.

Also in this alternative view of the universe, as I look further back into my past event-horizon, I see a part of the universe that is much younger. Its sink-holes are much more homogeneously distributed. They haven't yet had time to gravitate to­wards each other. The flow of the æther is therefore much less radially aligned. Time is flowing in different directions. So the composite of the components of time flowing towards me run slower. Electromagnetic radiation from that epoch there­fore appears red-shifted.

My sense of a collapsing universe continues into the realm of material objects. These too appear to be converging towards me like flakes of falling snow. Dust is thought to have collapsed - under the influence of what is perceived as gravita­tional attraction - to form rocks, asteroids, planets and stars. The orbits of these objects gradually collapse until they collide and coalesce. It seems therefore that the material universe too is in a gradual state of collapse.

Of course, we know that the radius of the Moon's orbit around the Earth is, at the present time, increasing. But this is because the Moon is being continually pushed into a higher orbit, via ocean tide gravitational coup­ling, by the Earth's fast rotation. Eventually, the Earth's rate of rotation will diminish and the Moon's orbit will decay. And collapsing stars ex­plode. But the energy of their explosions is always far less than the energy of the gravitational collapse which caused the explosion. Most becomes trapped in a black hole or neutron star.

This alternative, and highly subjective, personal view of the universe is explained in greater detail in my series of essays about The Universe. The collapsing universe, which I have just described, would seem to have only a transient existence. It is not cyclic like the days and nights of Brahma. It is not eternal. How do I feel about that? Not too bad. Perhaps it has only a temporary purpose - a transitory signifi­cance - which, once fulfilled, will no longer require it.

Significance of The Universe

The universe has significance only from the point of view of a conscious entity that is perceiving it. As a conscious entity, I am constrained to perceive the universe, along my current event-horizon, from the point in space where I am currently located.

In my reduced-dimension model, the surface area of the inflating universe-now sphere represents the expanding space within the universe. It is easy to visualise that, upon the surface of this sphere, any point has exactly the same status as any other point thereon. There is no "zero-point". There is no absolute point of refer­ence. It is a relativistic universe. Consequently, although each perceives it from his slightly different point of view, the universe should appear, to every conscious observer, to behave in exactly the same way. Thus, all conscious observers are equal. None is king.

The universe is therefore such that I can perceive you only provided that you are within my past event-horizon at the time. I can therefore only receive a message from you that you sent at a time in my past. You can only receive from me a message that I sent at a time in your past. Consequently, for us to be able to engage in full-duplex communication, our messages must traverse consecutive event-horizons that leap-frog each other as the universe-now sphere expands with time. It is this profound property of the universe that realises the possibility of commun­ication between conscious entities.

A poignant corollary to all this is that I, as a conscious entity, exist exclusively at some point on the universe-now sphere. That point coincides with the "North Pole" of my event-horizon. From my point of view, the point at which my conscious awareness is located is the oldest point in the universe. All that I perceive is in my past. It is therefore closer to the time of the Big Band than I am. Consequently, for me, all else exists at places in the universe that are younger than the point where my conscious awareness is located. Consciousness, therefore, must only exist at the leading-edge of space-time. It is as if the hypothetical shell that bounds the expand­ing universe is itself the location - and indeed, the very essence - of consciousness. Consequently, if it be possible at all for conscious entities to communicate directly, that communication must take place along or through the surface membrane of that hypothetical shell.

The significance of the universe, from the point of view of conscious entities, such as we, is that it provides the means for us to perceive each other, to communicate and hence to relate. It is the universal fabric that connects conscious entities, which otherwise would be separated from each other in the dark silent prison of eternal isolation. But this universal fabric is not just like a radio link between individual consci­ousnesses. It also provides the context of the language in which we communicate and the very essence of the content of what we convey to each other. This, in consequence, becomes the very essence of what we are individually as conscious entities.

The spatial structure of the universe, and our ability to move independently within it, benignly regulate the intensity with which we may communicate and relate. Spatial proximity facilitates intense exchange between us. This intensity diminishes rapidly with increasing distance. When we are close, we can communicate with an all-consuming intensity. When we are far apart, we can still communicate but without it consuming all our attention. It affords each of us the freedom to gauge the degree of socialisation or solitude he desires or requires at the time. The uni­verse thus facilitates our spiritual development or evolution as conscious beings. But it is up to each of us to deploy this facility wisely and constructively, or foolishly and destructively.

Though the universe provides the means for us to communicate and relate, this is only really feasible within the confines of Planet Earth. If you were to visit Mars while I remained on Earth, there would be a long delay between me speaking to you and my hearing your response. This could be anything between 6 and 45 minutes, depending on the distance between Earth and Mars at the time. This is impractical for carrying on any kind of conversation, although it would be quite adequate for us to correspond by email. The universe is so vast that many people think that there is a good chance that some other planets could be host to intelligent life. If so, could we converse with them by radio and hence develop bene­ficial relationships with them too?

As for what the universe is and how it functions, we can never truly know. To do so, we would have to be able to observe it from its outside, which, since we are part of it, we can never do. We can only speculate. Consequently, all ideas about the uni­verse - whether they be the current collective vogue of cloistered academia or the idle mental meanderings of a lay-theorist like myself - must necessarily be sub­jective.


Parent Page | © 18 November 2010, 17 October 2012 Robert John Morton