Once upon a time, the world was flat. Or at least, they told us it was. It also stood at the very centre of a cosmos which dutifully and subserviently wheeled around us once a day. In the world of the Church, the stars were all embedded in a series of concentric crystal spheres, and in an alarming display of Christian self-deception the moon, despite all its naked-eye markings, was pure and unblemished.
This was the universe of the Christian, whose dark reign occupied the centuries between the enlightened times of the Greeks, with their mathematics and geometry, and our own modern times where the benefits of science are again available to all and church congregations around the world are finally dwindling. Anybody during this dark period who dared to think for himself and differ with their view, was to be persecuted and murdered, frequently by having their poor bodies burned up.
But thankfully, there have always been courageous and spirited people who have never been tolerant of darkness of oppression and who have always been prepared to risk all to achieve freedom: of expression, of action and of thought.
One such person was Nicholas Copernicus, who in the 15th century noticed that Mercury and Venus never seemed to stray far in the sky from the sun. But if the entire cosmos faithfully revolved around the earth, then both planets should be visible from time to time in the south at midnight, opposite the sun in the sky.
It became fairly obvious that the planets were going around the sun, not the earth, and that the orbits of Mercury and Venus lay within the orbit of the earth. Copernicus re-drew the solar system, with the sun in the centre and the planets going around in circular heliocentric orbits. This model also finally explained a phenomenon called "loops of retrogression" whereby from time to time a planet would actually seem to stop in the sky, turn around, and go back the way it came, before stopping again and resuming its original motion. This had baffled the ancients, and the Church, but proved to be nothing but the geometrical effect, as the earth in its own orbit races past the planet, so that the planet seems to pass first one way against the starry background, and then the other.
The achievement of breaking away from the oppressive views of the Church had been intellectually very easy, due to the clearly erroneous nature of those views, but humanly very difficult and dangerous because of the oppression, the tool by which, in the presence of ignorance of the real reasons for nature’s phenomena, the Church had retained its grip on power.
But refinements were needed. Johannes Kepler soon noticed that the planets didn't seem to follow orbits which were truly circular. He went to see the Danish astronomer Tycho Brahe who, in those pre-telescopic days had designed and built some extremely accurate devices for measuring the motions and positions of celestial objects. Tycho lacked Kepler's mathematical dexterity as Kepler lacked Tycho's apparatus. And so, they worked together. Tycho supplied the observational results, and Kepler racked his brains to try fit these into an equation.
Kepler knew that the orbits weren't perfect circles. Tycho's planets would sometimes speed up, sometimes slow down (even after correction had been made for the motion of the earth), which they would not do if the orbits were circular. Eventually, he discovered that the orbits were all in fact ellipses, with the sun at one focus and nothing at the other, that they all swept out equal sectorial areas of their ellipses in equal times, and that the square of their orbital periods were proportional to the cube of their distances from the sun. These equations, Kepler's Laws as we call them, still hold good today; NASA still use them every time they send a space craft out into the cosmos, and still disregard Einstein's relativistic corrections to the laws as being too small to be of significance except at stupendous velocities which we still cannot reach.
Then came Isaac Newton. He discovered that the moon is held in its orbit around the earth by an inward force which counteracts the outward "centrifugal" force (which tends to throw you outwards when you speed round a bend), and that that inward force was the same force-- gravity-- which makes an apple fall from a tree. He also first analysed light, using a spectrometer, and discovered that "white light" is merely an illusion, an optical effect on our retinas, white light itself being a mixture of light waves of all the primary colours. He invented reflecting telescopes, co-invented calculus (fluxions, he called it), and finally proved mathematically that a particle injected into a captured state of motion around the sun would indeed move in an ellipse.
After Newton, little further change of any profound nature took place until the late 19th century, and Newton's orderly, mathematically driven cosmos ticked away in peace.
The speed of light had first been measured by Romer in 1675, and by the 1880s it had been discovered, strangely, that the speed at which light reaches you from an object is always precisely the same, regardless of whether the object is speeding towards or away from you. This was indeed odd. It was reasoned therefore that light must travel through an invisible, mass-less medium which must pervade the entire cosmos. This medium was called the ether.
Michelson attempted to detect this ether by designing a cross-shaped apparatus whereby the speed of light was measured first in one direction and then at 90 degrees to that direction, so that the motion of the earth through the ether would reveal a difference in his measured results. But strangely the results were the same.
Albert Einstein therefore concluded that the ether does not exist, and that there must be a geometrical interpretation of the fact that the speed of light is the same in all inertial frames irrespective of any relative motion between those frames.
By this time, many spooky things had been noticed about this cosmos of ours. For example, if we travel in a car at 30 kph and then throw an object out of the front of the car at 20 kph (relative to the car), then relative to the road the object would be traveling at 30 + 20 = 50 kph. But that can't be right. Let us suppose that we could throw an object out of the front of the car at 60% of the speed of light, and also that the car was traveling at a further 60% of light speed. That means that the object would be traveling at 120% of light speed, which is impossible because it has been proven that no material object can exceed the speed of light. More basic spookiness than this had also been known much earlier. Does the cosmos go on forever? How can anything be infinitely big? Can we imagine that? And why is the sky dark at night? After all, if the cosmos is infinite in extent, and contains an infinite number of stars, truly without end, then no matter how incredibly faint each point of light may be, and infinite number of them --infinite, without end-- should still make the sky infinitely bright. So why's it dark, then?
In the early part of the 20th century, at just about the time that Einstein was writing off the ether and propounding his Special and General theories of Relativity an American astronomer, Edwin Hubble, noticed something else which was very profound. Using the powerful Newtonian reflector telescope at Mount Wilson in California, he discovered that all the galaxies were rushing away from each other. That is not to say that they are all rushing away from a specific point in the cosmos. It's spookier than that --they are all rushing away from each other. It was as though each was equally entitled to consider itself at the centre of a vast volume and everything was rushing away from it.
And thus, the Big Bang theory was born.
Albert Einstein described the cosmos as a four-dimensional space-time continuum, and many physicists have since written books about, and have attempted to describe, this cosmological structure, the great majority of them succeeding in achieving little but the complete mesmerisation of their lay readers. Thankfully, I have long been described (accurately, I hope) as a relatively (excuse the pun) clear explainer, and so here I would like to put this observation to the test and describe Einstein's continuum in such a manner that it might be readily understood.
Here, at last, after the monstrous 2,000 year interruption of Christianity, we can at last re-marry the geometry of the ancient Greeks, and the spooky mysteries of the cosmos which they must have seen, to present day science.
Suppose we have a football, just an ordinary sphere, in front of us. We notice that it has a surface which is finite, in other words it only has a fixed number of square centimetres to it, and if you were to stick postage stamps all over it you would eventually be able to fill it up. But we also notice that the same surface is unbounded, in other words there is no end to it.
The ball’s surface has of course 2 dimensions: length, and breadth. If you try to move in a 3rd dimension, depth, then you leave the surface of the sphere. And so the surface itself only therefore has the 2 dimensions of length and breadth
If you could make yourself really tiny (or the sphere really large), and stand on the surface, you would find yourself standing on what appeared to be a flat plane. Suppose that while you are there, you happen upon some local inhabitants. These beings are flat, 2 dimensional beings who have no perception of the 3rd dimension of depth. They are very good at flat geometry, and stuff like that, but don't try explaining depth to them, or you will be wasting your time. Let us call them Flatlanders.
Their cosmos is a flat plain, which appears to them to extend onwards forever.
One day, however, one of them sets off exploring. He starts walking, and just keeps walking in the same direction on his flat plane, being very careful not to change his direction at all. After a very long time, to his absolute astonishment, he eventually sees something ahead of him. It is his own house, where he started off from.
He concludes that there is something very spooky about his cosmos.
Then, a flat scientist friend of his draws a small triangle on the ground, and, measuring all the angles, he sees that, as in the case of all triangles, they add up to 180 degrees. But when he draws an enormous triangle, and measures its angles, he finds to his horror they add up to more than 180 degrees. Next, he draws a small circle on the ground and divides its circumference by its diameter. He gets pi (=3.141857...) as he would expect. But then, when he repeats the experiment with a huge circle, he is again horrified when he gets a smaller number than pi.
Of course, if we look down on them from above, ie through a 3rd dimension (depth) which they cannot understand, then we can see their folly. The explorer came upon his own house because he had walked completely around the globe on which he is living. And the scientist could not have understood that triangles and circles drawn on the surface of a sphere always have angles which add up to more than 180 degrees and circumference to diameter ratios less than pi.
The truth is, of course, that their flat plane curves round upon itself through a dimension (#3--depth) which is one dimension higher than the 2 (length and breadth) which they can understand.
If they had done further experiments, they would also have noticed that automatic probes set off along the ground in all directions from the same starting point would, without any of them changing direction, run together again at a counterpoint in their cosmos. For example if they all set off from their north pole, they would all travel due south all the time, and collide at the south pole. In their flat world, this would have completely staggered the Flatlanders.
Now the point is, that our own cosmos is just the same as theirs, -- except that everything here is one dimension higher.
In our cosmos, a spaceman setting off in a starship and never changing direction will eventually come back to where he started. And a number of probes, taking off into space in all directions, up, down, sideways, obliquely .... will all eventually-- without ever changing direction-- run together again at a counterpoint in the cosmos. Huge triangles drawn between galaxies, upways, downways, sideways, obliquely, will have angles the sum of which exceeds 180 degrees by more and more the bigger they get, and pi will get smaller and smaller the bigger the circles we draw.
However our cosmos is different from theirs in one key respect-- it is expanding, and all the galaxies are behaving as though each was at the centre and the others were all rushing away from it.
But if we go back to the flatlanders' world, we can at last understand this. Imagine the flatlanders went round with buckets of paint, and painted pictures of galaxies on the ground all over the surface of their world. Now imagine that somebody stuck a pump into their spherical football and started to blow it up. As their ball expanded, the galaxies painted all over the surface would all start to move away from each other, and irrespective of which galaxy you decided to stand at and call your own, all the others would seem to be rushing away from that one.
And that is exactly what is happening with the galaxies in our cosmos -- except of course that everything is one dimension higher. And of course, the expansion of our cosmos was due not to a huge pump, but to a huge explosion down in the centre of the football.
Now sometimes people ask, "Whereabouts in our cosmos did the Big Bang happen? Can we still see the place where Creation took place? Could we actually go there someday?".
Well we can see from the flatlanders' cosmos that the place where their expansion started was in the centre of the football, and not at any point on the surface. But only the surface of their ball is their cosmos, and the centre of the ball lies outside their cosmos along a direction (depth) which is one dimension higher than they can understand. They can search their surface world as much as they like, and nowhere will they find the place where the expansion began. It really began beneath their feet-- but they can't understand depth, because that is at 90 degrees to all the movement they can comprehend.
Likewise, in our cosmos, the source of the Big Bang, the place where Creation happened, is also nowhere to be seen in our 3-dimensional space. Just like the Flatlanders, we too live in a cosmos where the site of the expansion lies off in a direction which is one dimension higher than we can understand. Einstein called this fourth dimension Time. But really it is just a direction, which lays at 90 degrees to all the movement we can comprehend. You could mark it out with a measuring rod, just as you can the other three. Or you could rotate a 4-dimensional grid system (x,y,z,t), so that the x-axis becomes the z, the z the t, and the t the y and the y becomes the x; in that respect, the axes (including Time) are all equivalent and there is nothing spooky about any one of them more than any other.
But in a sense we too are "Flat"-landers; like them we cannot imagine that extra dimension which we need to picture our cosmos clearly. My university physics tutor once put it admirably: "Time?", he said, "Piece of cake! Imagine 3 axes all mutually perpendicular to each other, then imagine a 4th axis perpendicular to all three"!
You can imagine the roar of laughter.
Well, that is pretty much the current state of affairs with regard to the shape of our cosmos. But there is a problem.
Now wouldn't you feel a Turnip if you ever went into enormous depth and complexity to explain something, and then a little kid came along and asked one simple question which not only you couldn't answer, but also shot your theory down in flames? Well I'm afraid Cosmology is presently in just such a position. Here's the question:-
"If
the cosmos is Everything, (and by the definition of Everything there cannot be
anything outside it), and if it is expanding, -- then what is it expanding out
into?"
Er….oh.
Cosmology does not have an answer to this. But seeing as this is my old university subject I would like to venture to suggest that I do.
Let's go back to the Flatlanders' expanding football. The surface of the ball is of course the 2-dimensional world within which the Flatlanders live, and the 3rd dimension is a line at 90 degrees to the surface, which joins the surface to the centre of the ball..
But let us now simulate our own cosmos, by increasing everything by one dimension, whilst at the same time retaining the football as our basic working model. The first 2 dimensions would now be represented by a circle drawn around the ball, like a line of latitude on a globe. Travelling anywhere along this latitude circle would now represent movement in the first 2 dimensions, while venturing along the surface of the ball at 90 degrees to this circle would represent movement in the 3rd dimension. The 4th dimension would lay at 90 degrees to the previous three, and that would be represented by a line joining the surface of the ball to its centre, as we have already seen.
But of course this ball is expanding. And it can't do that because the volume of the ball is supposed to contain Everything.
So let us go one dimensional stage further, and imagine that a latitude circle around the football represents the first three dimensions, while a line striking out across the surface of the football at 90 degrees to this, ie parallel to a line of longitude on the football, represents the 4th dimension (Time). Then, the line joining the surface of the football to its centre would be a 5th dimension. So on this model all the galaxies in our three-dimensional space would lay, and move, along the circumference of the latitude circle.
Now suppose that a Big Bang happened at the "north pole" of the football, and a circle spread out from that, like an ever-increasing latitude circle heading down towards the football's equator. As the expanding circle gets bigger, all the galaxies around the circumference of the circle will move apart, and if you hold the football in your hands you can rotate it as you please to consider any particular galaxy to be at the centre of your field of view, and all the others to be moving away from it.
The direction of travel of any point on this expanding latitude circle is due south, at 90 degrees to all directions you would travel if you followed the circumference of the circle, and so this "north-south" direction on the surface of the football is the 4th dimension (Time).
But the point is this: on this model, the football itself doesn't have to expand! It just remains the same old size, as time folds round on itself (from "pole to pole").
We can make some pretty mind-boggling predictions from this.
First, the cosmos will not just expand forever, even if the rate of expansion is accelerating (as we now believe it is). Accelerating or slowing down, there will be an inevitable Big Crunch when the latitude circle passes the football's equator, keeps heading on south, and then implodes on itself at the football's south pole.
Second, the very notion of whether there is enough matter in the cosmos to halt the expansion is a folly. The football's latitude circle containing all the galaxies is moving "north to south"--- at 90 degrees to any 3-dimensionally applied force such as gravity, which only acts around the circumference of the latitude circle. So the vectorial component of any such force in the direction of the latitude circle's movement is zero and therefore neither gravity nor the postulated repulsive force (another force which may be acting around the circumference of the latitude circle) can be having any effect on the expansion.
Third, if we examine the distribution of galaxies around the latitude circle, we see that both gravity, (which tends to pull the galaxies round the circumference of the latitude circle towards each other) and the postulated repulsive force (which tends to push the galaxies round the circumference of the latitude circle away from each other) will only achieve the same effect-- a "diamond ring" phenomenon where part of the circumference of the latitude circle contains a greater concentration of galaxies. This may of course result in a premature Big Crunch taking place at any arbitrary point on the football which the latitude circle was passing through at the time, immediately followed by another Big Bang, and a new circle of galaxies will emanate out from there on its way towards its antipodean point on the football. In other words, the site of this new Big Bang will become the new North Pole of the football, and the opposite point on the football will become the new South Pole. It could well be, that these Bangs and Crunches are happening all over the time-surface of the football.
But the point is, that the football itself is not expanding!! And so the little kid's question is answered.
Fourth, when a Big Bang happens on the surface of the football, there may be more than one latitude circle emanating from it. There may be many concentric latitude circles, separated in time like parallel universes, having established their spacing by each having bounced off the one in front only to get hit by the one behind, in much the same way as concentric shock waves from a dynamite explosion form.
Fifth, hyperspace travel will necessitate travelling not in the 4th dimension, but in the 5th, as to get from one part of the latitude circle to another part of the same latitude circle by the shortest route will mean having to go inside the football (5th dimension), but not having to go further north or south on the football (4th dimension).
Strings will be lines laid out on the surface of the football and membranes will be entire new football surfaces either above or below the original one, like concentric (but still not expanding!) footballs. These membranes would of course be separated in the 5th dimension. Naturally if ever another football surface (=membrane) should touch ours, then matter and energy could leak from one to the other. There may therefore be some particles in our cosmos which did not originate here and which will remain aloof from the equations which are supposed to predict the particles which formed here.
Notice that we do not need any more overall dimensions.
In conclusion therefore, on my model of the cosmos the greater cosmos itself is a super-sphere (the "football") which possesses 5 dimensions. The cycle of Big Bang (occurring at one of the football's poles), followed by a latitude circle of matter expanding out towards the football's equator, (expanding 3-D space), followed by the latitude circle then passing the equator and converging towards the other pole (contracting 3-D space), where a Big Crunch takes place, to be followed then by another Big Bang...is endless. (This entire system may be being driven by the presence of a staggeringly large concentration of matter at the centre of the football; for example, by way of analogy I have noticed that, if the Earth were massive enough, then an explosion of small particles in space high above the North Pole would lead to those particles emanating outwards in a contained circle or ring, which would then pass over every latitude circle on the Earth's surface, before running together again high over the Earth's South Pole. This is a remarkable lower-dimensional parallel to what may be happening in the greater cosmos at large). The football itself has always existed, as time (the surface of the football), is curved round upon itself and is therefore finite yet unbounded (i.e endless). The football cannot thus be measured against a background of time, as time is merely a subordinate feature of the football. And the football itself is neither expanding nor contracting.
Again, no matter what your theory of the cosmos explains, it is bound to be wrong if it can't even answer the basic question of what the cosmos is supposed to be expanding out into. At least my theory,-- unlike many other current theories-- does explain that. However as to whether the rest of the theory is also correct, only time-- and meticulous observation-- will tell.
Prediction (#1)
It follows from my theory, that the rate of expansion of the 3-dimensional cosmos is (a) accelerating, and (b) accelerating at a decreasing rate. This is because in the real world everything in the cosmos rotates, and in terms of good old commonsense, -- and there will always be room in science for commonsense -- it would be hard to imagine that the near-singularity from which a Big Bang occurs, would not be rotating at an incredible rate as it originally begins to form during the previous Big Crunch, and as it explodes. This means that the latitude circle of matter emanating outwards from a Big Bang will itself rotate as it goes, and so the centripetal force on the latitude circle (= 3-dimensional space full of galaxies) will cause that latitude circle to accelerate towards the football's equator. However this acceleration will be greatest near the football's poles, as the turning circle is sharper there, and will decrease as the latitude circle expands outwards and approaches the football's equator. (Of course when the latitude circle of matter reaches the equator, it will by then have acquired the impetus to carry on going and eventually reach the opposite pole, where it will crash in on itself as a Big Crunch, which immediately precedes the next Big Bang).
Measurements of the rate of expansion of the 3-D cosmos could be made using distant galaxies, and the expansion rate for 10 billion years ago could be compared to that for 9 billion years ago, that for 9 billion years ago compared to that for 8 billion years ago...etc.
Expect a decrease in the rate of acceleration.
Prediction (#2)
This theory also predicts that the current supposition that the cosmos is "open" and will expand outwards forever until the skies become void of stars...is a folly. (But then, we already knew this..."expand outwards into what?"). Irrespective of the measured expansion rate of the cosmos, and of the acceleration rate of that expansion, there will come a time when the galaxies are nevertheless all running together again (as the latitude circle passes the football's equator) and heading for another Big Crunch at the football's opposite pole.
The envisaging of a repulsive force causing the galaxies to accelerate away from each other in 3-D space is also a folly. This acceleration is, as we have seen, merely a feature of the geometry of the football and of the rotational forces involved in each Big Bang. Neither gravity nor the postulated repulsive force can have any vectorial relevance to the expansional/contractional behaviour of the cosmos, as these forces only act around the latitude circle, and not along the direction of the Pole-Pole movement of the galaxies in the latitude circle, which movement is at 90 degrees to the gravitational and to any repulsive forces. (We have always known that gravitation does not act through the 4th (time) dimension, the direction along which the 3-D cosmos is expanding. For example, take a large gravitating mass and place it near to you. You feel the gravitational pull. Now, at a subsequent time, say, 2 minutes later, remove it. Do you still feel the pull?? Course you don't. (Think about it)).*
--- Michael Alan Marshall
*
Only 2 minutes away in time, and right next to you in space, there's a huge
gravitating object. But you don't feel a thing. Therefore gravity cannot
possibly extend through time. This in turn verifies the sheer folly of
considering gravity to be relevant to the expansion of the cosmos, as this
expansion takes place at 90 degrees to all 3 spatial axes, and gravity's
vectorial component in that direction is therefore zero.