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The World is Just a Great Big Onion...

Immo Hüneke

Ever since studying Astrophysics at University, I’ve carried this theory around with me, and this is my chance to discuss it with a wider audience. I happened upon this theory as a result of putting together a small number of pieces of a puzzle. It also supplies the answer to a problem once posed by Isaac Asimov, when he observed that if all the matter in the Universe was once concentrated at a single point (just before the Big Bang), it would certainly be dense enough to form a black hole. Since nothing can ever escape from a black hole, we must still be inside it!

Here’s the first piece of the puzzle. You’ve all heard the now well-known view that the universe is composed of three spatial dimensions plus an extra time dimension. Few of us think intuitively in four dimensions, so to keep it simple, we tend to just ignore one or more of the spatial dimensions (which are all considered equivalent anyway). For instance, most people at some time or other have encountered life history charts like the following, which illustrates two particles (A and B) being in the same place, moving apart, and moving back together at a new position.

Most explanations of Einstein’s Special Relativity theory rely on similar diagrams. It’s all good old-fashioned cartesian co-ordinate systems. However, when you get into General Relativity, then everything gets rather murky. Einstein’s equations (which are today borne out by experiment) show that “space becomes curved” in the vicinity of a massive object. This has curious effects such as slowing down time, bending light beams and so on.

Because people generally can’t easily visualise what is meant by the curvature of space (after all, space is a vacuum, isn’t it, so how can it have any sort of shape?) popular science writers resort to analogies such as a rubber sheet suspended at the edges. Once again, this idea removes one of the three spatial dimensions to make the visualisation possible.

In this analogy, the flat rubber sheet (usually depicted with a rectangular matrix of grid lines on it) represents “flat” i.e. undistorted space. When a mass, such as a heavy ball bearing, is dropped onto the sheet, gravity pushes it downwards and distorts the sheet around it into a sort of inverted bell shape. If you roll another mass, such as a little ball bearing, across the sheet towards the large mass, it may fall down the funnel and be “captured” by the larger object. If it is moving fast enough, though, it will merely be deflected slightly by entering the larger mass’s region of influence.

The elastic distortion of a rubber sheet by masses under gravity can be modelled mathematically by the same set of equations as gravitational distortion of space itself. In the absence of friction, the behaviour of the small and large masses on the rubber sheet closely resembles that of free masses moving through space. The fact that they distort the space around them proportionately to their mass accounts for the effect we feel as gravity.

Intuitively, the larger the mass, the more it will distort the rubber sheet. It’s exactly the same in three-dimensional space. See the next illustration, which is meant to show an edge-on view of a small rubber sheet universe.

Note that the slope of the rubber surface becomes progressively steeper close to the mass itself. It is steepest at the edge of the mass – but further in, it flattens out again until at the very centre of the mass, there is no gravitational pull in any direction. Obviously, if the mass is dense then its edge (i.e. surface, in 3D space) will be closer to its centre and further down the slope. Therefore the denser the mass, the steeper the slope of the rubber sheet (i.e. the more curved the space) at its surface.

Now, there are some pretty concentrated masses out there in space. Some of them are so dense that the slope of the rubber sheet at their surface actually becomes vertical. These things are called black holes, and I’ll come back to them in a little while.

Now think for a moment. When considering the rubber sheet analogy, we blithely assumed that there was a third dimension, so that we could look at the sheet from above and below and see its distortion. Had we been two-dimensional creatures who were part of the rubber-sheet universe, we would have been able to see only the two spatial dimensions marked out by the grid lines on the sheet: we would have been unaware of the third dimension (except indirectly, if there were a two-dimensional Einstein to recognise that our two-dimensional space was somehow curved, causing the attractive effect between masses).

If real-world, three-dimensional space is curved in the way Einstein says, that means there must be a fourth dimension through which it curves. Four-dimensional creatures would be able to look down at our three spatial dimensions and see their curvature directly. Well, as I said at the beginning, there is such a fourth dimension: it is the dimension of time (the temporal dimension).

So far, so good. We are beginning to get an inkling why time dilation occurs when space is curved. I said before that the three dimensions of space are considered equivalent, i.e. interchangeable. There is not even any obvious X, Y, or Z axis to use as a reference line ­– all the equations work equally well if you use any arbitrary reference axis and make the other two axes mutually perpendicular with it. If you consider an arbitrary vector, it can always be resolved into X, Y, and Z components. If you rotate the reference frame, the same vector resolves to different components, but its magnitude and direction are unchanged.

The same is not true of the time axis! There is definitely something different about time. For instance, as many writers have noted, we cannot voluntarily move along this axis in either direction. The notion of rotating the reference frame makes no sense here: a vector in 3D space can never be resolved into some X, Y, Z, and T components.

So, time cannot be arbitrarily interchanged with the spatial axes. But as we noted before, if it is a proper dimension, its axis must be perpendicular to the other three. Therefore, to return to the rubber sheet analogy, the direction of time everywhere along the rubber surface is normal to it (perpendicular to the surface at any given point). The time vector may therefore point in different directions, depending where in the Universe you happen to be!

This has the consequence that, if we were both in the same rubber-sheet universe, I could look across the sheet at you and find your time axis pointing in a slightly different direction to mine. See the next picture.

Of course, the description I just gave is an external view of the situation. From within the rubber-sheet universe, I would first of all say that in the time it took for one second to tick past on your clock, nearly two seconds had passed in mine (see the dotted arrows). In other words, your time has “dilated”. Moreover, I would say that you look a bit squashed.

You, of course, would say exactly the same things about me. That’s what Relativity is all about.

Another piece of the puzzle is the well-known fact that the Universe is expanding. There’s a well-known effect known as the red shift, which was discovered by an astronomer called Hubble. Hubble’s constant is the number that relates how distant something is to the speed with which it is receding from the observer. This speed of recession causes light emanating from a distant source to drop in frequency, exactly the way in which the engine note of a bike seems to drop an octave as it roars past you, even though the note that the rider hears stays constant in pitch (in acoustics, this is known as the Doppler effect).

It is, incidentally, a little-publicised fact that very distant objects in the Universe have red shifts so enormous that they would have to be receding at four times the speed of light. This is of course impossible, but may be explained instead by the time dilation effect, assuming that the time axis at distant points in the universe is way out of alignment with ours.

The red shift is normally explained by the notion that the Universe is expanding, very rapidly, as a result of a primordial explosion known as the Big Bang. To my mind, that has never been a very satisfactory explanation – explosions only happen in real 3D space, where the resultant gases have some sort of pre-existing volume into which they can expand.

Astronomers have looked in vain for an “edge” to the Universe, which there would have to be if there were some sort of expanding shock wave centred on the site of the original explosion. The fact that the Universe looks uniformly the same in all directions suggests either the extremely unlikely explanation that we are slap bang in the middle (i.e. where the Big Bang actually occurred), or more likely, that there simply isn’t any edge. If there is no edge, then the Universe must be curved completely around on itself.

In the same way, ancient Mariners before Columbus expected to find an edge to the Earth if they sailed far enough to the West. We now know that the Earth is a globe, its surface being two-dimensional on a macroscopic scale and uniformly curved through a third to form a finite, closed surface with no edges. Does this begin to sound familiar?

Why should we assume any more complicated shape for the Universe, such as a torus, when a simple sphere will do? It would be entirely consistent with observations.

My theory then, which I think of as the Onion Model of the Universe, goes like this. The three spatial dimensions are all finite, yet without beginning or end – in other words they are curved around on themselves. The time dimension is measured (on a macroscopic scale) from the centre of the Universe outwards. If you ignore one spatial dimension, you could imagine a sphere which is growing over time, putting on layer after layer in the manner of an onion.

The past history of the Universe, like the sequence of inner layers of an onion, is fixed and immutable. The future could take many different potential shapes until it happens.

If you were able to follow the time axis backwards, you would be moving towards the centre of the Universe. What lies before the Big Bang? The question is meaningless – when you reach the origin in this co-ordinate system and carry on in the same direction, you start to move forward in time again but in a diametrically opposite part of the Universe. See the next diagram. It shows that a more appropriate co-ordinate system for the real Universe is not cartesian, but spherical polar, with time corresponding to the radius.

The distance along the circumference of a circle is related to its radius by the well known constant 2π. In other words, as the circle gets bigger, any two points on it will move apart at a constant rate. If you think about the Universe again, then as time increases, the circumference will inevitably increase – the rate of its increase being constant with time. The interesting thing is that astronomical observations seem to suggest that the rate of expansion of the Universe is indeed constant, to within the margins of observational error.

Another interesting result of this model is that the observable Universe must be less than half of the total. If you imagine a point 90 degrees away from you on the cosmic polar co-ordinate system, then its time axis will be perpendicular to yours – in other words, time (as seen from your position) would seem to be standing still. However, you can’t observe this: a photon emitted from there could never ever reach your position, because it will be travelling parallel to your time axis! At any position more than 90 degrees away from you, time would appear to be running backwards!

Of course, the Universe can’t be just a smooth sphere. Its distribution of matter is not uniform, and hence there are local regions of excess curvature. I visualise these as dimples in the surface – like the pores of an orange, or the craters of the Moon. Black holes are interesting in this context. The accepted theory is that the curvature of space near a black hole becomes so severe that the time axis points perpendicularly towards the centre of gravity. Thus an object close to a black hole will find itself carried (by time or by gravity, whichever way you look at it) towards the centre. The black hole is thus a sort of anti-Universe: the time axis points towards its centre rather than away from it! Presumably the point where all the time axes meet is the end of time (locally at any rate).

Another way of looking at this is using the rubber sheet analogy. It’s as if a ball bearing on the sheet were so heavy that it made an infinitely deep hole! In our spherical Universe, this would mean that the black hole tunnels back through the history of its region of space towards the origin of time! In fact, the mathematics of black holes show the time contour curving down towards the centre of gravity and beyond (see the next picture).

This paradoxical result of the mathematical equations has been interpreted as meaning that if you fall into a black hole in the right way, you could emerge at a totally different point in the Universe. In the onion model, I suppose this could be at the “antipodes” of the cosmic globe.

Supposing there were multiple Universes? Imagine rows of onions growing in a field. If they are close together, then there will come a time when they grow big enough to come into contact. If they are unable to move apart, then growth at the point of contact will stop. Assuming growth elsewhere continues at the constant rate, a flat spot will develop between the onions.

Translated to the real Universe, this would mean that time would come to a sudden halt all over a spherical region of space, which would rapidly expand like the flat spot on the onion. Its rate of expansion would gradually slow down as the edge of the stasis zone grows further from the original point of contact – it would never stop growing, yet the Universe as a whole would be growing faster. Thus the future of the Universe seems assured, unless of course there are many other Universes growing all around ours.

There are still some puzzles, though. One is the universally constant speed of light. If you visualise photons as wave-like disturbances on the surface of this cosmic sphere, then you get quite a good image of the way light propagates from one point to another (see the picture below, which illustrates a very small region of space so that its curvature is not noticeable).

What properties of the space-time continuum govern the rate of propagation of this disturbance? What happens to it as it gradually enters regions of space where the time axis points in a different direction? (I suspect that it becomes smeared out and its energy dissipated, resulting in a perceived red shift). I have an intuition that more powerful mathematics than mine are needed to get a grasp on the behaviour of a step-like disturbance in such a medium.

Mass itself would seem to be just such a step-like disturbance, but somehow it doesn’t propagate horizontally (at least, not at the constant rate that photons do). How come multiple particles can add up to a much greater curvature than one alone? As far as I’m aware, Relativity is a bit cagey on this question too. However, the notion that fundamental particles are nothing more than photons which continually bounce back and forth between tightly defined boundaries has some appeal.

To sum up, I think I have presented a view of the Universe which is elegant and simple, and which goes a bit further in explaining some fundamental observations than the existing ones. However, I have no doubt that it is a long way from being a complete and consistent theory.

I won’t go into the religious aspects of this view of the world, although I have thought about it. The mental picture of God as a cosmic gardener, tending His rows of onions, is quite amusing though.

Created Thu Oct 23 15:04:26 2003

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