9375

A common image used to explain the idea of the Universe expanding is of a balloon inflating, with the skin of the balloon representing space.  The balloon is covered in dots representing galaxies and as the balloon inflates, the galaxies recede from each other.  To an ant standing on one of the dots, everything is receding and she appears to be at the centre of the Universe.  Extending this image to the real Universe, rather than there being two dimensions across the curved skin of the balloon, there are three, but the constant recession of galaxies from each other would still be observed.

There are some other similar images used elsewhere in physics.  One of these is the idea that most of the eleven dimensions making up the Universe according to string theory are “rolled up”, so space is in fact “thicker” in these extra dimensions than it seems, but still so thin that we fail to notice these other dimensions directly.  A further image is of space as an elastic sheet with mass causing depressions like a weight on a sheet of rubber, used to explain gravity in general relativity and linked to the balloon image above.

Like any metaphor, these images have their limits and beyond them they can become misleading.  In the case of the balloon, there is a misleading idea of a pre-existing hyperspace into which the Universe expands.  Whereas this might be so, the general relativity and the Big Bang theory don’t require it to be looked at in this way.  There need not be such a space and the Universe need not have an inside or an outside for this to work.  The reason for this flaw is the nature of the concept of space.  Space is not a container for objects but a set of relationships between them.  Looking at space as if it’s some kind of vast ocean of infinitely subtle substance in which physical objects float is erroneous.  Granted, it may be that space is entirely permeated by something tangible such as the Higgs Field or virtual particles, but the existence of space does not depend on this being so.

Space can be considered as an abstraction of two relationships somewhat like temperature.  Although there is a temperature scale on which items such as the boiling point of water or the transition temperature of helium to a superfluid can be placed, there is no physical object called “temperature”, though there could be physical scales or devices for measuring temperature.  Not would it generally make sense to refer to something as being outside the temperature scale, but simply as something to which the concept of temperature does not apply, such as the number seven or the experience of fascination.  Similarly, the balloon in the image lacks an interior and an exterior, and in a sense even a surface.

The physical qualities of an object or event can be further sophisticated with respect to temperature.  For instance, the boiling points of liquids tend to go up with pressure.  Pressure could be introduced as another axis on a graph of physical properties, showing things like the boiling point of water at the top of Mount Everest or on the shores of the Dead Sea.  Salinity could constitute a third dimension here.  However, there is no real plane or volume where these events or points are located.  Nobody would seriously suggest there was.

Space is similar.  It appears to express two things:  direction and distance.  It is convenient to talk about locations as if they are physical, but points in space are more like “gunpoint” than “Gibraltar Point”.  They are not literally located within the largest possible physical object named “Space”.

Consider the following three thought experiments:

1. Everything in the Universe shifts one metre in the same direction.

2. The Universe is completely empty.

3. A sphere of space one metre in radius is scooped out of the Universe somewhere.

All of these three experiments are meaningless on closer examination, but would mean something if space were a physical object.  In the first place, there is no way to ascertain that such a shift had taken place, assuming inertia and momentum would not apply, because there would be no way to measure the shift.  The same is true of the second thought.  An empty Universe contains no rulers, sextants or protractors.  If it contained a ruler and a sextant alone, space could be defined in terms of those two items but there are other conceivable worlds containing, for example, two identical featureless spheres, which have distance but no direction and therefore no space.  Are there possible worlds with direction but no distance?  I don’t know.  The final example indicates that there is something wrong with thinking of space as a thing, although it also happens to be the closest of the three to having a meaning.  If space is a thing, scooping out a sphere is for some reason immediately followed by it “growing back” instantly.  Also, this sphere which is scooped out is somehow able to occupy the same space as another bit of space.  Higher dimensions are not a solution to this – simply imagine a hypersphere.  Having said that, there is a sort of sense to it because it could be taken as an outlandish way of describing moving everything in the Universe a metre closer centred about a particular point, assuming that the sphere is empty.  If it isn’t, the objects within the sphere would have to relocate to their antipodes on the surface of a sphere of the same radius as the distance to the centre of the sphere.  Also, this account assumes Euclidean space.

All of these are important because they show the shortcomings of a view of space as a physical object shown by the balloon metaphor.  I’m not suggesting for a moment that they were intended seriously, or for that matter that the theories behind the images are true or false, but taking them that literally gets you nowhere and is misleading, except to illustrate that space is an abstraction of relationships and not a “thing”.

It so happens that an expanding Universe is a good way to illustrate the relational nature of space, even if the real Universe is not expanding.  It also happens that the Creationist hyperbolic model of space works equally well, but i don’t really want to go there.

At first glance, on the scale on which humans are accustomed to thinking, the distance between two objects simply varies between zero and infinity, that is, it has no upper limit.  The Big Bang theory claims something different:  that at any point in time, there is a finite maximum distance between objects, that that distance has been increasing for some time now and that any two objects surround each other in all directions.  The expansion of the Universe is simply the increase in the maximum possible distance between two objects.  There could be variants.  It might be that the maximum distance will begin to decrease, that its rate of increase will slow or that it was decreasing in the past.  One thing, however, it definitely does not claim is that the Universe is literally expanding into a pre-existing hyperspace (although i suppose it might be).

What’s not clear about this, intriguingly, is whether distance and direction are all that space expresses.  There might be other things involved.  It isn’t clear whether two separate locations can be at the same distance and direction from a third without being in the same place.  It might be, however, that such a situation would entail that space is not simply an abstraction of relationships, which would imply that it is in fact not possible.

So to imagining that notorious moment when the Earth was wrapped in bandages.  Possibly a good idea if we think we are hurting the planet, but anyway, the idea is this:  if you could somehow produce a strand of stationary massless bandages of any length you wanted and proceed to wrap them around Earth evenly, and assuming the Universe was otherwise empty, you would have surrounded yourself in bandages and be in the process of reducing the maximum distance at that time between the surface of the bandages.  If the Universe turned out to be expanding more slowly than the rate at which the layers of bandages were being laid down, you would eventually find that you were inside a hollow, gradually shrinking ball of bandages rather than outside them.  This can be made sense of thus:  everything is in all directions from everything else – in other words it surrounds everything else – and there is a finite maximum distance.

Eventually, the only way outwards is inwards.