“What Is The Universe Expanding Into?”

Steve, I wrote this with you in mind.

Yahoo Answers is, as I mentioned previously, about to die, although it’s a death by a thousand cuts. In the past I’ve used this blog to put more thoroughly thought-out answers to frequently-asked questions on the site, so I’ve probably addressed this before, but right now I have a different and perhaps less dogmatic take on this question than I usually adopt. Before I go on, I should probably insert the standard diagram people put in nowadays when talking about the Big Bang:

Strictly speaking, this diagram is inaccurate because it shows a two-dimensional projection of a three-dimensional model of a four-dimensional set of circumstances. Take the barred spiral galaxy at top right. If the X-axis is supposed to be time, we should be concluding that the left hand arm of that galaxy happens first, then the end of the right hand arm and the nucleus, and finally the middle of the right hand arm. Also, space is two-dimensional in this picture when for most practical large-scale purposes it really has three dimensions. In other words, this isn’t so much a diagram as an illustration intended to communicate the history of the Universe since the Big Bang. You can’t take it too seriously. It has an artistic, creative aspect.

One possibly inaccurate, because it isn’t really intended to be that accurate, feature of this diagram is the way it shows space. It’s a black rectangle into which the Universe is expanding. There is an outside to this Universe, and at that point you’d be forgiven for asking, if the Universe is everything, what’s the blackness outside it supposed to be? Why is that not also the Universe? The Jains, of all people, had an answer to this. They believed that the Universe as we know it was suffused with a substance which made movement possible, but was surrounded by infinite space from which this was absent. Nowadays, maybe we could do something similar with the idea of dark energy, the apparent force which causes the Universe’s expansion to accelerate. The above picture has a literal “bell end”. It flares out rather than widening steadily or perhaps slowing down from left to right. This is the influence of dark energy, as it represents accelerating expansion. I suppose it’s possible to think of the Universe as infinite space with at least one region where dark energy is active. However, this is neither how I think of it nor, as far as I know, the way scientists do.

Before I go on, I want to make a point about the nature of science at this scale. In certain circumstances, rational thought is “bigger” than science. Maths is one example of that. There’s plenty of pure mathematics which seems to have no practical application and even applied maths doesn’t need to be tested by observation if it’s proper pure maths. For instance, it’s a mathematical truth that any roughly spherical planet covered by an atmosphere must have at least two points on its surface where there’s no wind at any moment, although these points may move. However, our oceans needn’t have any points where there’s no current because there’s land on this planet. Likewise, a doughnut-shaped planet needn’t have any such locations, nor need any planet with at least two mountains high enough to stick up into the stratosphere. There’s no need to observe any planets to prove this because it’s a mathematical fact. I’m not entirely sure about this, but I suspect that cosmology may also have aspects of this: it may not be possible to approach the nature of the Universe entirely scientifically because there’s by definition only one example of the Universe and it can’t be compared to others. This is a particular view of the nature of the Universe which either includes the Multiverse as part of the Universe or in some way demonstrates that this Universe is all there is. There are a number of conceivable ways in which there could be other universes, but some of the arguments for it not only rely on logic and maths but also require that they cannot be observed even in principle. For this reason, without disrespecting the field, there’s a way in which cosmology cannot be scientific. James Muirden once said:

The Universe is a dangerous place – a sort of abstract wilderness embracing the worlds of physics, astronomy, metaphysics, biology and theology. These all subscribe to the super-world of cosmology, to which students of these various sciences can contribute. Strictly speaking there is no such person as a ‘cosmologist,’ for the simple reason that nobody can be physicist, astronomer, metaphysicist, biologist and theologian at the same time.

James Muriden, ‘The Handbook Of Astronomy’ 1964.

It isn’t clear though whether something which is outside the realm of science will always remain there, and in this view, it may be that there’s not in principle something imponderable about cosmology if the mind pondering it is sufficiently powerful, but simply that the span of disciplines is too broad for anyone to grasp. There certainly seem to be cosmologists nowadays, but maybe they’re cosmologians.

Although I don’t want to dwell on that, I do want to point out that it isn’t immediately obvious what space and time are. The nature of space in particular seems to depend on observation. It’s possible to doubt the existence of space but not the passage of time, since as far as we know we are disembodied viewpoints imagining the world but we can only do that imagining if time passes. This is in spite of the fact that spacetime is unified, so it isn’t clear how we’re immediately confronted with time but not space. Maybe there are more advanced minds in the Universe who experience both with the same immediacy. But there are, in any case, at least two different ways of thinking of space and this is what I usually based my answer on.

Space can be thought of as a thing or a relationship. That is, it could be understood as a container, as it were, in which objects are located, but also an object in itself. The Universe clearly is an object, but that doesn’t mean it’s made of space and studded with galaxies like spotted dick. There is a famous “balloon” analogy applied to space, which views the galaxies as spots on the surface which move apart from each other as the balloon inflates. This makes it sound like there’s a hyperspace into which the Universe is expanding, but this may not be the case.

In maths and physics, the concept of space is often used to make arcane ideas simpler. For instance, up, down, top and bottom quarks seem to refer to direction and location, but of course they don’t. They’re just called that to indicate that they are related to each other more closely than they are to other quarks. Likewise, we might talk about the temperature rising and falling, but that doesn’t mean there’s a spatial dimension called temperature. This can even be taken into the realm of space itself. We impose the idea of several dimensions on the idea of direction and temporal precedence, but there are reasons to suppose that this is mere convenience.

Suppose space is an actual thing. What would happen if there was a tear in it? It would surely mean that one could go into that tear, wouldn’t it? But how could that happen if there was no space there, since it’s torn? Does it mean anything to say that you can take a one metre sphere out of space? What happens when you move “into” it? How would it be different from a point? This suggests that there’s a flaw in thinking of space as the fabric of the Universe.

Consequently, space can be thought of as a combination of direction and location. Location can be described, more or less, using three numbers, although since there are higher dimensions this doesn’t work perfectly. It is, however, true, that relative to one’s current position a list of numbers is sufficient to describe where something else is. This tells you how far away something else is and in what direction. However, there is no absolute position. The Universe has no centre, or its centre is everywhere. This would also be true if space is infinite but it isn’t. However, as I’ve just said, space cannot have an outside, so how can this be?

The answer is that there is a maximum distance between two points, after which the direction between them reverses. This follows from the fact that the parallel postulate is incorrect: parallel lines do in fact meet at an enormous distance in most circumstances, and nearer than that in special circumstances to do with extremely high gravity. These are just properties of that group of qualities we refer to as space or spacetime, in a similar sense to addition working the same way either way round and subtraction not. When it’s said that space is expanding, all that means is that the maximum possible distance between two locations is increasing. That doesn’t imply that any actual object is expanding. A further clue to this being so is that although it’s impossible to travel faster than light, sufficiently distant objects do recede from each other at superluminal speeds. This would be impossible if space was an object unless the mass of such an object could only be expressed by a number on the complex number plane, but the distance between nearby locations increases at less than the speed of light, at a specific distance at the speed of light and at a greater distance greater than the speed of light. This is impossible for a single object because it would have to have real mass in small quantities, zero mass at the volume of the observable Universe and imaginary mass at greater than that volume. I have to say that’s an interesting set of properties and I’m not sure if it really is impossible.

The point is that in this view the Universe has no outside or, in terms of hyperspace, no interior. It clearly does have a three-dimensional interior, but not an interior in terms of a larger set of large dimensions. This account is slightly complicated by the fact that as well as time there are tiny further dimensions, but it usually makes more sense to measure the length of a pencil line than its area.

That’s an expanded version of my usual answer to the question “what is the Universe expanding into?” but it could be wrong. The reason it might be wrong is fascinating, and therefore probably not valid, but here it is anyway: ‘Brane Theory.

You might think at first that Brane Theory is just “Brain Theory” spelt wrong. That would be funny, but sadly it’s not so. Brane Theory is an extension of string theory and although I’m not afraid of maths, I can’t understand it fully. I’ve already mentioned the issue of extra dimensions which are, however, tiny. Brane theory uses this idea to explain why gravity is so much weaker than the other forces, if indeed it is a force. It isn’t immediately clear to observation, but there seem to be three major forces in the Universe plus gravity: electromagnetism, the strong force and the weak force. Of these, electromagnetism is obvious except that it may not be realised that light is part of electromagnetism. The strong force prevents atoms other than hydrogen from exploding as soon as they form, since their nuclei are made up of positively charged particles which repel each other. The weak force is a bit more obscure, and might be better described as the weak interaction because it doesn’t involve attraction or repulsion. It amounts to a tiny force field which occurs when radioactive decay involves atoms emitting beta particles, which are fast electrons. When a nucleus releases an electron, because it’s negatively charged and there are no negatively charged particles in the nucleus, a neutron becomes a proton, or the nucleus emits a positron and a proton becomes a neutron. In the former case it means the element moves one place up the periodic table. But nothing is pushing or pulling, which makes it confusing. The strong and weak nuclear forces are very small scale in their range, only operating within atomic nuclei, and for some reason the strong nuclear force is 128 times weaker at double the distance. Electromagnetism is more straightforward, probably because we experience it ourselves directly and obviously in the form of light, current, magnets, compasses, lightning and so on, and it diminishes like gravity, following the inverse square law. That is, for example, a light source emitting light all around it such as the Sun will do so in a sphere and because a sphere twice the size has four times the volume, it will be a quarter as bright from twice as far away. Gravity may not even be a force at all, but the distortion of spacetime by mass, and is anomalously weak. A magnet can pick up a piece of iron against gravity even if the magnet only has a mass of one gramme, yet Earth’s mass is nearly six quintillion (long scale) times the mass of the magnet. That’s ridiculously weak.

Brane theory, at least sometimes, attempts to solve the problem of gravity being as weak as it is by using extra dimensions. Instead of exerting a force in three-dimensional space, gravity may be doing so in hyperspace, which means that instead of weakening due to the geometry of a sphere, it does so due to the geometry of a higher, multidimensional cousin of a sphere, but the other forces are confined to three-dimensional space, in a thin membrane, hence the name “Brane Theory”, which is of course expanding in hyperspace. It’s also theorised that just after the Big Bang, in the part of the above diagram labelled “inflation”, this Universe collided with another one, causing this inflation.

So in other words, perhaps it isn’t a silly question to ask what the Universe is expanding into. This still doesn’t require space to be a thing, but makes the galaxies and stars into a thin, three-dimensional skin on a four-dimensional or multidimensional bubble. The answer is therefore possibly that the Universe is expanding in hyperspace, which is also not a thing but a way of describing distances and directions which need more than three numbers relative to where you are.

A few bits and pieces I want to clear up. This might all be thrown up in the air by the recent discovery of the way muons precess, because that suggests that the standard model of particle physics is wrong. And finally, I may have got this wrong myself. That is, what I just said might turn out to be nothing like what Brane Theory actually is. But note this: it’s maths and I’m not afraid of it. Lots of people are afraid of maths, and think they’re no good at it. I may well also be no good at maths, but I’m not afraid of it. This is a tangential point but very important, and probably has more bearing on everyday life that Calabi-Yau manifolds and stuff have anyway.