Sodding Phosphorus!

Here is a sample of the aforesaid element:

Phosphorus has two main forms, or allotropes. When first extracted, it’s white and extremely toxic. The form illustrated above is red phosphorus of course. Left to itself, white phosphorus gradually turns into its red form, which is why the so-called “white” allotrope usually looks yellow:

By BXXXD, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=1096986

This is not, however, supposed to be “all about phosphorus”. Rather, it’s about two issues which affect the element, both to do with life, one on this planet and one in the Universe generally.

I’ll start by explaining the importance of phosphorus to life as we know it. There are six elements making up most of the body of a living organism on Earth. These are carbon, hydrogen, oxygen, nitrogen, sulphur and phosphorus. Carbon is important because it can form chains and rings from which complex molecules can be built. It’s notable that even though silicon is far more abundant on this planet than carbon, life is nonetheless carbon-based. This is to do with things like carbon’s ability to link itself into chains, form double and triple bonds with other atoms, the fact that its atoms are small compared to silicon and the difficulty of getting silicon out of molecules such as silica which may be formed as a result of any putative biochemical processes. Carbon dioxide, the analogue of silicon, is a gas at fairly low temperatures and can be incorporated into other structures. It so happens that I do think silicon-based life is possible, but it would have to be created artificially and exist in some kind of closed environment whose contents were carefully selected. The chances of silicon-based life arising without intelligent intervention are very low. The greater terrestrial abundance of another element should be considered again here, but not right now. Hydrogen and oxygen are of course the constituents of water, a compound which is really unusual in many ways, such as its unusually high melting and boiling points on the surface of this planet, its ability to dissolve other compounds and the fact that it gets less dense as it cools below 4°C. These properties mean respectively that the chemical reactions needed for life as we know it can occur at a temperature where there’s enough energy for them to take place but not so much that they’d be unstable, that the compounds are in a liquid medium conducive to reactions in the first place and that the oceans, lakes and rivers don’t freeze solid from the bottom up. The two constituents are useful in their own right. Oxygen and hydrogen are components of countless compounds, including carbohydrates, amino acids, proteins and fats. Oxygen, unlike chlorine which has been considered as a possible alternate breathing gas for alien life, can form two bonds, meaning that it isn’t the dead end single-bonding atom which the halogens are. Nitrogen is a essential component of protein via its presence in amino acids. Amino acids have a carbon connected to a carboxyl group and an amino group, which can bond together to form chains, and a functional group such as a benzene ring or a sulphur atom which can have other biological functions. Proteins, in other words. There are also chemicals called alkaloids which occur mainly in plants and vary a lot, which have striking pharmacological effects, and the nucleotides are also rings containing nitrogen, encoding genes in DNA and RNA. Nitrogen is actually so reactive that it bonds strongly to other atoms, including other nitrogen atoms, and consequently it’s vital that various organisms can uncouple it and combine it for the benefit of the rest of the biosphere. This is known as nitrogen fixation and is performed mainly by bacteria and certain plants, and also by lightning, but if life had to rely on lightning to do this, it would not be widespread and nitrogen fixed by lightning would be the limiting factor in global biomasse. Sulphur is significantly found in a couple of amino acids and allows proteins to form more complex shapes as are needed, for example, by enzymes and hormone receptors, because they form bridges with other amino acids making the molecule tangle usefully together. It’s also found in hair, nails and various other substances such as the substances responsible for the smell of garlic and onions. Sulphur is actually a bit of an exception in the chief elements required for life because sometimes it can be substituted by either selenium or tellurium, and there are amino acids which have these elements in sulphur’s place, but both of them are much scarcer than sulphur.

Then there’s phosphorus. Phosphorus has more limited functions than the others but these are incredibly vital. It forms part of adenosine triphosphate, which organisms use to transfer energy from respiration to the other functions of the body. It also forms part of the double layers of molecules which form membranes and allow controlled and specialised environments to exist in which the chemical reactions essential to life take place, and also enables substances to be packaged, as with neurotransmitters. Thirdly, it forms the strands of sugar phosphate which hold DNA and RNA together, so even if it didn’t do anything else, some kind of method would have to exist to store genetic information. This is perhaps the least vital role though. A more restricted role is found in most vertebrates, in that it forms part of the mineral matrix of bones and teeth, but there’s plenty of life that doesn’t do this and the usual substances used to make hard parts of animals are silicates and calcium carbonate, among other rarer examples such as iron pyrite. Nonetheless, humans need phosphorus for that reason too, as do our close relatives. However, even the closely related sea urchins use calcium carbonate instead.

Hence several facts emerge from all this. One is that an apparently similar and more abundant element can’t necessarily be used for a similar function, assuming here that life can start from scratch. Another is that elements can get themselves into such a strongly bound state that it would take too much energy to use them for it to be worth it for life. A third is that life will sometimes substitute another element for the one it usually employs if it can. If a rare element is used, there’s usually a good reason for it.

Now the first problem with phosphorus is that it’s much more abundant inside a living thing than in its non-living environment, and the cycle that replenishes it is very slow. Phosphorus usually becomes available to the biosphere on land as a result of continental drift, the formation of mountains and erosion and weathering, and it’s lost to the land when it’s washed into rivers and the sea, where it disappears into sediment before becoming available again millions of years later. In the sea, it’s less of a problem but still a significant one because it’s only available to life as phosphates and it’s often found as phosphides instead. Ironically, there’s also an overabundance problem with phosphates in fertilisers being washed into bodies of water and leading to algal blooms, which can in fact be of cyanobacteria rather than algæ as such. Since some microörganisms can produce extremely powerful toxins, this can lead to massive marine die-offs and contaminated sea food. Where I live, a nearby reservoir was afflicted by an algal bloom and had to be closed off for quite some time, and this can also poison wildlife on land. These can also lead to high biochemical oxygen demand, which is where all the oxygen gets used up and the water becomes anoxic, which is incidentally a cause of mass extinctions, though on a much larger scale, in the oceans. This happens because phosphorus is relatively scarce and a significant limiting factor in how much life is possible in a given area, so a sudden influx of usable phosphate is likely to cause a chemical imbalance.

The Alchemist Discovering Phosphorus, Joseph Wright, 1771 and 1795.

This painting is thought to refer to the discovery of the element by Hennig Brand in 1669. Brand discovered it when searching for the Philosopher’s Stone, by heating boiled down urine and collecting the liquid which dripped off it. It turns out that this is actually quite an inefficient process and it’s possible to extract a lot more of the phosphorus by other means. The allotrope illustrated in the painting is unfortunately the highly toxic and dangerous white variety, so the alchemist is putting himself in peril by kneeling so close to the retort. The point to remember in all this is that phosphorus is found in urine, not in huge amounts but enough. This points towards a particular problem, highlighted by Isaac Asimov in his 1971 essay ‘Life’s Bottleneck’, which points out that humans “may be able to substitute nuclear power for coal, and plastics for wood, and yeast for meat, and friendliness for isolation—but for phosphorus there is neither substitute nor replacement”. Urine goes down the toilet and is flushed into the sewers, processed in sewage farms and the phosphorus from it ends up in the sea. It does gradually return to the land in biological ways. For instance, a seagull may die on land and her bones may become part of the terrestrial ecosystem, or she might just poo everywhere and return it that way, but the occasional gull or tern conking out in Bridlington is no compensation for millions of people flushing the loo several times a day. By doing this, we are gradually removing phosphorus from the land and returning it to the sea, whence it won’t return on the whole for millions of years.

Two ways round this suggest themselves. One is to eat more sea food. For a vegan, this is unfeasible and in any case fishing causes a lot of plastic pollution and is unsustainable, but of course it is possible to eat seaweed, and I do this. The other is not to allow urine into sewage in the first place or to process sewage differently. I have been in the habit of dumping urine in the garden, although I haven’t done this as much recently. It also contains potassium, and in particular fixed nitrogen, so in diluted form it is indeed useful for raising crops. However, this is on a small scale and a better system might be to process the sewage differently and put it on the land, being careful to ensure that harmful microbes and medication have been neutralised before doing so. Regarding seaweed, dulse, for example, is 3% of the RDI of phosphorus by dried weight, compared to the much lower amounts in most fish. Cuttlefish is the highest marine animal source. Human urine averages 0.035%, so you’d have to eat a lot of seaweed. However, in isolation, if you don’t, there will be a constant loss of phosphorus to the land. Guano is one solution, but not ideal and only slowly renewable.

The other problem with phosphorus follows from the same scarcity and the same use in living systems, but is more cosmic in scale, and I personally find it more worrying: phosphorus is rare on a cosmic level. In a way, all atomic matter is rare in this sense because the Universe is, as the otherwise really annoying Nick Land once said, “a good try at nothing” (apparently nobody has ever quoted that before, so that’s a first!). The cosmic abundance of the different elements looks like this:

The Y axis is a logarithmic scale, so for instance hydrogen is about ten times as abundant as helium and even in terms of mass is more common than any other element except helium. One notable thing about this graph other than the clear rapid decline in abundance with atomic number (the X axis) is that it zig-zags because even-numbered elements are more frequently found than their odd-numbered neighbours. This is because many elements are formed by the collision of α particles, which consist of two protons and two neutrons. Phosphorus is flanked by Silicon and Sulphur on here, though it isn’t specifically marked, and its atomic number is fifteen, i.e. an odd number. Chlorine, which is quite common in living things because it’s part of salt, is less common still.

Elements are formed in various ways, and this relates to how common they are. The Big Bang led to the formation of mainly hydrogen and helium a few minutes later, as soon as the Universe was cool enough to allow their nuclei to hold together and their nucleons to form, although they would’ve been ionised for quite some time rather than being actual atoms. Small amounts of lithium and beryllium formed in the same way, and if the graph is anything to go by this looks like it might’ve been the main way beryllium in particular formed. Then the stars formed and the pressure inside them led to helium nuclei in particular being pushed together to form heavier elements. The crucial step in this phase is the formation of calcium when three helium nuclei collide. Then, a number of other things happen. The star may end up going supernova and scattering its heavier elements through the local galactic neighbourhood. It may also form new elements in the process of exploding through radiation. This was until fairly recently thought to be the main means heavier elements were formed, but another way has recently been discovered. When a star not quite massive enough to become a black hole collapses, it forms into what is effectively a giant atomic nucleus the size of a city known as a neutron star. When these collide, they kind of “splat” into lots of droplets. Neutrons are only stable within atomic nuclei. Outside them they last about a quarter of an hour before breaking down, and they often become protons in doing so. This means that many of the neutronium droplets form into heavier elements, which are then pushed away by an unimaginably powerful neutrino burst from the neutron stars and again scattered into the galactic neighbourhood. Two elements, beryllium and boron, are mainly formed by cosmic rays splitting heavier atoms. Some, particularly transition metals such as chromium and manganese, formed in white dwarf stars which then exploded, and technetium along with all the heaviest elements, have been generated by human activity.

At first, the abundance of phosphorus didn’t seem to be a big problem. However, after studying supernova remnants, scientists at Cardiff University seem to have found that there is a lot less produced in supernova than had been previously thought. This means that phosphorus is likely only to be as common as it is here in this solar system in star systems which formed near the right kind of supernova to generate it in relatively large amounts. Couple this with the essential function of phosphorus in DNA, RNA, membranes and ATP, particularly the last, and it seems to mean that at this point in the history of the Universe, life as is well-known on Earth is likely only to be found in initially localised areas, surrounded by vast tracts of lifeless space. The systems containing life would gradually separate and spread out through the Galaxy due to the migration of the stars as they orbit the centre of the Milky Way, but they would remain fairly sparse. However, as time goes by and the Universe ages, there will be more such supernovæ and phosphorus will slowly become more common, making our kind of life increasingly likely. If life always does depend on phosphorus, we may simply be unusually early in the history of the Universe, and in many æons time there will be much more life. This possible limitation may have another consequence. We may be living in a star system isolated from others which are higher than average in phosphorus, meaning that to exist as biological beings with a viable ecosystem around us elsewhere, we would either have to take enough phosphorus with us or make our own, and even the several light years between stars which we already find intimidating is dwarfed by the distances between phosphorus-rich systems in the Galaxy, which may once have been near us but no longer are, and not only do we have to schlep ourselves across the void, but also we have to take a massive load of phosphorus with us wherever we go.

But that is biological life as we know it. A couple of other thoughts occur. One is that there could conceivably be life as we don’t know it. This doesn’t work as well if the substitution of phosphorus is the main difference, because if that could happen, it presumably would’ve happened with us, and it didn’t, because other elements with similar functions would’ve worked better if they were more abundant and out-competed with the life which actually did arise unless there’s something about this planet which does something else like lock the possible other options away chemically or something. However, there could just be drastically different life, based perhaps on plasma instead of solid and liquid matter on planets and moons, which has no need for phosphorus or even chemistry, on nuclear reactions taking place between nucleons on the surface of a neutron star as suggested by Robert L Forward’s SF book ‘Dragon’s Egg’, or even nuclear pasta inside neutron stars. Maybe it isn’t that life is rare in the Universe, but that life as we know it is, partly because it needs to use phosphorus.

There is another possibility. We are these flimsy wet things crawling about a planet somewhere in the Galaxy, but we’ve also made machines. In our own history, we are the results of genes, and perhaps also mitochondria and flagella, concealing themselves inside cells and proceeding to build, through evolution, relatively vast multicellular machines to protect themselves. Maybe history is about to repeat itself and we are going to build our own successors, or perhaps symbionts, in the form of AI spacecraft which go out into the Universe and reproduce. Perhaps machine life is common in the Galaxy and we’re just the precursors. There is an obvious problem with this though, mentioned a long time ago: what’s to stop swarms of self-replicating interstellar probes from dismantling planets and moons and making trillions of copies of themselves? If this arises through a mutated bug in their software, it would be to their advantage, and they could be expected to be by far the most widespread “life” in the Universe. Yet this doesn’t seem to have happened. If it hasn’t, maybe the beings which built these machines never existed either. Or maybe they’re just more responsible than we are.

It Might Be Nothing

I don’t know how long this is going to be because it’s a bit of a thought dump, which actually everything on here is supposed to be, so this is actually more in the spirit of the intention of this blog than usual, to some extent. Then again, most of what I put on here is a bit like that – unstructured stream of consciousness stuff with a small readership.

But someone has said something which has made me think, and I was already thinking about this. They were concerned that they might be a figment of the imagination.

Let’s start from the beginning.

Everything used to be in the same place. Then something happened and things started being in different places. Supposèdly, anyway. This was the Big Bang. I’ve just come out of the other side of a phase of not believing in the Big Bang but now I think it probably did happen because it was preceded by a infinitely long period of time going backwards. The reason I didn’t believe in the Big Bang was that given that time is eternal and the conditions of the Big Bang can arise spontaneously by quantum events at any time, very improbably, the chances of being within measurable distance of the beginning of the Universe are zero. This is, incidentally, not the same as impossible. Infinitely improbable events happen all the time. If someone were to flip a coin forever the sequence of heads and tails they produce would have a probability of zero but it would have to be a particular sequence, and the Universe, in some places, does kind of consist of a figurative coin being flipped forever in the sense that there are random quantum fluctuations. However, there are infinitely more of these random fluctuations than the actual event they mimic, so you can be certain that we are not near the beginning of the Universe. However, the idea that we are in a habitable period of the Universe’s history is entirely different. In this case we’re not near the beginning, just near an event following the collapse (backwards expansion actually) of the Universe followed by a Big Bang, which probably happens a lot. This is fine because it eliminates the possibility of us being infinitely special. We’re just living in the period where it’s possible for us to exist instead, and so now I kind of believe in the Big Bang again.

Yesterday I mentioned cosmic strings. Since I’ve only just said what they are, or what I think they are, I’m going to go into that again just briefly this time. Cosmic strings are basically wrinkles or cracks in space which didn’t collapse down to the three dimensions we’re familiar with nowadays but stayed more like the early Universe, and as such are either very massive or very “anti-massive” and tend to warp space. This depends on string “theory” because of the extra dimensions, or rather it’s related to it. This made me wonder if it’s actually more than this. I should point out here that this is now just me, a philosopher and herbalist, thinking and not a physicist.

Up until I was thirteen, I used to believe that fermions were tiny vortices in space time, and that bosons, including light, were gravitational waves. Just to explain that briefly, bosons carry force and fermions are stuff, such as protons, neutrons and electrons. This happens to be similar to a nineteenth century theory of atoms that they were vortices in the æther, which was the medium believed to carry light. At this time, I seemed to have been assuming that space was a thing rather than a relationship, because presumably if something could swirl about it had to be something.

I was at some point disabused of this model by my physics teacher. Incidentally, to get a bit home-eddy (geddit?), this was the same physics teacher who inadvertently killed my interest in physics after an optics lesson about refractive indices, which by that point I’d known about for more than half my life, when I asked him why anything was transparent and he said “you don’t need to know that at O-level”, the problem being that he was of course constrained by time and resources to teach O-level physics and was therefore unable to help me pursue my highly motivated curiosity. Nowadays I still have no idea why some matter is transparent and some opaque. It would make sense to me if everything was opaque or everything transparent, and I can to some extent understand translucency, but I don’t understand why there’s a difference. Also, I only understand structural colour. I get that some atoms absorb or emit certain wavelengths of electromagnetic radiation when their electrons change energy level, but beyond that I get stuck. This has been going on for more than three dozen years now and it really bugs me sometimes.

It’s important to be aware of the patterns one’s mind tends to fall into because of how it’s predisposed to function. For instance, as a child I used to have a habit of trying to imagine two-dimensional phenomena in three or more dimensions. This initially gave me a frisson of intellectual superiority but after a short while I got worried that I was falling into a rigid mental tendency in this area. This, of course, was the mind of a nine year old child, so perhaps it reflects a developing brain rather than some ingrained issue. Nonetheless, it’s helpful to be suspicious of one’s own thought processes and try to step outside them sometimes, although literally speaking that’s impossible as one is still having thoughts about having thoughts. But it’s about self-awareness, and that’s definitely important. I bring this up because what I’m about to say seems quite like my childish vortex notion of matter.

Cosmic strings are supposed to be pinched-up wrinkles in space. They form into loops when they intersect with themselves, so presumably by now there are loads of looped strings around the Universe formed from former strings, and for all I know they also merge and become bigger strings or loops once again. But also, I couldn’t help thinking that these enormous strings, some gigaparsecs long apparently, really sound like superstrings, and that maybe at some other juncture in the early Universe after the Big Bang space was just really scruffed up and wrinkly, and this led to the formation of elementary particles, perhaps as different knots or maybe vibrating at different rates, which were nothing other than really tiny cosmic strings or loops. I would like to believe that this is what string theory is, but to be honest I have no idea at all other than the stuff in my own head, so I dunno, maybe. Little loops of vibrating multidimensional space?

I am purposely avoiding doing any research for this post. I’m as interested in the process giving rise to my thoughts, and therefore those of other people, as I am in the ideas themselves here, and I don’t want to set off the “someone else’s idea” alarm, so I’m not reading up on this right now.

What is the nature of space-time? Space stops everything from being in the same place and time stops everything from happening at once. There are other ways of measuring things based on space and time, such as temperature and weight. The absolute temperature scale begins at the lowest possible temperature, and it works like this. It was discovered that at the freezing point of water a gas had a particular volume, which was 1/273 smaller at -1°C, 2/273 smaller at -2 and so on, so the question arose, what happens at -273? It’s actually -273.15, but that would involve more accurate measurement than was possible at the time. The answer is quite simple. It always takes the same energy to reduce temperature by a certain proportion, or alternatively, the same energy is always lost when temperature goes down by the same proportion, so reducing temperature from 100°C to about -86°C, which is halving the temperature from 373 to 186.5 above absolute zero, takes as much energy as reducing it from -273.14°C to -273.145°C, so absolute zero can never be reached. Hence there are no negative absolute temperatures. Not every quantity measured can be negative. Mass might be an example of this. Nonetheless it makes sense to think of temperatures as located along a line, and the differences between them as measured along this line. After all, that’s what a thermometer is. Likewise with weight and a spring balance, the weight of an object is measured along a line. We abstract these quantities in terms of a dimension.

(Honest units on the left, pretend ones on the right)

(Honest units on neither side but left slightly more sensible than right)

Now a ruler could be the same kind of device, as could a protractor. They measure something, but that doesn’t make that thing any more of a “thing” than temperature, weight or pressure. Length, width and breadth are quantities along with direction, and from those we abstract the idea that there is a “thing” called space, and likewise from clocks, stopwatches and calendars we abstract the idea of the quantity we measure with those into a “thing” called time, and of course the two are related, and they do exist, but maybe they’re not things.

Why would it be a good idea not to think of space-time as a thing?

There’s a question which seems to betray a misunderstanding of the nature of space and time yet is constantly asked: what is the Universe expanding into? The reason this question gets asked is probably due to the idea of the expanding Universe being illustrated as an inflating balloon, which makes it sound like there is a larger, higher dimensional hyperspace into which the Universe is expanding. I’ve long maintained that this isn’t so. In fact the idea of the expanding Universe is that the maximum possible distance between two points is always increasing, and that beyond a certain distance the direction of an object reverses. This is true on a spherical surface if you think of it as flat, but for different reasons, so for example the maximum possible distance between two locations on Earth is (almost by definition) 20 000 km, and if you are on the equator and someone else near your antipodes is walking West, they will be East of you once they pass it. In the case of the Universe, however, it’s a property of space implied by geometry not being Euclidean and space is not a “thing” in the same way as Earth’s surface is. Consequently, although the Universe seems to have the topology of a hypersphere, there is no geometrical real hypersphere corresponding to that topology.

Or so I thought. I should point out that not everyone thinks this way. There is a thing called “‘brane theory”, where “‘brane” is short for “membrane”. According to this theory, there really is a hyperspace in which this universe and many others are expanding, and when they touch and cross each other new universes are made. Incidentally you should check that – I’m not looking anything up for the purposes of this exercise, but I think that’s what brane theory is. It’s also an amusingly similar word to “brain”, which is an intrinsically funny word. If brane theory is correct, that really is what the Universe is like and space is actually a thing.

Now to get back to superstring theory, which I admit I may have got completely wrong. If particles are superstrings, and superstrings are topological defects in the same way as cosmic strings are, then all matter is, is swirly bits of space, and the problem with that is that if space and time are not really “things”, there’s nothing to swirl and nothing to be anywhere or happen at a particular time, and there just is no time or space. So, huh? Does this mean that space-time is actually a thing, or just that I have misunderstood superstrings? Or, does it mean string theory is flawed? Probably not the last one.

With Strings Attached

Time and faster than light travel have for a long time been thought impossible. Before Einstein, nobody realised there was a cosmic speed limit so the issue of travelling at any speed would’ve been considered merely a problem of giving something enough energy to force it to do so. This was ultimately proven wrong due to a chain of reasoning beginning with the observation that light travels at the same speed in a vacuum regardless of how fast an observer is moving. As for time travel, this has existed as a literary trope for centuries, in the form of visions and dreams of the future or sleeping for a long time. Even the Bible has time travel in a sense, because it has prophecy and the resurrection. I’m personally inclined to regard dreams as not anchored to our own perception of the passage of time and am aware that they are sometimes precognitive. That is, I don’t just speculate that they might be: I assert that people have dreams which predict the future. I don’t know exactly how that works but a true sceptic will accept an incontrovertible fact and look for an explanation. K-skeptics will often deny facts if they don’t fit theories.

It took a long time for literature to get round to imagining time travel into the past rather than the future. H G Wells had his time traveller go into the future and report back, but although he is speculated to have gone into the past and disappeared permanently from the nineteenth Christian century, and the narrator speculates thus:

It may be that he swept back into the past, and fell among the blood-drinking, hairy savages of the Age of Unpolished Stone; into the abysses of the Cretaceous Sea; or among the grotesque saurians, the huge reptilian brutes of the Jurassic times. He may even now—if I may use the phrase—be wandering on some plesiosaurus-haunted Oolitic coral reef, or beside the lonely saline lakes of the Triassic Age.

H G Wells, ‘The Time Machine’, 1895

The very obvious big problem with upstream time travel is that it appears to cause paradoxes, that is, one can kill one’s own ancestor. There is a related paradox that one can take an item from the present day and leave it in the past, so that it becomes token-identical with it and has no origin, but these are really the same problem. However, there is a startling oddity regarding upstream time travel and physics which is not present with faster than light travel: nothing seems to rule it out in principle. There are practical difficulties in building time machines but they don’t appear to rely on problems related to time travel itself. It’s as if the problem with travelling faster than light were to do with sufficiently streamlining a spacecraft because space was filled with a tenuous gas rather than it being a fundamental issue with the nature of reality, but at first glance the idea of travelling faster than light seems less problematic than going backwards in time.

There may also be a close connection between the two problems. I’ve also failed to state the exact issue with travelling faster than light, because in fact there is nothing stopping an object from moving at the speed of light or even faster than it provided certain properties of an unusual nature are physically possible. What is impossible is for any object currently moving slower than light to reach the speed of light, any object currently moving faster than light to decelerate to the speed of light and any object currently moving at the speed of light to accelerate or decelerate. This is not the same thing as it being impossible to move faster than light. There are also a few anomalies that suggest superluminal travel, such as the fact that when a particle moves through barriers their location is “blurred” such that the time taken to travel the distance has a low but not zero probability of being ahead of where it would be if it had moved at the speed of light from its previous location, and there are jets emitted from galaxies which seem to move faster than light, although that’s an optical illusion caused by foreshortening, because the speed of light is finite and a fast jet approaching us will be visible earlier than expected due to the shorter distance travelled by the light leaving it.

Before I get going on the other bit, I want to make an observation which I’m sure can be explained in accordance with relativity but whose explanation I’m unaware of. As an object accelerates, it becomes foreshortened in the direction of movement and increases in mass. I would expect a sufficiently foreshortened and massive object to be smaller than the size required to make it a black hole, which would then warp space. If this happens, what stops objects near the speed of light from opening wormholes in space and slipping through them faster than light? I can’t have been the first person to have thought of this so I presume there’s an answer. I just don’t know what it is.

Geometry as it actually is, as opposed to Euclidean geometry, which maintains falsely that parallel lines meet at infinity rather than converging or diverging as they really do, is substantially the study of what follows from distances and angles between items. Movement is not the same thing as an increase in distance. This crucial point is what allows the Universe to expand at a rate which over great distances is greater than the speed of light. No actual matter within the Universe needs to move faster than light. I’ll try to illustrate what I mean. If two rocks are located just outside the event horizon of a black hole and it moves away from them, the distance between them will change but neither of them will have moved, because the space warp created by the black hole will lessen.

This is the principle on which the Alcubierre Warp Drive is based, and at this point it’s fair to point out that a warp drive could also be used to travel, or rather modify one’s location, slower than light. It works by changing the geometry of space around the object to be moved. Clearly objects will tend to fall towards massive bodies in their vicinity, which is because they warp space in front of them, but this doesn’t help them get places unless those places are somewhere between the object and the massive body. However, this also contracts space. If space could also be expanded behind the object, relocation is possible over a period less than that required for light to travel between the initial and final locations of the object. The only trouble is, this requires negative mass. If positive mass, such as a black hole, reduces the space around it, negative mass should increase it. I’m personally suspicious of this idea for all sorts of reasons. If this kind of warp drive is possible, it also makes gravity control, antigravity, tractor beams and practically limitless energy possible, and this just sounds too good to be true. It sounds like the kind of thing which ought to be ruled out by the laws of physics because it would solve so many problems. It means we would be able to effectively travel faster than light, have antigravity, spacecraft with their own vertical gravity fields and we’d never need to worry about generating electricity again. I realise this is not a scientific objection, but so much hangs on it, it just feels wrong. The catch is that nobody knows if negative mass is a thing. Also, relocating something faster than light is stepping outside the light cone and this influences the order in which things happen. This means that a simultaneous event can become earlier and be interfered with even though it’s known by observation what its consequences are already. This is still an issue even with the Alcubierre warp drive: it kind of turns a spacecraft into a time machine. It’s not a good thing, incidentally. It suggests there’s a reason it wouldn’t work.

I’ll turn now to the related subject of cosmic strings. A few comments need to be made here about the relationship between these and the strings of string theory. I’ll talk about string theory first, also known as “superstring theory”.

According to string theory, the fundamental component of the Universe is loops of string which vibrate in different ways. The differences in vibration manifest as particles with different properties. These loops operate in a ten-dimensional space, or possibly eleven, but six of those dimensions are a maximum of 10^-33 centimetres in size. They are, like the three dimensions of the space we’re familiar with, curved back on themselves. One of the main points of string theory is to provide a grand unified theory which accounts for both the standard model (all that quantum stuff and particles) and gravity, and it does do that, but one drawback is that it seems untestable. It’s also been criticised for predicting the existence of 10⁵⁰⁰ universes, each with their own laws of physics, and fails to explain why we’re in this one. I’m no expert, but I would’ve thought that the answer is that the others are uninhabitable and that life and intelligence can’t arise in them, or that there are rather few of them. Objecting to it on those grounds is a bit like objecting to the idea of outer space because we live on a particular planet. The theory is also far from elegant, but that objection is kind of æsthetic. Other physicists claim that we are too attached to elegance and that there’s no reason why the Universe should be like that. However, more seriously no version of string theory explains the expansion of the Universe, and it doesn’t make useful predictions about the nature of physical reality.

The mathematics of string theory, however, can be applied elsewhere, including to other kinds of “string”, and the question arises of whether there is a direct connection between superstrings and cosmic strings or merely a mathematical one, and of course the main focus of this post is the latter type of string. I can see a similar incident in the early Universe causing both superstrings and strings, but I lack the scientific “knowledge” (which it isn’t because it’s empirical science, hypothetically) to know if I’m saying something sensible about it. Cosmic strings are basically topological entities, and are one of four types of object which emerged just after the Big Bang, and I’m going to present my idea here for what it’s worth. What if the same kind of process led to the formation of extremely small cosmic strings before the large ones emerged? Maybe not, I don’t know.

There are, as I said, supposed to be four types of entity known as topological defects in space. These defects can be studied to some extent because they also occur in other situations, such as in liquid crystals, which makes me wonder if there are some in front of me right now, and microvortices in helium II and other superfluids as mentioned here. Strings are thought to have appeared 10^-35 seconds after the Big Bang and are “defects” in space, which appeared because the Big Bang was a phase change analogous to a liquid freezing in the sense that the primordial chaos became an ordered Universe, and just as cracks appear in ice as it freezes from the apparently homogenous water, so do topological defects appear in space. They’re similar to whorls in hair and partings as well, in the sense that there’s a polarity to each point in space which may be oriented in different directions in different regions.

I’m going to have to confess to not being confident that I’ve got the following right.

Space, according to string theory, has ten or eleven dimensions. At the point of the Big Bang, all of these dimensions were of zero size, so in other words they didn’t exist and presumably immediately after, or rather as soon as size had any meaning, they were equal in size but also non-Euclidean, curled up on themselves. At 10^-35 seconds, over most of space the extra dimensions collapsed, but not the the same extent in certain regions, as far as anyone can tell at random, and the regions where space was “normal” began to expand until they almost came into contact with each other. Where they did this, they stayed very slightly separated, by a distance smaller than the size of an atomic nucleus. These took different forms. They may be almost points, corresponding somewhat to particles, lines, which are the cosmic strings, domain walls, which are two-dimensional and textures, which are regions of variation liable to collapse. Presumably textures no longer exist because they were formed 13.8 æons ago and being unstable can surely not have survived. Incidentally, the initial topological defects are now much larger and may, for example, stretch across the entire observable Universe because it’s expanded.

There are a few things I don’t understand at all here. In particular, I think I don’t understand why a point defect would be a magnetic monopole. If all this is about is magnetism, like the magnetic field of the Universe as it were, I can see that there could be points from which everywhere is north or south in the magnetic sense, and an analogy could even be made with the poles of a planet as positions whence everywhere is south or north. However, this seems to be about more than mere magnetism, which leads me to contemplate whether there are other kinds of “monopole”, which we would be familiar with involving other forces such as quantum black holes, which are tiny black holes theorised to have existed since the early Universe. But I honestly don’t get this bit.

It’s also important to note that although these things are in a sense one- or two-dimensional, this is not the same as them being literally perfectly straight or flat. Rather, they’re crooked lines, able to swirl around, and irregular bumpy surfaces. Where a cosmic string intersects with itself, it pinches off a loop because it’s able to penetrate itself, leaving the rest of the string to “heal” and continue.

A circle drawn round a cross-section of a cosmic string would not have 360°. This is, I think, because the space in the vicinity to one of these objects is far from Euclidean, in turn because the multiple dimensions of the Universe have been retained at a larger size than in most of space. Hence it’s a spatial anomaly – a small piece of hyperspace. However, just as there can be north and south magnetic monopoles, there can be cosmic strings with more than 360° circumference and others with less than 360°. Because gravity is the warping of space-time, this means two things, depending on the type of string (and I presume this also applies to domain walls). One type is extremely dense – one quote is that an inch of cosmic string, with the width of a proton, is as massive as Mount Everest, which is around 160 gigatonnes an inch or 50 gigatonnes a centimetre. They’re also under a lot of tension and vibrate, meaning that they’re going to give off gravitational waves if they exist, and these can be detected now. Thus it’s possible to look for a confirming instance in gravitational waves, which are disturbances in the curvature of space-time. Another way to find them would be to look for a line of stars with twin images, where the light has been refracted either side of the string.

As is probably clear, I don’t know what these things are in detail but the relevant aspect is that the ones whose circumference is less than that of a circle would have negative mass. Now imagine a situation where a cosmic string, or possibly a domain wall, with negative mass, is near either a black hole or a topological defect with positive mass. This is a “warp field”, or rather the space between the two is. It’s tipped ana (four-dimensional direction number 1) behind and kata (four-dimensional direction number 2) in front. Therefore items small enough to be completely covered on both sides would be able to “move” faster than light. This could be taken to mean that cosmic strings can’t exist. There’s also a problem with movement, as it seems it would be very difficult to move a cosmic string with positive mass at all, let alone near the speed of light. On the other hand, it might be moving of its own accord, and this makes me wonder whether the mass that a topological defect has is the same as that of ordinary matter, because rather than being matter it just is a warp in space, which we already know can move faster than light. I don’t know the answer to this.

Then there’s time travel, and this is not my idea. Apparently there are two ways to travel in time using cosmic string. Firstly, because they’re so dense, time slows down near them in the same way as it does near a black hole, meaning that just staying close to one would be tantamount to travelling faster downstream in time than one is anyway, although the chances of much physical matter of the familiar variety, such as the stuff our bodies are made of, seem pretty slim. That doesn’t stop a signal from travelling though. Secondly, in a mechanism I don’t understand and with an enormous amount of energy, a spaceship near two crossing strings could travel into the past, and again the spaceship can be replaced by a signal. Information from the future is just as likely to cause paradoxes as matter, so this is a problem. Also, teleportation is often thought of as using signals, so if teleportation through matter transmission is possible, physical objects would be able to travel in time, or at least be cloned. As usual with time machines, you wouldn’t be able to travel back before the formation of the machine, but it’s possible that these could form by chance, and since they date from the early Universe, that’s not really a problem.

And no, I do not know how to overcome the paradoxes this would apparently cause. I merely present it as I received it.

The Anti-Universe

A prominent mythological theme is that of time being cyclical. For instance, in Hinduism there is a detailed chronology which repeats endlessly. Bearing in mind that the numbers used in mythological contexts are often mainly there to indicate enormity or tininess, there is the kalpa, which lasts 4 320 million years and is equivalent to a day in Brahma’s life. There are three hundred and sixty of these days in a Brahman year, and a hundred Brahman years in a Brahman lifetime, after which the cycle repeats. Within a Brahman Day, human history also repeats a cycle known as the Yuga Cycle, which consists of four ages, Satya, Treta, Dvapara and Kali. The names refer to the proportion of virtue and vice characterising each age, so Satya is perfect, life is long, everyone is kind to each other, wise, healthy and so on, satya meaning “truth” or “sincerity”, Treta is “third” in the sense of being three quarters virtue and one quarter vice, Dvapara is two quarters of each and Kali, unsurprisingly the current age, is the age of evil and destruction. Humans start off as giants and end as dwarfs. Then the cycle repeats. Thus there are cycles within cycles in Hindu cosmology.

The Maya also have a cyclical chronology, including the Long Count, in a cycle lasting 63 million years. Probably the most important cycle in Mesoamerican calendars is the fifty-two year one, during which the two different calendars cycle in and out of sync with each other. The Aztecs used to give away all their possessions at the end of that period in the expectation that the world might come to an end.

The Jewish tradition has a few similar features as well. Firstly, it appears to use the ages of people to indicate their health and the decline of virtue. The patriarchs named in the Book of Genesis tend to have shorter and shorter lives leading up to the Flood, which ends the lives of the last few generations before it, including the 969-year old Methuselah. Giants are also mentioned in the form of the Nephilim, although they are seen as evil. I wonder if this reflects the inversion of good and evil which took place when Zoroastrianism began, where previously lauded deities were demonised. There is also a cycle in the practice of the Jubilee, consisting of a forty-nine year Golden Jubilee and a shorter seven year Jubilee, and obviously there are the seven-day weeks, which we still have in the West.

The Hindu series of Yugas also reflects the Greek tradition of Golden, Silver, Bronze and Iron Ages, which was ultimately adopted into modern archæology in modified form as the Three-Age System of Stone, Bronze and Iron. The crucial difference between the Hindu and Greek age system and our own ideas of history is that they both believed in steady decline whereas we tend to be more mixed. We tend to believe in progress, although our ideas of what constitutes that do vary quite a lot. In a way, it makes more sense to suppose that everything will get worse, although since history is meant to be cyclical it can also be expected to get better, because of the operation of entropy. Things age, wear out, run down, burn out and so on, and this is the regular experience for everyone, no matter when they’re living in history, and it makes sense that the world might be going in the same direction. On the longest timescale of course it is, because the Sun will burn out, followed by all other stars and so on.

Twentieth century cosmology included a similar theory, that of the oscillating Universe. It was considered possible that the quantity of mass in the Universe was sufficient that once it got past a certain age, gravity acting between all the masses in existence would start to pull everything back together again until it collapsed into the same hot, dense state which started the Universe in the first place. There then emerge a couple of issues. Would the Universe then bounce back and be reborn, only to do it again in an endless cycle? If each cycle is an exact repetition, does it even mean anything to say it’s a different Universe, or is it just the same Universe with time passing in a loop?

This is not currently a popular idea because it turns out that there isn’t enough mass in the Universe to cause it to collapse against the Dark Energy which is pushing everything apart, so ultimately the objects in the Universe are expected to become increasingly isolated until there is only one galaxy visible in each region of the Universe where space is expanding relatively more slowly than the speed of light. This has a significant consequence. A species living in a galaxy at that time would be unaware that things had ever been different. There would be no evidence available to suggest that it was because we can currently see the galaxies receding, and therefore we can know that things will be like that one day, but they would have no way to discover that they hadn’t always been like this. This raises the question of what we might have lost. We reconstruct the history of the Universe based on the data available to us, and we’re aware that we’re surrounded by galaxies which, on the very large scale, are receding from each other, so we can imagine the film rewinding and all the stars and galaxies, or what will become them, starting off in the same place. But at that time, how do we know there wasn’t evidence of something we can no longer recover which is crucial to our own understanding of the Universe?

Physics has been in a bit of a strange state in recent decades. Because the levels of energy required cannot be achieved using current technology, the likes of the Large Hadron Collider are not powerful enough to provide more than a glimpse of the fundamental nature of physical reality. Consequently, physicists are having to engage in guesswork without much feedback, and this applies also to their conception of the entire Universe. I’ve long been very suspicious about the very existence of non-baryonic dark matter. Dark matter was originally proposed as a way to explain why galaxies rotate as if they have much more gravity than their visible matter, i.e. stars, is exerting. In fact, if gravity operates over a long range in the same way as it does over short distances, such as within this solar system or between binary stars, something like nine-tenths of the mass is invisible. To some extent this can be explained by ordinary matter such as dust, planets or very dim stars, and there are also known subatomic particles such as the neutrinos which are very common but virtually undetectable. The issue I have with non-baryonic dark matter, and I’ve been into this before on here, is that it seems to be a specially invented kind of matter to fill the gap in the model which, however, is practically undetectable. There’s another possible solution. What makes this worse is that dark matter is now being used to argue for flaws in the general theory of relativity, when it seems very clear that the problem is actually that physicists have proposed the existence of a kind of substance which is basically magic.

If you go back to the first moment of the Universe, there is a similar issue. Just after the grand unification epoch, a sextillionth (long scale) of a second after the Big Bang, an event is supposed to have taken place which increased each of the three extensive dimensions of the Universe by a factor of the order of one hundred quintillion in a millionth of a yoctosecond. If you don’t recognise these words, the reason is that these are unusually large and small quantities, so their values aren’t that important. Some physicists think this is fishy, because again something seems to have been simply invented to account for what happened in those circumstances without there being other reasons for supposing it to be so. They therefore decided to see what would happen if they used established principles to recreate the early Universe, and in particular they focussed on CPT symmetry

CPT symmetry is Charge, Parity and Temporal symmetry, and can be explained thus, starting with time. Imagine a video of two billiard balls hitting and bouncing off each other out of context. It would be difficult to tell whether that video was being played forwards or backwards. This works well on a small scale, perhaps with two neutrons colliding at about the speed of sound at an angle to each other, or a laser beam reflecting off a mirror. Charge symmetry means that if you observe two equally positively and negatively charged objects interacting, you could swap the charges and still observe the same thing, or for that matter two objects with the same charge could have the opposite charges and still do the same thing. Finally, parity symmetry is the fact that you can’t tell whether what you’re seeing is the right way up or upside down, or reflected. All of these things don’t work in the complicated situations we tend to observe because of pesky things like gravity and accidentally burning things out by sticking batteries in the wrong way round or miswiring plugs, but in sufficiently simple situations all of these things are symmetrical.

But there is a problem. The Universe as a whole doesn’t seem to obey these laws of symmetry. For instance, almost everything we come across seems to be made of matter even though there doesn’t seem to be any reason why there should be more matter than antimatter or the other way round, and time tends to go forwards rather than backwards on the whole. One attempt to explain why matter seems to dominate the Universe is that for some reason in the early Universe more matter was created than antimatter, and since matter meeting antimatter annihilates both, matter is all that’s left. Of course antimatter does crop up from time to time, for instance in bananas and thunderstorms, but it doesn’t last long because it pretty soon comes across an antiparticle in the form of, say, an electron, and the two wipe each other off the map in a burst of energy.

These physicists proposed a solution which does respect this symmetry and allows time to move both forwards and backwards. They propose that the Big Bang created not one but two universes, one where time runs forwards and mainly made of matter and the other where time goes backwards and is mainly made of antimatter, and also either of these universes is geometrically speaking a reflection of the other, such as all the left-handed people in one being right-handed in the other. This explains away the supposèd excess of matter. There’s actually just as much antimatter as matter, but it swapped over at the Big Bang. Before the Big Bang, time was running backwards and the Universe was collapsing.

In a manner rather similar to the thought that an oscillating Universe could be practically the same as time running in a circle because each cycle might be identical and there’s no outside to see it from, the reversed, mirror image antimatter Universe is simply this one running backwards with, again, nothing on the outside to observe it with, and therefore for all intents and purposes there just is this one Universe running forwards after the Big Bang, because it’s indistinguishable from the antimatter one running backwards. On the other hand, the time dimension involved is the same as this one, and therefore it could just be seen as the distant past, which answers the question of what there was before the Big Bang: there was another universe, or rather there was this universe. It also means everything has already happened.

But a further question arises in my head too, and this is by no means what these physicists are claiming. As mentioned above, one model of the Universe is that it repeats itself in a cycle. What we may have here is theoretical support for the idea of a Universe collapsing in on itself before expanding again. That’s the bit we can see or deduce given currently available evidence. However, in the future, certain evidence will be lost because there will only be one visible galaxy observable, and the idea of space expanding will be impossible to support even though it is. What if one of the bits of evidence we’ve already lost is of time looping? Or, what if time just does loop anyway? What if time runs forwards until the Universe reaches a maximum size and then runs backwards again as it contracts? There is an issue with this. There isn’t enough mass in the Universe for it to collapse given the strength of dark energy pushing it apart, but of course elsewhere in the Multiverse there could be looping universes due to different physical constants such as the strength of dark energy or the increased quantity of matter in them, because in fact as has been mentioned before there are possible worlds where this does take place. Another question then arises: how does time work between universes? Are these looping universes doing so now in endless cycles, or are they repeating the same stretch of time? Does time even work that way in the Multiverse, or is it like in Narnia, where time runs at different speeds relative to our world?

It may seem like I’ve become highly speculative. In my defence, I’d say this. I have taken pains to ignore my intuition in the past because I believed it was misleading. However, there appears to be an intuition among many cultures that time does run in a cycle, and the numbers these cultures produce are oddly similar. The Mayan calendar’s longest time period is the Alautun, which lasts 63 081 429 years, close to the number of years it’s been since the Chicxulub Impact, which coincidentally was nearby and wiped out the non-avian dinosaurs. The Indian kalpa is 4 320 million years in length, which is again quite close to the age of this planet. Earth is 4 543 million years old and the Cretaceous ended 66 million years ago, so these figures are 4.6% out in the case of the Maya and 5% for the kalpa. Of course it may be coincidence, and the idea of time being cyclical may simply be based on something like the cycle of the day and night or the seasons through the year, but since I believe intuitive truths are available in Torah and the rest of the Tanakh, I don’t necessarily have a problem with other sources. Parallels have of course been made between ancient philosophies and today’s physics before, for example by Fritjof Capra in his ‘The Tao [sic] Of Physics’. Although much of what he says has been rubbished by physicists since, there is a statue of Dancing Shiva in the lobby at CERN and one quote from Capra is widely accepted:

“Science does not need mysticism and mysticism does not need science. But man needs both.”

“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.