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.