One of the best things about the internet is that it gives the public unprecedented access to the cutting edge of science. For example, on Friday I uploaded my entire PhD thesis, “Causality Violation and Nonlinear Quantum Mechanics”, to the arXiv, where it can now be read by my contemporaries, colleagues, parents, neighbours and any pets that can read human-speak. The downside is, as my parents pointed out, my thesis is not written in English but in gobbledegook that makes no sense to anybody outside of the quantum physics community. So, while most work at the cutting edge of physics is available to anyone to read, almost nobody can understand it — and those who can, have access to journal subscriptions anyway! Oh, the irony. In order to remedy this problem, I’ve decided to translate my thesis from jargon into words that most people can understand (I’m not the first one to have this idea – check out Scott Aaronson’s description of his own research using the 1000 most common words in English).
Like any PhD thesis, my work is on a really small, pigeonhole topic that is part of a much bigger picture — like one brick in the wall of a huge building that is being constructed. I’ll start by talking about the whole building, which represents all of physics, and then slowly zoom in on the single, tiny brick that I focused on intensely for three and a half years. One thing about doing a PhD is that it teaches you to be very Zen about your work. We can’t all expect to be like Einstein, who single-handedly constructed an entire wing of the building — us regular scientists have to content ourselves with the laying of a single brick. In the end, the whole structure will only stand if every single brick is placed carefully and correctly. Sherlock Holmes once observed that, from a single drop of water, “a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other. So all life is a great chain, the nature of which is known whenever we are shown a single link of it.” In the same way, the contribution of just a single brick to the building of physics is significant. After all, one cannot know how to place the individual brick without having first consulted the blueprint of the entire building. In this sense, the individual brick is as significant as the entire structure.
But enough philosophical mumbo-jumbo! Let’s get concrete. Modern physics can be roughly divided up into two separate theories. The first is Einstein’s theory of gravity, called General Relativity. This theory applies to all heavy objects that are affected by gravity, like planets, galaxies, and your mum. The theory says that heavy objects cause space and time to bend and curve around them in a special way. When the objects move through this curved space-time, they follow paths that bring them closer together, creating the appearance of an attractive force — the “force” normally known as gravity. If you want to fly rockets through space or deduce how the galaxy formed, or predict how heavy objects move around each other in space, you need this theory.
The other theory is Quantum Mechanics. This governs the behaviour of things that are very small, like atoms and the smaller parts of atoms. It turns out that even light is composed of a vast number of very small particles, called photons. If you have a very weak source of light that emits only a few photons at a time, it too is described by quantum mechanics. All quantum particles possess wave-like behaviour under certain conditions, which is described by something called the “wave-function” of the particle. Since we are made entirely out of atoms, you might ask: how come our bodies are not governed by quantum mechanics too? The answer is that, although in theory there could be a wave-function for larger objects like human bodies, in practice it is extremely difficult to create the special conditions needed to see the quantum behaviour of such large collections of atoms. The process whereby quantum effects become harder to observe in bigger objects is called “decoherence”, and it is still not completely understood.
Now comes the interesting part: it turns out that gravity is very weak. We can feel the Earth’s gravitational pull because the Earth is really, really heavy. But, in theory, you and I are also heavy enough to cause space-time to bend, just a little bit, around our bodies. This means you should be pulled towards me by gravity, and I towards you. However, because we are not nearly as heavy as the Earth, our gravitational pull on each other is far too weak for us to notice (though people have observed the gravitational attraction between large, heavy balls suspended by wires). By the time you get down to molecules, atoms and quantum mechanics, the gravitational force is so tiny that it can be completely ignored. On the other hand, because of decoherence, quantum mechanics can usually be ignored for anything much larger than molecules. This means that it is very rare to find a situation in which both quantum effects and gravitational effects both need to be taken into account; it is almost always a case of just one or the other.
The trouble is, if there were an in-between situation where both theories become significant, we do not know how quantum mechanics and gravity would overlap. One example is when a star becomes so heavy that it collapses under its own gravity into a black hole. The singularity at the centre of the hole is small enough that quantum mechanics should become important. As for being heavy, well, a black hole is so heavy that even light cannot go fast enough to escape from its gravitational attraction. Another in-between case would occur if we ever manage to make instruments that can measure space and time to extremely high accuracy, at a level called the “Planck scale”. If we are ever able to measure such tiny distances and times, we might expect to observe the curving of space-time due to very low-mass objects like atoms. So far, such precision is beyond our technology, and black holes have only been observed very indirectly. But when we finally do begin to probe these things, we will need a theory to describe them that incorporates both gravity and quantum mechanics together — a theory of “quantum gravity”. But despite roughly a hundred years of effort, we still do not have such a theory.
Why is it so hard to do quantum mechanics and gravity at the same time? This question alone is the subject of much debate. For now, you’ll just have to take my word that you can’t simply mash the two together (it has something to do with the fact that “space-time” is no longer clearly defined at the Planck scale). One approach is to consider a specific example of something that needs quantum gravity to describe it, like a black hole, and then try to develop a kind of “toy” theory of quantum gravity that describes only that particular situation. Once you have enough toy theories for different situations, you might be able to stick them together into a proper theory that includes all of them as special cases. This is easier said than done — it relies on us being able to come up with a wide variety of “thought experiments” that combine different aspects of quantum mechanics and gravity. But thought experiments like these are very rare: you’ve got black holes, Roger Penrose’s idea of a massive object in a quantum superposition, and a smattering of lesser known ideas. Are there any more?
This is where I come in. The idea for my PhD thesis comes from a paper that I stumbled across as an undergraduate at the University of Melbourne. The paper, by Tim Ralph, Gerard Milburn and Tony Downes of the University of Queensland, proposed that Earth’s own gravitational field might be strong enough to cause quantum gravity effects in experiments done on satellites. In particular, the difference between the strength of gravity at ground-level and at the height of the orbiting satellite might be just enough to make the quantum particles on the satellite behave in a very funny “non-linear” way, never before seen at ground level. Why might this happen? This is where the story gets bizarre: the authors got their idea after looking at a theory of time-travel, proposed in 1991 by David Deutsch. According to Deutsch’s theory, if space and time were bent enough by gravity to create a closed loop in time (aka a time machine), then any quantum particle that travelled backwards in time ought to have a very peculiar “non-linear” behaviour. Tim Ralph and co-authors said: what if there was only a little bit of space-time curvature? Wouldn’t you still expect just a little bit of non-linear behaviour? And we can look for that in the curvature produced by the Earth, without even needing to build a time-machine!
I was so fascinated by this idea that I immediately wrote to Tim Ralph. After some discussions, I visited Brisbane for the first time to meet him, and soon afterwards I began my PhD at the Uni of Queensland under Tim’s supervision. My first task was to understand Deutsch’s model of time-travel in more detail. (Unfortunately, the idea of time-travel is notorious for attracting crackpots, so if you want to do legitimate research on the topic you have to couch it in jargon to convince your colleagues that you have not gone crazy — hence the replacement of “time-travel” with the more politically-correct term “causality violation” in the title of my thesis). David Deutsch is best known for being one of the founding fathers of the idea of a quantum computer. That gave him enough credibility amongst physicists that we were willing to listen to his more eccentric ideas on things like Everett’s many-worlds interpretation of quantum mechanics, and the quantum mechanics of time-travel. On the latter topic, Deutsch made the seminal observation that certain well-known paradoxes of time travel — for instance, what happens if you go back in time and kill your past self before he/she enters the time machine — could be fixed by taking into account the wave-function of a quantum particle as it travels back in time.
Roughly speaking, the closed loop in time causes the wave-function of the particle to loop back on itself, allowing the particle to “interact with itself” in a non-linear way. Just like Schrödinger’s cat can be both dead and alive at the same time in a quantum superposition, it is possible for the quantum particle to “kill it’s past self” and “not kill it’s past self” at the same time, thereby apparently resolving the paradox (although, you might be forgiven for thinking that we just made it worse…).
Here was a prime example of a genuine quantum gravity effect: space-time had to be curved in order to create the time-machine, but quantum mechanics had to be included to resolve the paradoxes! Could we therefore use this model as a new thought experiment for understanding quantum gravity effects? Luckily for me, there were a few problems with Deutsch’s model that still needed to be ironed out before we could really take seriously the experiment proposed by Ralph, Milburn and Downes. First of all, as I mentioned, Deutsch’s model introduced non-linear behaviour of the quantum particle. But many years earlier, Nicolas Gisin and others had argued that any non-linear effects of this type should allow you to send signals faster than light, which seemed to be against the spirit of Einstein’s theory of relativity. Secondly, Deutsch’s model did not take into account all of the quantum properties of the particle, such as the spread of the particle’s wave function in space and time. Without that, it remained unclear whether the non-linear behaviour should persist in Earth’s gravitational field, as Ralph and co-authors had speculated, or whether the space-time spread of the wave-function would some how “smear out” the non-linearity until it disappeared altogether.
In my thesis, I showed that it might be possible to keep the non-linear behaviour of the Deutsch model while also ensuring that no signals could be sent faster than light outside of the time-machine. My arguments were based on some work that had already been done by others in a different context — I was able to adapt their work to the particular case of Deutsch’s model. In addition, I re-formulated Deutsch’s model to describe what happens to pulses of light, such that the space-time spread of the light could be taken into account together with the other quantum properties of light. Using this model, I showed that even if a pulse of light were sent back in time without interacting with its past self at all (no paradoxes), the wave-function of the light would still behave in a non-linear way. Using my model, I was able to describe exactly when the non-linear effects would get “smeared out” by the wave-function, and confirmed that the non-linear effects might still be observable in Earth’s gravitational field without needing a time-machine, thereby lending further support to the speculative work of Ralph and co. that had started it all.
So, that’s my PhD in a nutshell! Where to next? Right now I have decided to calm down a little bit and steer towards less extreme examples of a quantum gravity thought experiments. In particular, rather than looking at outright “causality violation”, I am investigating a peculiar effect called “indefinite causality”, in which space-time is not quite curved enough to send anything backwards in time, but where it is also not clear which events are causes and which ones are their effects. Hopefully, I’ll be able to understand how quantum mechanics fits into this weird picture — but that’s a topic for another post.