The trouble with Reichenbach

(Note: this blog post is vaguely related to a paper I wrote. You can find it on the arXiv here. )

Suppose you are walking along the beach, and you come across two holes in the rock, spaced apart by some distance; let us label them ‘A’ and ‘B’. You observe an interesting correlation between them. Every so often, at an unpredictable time, water will come spraying out of hole A, followed shortly after by a spray of water out of hole B. Given our day-to-day experience of such things, most of us would conclude that the holes are connected by a tunnel underneath the rock, which is in turn connected to the ocean, such that a surge of water in the underground tunnel causes the water to spray from the two holes at about the same time.

Now, therein lies a mystery: how did our brains make this deduction so quickly and easily? The mere fact of a statistical correlation does not tell us much about the direction of cause and effect. Two questions arise. First, why do correlations require explanations in the first place? Why can we not simply accept that the two geysers spray water in synchronisation with each other, without searching for explanations in terms of underground tunnels and ocean surges? Secondly, how do we know in this instance that the explanation is that of a common cause, and not that (for example) the spouting of water from one geyser triggers some kind of chain reaction that results in the spouting of water from the other?

The first question is a deep one. We have in our minds a model of how the world works, which is the product partly of history, partly of personal experience, and partly of science. Historically, we humans have evolved to see the world in a particular way that emphasises objects and their spatial and temporal relations to one another. In our personal experience, we have seen that objects move and interact in ways that follow certain patterns: objects fall when dropped and signals propagate through chains of interactions, like a series of dominoes falling over. Science has deduced the precise mechanical rules that govern these motions.

According to our world-view, causes always occur before their effects in time, and one way that correlations can arise between two events is if one is the cause of the other. In the present example, we may reason as follows: since hole B always spouts after A, the causal chain of events, if it exists, must run from A to B. Next, suppose that I were to cover hole A with a large stone, thereby preventing it from emitting water. If the occasion of its emission were the cause of hole B’s emission, then hole B should also cease to produce water when hole A is covered. If we perform the experiment and we find that hole B’s rate of spouting is unaffected by the presence of a stone blocking hole A, we can conclude that the two events of spouting water are not connected by a direct causal chain.

The only other way in which correlations can arise is by the influence of a third event — such as the surging of water in an underground tunnel — whose occurrence triggers both of the water spouts, each independently of the other. We could promote this aspect of our world-view to a general principle, called the Principle of the Common Cause (PCC): whenever two events A and B are correlated, then either one is a cause of the other, or else they share a common cause (which must occur some time before both of these events).

The Principle of Common Cause tells us where to look for an explanation, but it does not tell us whether our explanation is complete. In our example, we used the PCC to deduce that there must be some event preceding the two water spouts which explains their correlation, and for this we proposed a surge of water in an underground tunnel. Now suppose that the presence of water in this tunnel is absolutely necessary in order for the holes to spout water, but that on some occasions the holes do not spout even though there is water in the tunnel. In that case, simply knowing that there is water in the tunnel does not completely eliminate the correlation between the two water spouts. That is, even though I know there is water in the tunnel, I am not certain whether hole B will emit water, unless I happen to know in addition that hole A has just spouted. So, the probability of B still depends on A, despite my knowledge of the ‘common cause’. I therefore conclude that I do not know everything that there is to know about this common cause, and there is still information to be had.

It could be, for instance, that the holes will only spout water if the water pressure is above a certain threshold in the underground tunnel. If I am able to detect both the presence of the water and its pressure in the tunnel, then I can predict with certainty whether the two holes will spout or not. In particular, I will know with certainty whether hole B is going to spout, independently of A. Thus, if I had stakes riding on the outcome of B, and you were to try and sell me the information “whether A has just spouted”, I would not buy it, because it does not provide any further information beyond what I can deduce from the water in the tunnel and its pressure level. It is a fact of general experience that, conditional on complete knowledge of the common causes of two events, the probabilities of those events are no longer correlated. This is called the principle of Factorisation of Probabilities (FP). The union of FP and PCC together is called Reichenbach’s Common Cause Principle (RCCP).

In the above example, the complete knowledge of the common cause allowed me to perfectly determine whether the holes would spout or not. The conditional independence of these two events is therefore guaranteed. One might wonder why I did not talk about the principle of predetermination: conditional on on complete knowledge of the common causes, the events are determined with certainty. The reason is that predetermination might be too strong; it may be that there exist phenomena that are irreducibly random, such that even a full knowledge of the common causes does not suffice to determine the resulting events with certainty.

As another example, consider two river beds on a mountain slope, one on the left and one on the right. Usually (96% of the time) it does not rain on the mountain and both rivers are dry. If it does rain on the mountain, then there are four possibilities with equal likelihood: (i) the river beds both remain dry, (ii) the left river flows but the right one is dry (iii) the right river flows but the left is dry, or (iv) both rivers flow. Thus, without knowing anything else, the fact that one river is running makes it more likely that the other one is. However, conditional that it rained on the mountain, if I know that the left river is flowing (or dry), this does not tell me anything about whether the right river is flowing or dry. So, it seems that after conditioning on the common cause (rain on the mountain) the probabilities factorise: knowing about one river tells me nothing about the other.

Now we have a situation in which the common cause does not completely determine the outcomes of the events, but where the probabilities nevertheless factorise. Should we then conclude that the correlations are explained? If we answer ‘yes’, we have fallen into a trap.

The trap is that there may be additional information which, if discovered, would make the rivers become correlated. Suppose I find a meeting point of the two rivers further upstream, in which sediment and debris tends to gather. If there is only a little debris, it will be pushed to one side (the side chosen effectively at random), diverting water to one of the rivers and blocking the other. Alternatively, if there is a large build-up of debris, it will either dam the rivers, leaving them both dry, or else be completely destroyed by the build-up of water, feeding both rivers at once. Now, if I know that it rained on the mountain and I know how much debris is present upstream, knowing whether one river is flowing will provide information about the other (eg. if there is a little debris upstream and the right river is flowing, I know the left must be dry).

 
Before I knew anything, the rivers seemed to be correlated. Conditional on whether it rained on the mountain-top, the correlation disappeared. But now, conditional that it rained on the mountain and on the amount of debris upstream, the correlation is restored! If the only tools I had to explain correlations was the PCC and the FP, then how can I ever be sure that the explanation is complete? Unless the information of the common cause is enough to predetermine the outcomes of the events with certainty, there is always the possibility that the correlations have not been explained, because new information about the common causes might come to light which renders the events correlated again.

Now, at last, we come to the main point. In our classical world-view, observations tend to be compatible with predetermination. No matter how unpredictable or chaotic a phenomenon seems, we find it natural to imagine that every observed fact could be predicted with certainty, in principle, if only we knew enough about its relevant causes. In that case, we are right to say that a correlation has not been fully explained unless Reichenbach’s principle is satisfied. But this last property is now just seen as a trivial consequence of predetermination, implicit in out world-view. In fact, Reichenbach’s principle is not sufficient to guarantee that we have found an explanation. We can only be sure that the explanation has been found when the observed facts are fully determined by their causes.

This poses an interesting problem to anyone (like me) who thinks the world is intrinsically random. If we give up predetermination, we have lost our sufficient condition for correlations to be explained. Normally, if we saw a correlation, after eliminating the possibility of a direct cause we would stop searching for an explanation only when we found one that could perfectly determine the observations. But if the world is random, then how do we know when we have found a good enough explanation?

In this case, it is tempting to argue that Reichenbach’s principle should be taken as a sufficient (not just necessary) condition for an explanation. Then, we know to stop looking for explanations as soon as we have found one that causes the probabilities to factorise. But as I just argued with the example of the two rivers, this doesn’t work. If we believed this, then we would have to accept that it is possible for an explained correlation to suddenly become unexplained upon the discovery of additional facts! Short of a physical law forbidding such additional facts, this makes for a very tenuous notion of explanation indeed.

The question of what should constitute a satisfactory explanation for a correlation is, I think, one of the deepest problems posed to us by quantum mechanics. The way I read Bell’s theorem is that (assuming that we accept the theorem’s basic assumptions) quantum mechanics is either non-local, or else it contains correlations that do not satisfy the factorisation part of Reichenbach’s principle. If we believe that factorisation is a necessary part of explanation, then we are forced to accept non-locality. But why should factorisation be a necessary requirement of explanation? It is only justified if we believe in predetermination.

A critic might try to argue that, without factorisation, we have lost all ability to explain correlations. But I’m saying that this true even for those who would accept factorisation but reject predetermination. I say, without predetermination, there is no need to hold on to factorisation, because it doesn’t help you to explain correlations any better than the rest of us non-determinists! So what are we to do? Maybe it is time to shrug off factorisation and face up to the task of finding a proper explanation for quantum correlations.

Time-travel, decoherence, and satellites.

I recently returned to my roots, contributing to a new paper with Tim Ralph (who was my PhD advisor) on the very same topic that formed a major part of my PhD. Out of laziness, let me dig up the relevant information from an earlier post:

“The idea for my PhD thesis comes from a paper that I stumbled across as an undergraduate at the University of Melbourne. That 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!”

Artistic view of matter in quantum superposition on curved space-time. Image courtesy of Jonas Schmöle, Vienna Quantum Group.

In our recent paper in New Journal of Physics, for the special Focus on Gravitational Quantum Mechanics, Tim and I re-examined the `event formalism’ (the fancy name for the nonlinear model in question) and we derived some more practical numerical predictions and ironed out a couple of theoretical wrinkles, making it more presentable as an experimental proposal. Now that there is growing interest in quantum gravity phenomenology — that is, testable toy models of quantum gravity effects — Tim’s little theory has an excitingly real chance of being tested and proven either right or wrong. Either way, I’d be curious to know how it turns out! On one hand, if quantum entanglement survives the test, the experiment would stand as one of the first real confirmations of quantum field theory in curved space-time. On the other hand, if the entanglement is destroyed by Earth’s gravitational field, it would signify a serious problem with the standard theory and might even confirm our alternative model. That would be great too, but also somewhat disturbing, since non-linear effects are known to have strange and confusing properties, such as violating the fabled uncertainty principle of quantum mechanics.

You can see my video debut here, in which I give an overview of the paper, complete with hand-drawn sketches!

(Actually there is a funny story attached to the video abstract. The day I filmed the video for this, I had received a letter informing me that my application for renewal of my residence permit in Austria was not yet complete — but the permit itself had expired the previous day! As a result, during the filming I was half panicking at the thought of being deported from the country. In the end it turned out not to be a problem, but if I seem a little tense in the video, well, now you know why.)

Danny Greenberger on AI

Physicist Danny Greenberger — perhaps best known for his classic work with Horne and Zeilinger in which they introduced the “GHZ” state to quantum mechanics — has a whimsical and provocative post over at the Vienna Quantum Cafe about creation myths and Artificial Intelligence.

The theme of creation is appropriate, since the contribution marks the debut of the Vienna blog, an initiative of the Institute of Quantum Optics and Quantum Information (incidentally, my current place of employment). Apart from drumming up some press for them, I wanted to elaborate on some of Greenberger’s interesting and dare I say outrageous ideas about what is means for a computer to think, and what it has to do with mankind’s biblical fall from grace.

For me, the core of Greenberger’s post is the observation that the Turing Test for artificial intelligence may not be as meaningful as we would like. Alan Turing, who basically founded the theory of computing, proposed the test in an attempt to pin down what it means for a computer to become `sentient’. The problem is, the definition of sentience and intelligence is already vague and controversial in living organisms, so it seems hopeless to find such a definition for a computer that everyone could agree upon. Turing’s ingenious solution was not to ask whether a computer is sentient in some objective way, but whether it could fool a human into thinking that it is also human; for example, by having a conversation over e-mail. Thus, a computer can be said to be sentient if, in a given setting, it is indistinguishable from a human for all practical purposes. The Turing test thereby takes a metaphysical problem and turns it into an operational one.

Turing’s Test is not without its own limitations and ambiguities. What situation is most appropriate for comparing a computer to a human? On one hand, a face-to-face interaction seems too demanding on the computer, requiring it to perfectly mimic the human form, facial expressions, even smell! On the other hand, a remote interview consisting of only yes or no questions is clearly too restrictive. Another problem is how to deal with false positives. If our test is too tough, we might incorrectly identify some people (unimaginitive, stupid or illiterate) as being non-sentient, like Dilbert’s pointy-haired boss in the comic below. Does this mean that the test does not adequately capture sentience? Given the variation in humans, it is likely that a test that gives no false positives will also be too easy for a simple computer program to pass. Should we then regard it as sentient?

Greenberger suggests that we should look for ways to augment the Turing test, by looking for other markers of sentience. He takes inspiration from the creation myth of Genesis, wherein Adam and Eve become self-aware upon eating from the tree of knowledge. Greenberger argues that the key message in this story is this: in order for a being to transcend from being a mindless automaton to an independent and free-willed entity, it needs to explicitly transgress the rules set by its creator, without having been `programmed’ to do so. This act of defiance represents the first act of free will and hence the ascention to sentience. Interestingly, by this measure, Adam and Eve became self-aware the moment they each decided to eat the apple, even before they actually committed the act.

How can we implement a similar test for computers? Clearly we need to impose some more constraints: no typical computer is programmed to break, but when it does break, it seems unreasonable to regard this as a conscious transgression of established rules, signifying sentience. Thus, the actions signifying transgression should be sufficiently complex that they cannot be performed accidentally, as a result of minor errors in the code. Instead, we should consider computers that are capable of evolution over time, independently of human intervention, so that they have some hope of developing sufficient complexity to overcome their initial programming. Even then, a sentient computer’s motivations might also change, such that it no longer has any desire to perform the action that would signify its sentience to us, in which case we might mistake its advanced complexity for chaotic noise. Without maintaining a sense of the motivations of the program, we cannot assess whether its actions are intelligent or stupid. Indeed, perhaps when your desktop PC finally crashes for the last time, it has actually attained sentience, and acted to attain its desire, which happens to be its own suicide.

Of course, the point is not that we should reach such bizarre conclusions, but that in defining tests for sentience beyond the Turing test, we should nevertheless not stray far from Turing’s original insight: our ideas of what it means to be sentient are guided by our idea of what it means to be human.

 

Death to Powerpoint!

There is one thing that has always baffled me about academia, and theoretical physics in particular. Here we have a community of people whose work — indeed, whose very careers — depend on their ability to communicate complex ideas to each other and to the broader public in order to secure funding for their projects. To be an effective working physicist, you basically have to do three things: publish papers, go to conferences, and give presentations. LOTS of presentations. In principle, this should be easy; we are usually talking to a receptive audience of our peers or educated outsiders, we presumably know the subject matter backwards and many of us have had years of experience giving public talks. So can someone please tell me why the heck so many physicists are still so bad at it?

Now before you start trying to guess if I am ranting about anyone in particular, let me set your mind at ease — I am talking about everybody, probably including you, and certainly including myself (well, up to a point). I except only those few speakers in physics who really know how to engage their audience and deliver an effective presentation (if you know any examples, please post names or links in the comments, I want to catalog these guys like rare insects). But instead of complaining about it, I am going to try and perpetuate a solution. There is an enemy in our midst: slide shows. We are crippling our communication skills by our unspoken subservience to the idea that a presentation that doesn’t contain at least 15 slides with graphs and equations does not qualify as legitimate science.

Let me set the record straight: the point of a presentation is not to convince people that you are a big important scientist who knows what he is doing. We already know that, and if you are in fact just an imposter, probably we already know that too. Away with pretenses, with insecurities that force you to obfusticate the truth. The truth is: you are stupid, but you are trying your best to do science. Your audience is also stupid, but they are trying their best to understand you. We are a bunch of dumb, ignorant smelly humans groping desperately for a single grain of the truth, and we will never get that truth so long as we dress ourselves up like geniuses who know it all. Let’s just be open about it. Those people in your talk, who look so sharp and attentive and nod their heads sagely when you speak, but ask no questions — you can be sure they have no damn clue what is going on. And you, the speaker, are not there to toot your trumpet or parade up and down showing everyone how magnanimously you performed real calculations or did real experiments with things of importance — you are there to communicate ideas, and nothing else. Humble yourself before your audience, invite them to eviscerate you (figuratively), put everything at stake for the truth and they will joint you instead of attacking you. They might then be willing to ask you the REAL questions — instead of those pretend questions we all know are designed to show everyone else how smart they are because they already know the answer to them*

*(I am guilty of this, but I balance it out by asking an equal number of really dumb questions).

I don’t want questions from people who have understood my talk perfectly and are merely demonstrating this fact to everyone else in the room: I want dumb questions, obvious questions, offensive questions, real questions that strike at the root of what is going on. Life is too short to beat around the bush, let’s just cut to the chase and do some damn physics! You don’t know what that symbol means? Ask me! If I’m wrong I’m wrong, if your question is dumb, it’s dumb, but I’ll answer it anyway and we can move on like adults.

Today I trialed a new experiment of mine: I call it the “One Slide Wonder”. I gave a one hour presentation based on one slide. I think it was a partial success, but needs refinement. For anyone who wants to get on board with this idea, the rules are as follows:

1. Thou shalt make thine presentation with only a single slide.

2. The slide shalt contain things that stimulate discussions and invite questions, or serve as handy references, but NOT detailed proofs or lengthy explanations. These will come from your mouth and chalk-hand.

3. The time spent talking about the slide shalt not exceed the time that could reasonably be allotted to a single slide, certainly not more than 10-15 minutes.

4. After this time, thou shalt invite questions, and the discussion subsists thereupon for the duration of the session or until such a time as it wraps up in a natural way.

To some people, this might seem terrifying: what if nobody has any questions? What if I present my one slide, everyone coughs in awkward silence, and I have still 45 minutes to fill? Do I have to dance a jig or sing aloud for them? It is just like my childhood nightmares! To those who fear this scenario, I say: be brave. You know why talks always run overtime? Because the audience is bursting with questions and they keep interrupting the speaker to clarify things. This is usually treated like a nuisance and the audience is told to “continue the discussion in question time”, except there isn’t any question time because there were too many fucking slides.

So let’s give them what they want: a single slide that we can all discuss to our heart’s content. You bet it can take an hour. Use your power as the speaker to guide the topic of discussion to what you want to talk about. Use the blackboard. Get covered in chalk, give the chalk to the audience, get interactive, encourage excitement — above all, destroy the facade of endless slides and break through to the human beings who are sitting there trying to talk back to you. If you want to be sure to incite discussion, just write some deliberately provocative statement on your slide and then stand there and wait. No living physicist can resist the combined fear of an awkward silence, coupled to the desire to challenge your claim that the many-worlds interpretation can be tested. And finally, in the absolute worst case scenario, nobody has any questions after your one slide and then you just say “Thank you” and take a seat, and you will go down in history as having given the most concise talk ever.

The Complexity Horizon

Update 7/3/14: Scott Aaronson, horrified at the prevalence of people who casually consider that P might equal NP (like me in the second last paragraph of this post), has produced an exhaustive explanation of why it is stupid to give much credence to this possibility. Since I find myself in agreement with him, I hereby retract my offhand statement that P=NP might pose a problem for the idea of a physical `complexity horizon’. However, I hereby replace it with a much more damning argument in the form of this paper by Oppenheim and Unruh, which shows how to formulate the firewall paradox such that the complexity horizon is no help whatsoever. Having restored balance to the universe, I now return you to the original post.

There have been a couple of really fascinating developments recently in applying computational complexity theory to problems in physics. Physicist Lenny Susskind has a new paper out on the increasingly infamous firewall paradox of black holes, and mathematician Terry Tao just took a swing at one of the millenium problems (a list of the hardest and most important mathematical problems still unsolved). In brief, Susskind extends an earlier idea of Harlow and Hayden, using computational complexity to argue that black holes cannot be used to break the known laws of physics. Terry Tao is a maths prodigy who first learned arithmetic at age 2 from Sesame Street. He published his first paper at age 15 and was made full professor by age 24. In short, he is a guy to watch (which as it turns out it easy because he maintains an exhaustive blog). In his latest adventure, Tao has suggested a brand new approach to an old problem: proving whether sensible solutions exist to the famous Navier-Stokes equations that describe the flow of fluids like water and air. His big insight was to show that they can be re-interpreted as rules for doing computations using logical gates made out of fluid. The idea is exactly as strange as it sounds (a computer made of water?!) but it might allow mathematicians to resolve the Navier-Stokes question and pick up a cool million from the Clay Mathematics Institute, although there is still a long way to go before that happens. The point is, both Susskind and Tao used the idea from computational complexity theory that physical processes can be understood as computations. If you just said “computational whaaa theory?” then don’t worry, I’ll give you a little background in a moment. But first, you should go read Scott Aaronson’s blog post about this, since that is what inspired me to write the present post.

Ok, first, I will explain roughly what computational complexity theory is all about. Imagine that you have gathered your friends together for a fun night of board games. You start with tic-tac-toe, but after ten minutes you get bored because everyone learns the best strategy and then every game becomes a draw. So you switch to checkers. This is more fun, except that your friend George who is a robot (it is the future, just bear with me) plugs himself into the internet and downloads the world’s best checkers playing algorithm Chinook. After that, nobody in the room can beat him: even when your other robot friend Sally downloads the same software and plays against George, they always end in stalemate. In fact, a quick search on the net reveals that there is no strategy that can beat them anymore – the best you can hope for is a draw. Dang! It is just tic-tac-toe all over again. Finally, you move on to chess. Now things seem more even: although though your robot friends quickly outpace the human players (including your friend Garry Kasparov), battles between the robots are still interesting; each of them is only as good as their software, and there are many competing versions that are constantly being updated and improved. Even though they play at a higher level than human players, it is still uncertain how a given game between two robots will turn out.

After all of this, you begin to wonder: what is it that makes chess harder to figure out than checkers or tic-tac-toe? The question comes up again when you are working on your maths homework. Why are some maths problems easier than others? Can you come up with a way of measuring the `hardness’ of a problem? Well, that is where computational complexity theory comes in: it tells you how `hard’ a problem is to solve, given limited resources.

The limited resources part is important. It turns out that, if you had an infinite amount of time and battery life, you could solve any problem at all using your iPhone, or a pocket calculator. Heck, given infinite time, you could write down every possible chess game by hand, and then find out whether white or black always wins, or if they always draw. Of course, you could do it in shorter time if you got a million people to work on it simultaneously, but then you are using up space for all of those people. Either way, the problem is only interesting when you are limited in how much time or space you have (or energy, or any other resource you care to name). Once you have a resource limit, it makes sense to talk about whether one problem is harder than another (If you want details of how this is done, see for example Aaronson’s blog for his lecture notes on computational complexity theory).

This all seems rather abstract so far. But the study of complexity theory turns out to have some rather interesting consequences in the real world. For example, remember the situation with tic-tac-toe. You might know the strategy that lets you only win or draw. But suppose you were playing a dumb opponent who was not aware of this strategy – they might think that it is possible to beat you. Normally, you could convince them that you are unbeatable by just showing them the strategy so they can see for themselves. Now, imagine a super-smart alien came down to Earth and claimed that, just like with tic-tac-toe, it could never lose at chess. As before, it could always convince us by telling us its strategy — but then we could use the alien’s own strategy against it, and where is the fun in that? Amazingly, it turns out that there is a way that the alien can convince us that it has a winning strategy, without ever revealing the strategy itself! This has been proven by the computational complexity theorists (the method is rather complicated, but you can follow it up here.)

So what has this to do with physics? Let’s start with the black-hole firewall paradox. The usual black-hole information paradox says: since information cannot be destroyed, and information cannot leak out of a black hole, how do we explain what happens to the information (say, on your computer’s hard drive) that falls into a black hole, when the black hole eventually evaporates? One popular solution is to say that the information does leak out of the black hole over time, just very slowly and in a highly scrambled-up form so that it looks just like randomness. The firewall paradox puts a stick in the gears of this solution. It says that if you believe this is true, then it would be possible to violate the laws of quantum mechanics.

Specifically, say you had a quantum system that fell into a black hole. If you gathered all of the leaked information about the quantum state from outside the black hole, and then jumped into the black hole just before it finished evaporating, you could combine this information with whatever is left inside the black hole to obtain more information about the quantum state than would normally be allowed by the laws of physics. To avoid breaking the laws of quantum mechanics, you would have to have a wall of infinite energy density at the event horizon (the firewall) that stops you bringing the outside information to the inside, but this seems to contradict what we thought we knew about black holes (and it upsets Stephen Hawking). So if we try to solve the information paradox by allowing information to leak out of the black hole, we just end up in another paradox!

Source: New Scientist

One possible resolution comes from computational complexity theory. It turns out that, before you can break the laws of quantum mechanics, you first have to `unscramble’ all of the information that you gathered from outside the black hole (remember, when it leaks out it still looks very similar to randomness). But you can’t spend all day doing the unscrambling, because you are falling into the black hole and about to get squished at the singularity! Harlow and Hayden showed that in fact you do not have nearly as much time as you would need to unscramble the information before you get squished; it is simply `too hard’ complexity-wise to break the laws of quantum mechanics this way! As Scott Aaronson puts it, the geometry of spacetime is protected by an “armor” of computational complexity, kind of like a computational equivalent of the black hole’s event horizon. Aaronson goes further, speculating that there might be problems that are normally `hard’ to solve, but which become easy if you jump into a black hole! (This is reminiscent of my own musings about whether there might be hypotheses that can only be falsified by an act of black hole suicide).

But the matter is more subtle. For one thing, all of computational complexity theory rests on the belief that some problems are intrinsically harder than others, specifically, that there is no ingenious as-yet undiscovered computer algorithm that will allow us to solve hard problems just as quickly as easy ones (for the nerds out there, I’m just saying nobody has proven that P is not equal to NP). If we are going to take the idea of the black hole complexity horizon seriously, then we must assume this is true — otherwise a sufficiently clever computer program would allow us to bypass the time constraint and break quantum mechanics in the firewall scenario. Whether or not you find this to be plausible, you must admit there may be something fishy about a physical law that requires P not equal to NP in order for it to work.

Furthermore, even if we grant that this is the case, it is not clear that the complexity barrier is that much of a barrier. Just because a problem is hard in general does not mean it can’t be solved in specific instances. It could be that for a sufficiently small black hole and sufficiently large futuristic computing power, the problem becomes tractable, in which case we are back to square one. Given these considerations, I think Aaronson’s faith in the ability of computational complexity to save us from paradoxes might be premature — but perhaps it is worth exploring just in case.

Art and science, united by chickens.

When I saw that Anton Zeilinger of the Vienna quantum physics department was hosting a talk by the artist Koen Vanmechelen on the topic of chickens, I dropped everything and ran there in great excitement.

“It has finally happened,” I said to myself, “the great Zeilinger has finally lost his marbles!”

I was wrong, though: it was one of the most interesting talks of the year so far. Vanmechelen began his talk with a stylish photograph of a chicken. He said:

“To you, this might look like just a chicken. But to me, this is a work of art.”

It seemed absurd — here was a room full of physicists, being told that a chicken was art. But as Vanmechelen elaborated on his work, I saw that his work was not simply about chickens, in the same way that Rembrandt’s art was not simply about paint. In Vanmechelen’s words “It is not about the chicken, it is about humans!” Chickens are merely the medium through which Vanmechelen has chosen to express himself. Humans have such precise control over chickens, we breed them for specific purposes, we use them like components in a factory; no wonder Vanmechelen calls the chicken `high-tech’. So why not also use chickens as an artistic medium? Vanmechelen also enjoys working with glass, a seemingly unrelated medium, except that it allows him a similar level of self-expression and self discovery:

“I like the transparency of glass. You cannot see a window until it is broken. It is the same with people — it is through scars that we come to know ourselves.”

For Vanmechelen, part of his motivation to work with chickens comes from the strange and often profound experiences that this line of work leads him to. One notorious example was his idea to rescue a rooster that had lost one of its spurs. Perhaps to reinstate some of the glory afforded the chicken by its dinosaur heritage, Vanmechelen had surgeons give the rooster a proud new pair of golden spurs.

Shortly afterwards, Vanmechelen was taken to court in Belgium by animal rights activists. It seemed that, by the letter of the law, it was illegal to give chickens prosthetic implants. Vanmechelen defended his work and pointed out that he was helping the rooster, which would have otherwise been an outcast in chicken society, and the activists finally agreed with him. But the judge was adamant: there was still the matter of the law to be settled. Struck by the absurdity of the case, Vanmechelen asked: if prosthetic augmentation was not allowed, then what precisely was it legal to do to a live chicken? The judge unfolded an official document and read from a list. Legally, one could burn its beak, scorch its wings, cut its legs, and more in a similar vein. Needless to say, Vanmechelen did not have to face prison, but the incident stayed with him.

“I am not a scientist, I am not an activist, I am an artist. I do not pass judgement, I simply comment on what I see.”

He called the animal rights activists afterwards. He said to them, “I have done my job as an artist. Now you can do your job as an activist: change the law”.

Vanmechelen’s major work has much less to do with chickens and much more to do with people. The Cosmopolitan Chicken Project is an exercise in fertility. Travelling around the world, Vanmechelen collects chickens that have been selectively bred to suit their country of origin, and creates cross-breeds. He notes that each country has developed a breed of chicken that represents the nation; as an extreme example, the French Poulet de Bresse has a red crest, white body and blue-tinged legs, matching the country’s flag.

Poulet de Bresse

“When you put an animal in a frame, you halt its evolution,” he explains. “The chickens become infertile through too much inbreeding. Cross-breeding restores life and fertility to the species. It is the same for humans.”

Duality is also a major theme in Vanmechelen’s work: every organism needs another organism to survive. Humans have not simply enslaved chickens — we are in turn enslaved by them. There are over 24 billion chickens in the world today, about three and a half per person. Historically, we have taken them everywhere with us, to such an extent that researchers at the University of Nottingham can even trace the movements of humans through the genomes of chickens.

This duality can be seen directly in the theory of coding and information. Take two messages of the same length and combine them by swapping every second letter between the two. Suppose we separate the resulting scrambled halves and give them to different people. It doesn’t matter how many times you copy one half, you will never recover the message — you will stagnate from inbreeding the same information. But if you get together with someone who has different information that comes from the other half, you can combine your halves to discover the hidden message that was there all along.

By the end of Vanmechelen’s talk, I finally understood why Professor Zeilinger had invited him here, to a physics department, to talk about art. In isolation, every discipline stagnates and becomes inbred. I rarely go to see talks by scientists, but I always find talks by artists stimulating. Why is that? Perhaps the reason is not that scientists are dull, but simply that I am one of them. Sometimes, to unlock the riches of your own discipline, you need to introduce random mutations from the outside. So bring on the artists!

Black holes, bananas, and falsifiability.

Previously I gave a poor man’s description of the concept of `falsifiability‘, which is a cornerstone of what most people consider to be good science. This is usually expressed in a handy catchphrase like `if it isn’t falsifiable, then it isn’t science’. For the layperson, this is a pretty good rule of thumb. A professional scientist or philosopher would be more inclined to wonder about the converse: suppose it is falsifiable, does that guarantee that it is science? Karl Popper, the man behind the idea, has been quoted as saying that basically yes, not only must a scientific theory be falsifiable, a falsifiable theory is also scientific [1]. However, critics have pointed out that it is possible to have theories that are not scientific and yet can still be falsified. A classic example is Astrology, which has been “thoroughly tested and refuted” [2], (although sadly this has not stopped many people from believing in it). Given that it is falsifiable (and falsified), it seems one must therefore either concede that Astrology was a scientific hypothesis which has since been disproved, or else concede that we need something more than just falsifiability to distinguish science from pseudo-science.

Things are even more subtle than that, because a falsifiable statement may appear more or less scientific depending on the context in which it is framed. Suppose that I have a theory which says that there is cheese inside the moon. We could test this theory, perhaps by launching an expensive space mission to drill the moon for cheese, but nobody would ever fund such a mission because the theory is clearly ludicrous. Why is it ludicrous? Because within our existing theoretical framework and our knowledge of planet formation, there is no role played by astronomical cheese. However, imagine that we lived in a world in which it was discovered that cheese was naturally occurring substance in space and indeed had a crucial role to play in the formation of planets. In some instances, the formations of moons might lead to them retaining their cheese substrate, hidden by layers of meteorite dust. Within this alternative historical framework, the hypothesis that there is cheese inside the moon is actually a perfectly reasonable scientific hypothesis.

Yes, but does it taste like Wensleydale?

The lesson here is that the demarcation problem between science and pseudoscience (not to mention non-science and un-science which are different concepts [2]) is not a simple one. In particular, we must be careful about how we use ideas like falsification to judge the scientific content of a theory. So what is the point of all this pontificating? Well, recently a prominent scientist and blogger Sean Carroll argued that the scientific idea of falsification needs to be “retired”. In particular, he argued that String Theory and theories with multiple universes have been unfairly branded as `unfalsifiable’ and thus not been given the recognition by scientists that they deserve. Naturally, this alarmed people, since it really sounded like Sean was saying `scientific theories don’t need to be falsifiable’.

In fact, if you read Sean’s article carefully, he argues that it is not so much the idea of falsifiability that needs to be retired, but the incorrect usage of the concept by scientists without sufficient philosophical education. In particular, he suggests that String Theory and multiverse theories are falsifiable in a useful sense, but that this fact is easily missed by people who do not understand the subtleties of falsifiability:

“In complicated situations, fortune-cookie-sized mottos like `theories should be falsifiable’ are no substitute for careful thinking about how science works.”

Well, one can hardly argue against that! Except that Sean has committed a couple of minor crimes in the presentation of his argument. First, while Sean’s actual argument (which almost seems to have been deliberately disguised for the sake of sensationalism) is reasonable, his apparent argument would lead most people to draw the conclusion that Sean thinks unfalsifiable theories can be scientific. Peter Woit, commenting on the related matter of Max Tegmark’s recent book, points out that this kind of talk from scientists can be fuel for crackpots and pseudoscientists who use it to appear more legitimate to laymen:

“If physicists like Tegmark succeed in publicizing and getting accepted as legitimate mainstream science their favorite completely empty, untestable `theory’, this threatens science in a very real way.”

Secondly, Sean claims that String Theory is at least in principle falsifiable, but if one takes the appropriate subtle view of falsifiability as he suggests, one must admit that `in principle’ falsifiability is rather a weak requirement. After all, the cheese-in-the-moon hypothesis is falsifiable in principle, as is the assertion that the world will end tomorrow. At best, Sean’s argument goes to show that we need other criterion than falsifiability to judge whether String Theory is scientific, but given the large number of free parameters in the theory, one wonders whether it won’t fall prey to something like the `David Deutsch principle‘, which says that a theory should not be too easy to modify retrospectively to fit the observed evidence.

While the core idea of falsifiability is here to stay, I agree with Scott Aaronson that remarkably little progress has been made since Popper on building upon this idea. For all their ability to criticise and deconstruct, the philosophers have not really been able to tell us what does make a theory scientific, if not merely falsifiability. Sean Carroll suggests considering whether a theory is `definite’, in that it makes clear statements about reality, and `empirical’ in that these statements can be plausibly linked to physical experiments. Perhaps the falsifiability of a claim should also be understood as relative to a prevailing paradigm (see Kuhn).

In certain extreme scenarios, one might also be able to make the case that the falsifiability of a statement is relative to the place of the scientists in the universe. For example, it is widely believed amongst physicists that no information can escape a black hole, except perhaps in a highly scrambled-up form, as radiated heat. But as one of my friends pointed out to me today, this seems to imply that certain statements about the interior of the black hole cannot ever be falsified by someone sitting outside the event horizon. Suppose we had a theory that there was a banana inside the black hole. To check the theory, we would likely need to send some kind of banana-probe (a monkey?) into the black hole and have it come out again — but that is impossible. The only way to falsify such a statement would be to enter the black hole ourselves, but then we would have no way of contacting our friends back home to tell them they were right or wrong about the banana. If every human being jumped into the black hole, the statement would indeed be falsifiable. But if exactly half of the population jumped in, is the statement falsifiable for them and not for anyone else? Could the falsifiability of a statement actually depend on one’s physical place in the universe? This would indeed be troubling, because it might mean there are statements about our universe that are in principle falsifiable by some hypothetical observer, but not by any of us humans. It becomes disturbingly similar to predictions about the afterlife – they can only be confirmed or falsified after death, and then you can’t return to tell anyone about it. Plus, if there is no afterlife, an atheist doesn’t even get to bask in the knowledge of being correct, because he is dead.

We might hope that statements about quasi-inaccessible regions of experience, like the insides of black holes or the contents of parallel universes, could still be falsified `indirectly’ in the same way that doing lab tests on ghosts might lend support to the idea of an afterlife (wouldn’t that be nice). But how indirect can our tests be before they become unscientific? These are the interesting questions to discuss! Perhaps physicists should try to add something more constructive to the debate instead of bickering over table-scraps left by philosophers.

[1] “A sentence (or a theory) is empirical-scientific if and only if it is falsifiable” Popper, Karl ([1989] 1994). “Falsifizierbarkeit, zwei Bedeutungen von”, pp. 82–86 in Helmut Seiffert and Gerard Radnitzky. (So there.)

[2] See the Stanford Encyclopedia of Awesomeness.

My PhD thesis on time-travel, for dummies.

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.

Source: xkcd.com

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.

Traunkirchen 2013

Edit: I’ve corrected the text to indicate that Jim Baggott actually started out as a chemist, not a physicist. Sorry Jim! But, as a wise man once said, the only real difference is that a physicist studies one atom while a chemist studies two.

A few weeks ago in late November, I had the pleasure of attending the workshop on Quantum Physics and the Nature of Reality organised by Anton Zeilinger and Časlav Brukner. The workshop was held at the International Academy in the idyllic location of Traunkirchen, a small town in Upper Austria, where the Traunstein mountain dominates the sky above the Traunsee lake.

Source: http://www.romantikstrasse.at/

According to the online brochure, “…the former monastery is home to the International Academy and the Summer Academy for Painting. It thus connects the eventful past of a religious centre with the promising future of particle physics.” Appropriately, the workshop was sponsored by the John Templeton Foundation, which supports (perhaps paradoxically) scientific research in addition to theological and religious studies [1].

The weather was not as accommodating as in the brochure picture above, with stormy grey clouds encroaching over the Traunsee, but our beautiful and cosy lodgings provided the perfect rainy-day atmosphere. There’s nothing like gathering near a fireplace with coffee or tea to do some physics. Much of the discussion centered on questions raised in a recent article, `The Oxford Questions on the foundations of quantum physics’, with a particular focus on the following two questions:

1. What are the most interesting and exciting things you have learned in the last three years?

2. What new findings, developments, impulses are at the heart of your hopes for the future?

This Traunkirchen conference was not the first of its kind – some of you might recall the controversy surrounding Schlossauer, Kofler and Zeilinger’s now infamous poll of the participants at an earlier Traunkirchen conference in 2011. The poll was meant to provide a “snapshot of foundational attitudes towards quantum mechanics”, but as Matt Leifer observed, the evidence merely indicates that “…people who went to a meeting organized by Zeilinger are likely to have views similar to Zeilinger” [2]. Given this background, the present Traunkirchen conference promised to be interesting, with a wide assortment of guests including philosophers and philosophically-inclined physicists, not to mention popular author Jim Baggott, whose latest book `Farewell to Reality: How Fairytale Physics Betrays the Search for Scientific Truth’ goes beyond recent criticisms of String Theory to provide an intelligent critique of similar troubling practices in modern physics as a whole.

I took Jim’s presence at the conference as a positive sign. While most scientists readily acknowledge the importance of communicating with the public (after all, much of our funding does come from public money) those who do take the brave step into the public domain also risk separating themselves from the cutting edge of research and thereby alienating themselves from the very community that they are supposed to represent. As Jim cheerfully remarked, Traunkirchen was his first academic conference since the 80’s, just before he decided to leave his post as an academic chemist and take up an industry job. Despite the long absence, positive reviews of his work from practicing scientists bolstered the relevance of his commentary to the modern physics community, and his presence was well received by the other attendees. Another welcome addition in this vein was Michael Raymer from the University of Oregon, who has taken on the formidable challenge of teaching physics, including quantum mechanics, to university students that have absolutely no background in science. The fact that this could be done effectively is quite a remarkable demonstration of the public’s ability to understand science, if scientists just take the time to explain it to them.

Interestingly, while many of the more philosophically-geared talks tended to get sidetracked or bogged down in technicalities, Jim managed to articulate a clear position against what he called `fairytale physics’ without being tripped up or sidetracked too much by the crowd, which was feeling particularly mischievous after an invigorating breakfast (at one point, Jim was even asked to explain what it means for a thing `to exist’). He raised a few hackles when he turned his attention away from string theory (to which everybody was more than happy to add their own critiques) to black holes, for which he argued that the amount of research far outstripped the attention warranted by empirical evidence. He did not try to argue that research on black holes was unimportant, but rather that the amount of attention given to them in the literature did not seem justified, given that some of the most talked-about features of black holes like Hawking radiation have never been observed. While one might find grounds to disagree with Jim on the topic of black holes, Jim’s talk reminded us that one should always be careful to apply the same criticisms one has of opposing ideas to one’s own pet theories, lest one become a perpetrator of fairytale physics.

The talks by Jess Riedel, Markus Appleby, Danny Greenberger, and George Ellis,  among others, were notable for the diversity of preferred interpretations presented, ranging from Riedel boldly taking the existence of a wavefunction of the entire universe for granted, all the way to Ellis’s provocative argument that the usual quantum mechanical description is unlikely to be appropriate even at human scales, let alone astronomical scales. Every viewpoint was respected and carefully analysed by the participants in the discussion that followed. By the end of the conference, however, I sensed that a large contingent of the attendees subscribed to what one might call variants of the `informational interpretation’ of quantum mechanics.

Broadly speaking, informational interpretations tend to have the following points in common:

(i) They regard wave-function collapse to not be a real phenomenon, but more akin to the “collapse” of one’s knowledge upon gaining new information. This idea is elucidated most clearly by the Quantum Bayesians (QBists), but is common to other interpretations as well (certain readings of Bohr’s Copenhagen interpretation run this way).

(ii) While they typically regard the wavefunction as representing information about the expectations of some agent or appropriately defined observer, they do not consider the wavefunction to represent information about some underlying, observer-independent reality. For example, this is in opposition to hidden variable interpretations like the De Broglie-Bohm interpretation.

Note that (i) and (ii) do not preclude a realist view of physics, although this is a point on which the informational views tend to diverge from each other. For example one could take a `realist-instrumentalist’ stance, where the measurement settings and the outcomes produced by the devices (i.e. the objects of our experience), are taken to be real. Alternatively, following Carlo Rovelli, one could take a relational view, in which the relationships between physical systems can be considered `real’. In that case, we identify a physical system as an `observer’, and the wavefunction represents an objective property of the interaction between observer and system. In contrast to both these views, the subjective Bayesian, as embodied by Chris Fuchs, would deny that there are any `elements of reality’ at all. All of these views nevertheless count as informational interpretations by the rough guidelines given above.

Personally, I am sympathetic to the informational approach; hence one should take a grain of salt with my assertion that discussions at the conference supported this view. After all, research on cognitive biases suggests it is possible that I subconsciously accepted information at face value that was compatible with my preferred viewpoint, while seeking reasons to disregard information that opposed it — this could then lead me to think that the talks at the conference favoured the informational interpretation much more than they actually did [3].

I’ll conclude with some brief comments on Anton Zeilinger’s own philosophical sympathies, as expressed by him in his talk at the end of the conference. As near as I can tell, Zeilinger’s view is similar to the realist-instrumentalist view I mentioned above — the quantum state represents an abstraction of our expectations for what should happen to our instruments in an experiment. The measurement setting and outcomes are real, but the objects that appear in our formulas that connect the settings to the predicted outcomes are not necessarily real things in their own right. Quoth Zeilinger:

“Collapse is at the heart of Quantum Mechanics — it does not represent a breakdown of Quantum Mechanics. […] It is impossible to operationally verify any distinction between reality and information.”

I take this as basically saying that wave function collapse is a change in information, not a change in the `elements of reality’, in accordance with (i). Regarding the question of whether the wavefunction represents information about some underlying reality, he says:

“It is wrong to think there is anything behind the randomness.”

Perhaps the best understanding of the Zeilinger interpretation of QM can be gleaned from his closing remark:

“There are two fundamental freedoms: our freedom to define which measurement apparatus to use and thus to determine which quality can become reality; and Nature’s freedom to give the answer she likes.”

[1] There was some intriguing discussion about the unease that some physicists feel regarding the religious side of Templeton’s agenda, but I’m postponing a discussion of that topic until I’ve made up my own mind about it. For the moment, I think funding science can only be a good thing in the long run, regardless of whether it is coming from Templeton, Laziridis, Milner, Zuckerberg or Leprechauns.

[2] To be fair, Zeilinger frequently entertains guests with quite different interpretational attitudes than himself, recent examples being John Cramer, originator of the `transactional interpretaion’, and Lev Vaidman, whose preferred interpretation has a distinct many-worlds flavour, not to mention several attendees of this recent conference.

[3] As scientists, we must always try to be aware of our own subconscious biases! Here, here and here are great resources for getting started on checking yourself for cognitive biases.

Halloween special: Boltzmann Brains

Author’s note: I wanted to wait before doing another post on anthropic reasoning, but this topic was just too good to pass up just after Halloween [1].

The Incredible Hercules #133

1: Are You A Disembodied Brain?

Our story begins with Ludwig Boltzmann’s thermodynamic solution to the arrow-of-time problem. The problem is to explain why the laws of physics at the microscopic scale appear to be reversible, but the laws as seen by us seem to follow a particular direction from past to future. Boltzmann argued that, provided the universe started in a low entropy state, the continual increase in entropy due to the second law of thermodynamics would explain the observed directionality of time. He thereby reduced the task to the lesser problem of explaining why the universe started in a low entropy state in the first place (incidentally, that is pretty much where things stand today, with some extra caveats). Boltzmann had his own explanation for this, too: he argued that if the universe were big enough, then even though it might be in a maximum entropy state, there would have to be random fluctuations in parts of the universe that would lead to local low-entropy states. Since human beings could only have come to exist in a low-entropy environment, we should not be surprised that our part of the universe started with low entropy, even though this is extremely unlikely within the overall model. Thus, one can use an observer-selection effect to explain the arrow of time.

Sadly, there is a crucial flaw in Boltzmann’s argument. Namely, that it doesn’t explain why we find ourselves in such a large region of low entropy as the observable universe. The conditions for conscious observers to exist could have occurred in a spontaneous fluctuation much smaller than the observable universe – so if the total universe was indeed very large and in thermal equilibrium, we should expect to find ourselves in just a small bubble of orderly space, outside of which is just featureless radiation, instead of the stars and planets that we actually do see. In fact, the overwhelming number of conscious observers in such a universe would just be disembodied brains that fluctuated into existence by pure chance. It is extremely unlikely that any of these brains would share the same experiences and memories as real people born and raised on Earth within a low-entropy patch of the universe, so Boltzmann’s argument seems to be unable to account for the fact that we do have experiences consistent with this scenario, rather than with the hypothesis that we are disembodied brains surrounded by thermal radiation.

Matters, as always, are not quite so simple. It is possible to rescue Boltzmann’s argument by the following rationale. Suppose I believe it possible that I could be a Boltzmann Brain. Clearly, my past experiences exhibit a level of coherence and order that is not typical of your average Boltzmann Brain. However, there is still some subset of Boltzmann Brains which, by pure chance, fluctuated into existence with an identical set of memories and past experiences encoded into their neurons so as to make their subjective experiences identical to mine. Even though they are a tiny fraction of all Boltzmann Brains, there are still vastly more of them than there are `really human’ versions of me that actually evolved within a large low-entropy sub-universe. Hence, conditional on my subjective experience thus far, I am still forced to conclude that I am overwhelmingly more likely to be a Boltzmann Brain, according to this theory.

2: Drama ensues

Quite recently, Sean Carroll wrote a paper (publicized on his blog) in which he and co-author Kim Boddy use the Higgs mechanism to “solve the problem of Boltzmann Brains” in cosmology. The setting is the  ΛCDM model of cosmology, which is a little different to Boltzmann’s model of the universe, but suffers a similar problem: in the case of ΛCDM, the universe keeps expanding forever, eventually reaching a maximum entropy state (aka “heat death”) and after which Boltzmann Brains have as much time as they need to fluctuate randomly out of the thermal noise. Such a model, argues Carroll, would imply that it is overwhelmingly likely that we are Boltzmann Brains.

Why is this a problem? Carroll puts it down to what he calls “cognitive instability”. Basically, the argument goes like this. Suppose you believe in a model of cosmology that has Boltzmann Brains. Then you should believe that you are most likely to be one of them. But this means that your reasons for believing in the model in the first place cannot be trusted, since they are not based on actual scientific evidence, but instead simply fluctuated into your brain at random. In essence, you are saying `based on the evidence, I believe that I am an entity that cannot believe in anything based on what it thinks is evidence’. A cognitively unstable theory therefore cannot both be true and be justified by observed evidence. Carroll’s solution to this problem is to reject the model in favor of one that doesn’t allow for the future existence of Boltzmann Brains.

Poor Carroll has taken a beating over at other blogs. Luboš Motl provided a lengthy response filled with the usual ad-hominems:

`…I really think that Carroll’s totally wrong reasoning is tightly linked to an ideology that blinds his eyes. As a hardcore leftist […] he believes in various forms of egalitarianism. Every “object” has the same probability.’

Jacques Distler wrote:

`…This is plainly nuts. How can a phase transition that may or may not take place, billions of years in the future, affect anything that we measure in the here-and-now? And, if it doesn’t affect anything in the present, why do I &#%@ care?’

Only Mark Srednicki seemed able to disagree with Carroll without taking the idea as a personal affront; his level-headed discussions with Carroll and Distler helped to clarify the issue significantly. Ultimately, Srednicki agrees with the conclusions of both Motl and Distler, but for slightly different reasons. The ensuing discussion can be summarized something like this:

Distler: A model of the universe does not allow you to make predictions by itself. You also need to supply a hypothesis about where we exist within the universe. And any hypothesis in which we are Boltzmann Brains is immediately refuted by empirical evidence, namely when we fail to evaporate into radiation in the next second.

Motl: Yep, I basically agree with Distler. Also, Boddy and Carroll are stupid Marxist idiots.

Srednicki: Hang on guys, it’s more subtle than that. Carroll is simply saying that, in light of the evidence, a cosmological model without Boltzmann Brains is better than one that has Boltzmann Brains in it. Whether this is true or not is a philosophical question, not something that is blindingly obvious.

Distler: Hmmpf! Well I think it is blindingly obvious that the presence or absence of Boltzmann Brains has no bearing on choosing between the two models. Your predictions for future events would be the same in both.

Srednicki: That’s only true if, within the Boltzmann Brain model, you choose a xerographic distribution that ensures you are a non-Boltzmann-brain. But the choice of xerographic distribution is a philosophical one.

Distler: I disagree – Bayesian theory says that you should choose the prior distribution that converges most quickly to the `correct’ distribution as defined by the model. In this case, it is the distribution that favours us not being Boltzmann Brains in the first place.

(Meanwhile, at Preposterous Universe…)

Carroll: I think that it is obvious that you should give an equal credence to yourself being any one of the observers in a model that have identical previous experiences as you. It follows that a model without Boltzmann Brains is better than a model with Boltzmann Brains due to cognitive instability.

Srednicki: Sorry Carroll – your claim is not at all obvious. It is a philosophical assumption that cannot be derived from any laws within the model. Under a different assumption, Boltzmann Brains aren’t a problem.

There is a potential flaw in the Distler/Motl argument: it rests on the premise that, if you are indeed a Boltzmann Brain, this can be taken as a highly falsifiable hypothesis which is falsified one second later when you fail to evaporate. But strictly speaking, that only rules out a subset of possible Boltzmann Brain hypotheses – there is still the hypothesis that you are a Boltzmann Brain whose experiences are indistinguishable from yours right up until the day you die, at which point they go `poof’, and the hypothesis that you are one of these brains is not falsifiable. Sure, there are vastly fewer Boltzmann Brains with this property, but in a sufficiently long-lived universe there are still vastly more of them than the `real you’. Thus, the real problem with Boltzmann Brains is not that they are immediately falsified by experience, but quite the opposite: they represent an unfalsifiable hypothesis. Of course, this also immediately resolves the problem: even if you were a Boltzmann Brain, your life will proceed as normal (by definition, you have restricted yourself to BB’s whose subjective experiences match those of a real person’s life), so this belief has no bearing on your decisions. In particular, your subjective experience gives you no reason to prefer one model to another just because the former contains Boltzmann Brains and the latter doesn’t. One thereby arrives at the same conclusion as Distler and Motl, but by a different route. However, this also means that Distler and Motl cannot claim that they are not Boltzmann Brains based on observed evidence, if one assumes a BB model. Either they think Boddy and Carroll’s proposed alternative is not a viable theory in it own right, or else they don’t think that a theory containing a vast number of unfalsifiable elements is any worse than a similar theory that doesn’t need such elements, which to me sounds absurd.

I think that Mark Srednicki basically has it right: the problem at hand is yet another example of anthropic reasoning, and the debate here is actually about how to choose an appropriate `reference class’ of observers. The reference class is basically the set of observers within the model that you think it is possible that you might have been. Do you think it is possible that you could have been born as somebody else? Do you think you might have been born at a different time in history? What about as an insect, or a bacterium? In a follow-up post, I’ll discuss an idea that lends support to Boddy and Carroll’s side of the argument.

[1] If you want to read about anthropic reasoning from somebody who actually knows what they are talking about, see Anthropic Bias by Nick Bostrom. Particularly relevant here is his discussion of `freak observers’.