Bootstrapping to quantum gravity

Kepler

“If … there were no solid bodies in nature there would be no geometry.”
-Poincaré

A while ago, I discussed the mystery of why matter should be the source of gravity. To date, this remains simply an empirical fact. The deep insight of general relativity – that gravity is the geometry of space and time – only provides us with a modern twist: why should matter dictate the geometry of space-time?

There is a possible answer, but it requires us to understand space-time in a different way: as an abstraction that is derived from the properties of matter itself. Under this interpretation, it is perfectly natural that matter should affect space-time geometry, because space-time is not simply a stage against which matter dances, but is fundamentally dependent on matter for its existence. I will elaborate on this idea and explain how it leads to a new avenue of approach to quantum gravity.

First consider what we mean when we talk about space and time. We can judge how far away a train is by listening to the tracks, or gauge how deep a well is by dropping a stone in and waiting to hear the echo. We can tell a mountain is far away just by looking at it, and that the cat is nearby by tripping over it. In all these examples, an interaction is necessary between myself and the object, sometimes through an intermediary (the light reflected off the mountain into my eyes) and sometimes not (tripping over the cat). Things can also be far away in time. I obviously cannot interact with people who lived in the past (unless I have a time machine), or people who have yet to be born, even if they stood (or will stand) exactly where I am standing now. I cannot easily talk to my father when he was my age, but I can almost do it, just by talking to him now and asking him to remember his past self. When we say that something is far away in either space or time, what we really mean is that it is hard to interact with, and this difficulty of interaction has certain universal qualities that we give the names `distance’ and `time’.
It is worth mentioning here, as an aside, that in a certain sense, the properties of `time’ can be reduced to properties of `distance’ alone. Consider, for instance, that most of our interactions can be reduced to measurements of distances of things from us, at a given time. To know the time, I invariably look at the distance the minute hand has traversed along its cycle on the face of my watch. Our clocks are just systems with `internal’ distances, and it is the varying correspondence of these `clock distances’ with the distances of other things that we call the `time’. Indeed, Julian Barbour has developed this idea into a whole research program in which dynamics is fundamentally spatial, called Shape Dynamics.

Sigmund Freud Museum, Wien – Peter Kogler

So, if distance and time is just a way of describing certain properties of matter, what is the thing we call space-time?

We now arrive at a crucial point that has been stressed by philosopher Harvey Brown: the rigid rods and clocks with which we claim to measure space-time do not really measure it, in the traditional sense of the word `measure’. A measurement implies an interaction, and to measure space-time would be to grant space-time the same status as a physical body that can be interacted with. (To be sure, this is exactly how many people do wish to interpret space-time; see for instance space-time substantivalism and ontological structural realism).

Brown writes:
“One of Bell’s professed aims in his 1976 paper on `How to teach relativity’ was to fend off `premature philosophizing about space and time’. He hoped to achieve this by demonstrating with an appropriate model that a moving rod contracts, and a moving clock dilates, because of how it is made up and not because of the nature of its spatio-temporal environment. Bell was surely right. Indeed, if it is the structure of the background spacetime that accounts for the phenomenon, by what mechanism is the rod or clock informed as to what this structure is? How does this material object get to know which type of space-time — Galilean or Minkowskian, say — it is immersed in?” [1]

I claim that rods and clocks do not measure space-time, they embody space-time. Space-time is an idealized description of how material rods and clocks interact with other matter. This distinction is important because it has implications for quantum gravity. If we adopt the more popular view that space-time is an independently existing ontological construct, it stands to reason that, like other classical fields, we should attempt to directly quantise the space-time field. This is the approach adopted in Loop Quantum Gravity and extolled by Rovelli:

“Physical reality is now described as a complex interacting ensemble of entities (fields), the location of which is only meaningful with respect to one another. The relation among dynamical entities of being contiguous … is the foundation of the space-time structure. Among these various entities, there is one, the gravitational field, which interacts with every other one and thus determines the relative motion of the individual components of every object we want to use as rod or clock. Because of that, it admits a metrical interpretation.” [2]

One of the advantages of this point of view is that it dissolves some seemingly paradoxical features of general relativity, such as the fact that geometry can exist without (non-gravitational) matter, or the fact that geometry can carry energy and momentum. Since gravity is a field in its own right, it doesn’t depend on the other fields for its existence, nor is there any problem with it being able to carry energy. On the other hand, this point of view tempts us into framing quantum gravity as the mathematical problem of quantising the gravitational field. This, I think, is misguided.

I propose instead to return to a more Machian viewpoint, according to which space-time is contingent on (and not independent of) the existence of matter. Now the description of quantum space-time should follow, in principle, from an appropriate description of quantum matter, i.e. of quantum rods and clocks. From this perspective, the challenge of quantum gravity is to rebuild space-time from the ground up — to carry out Einstein’s revolution a second time over, but using quantum material as the building blocks.

Ernst Mach vs. Max Ernst. Get it right, folks.

My view about space-time can be seen as a kind of `pulling oneself up by one’s bootstraps’, or a Wittgenstein’s ladder (in which one climbs to the top of a ladder and then throws the ladder away). It works like this:
Step 1: define the properties of space-time according to the behaviour of rods and clocks.
Step 2: look for universal patterns or symmetries among these rods and clocks.
Step 3: take the ideal form of this symmetry and promote it to an independently existing object called `space-time’.
Step 4: Having liberated space-time from the material objects from which it was conceived, use it as the independent standard against which to compare rods and clocks.

Seen in this light, the idea of judging a rod or a clock by its ability to measure space or time is a convenient illusion: in fact we are testing real rods and clocks against what is essentially an embodiment of their own Platonic ideals, which are in turn conceived as the forms which give the laws of physics their most elegant expression. A pertinent example, much used by Julian Barbour, is Ephemeris time and the notion of a `good clock’. First, by using material bodies like pendulums and planets to serve as clocks, we find that the motions of material bodies approximately conform to Newton’s laws of mechanics and gravitation. We then make a metaphysical leap and declare the laws to be exactly true, and the inaccuracies to be due to imperfections in the clocks used to collect the data. This leads to the definition of the `Ephemeris time’, the time relative to which the planetary motions conform most closely to Newton’s laws, and a `good clock’ is then defined to be a clock whose time is closest to Ephemeris time.

The same thing happens in making the leap to special relativity. Einstein observed that, in light of Maxwell’s theory of electromagnetism, the empirical law of the relativity of motion seemed to have only a limited validity in nature. That is, assuming no changes to the behaviour of rods and clocks used to make measurements, it would not be possible to establish the law of the relativity of motion for electrodynamic bodies. Einstein made a metaphysical leap: he decided to upgrade this law to the universal Principle of Relativity, and to interpret its apparent inapplicability to electromagnetism as the failure of the rods and clocks used to test its validity. By constructing new rods and clocks that incorporated electromagnetism in the form of hypothetical light beams bouncing between mirrors, Einstein rebuilt space-time so as to give the laws of physics a more elegant form, in which the Relativity Principle is valid in the same regime as Maxwell’s equations.

Ladder for Booker T. Washington – Martin Puryear

By now, you can guess how I will interpret the step to general relativity. Empirical observations seem to suggest a (local) equivalence between a uniformly accelerated lab and a stationary lab in a gravitational field. However, as long as we consider `ideal’ clocks to conform to flat Minkowski space-time, we have to regard the time-dilated clocks of a gravitationally affected observer as being faulty. The empirical fact that observers stationary in a gravitational field cannot distinguish themselves (locally) from uniformly accelerated observers then seems accidental; there appears no reason why an observer could not locally detect the presence of gravity by comparing his normal clock to an `ideal clock’ that is somehow protected from gravity. On the other hand, if we raise this empirical indistinguishability to a matter of principle – the Einstein Equivalence Principle – we must conclude that time dilation should be incorporated into the very definition of an `ideal’ clock, and similarly with the gravitational effects on rods. Once the ideal rods and clocks are updated to include gravitational effects as part of their constitution (and not an interfering external force) they give rise to a geometry that is curved. Most magically of all, if we choose the simplest way to couple this geometry to matter (the Einstein Field Equations), we find that there is no need for a gravitational force at all: bodies follow the paths dictated by gravity simply because these are now the inertial paths followed by freely moving bodies in the curved space-time. Thus, gravity can be entirely replaced by geometry of space-time.

As we can see from the above examples, each revolution in our idea of space-time was achieved by reconsidering the nature of rods and clocks, so as to make the laws of physics take a more elegant form by incorporating some new physical principle (eg. the Relativity and Equivalence principles). What is remarkable is that this method does not require us to go all the way back to the fundamental properties of matter, prior to space-time, and derive everything again from scratch (the constructive theory approach). Instead, we can start from a previously existing conception of space-time and then upgrade it by modifying its primary elements (rods and clocks) to incorporate some new principle as part of physical law (the principle theory approach). The question is, will quantum gravity let us get away with the same trick?

I’m betting that it will. The challenge is to identify the empirical principle (or principles) that embody quantum mechanics, and upgrade them to universal principles by incorporating them into the very conception of the rods and clocks out of which general relativistic space-time is made. The result will be, hopefully, a picture of quantum geometry that retains a clear operational interpretation. Perhaps even Percy Bridgman, who dismissed the Planck length as being of “no significance whatever” [3] due to its empirical inaccessibility, would approve.

Boots with laces – Van Gogh

[1] Brown, Physical Relativity, p8.
[2] Rovelli, `Halfway through the woods: contemporary research on space and time’, in The Cosmos of Science, p194.
[3] Bridgman, Dimensional Analysis, p101.

Science, psychoanalyzed

“The problem for us is not, are our desires satisfied or not? The problem is, how do we know what we desire?”

-Slavoj Žižek

The most fundamental dramatic tension is the tension between the divided self. We have all on occasion experienced an internal dialogue like the following: `I ate the cookie despite myself. I knew it was wrong, but I couldn’t help myself. Afterwards, I hated myself’. On one hand, this dialogue makes sense to us and its meaning seems clear; on the other hand, it makes no sense without a division of the self. Who is the myself against whose wishes I eat the cookie? Who is the I that could not help myself? Who, afterwards, is hated, and who is the hater? To admit that the self can be both the subject and object of an action is equivalent to admitting that the self is divided.

Let us therefore deliver ourselves into the hands of Freud, who will lead us down a rabbit-hole of self-discovery. Who are these characters, the id, ego and superego? The id is the instinctive, reactive, animalistic part of the mind. It expresses emotion without reflection, it is wordless, mute, free of morals, shame or self-consciousness. The superego is the embodiment of laws and limitations. When the child learns that it is separate from the world, confined to a small, weak body and cannot have everything it wants – when it learns that it is at the mercy of beings far more powerful who dictate its life – it internalises these limitations and laws by creating the superego. The superego tells us what we are not allowed to do, where we cannot go, and what is forbidden by physical, moral or societal laws.

Freud

The fundamental tension between superego and id demands a mediator to decide whether to go with the desires of the id or follow the rules of the superego. This mediator, haplessly caught between the two, is our hero, ourselves: the ego. When the ego obeys the superego, the id is suppressed and frustrated, while the ego becomes more powerful and more strict in its demands. When the ego obeys the id instead, the satisfaction is short-lived, for the id knows only the present moment, and is hungry again no sooner it is fed. Meanwhile, the superego brings its vengeance on the ego for the transgression, afflicting it with guilt and feelings of inferiority. The id expresses our desires and fears, the superego expresses our judgements, and the ego determines how we respond in our actions. Before reading the end of this paragraph, take a moment to re-read the dialogue about the cookie and try to name the actors and the victims. Did you do it? The id wanted to eat the cookie, the superego knew it was wrong, and the ego ate it. The superego was helpless to stop the ego, but afterwards, it hated the ego, and punished it with feelings of guilt. Now it makes sense.

MBros

Humans have a curious obsession with the number three. There are three wise men, the holy trinity, the `third eye’ of Hinduism. Dramatic tension between fictional characters also frequently relies on combinations of three. It is an entertaining exercise (but not always fruitful) to identify the roles of id, ego and superego in famous triplets from mythology and fiction. Here is a puzzle for you. In Brisbane, I used to frequent a coffee house called Three Monkeys. Inside, they had amassed a collection of depictions and statuettes of the `Three Wise Monkeys’, a mystical image originating from Japan in which the first monkey has covered its eyes, the second its ears, and the last one its mouth. The image is typically associated with the maxim: see no evil, hear no evil, speak no evil, thought to originate from a similar passage in the Chinese Analects of Confucius. The puzzle is this: if the monkeys were to represent the different aspects of the divided self, which monkey is the id, which is the ego and which is the superego? Or does the comparison simply fail? My own answer is given at the end of this essay.

3monks

Tension is by nature unsustainable. It must eventually resolve itself in one of three ways: destruction, reconciliation, or transformation into a new kind of tension (which just means the destruction of some things and the reconciliation of others). Destruction can occur when the division between the id and superego is too extreme, tearing apart the ego with opposing forces. Since the ego exists only to mediate the conflict between the other two, a reconciliation of the id with the superego automatically conciliates the ego as well. This represents a dissolution of the ego, meaning a loss of the distinction between the self and the external world: the attainment of Nirvana in the eastern philosophies. In reality, however, most of us experience only a very small and partial conciliation of this type, a sort of secret collaboration between the superego and the id. This secret collaboration is at the core of science, so let us examine it in more detail.

The easiest way to appreciate the perverse but necessary collaboration between superego and id is to look at stories and films. There, the characters are nicely separated into roles that often reflect the roles of our divided selves. Take Batman and the Joker as depicted in Christopher Nolan’s film, The Dark Knight. The Joker is obviously a candidate for the id:

The Dark Knight
“Do I really look like a guy with a plan? You know what I am? I’m a dog chasing cars. I wouldn’t know what to do with one if I caught it. You know, I just… do things.”

Batman, although a vigilante, is a good fit for the superego: he is the true enforcer of law, both the judge and the executioner. In fact it is the police force, embodied by Commissioner Gordon, that best represents the ego in its unenviable position, caught between the two rogue elements. Given these roles, we finally understand this brilliant exchange:
Batman: Then why do you want to kill me?
Joker: I don’t want to kill you! What would I do without you? Go back to ripping off mob dealers? No, no, NO! No. You… you complete me.
You could not ask for a more perfect exposition of the mutual dependence of the superego and the id.

Sometimes the bond is more subtle. Consider one of fiction’s greatest characters: Sherlock Holmes. Not coincidentally, Holmes is a poster boy for scientists, with his strict adherence to a method based on evidence, reasoning and deduction. Quite obviously, he is a manifestation of the superego, leaving Watson to carry the banner of the ego. He wears it well enough, constantly being lectured and berated by Holmes, occasionally skeptical and rebellious but always respectful of Holmes’ superior judgement. Where, then, could the id be hiding? Therein lies a profound mystery, worthy of Holmes himself! One is tempted to point at Moriarty, the great enemy of Holmes – but the shoe does not fit. In Moriarty one finds exactly the kind of characteristics more typical of the superego: self-confidence verging on megalomania, mercilessness, a strict adherence to methodology. He is more like Holmes’s evil twin – the vindictive, cruel side of the superego – than the impulsive and chaotic id.

Holmes

My own theory is that Holmes is a much more subtle character than he first appears. Who is the Holmes that we find, lost in a wordless reverie, playing the violin? Who is the Holmes that disguises himself to play a prank on poor Watson – the Holmes who, indeed, delights in upsetting Watson with eccentric and erratic behaviour? Who is the Holmes that goes missing for days, only to be found curled up in a den of iniquity, his eyes clouded with Opium? I contend that Holmes has an instinctive, intuitive and sensitive side that embodies the id, working in harmony with his superego aspect. Indeed, the seedy side of Holmes – his indulgent, drug-taking, reckless aspect – is somehow essential to completing the portrait of his genius. We would not find him so credible, so impressive, so almost mystical in his virtuosity if it were not for this dark side.

The superego and id can indeed collaborate, but it is usually only in a secretive, almost illicit way as though neither can admit that it depends on the other. The superego turns a blind eye, allowing the id to run wild, and then acts surprised and disappointed when it discovers the transgression. Then ensues what is in essence a sadomasochistic mock-punishment, since the id secretly enjoys the flogging, and the superego knows it, but plays along. In short, the union between superego and id is possible through the hypocritical self-awareness of both parties that they depend on each other to exist. They throw themselves into their respective roles with even more gusto, maintaining as it were a secret conspiracy against the ego, keeping up the tension but with a knowing cynicism.

JekyllHyde
We now begin to see the first inklings of the mad scientist. The quintessential mad scientist is Dr. Jekyll and Mr. Hyde, whose two faces represent unmistakably a perverse union of superego and id; other examples in fiction abound. The mad scientist is in fact the manifestation in an individual character of the public’s view of scientific activity in general. Since (as Kuhn tells us) science is a human activity, its attributes can be traced to attributes of the human mind. In other words, science as an institution can be psychoanalyzed.
Science is defined on one hand by its rationality, its strict adherence to method, zero tolerance for transgression of its rules, and a claim to superiority in its judgements and conclusions about the world. On the other hand, science is a powerful vehicle for the realisation of our (human) fantasies: what technology is not born from the dream of a science-fiction nerd? Technology is transgressive in the same way that dreams are transgressive: there is no taboo in science, no political correctness, no boundaries. At its purest, science and technology is obscene, disturbing and visionary all at once. Medicine is born of the desire to be immortal, chemistry is born of our desire to have power over the substances and forces of the world, to make gold and riches from lead; physics is born of our desire to fly through the sky like a bird, to be invisible, telepathic, omnipotent. Biology promises us the power to make animals and other organisms serve our needs, and psychology offers us power over each other. Science, with all of its adherence to evidence, logic and deduction, remains silent on matters of its purpose, has nothing to suggest about the ends to which it should be used. There lies hidden the id of science: an amoral, primitive, instinctive drive of humanity, just like the indignant infant trying to come to terms with the world. Without an effective intermediary in the form of public discussion and deliberation over scientific advances, science risks becoming a Sherlock without a Watson, that is, a Dr. Jekyll and Mr. Hyde.

Of course, just as it does in the individual’s psyche, the scientific id also plays a beneficial role: it supplies the creative drive and aesthetic sensibility without which science would be impossible. This is why we cannot divorce the id from the superego in science without destroying science altogether. Eliminate the id from Science, and you are left with a stagnant dogma; eliminate the superego, the methodology and tools of rational inquiry, and you are left with mysticism and superstition. The philosophy of science does an injustice to the true mechanism of scientific progress by focusing too much on the methodology – how to evaluate evidence and test hypotheses – and neglecting to address the aesthetic side of science.

Rick and Morty
“Sometimes science is more art than science. A lot of people don’t get that.”

How do we generate hypotheses? Where do ideas come from? Scientists themselves often don’t acknowledge the role that instinct and intuition plays in proposing new theories – we tend to downplay it, or insist that science progresses without any creative input. If that were really true, computer programs could do science in the foreseeable future. But most of us consider the revolution of the machines to still be far away, for the simple reason that we don’t yet know how to teach computers to be creative and to select `good’ hypotheses from the vast pool of logically possible hypotheses. This is (so far) a uniquely human ability, which has everything to do with gut feelings, impulsive thoughts and secret desires. The philosophy of science would perhaps benefit greatly from a more careful examination of this hidden aspect of scientific progress.

My answer to the three monkey’s question is this: The monkey who cannot speak is the id, because the id is voiceless. That leaves the blind monkey and the deaf monkey. It boils down to a matter of opinion here, but the argument that appeals to me most is this one: the superego has a closer relationship with the id than the ego does. Since the blind monkey can neither see nor hear the id (because the id can’t talk), but the deaf monkey can at least see the id, it stands to reason that the deaf monkey is the superego and the blind monkey is the ego.

marx3monk

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.

Image credit: some douchebag
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.

thinks2

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).

thinks3

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.

mountain1

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).

mountain2

 
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.

So fuck off
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.

Jacques Pienaar’s guide to making physics (Pt.1)

PRINCIPLES AS TOOLS
(Not to be confused with using Principals as tools, which is what happens if your school Principal is a tool because he never taught you the difference between a Principal and a principle. Also not to be confused with a Princey-pal, who is a friend that happens to be a Prince).

`These principles are the boldly generalized results of experiment; but they appear to derive from their very generality a high degree of certainty. In fact, the greater the generality, the more frequent are the opportunities for verifying them, and such verifications, as they multiply, as they take the most varied and most unexpected forms, leave in the end no room for doubt.’ -Poincaré

 
One of the great things Einstein did, besides doing physics, was trying to explain to people how to do it as good as him. Ultimately he failed, because so far nobody has managed to do better than him, but he left us with some really interesting insights into how to come up with new physical theories.

One of these ideas is the concept of using `principles’. A principle is a statement about how the word works (or should work), stated in ordinary language. They are not always called principles, but might be called laws, postulates or hypotheses. I am not going to argue about semantics here. Just consider these examples to get a flavour:

The Second Law of Thermodynamics: You can’t build an engine which does useful work and ends up back in its starting position without producing any heat.

 
Landauer’s principle: you can’t erase information without producing heat.

 
The Principle of Relativity: It is impossible to tell by local experiments whether or not your laboratory is moving.

And some not strictly physics ones:

Shirky’s law: Institutions will try to preserve the problem to which they are the solution.

 
Murphy’s law: If something can go wrong, it will go wrong.

Stigler’s law: No scientific discovery is named after its original discoverer (this law was actually discovered by R.K. Merton, not Stigler).

 
Parkinson’s law: Work always expands to fill up the time allocated to doing it.
(See Wikipedia’s list of eponymous laws for more).

You’ll notice that principles are characterised by two main things: they ring true, and they are vague. Both of these properties are very important for their use in building theories.

Now I can practically hear the lice falling out as you scratch your head in confusion. “But Jacques! How can vagueness be a useful thing to have in a Principle? Shouldn’t it be made as precise as possible?”

No, doofus. A Principle is like an apple. You know what an apple is right?

hipstercat

Well, you think you do. But if I were to ask you, what colour is an apple, how sweet is an apple, how many worms are in an apple, you would have to admit that you don’t know, because the word “apple” is too vague to answer those questions. It is like asking how long is a piece of string. Nevertheless, when you want to go shopping, it suffices to say “buy me an apple” instead of “buy me a Malus domestica, reflective in the 620-750 nanometer range, ten percent sugar, one percent cydia pomonella“.

The only way to make a principle more precise is within the context of a precise theory. But then how would I build a new theory, if I am stuck using the language of the old theory? I can make the idea of an apple more precise using the various scientifically verified properties that apples are known to have, but all of that stuff had to come after we already had a basic vague understanding of what an “apple” was, e.g. a kind of round-ish thing on a tree that tastes nice when you eat it.

The vagueness of a principle means that it defines a whole family of possible theories, these being the ones that kind of fit with the principle if you take the right interpretation. On one hand, a principle that is too vague will not help you to make progress, because it will be too easy to make it fit with any future theory; on the other hand, a principle that is not vague enough will leave you stuck for choices and unable to progress.

The next aspect of a good principle is that it “rings true”. In other words, there is something about it that makes you want it to be true. We want our physical theories to be intuitive to our soft, human brains, and these brains of ours have evolved to think about the world in very specific terms. Why do you think physics seems to be all about the locations of objects in space, moving with time? There are infinitely many ways to describe physics, but we choose the ones we do because of the way our physical senses work, the way our bodies interact with the world, and the things we needed to do in order to survive up to this point. What is the principle of least action? It is a river flowing down a mountain. What is Newtonian mechanics? It is animals moving on the plains. We humans need to see the world in a special way in order to understand it, and good principles are what allow us to shoehorn abstract concepts like thermodynamics and gravitational physics into a picture that looks familiar to us, that we can work with.

That’s why a good principle has to ring true — it has to appeal to the limited imaginative abilities of us humans. Maybe if we were different animals, the laws of physics would be understood in very different terms. Like, the Newtonian mechanics of snakes would start with a simple model of objects moving along snake-paths in two dimensions (the ground), and then go from there to arbitrary motions and higher dimensions. So intelligent snakes might have discovered Fourier analysis way before humans would have, just because they would have been more used to thinking in wavy motions instead of linear motions.

Plissken

So you see, coming up with good principles is really an art form, that requires you to be deeply in touch with your own humanity. Indeed, principle-finding is part of the great art of generating hypotheses. It is a pity that many scientists don’t practice hypothesis generation enough to realise that it is an art (or maybe they don’t practice art enough?) It is also ironic that science tries so hard to eliminate the human element from the theories, when it is so apparent in the final forms of the theories themselves. It is just like an artist who trains so hard to hide her brush strokes, to make the signature of her hand invisible, even though the subject of the painting is her own face.

Ok, now that we know what principles are, how do we find them? One of the best ways is by the age-old method of Induction. How does induction work? It really deserves its own post, but here it is in a nutshell. Let’s say that you are a turkey, and you observe that whenever the farmer makes a whistle, there is some corn in your bowl. So, being a smart turkey, you might decide to elevate this empirical pattern to a general principle, called the Turkey Principle: whenever the farmer whistles, there is corn in your bowl. BOOM, induction!

Now, what is the use of this principle? It helps you to narrow down which theories are good and which are bad. Suppose one day the farmer whistles but you discover there is not corn in the bowl, but rather rice. With your limited turkey imagination, you are able to come up with three hypotheses to explain this. 1. There was corn in the bowl when the farmer whistled, but then somebody came along and replaced it with rice; 2. the Turkey Principle should be amended to the Weak Turkey Principle, which states that when the farmer whistles, food, but not necessarily corn, will be in the bowl; 3. the contents of the bowl are actually independent of the farmer’s whistling, and the apparent link between these phenomena is just a coincidence. Now, with the aid of the Principle, we can see that there is a clear preference for hypothesis 1 over 2, and for 2 over 3, according to the extent that each hypothesis fits with the Turkey Principle.

This example makes it clear that deciding which patterns to upgrade to general principles, and which to regard as anomalies, is again a question of aesthetics and artistry. A more perceptive turkey might observe that the farmer is not a simple mechanistic process, but a complex and mysterious system, and therefore may not be subject to such strong constraints with regards to his whistling and corn-giving behaviour as are implied by the Turkey Principle. Indeed, were the turkey perceptive enough to guess at the farmer’s true motives, he might start checking the tool shed to see if the axe is missing before running to the food bowl every time the farmer whistles. But this turkey would no doubt be working on hypotheses of his own, motivated by principles of his own, such as the Farmer-is-Not-to-be-Trusted Principle (in connection with the observed correlation of turkey disappearances and family dinner parties).

An example more relevant to physics is Einstein’s Equivalence Principle: that no local experiment can determine whether the laboratory is in motion, or is stationary in a gravitational field. The principle is vague, as you can see by the number of variations, interpretations, and Weak and Strong versions that exist in the literature; but undoubtedly it rings true, since it appears to be widely obeyed all but the most esoteric phenomena, and it gels nicely with the Principle of Relativity. While the Equivalence Principle was instrumental in leading to General Relativity, it is a matter of debate how it should be formulated within the theory, and whether or not it is even true. Much like hammers and saws are needed to make a table, but are not needed after the table is complete, we use principles to make theories and then we set them aside when the theory is complete. The final theory makes predictions perfectly well without needing to refer to the principles that built it, and the principles are too vague to make good predictions on their own. (Sure, with enough fiddling around, you can sit on a hammer and eat food off a saw, but it isn’t really comfortable or easy).

For more intellectual reading on principle theories, see the SEP entry on Einstein’s Philosophy of Science, and Poincare’s excellent notes.

Wigner has no friends in space

The title phrase of this post is taken from an article by Seth Lloyd that appeared on today’s arXiv, entitled “Analysis of a work of quantum art“. Lloyd was talking about an artwork in collaboration with artist Diemut Strebe, called `Wigner’s friends‘ in which a pair of telescopes are separated, one remaining on Earth and the other going to the International Space Station. According to Lloyd, Strebe motivates the work by appealing to the concepts of quantum superposition and entanglement, referring to physicist Eugene Wigner’s famous thought experiment in which one experimenter, Wigner’s friend, finds herself in a superposition prior to Wigner’s measurement. In Strebe’s scenario, both telescopes are aimed at interstellar space, and it is the viewers of the exhibition that are held responsible for collapsing the superposition of the orbiting telescope by observing the image on the ground-based telescope. The idea is that, since there is nobody looking at the orbiting telescope, the image on its CCD array initially exists in a quantum superposition of all possible artworks; hence Wigner has no friends in space. Before I discuss this intriguing work, let me first start a new art movement.

I was doing my PhD at the University of Queensland when my friend Aggie (also a PhD at that time) came to me with an intriguing problem. She needed to integrate a function over a certain region of three-dimensional space. This region could be obtained by slicing corners off a cube in a certain way, but Aggie was finding it impossible to visualize what the resulting shape would look like. Even after doing a 3D plot in Mathematica, she felt that there was something missing from the flattened projections that one had to click-and-drag to rotate. She wanted to know if I’d ever seen this shape before, and if I could maybe draw it for her or make one out of paper and glue (Weirdly, I have always had an undeserved reputation for drawing and origami). I did my best with paper and sticky-tape, but it didn’t quite come out right, so I gave up. In the end, she went and bought some plasticine and made a cube, then cut off the corners until she got the shape she wanted. Now that she could hold it in her hands, she finally felt that she understood just what she was dealing with. She went back to her computer to perform the integration.

At the time, it did not occur to me to ask “Is it art?” While its form was elegant, it was there to serve a practical purpose, namely to help Aggie (who probably did not once suspect that she was doing Art) in her calculation by condensing certain abstract ideas into a concrete form.

Soft Cube
© Malcolm Wright

Disclaimer: Before continuing, please note that I reject the idea that there can be a universal definition of Art. I further reject the (often claimed) corollary that therefore anything and everything can be Art. Instead, I posit that there are many different Arts, and just like living species, they are continually springing into existence, evolving into new forms, and going extinct. Just as a discussion about “what is a species” can lead to interminable and never-ending arguments, I posit that it is much better and more constructive to discuss “what is a lion”? Here, I am going to talk about, and attempt to define, something that might be called Science-Art, Technologism, Scientism, or something like that. Let’s go with `Zappism’, because it reminds me of things that supposedly go `zap’, but really don’t, like lasers.

So what is Zappism? Let me give some examples of what it is and what it is not. Every now and then, there are Art in Science exhibitions where academic researchers submit images of pretty things that they encountered in the course of their research. I include in this category colourful images of fractals, decorated graphs of pretty mathematical functions, astrophysical images of planets and stars and things, and basically anything where a scientist was just mucking around and noticed something beautiful and then made it into a graphic. For this stuff I would suggest the name “Scientific Found Art”, but it is not Zappism.

© Jonathan McCabe. An example of scientific found art.

Aggie’s shape might seem at first to fit the bill of found art, but there is a crucial difference: were the shape not pretty, it still would have served its purpose, which was to explore, in material form, scientific ideas that would otherwise have been elusive and abstract. A computer simulation of a fractal does not serve this purpose unless one also comes to understand the fractal better as a consequence of the simulation, and I’m not convinced this is true any more than one can understand a sentence better by writing it out in binary and then colouring it in.

Zappism is the art of using some kind of medium — be it painting, film, music, literature or something else — and using it to transform some ethereal and ungraspable Platonisms of science into things the human mind can more readily play with. Sometimes something is lost in translation, like adding unscientific `zap’ sounds to lasers, but this is acceptable as long as the core idea is translated — in the case of lasers, the idea that light can be focused into beams that can burn through things.

Many episodes of Star Trek exhibit Zappism. In the episode `Tuvix‘, the transporter merges two crew members into a single person, an incident that is explicitly explained by appealing to the way the transporter recombines matter. Similarly, Cronenberg’s film The Fly is classic Zappism, as is Spielberg’s Jurassic Park. Indeed, almost any science fiction that uses science in an active way almost can’t help but be Zappist. Science fiction can still fail to be Zappist if it uses the science as a kind of gloss or sugar-coating, instead of engaging with the science as a main ingredient. Star Wars is not really Zappist because it is not concerned with the mechanisms of the technology invoked. Luke and Darth might as well be using swords and riding on flying horses for all the story cares, making it is more like Science Fantasy (Why do lightsabers simply stop at a convenient sword-length?)

A science fiction movie can always ignore inconvenient facts, like conservation of momentum, or how there is no sound in space. These annoying truths are often seen as getting in the way of good action and drama. The truth is the opposite: it takes a creative leap of genius to see how to use these facts to the advantage of dramatic effects. The recent film Coherence does a brilliant job of using the idea of Schrodinger’s Cat to create a tense and frightening scenario. When film, art and storytelling are able to incorporate physical law in a natural and graspable way, we are one step closer to connecting the public to cutting-edge science.

Screen Shot 2015-01-08 at 9.57.10 PM
Actress Emily Baldoni grapples with Schrödinger’s equation in Coherence.

On the non-cinematic side, Koen Vanmechelen’s breeding program for cosmopolitan chickens, Maguire and collaborator’s epic project `Dr. Brainlove‘, and Theo Jansen’s Strandbeest could all be called examples of Zappism. But perhaps the most revealing examples are those that do not explicitly use physical technology for the scientific motive, but instead use abstract ideas. For these I cite Dali’s Persistence of Memory (and its Disintegration) with their roots in Relativity theory and Quantum Mechanics; the book Flatland by Edwin Abbott; Alice in Wonderland by Carroll; Gödel, Escher, Bach: An Eternal Golden Braid by Hofstadter, and similar books that bring abstract scientific or mathematical ideas into an imaginable form. A truly great work of Zappism was the invention of the Rubik’s Cube, by the Hungarian sculptor and mathematician Erno Rubik. Rubik conceived the cube as a solution to a more abstract structural design problem of how to rotate the parts of a cube in all three dimensions while keeping the parts connected.

Returning now to Strebe’s artwork `Wigner’s friends’, it should be remarked that the artwork is not a scientific experiment and there is no actual demonstration of quantum coherence between the telescopes. However, Seth Lloyd for some reason seems intent on defending the idea that maybe, just maybe, there is some tiny smidgen of possibility that there is something quantum going on in the experiment. I understand his enthusiasm: I also think it is a very cool artwork, and somehow the whole point of the artwork is its reference to quantum mechanics. But in order to plausibly say that something quantum was really going on in Strebe’s artwork, Lloyd is forced to invoke the Many Worlds interpretation, which to me is tantamount to begging the question — under that assumption isn’t my cheese sandwich also in a quantum superposition?

I don’t see why all this is necessary: when Dali painted the Disintegration of the Persistence of Memory, nobody was scrambling to argue that his oil paint was in a quantum superposition on the canvas. It would be just as absurd as insisting that Da Vinci’s portrait of the Mona Lisa actually contained a real person. There is a sense in which the artistic representation of a person is bound to physics — it is constrained to some extent by the way physical masses compose in three dimensional space — but the art of correct representation is not to be confused with the real thing. Even Mondrian, whose works were famously highly abstract, insisted that he was bound to the true representation of Nature as he saw it [1]. To me, Strebe’s artwork is a representation of quantum mechanics, put into a physical and graspable form, and that is what makes it Zappism. But is it good Zappism? That depends on whether the audience feels any closer to understanding quantum mechanics after the experience.

[1] “The masses generally find my work rather vague. I construct lines and color combinations on a flat surface, in order to express general beauty with the utmost awareness. Nature (or that which I see) inspires me . . . but I want to come as close as possible to the truth…” Source: http://www.comesaunter.com/2012/02/piet-mondrian-on-his-art.html

Ten Rules for Research

I see a lot of articles out there giving advice in the form of a list of rules. People have a fascination with rule lists. You’ve got the rules of Fight Club, the writer who uses a personal formula, policemen who follow “The Book” to the letter, gangsters with a personal code of ethics, and so on. So here’s my list of rules for being a scientist.

1. Keep reading everything.

2. The value of public speaking skills cannot be underestimated.

3. Remember the big questions that got you here in the first place.

4. Take philosophy seriously, but only the parts you can understand.

5. Sometimes, you just have to shut up and calculate.

6. Don’t distract yourself from the things you don’t know by working on things you do know.

7. The best defense against politics is integrity and a smile.

8. The more certain you are of a result, the more you should double check it.

9. If you aren’t curious to know the result of a calculation, it isn’t worth doing it.

10.  Ask dumb questions. If you are truly an idiot, you’ll be found out eventually, so you might as well satisfy your curiosity in the meantime.

In the end, I think Rule 1 is most important.  So, you should go and read Michael Nielsen’s classic advice to researchers, which is far more eloquent than the garbage you read on my blog.

Calvin and Hobbes
© 2013 Bill Watterson

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!

PicC

(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.)