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?

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.

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.

Why does matter curve space and time?

This is one of those questions that has always bugged me.

Suppose that, somewhere in the universe, there is a very large closed box made out of some kind of heavy, neutral matter. Inside this box a civilisation of intelligent creatures have evolved. They are made out of normal matter like you and me, except that for some reason they are very light — their bodies do not contain much matter at all. What’s more, there are no other heavy bodies or planets inside this large box aside from the population of aliens, whose total mass is too small to have any noticeable effect on the gravitational field. Thus, the only gravitational field that the aliens are aware of is the field created by the box itself (I’m assuming there are no other massive bodies near to the box).

Setting aside the obvious questions about how these aliens came to exist without an energy source like the sun, and where the heck the giant box came from, I want to examine the following question: in principle, is there any way that these aliens could figure out that matter is the source of gravitational fields?

Now, to make it interesting, let us assume the density of the box is not uniform, so there are some parts of its walls that have a stronger gravitational pull than others. Our aliens can walk around on these parts of the walls, and in some parts the aliens even become too heavy to support their own weight and get stuck until someone rescues them. Elsewhere, the walls of the box are low density and so the gravitational attraction to them is very weak. Here, the aliens can easily jump off and float away from the wall. Indeed, the aliens spend much of their time floating freely near the center of the box where the gravitational fields are weak. Apart from that, the composition of the box itself does not change with time and the box is not rotating, so the aliens are quickly able to map out the constant gravitational field that surrounds them inside the box, with its strong and weak points.

Like us, the aliens have developed technology to manipulate the electromagnetic field, and they know that it is the electromagnetic forces that keeps their bodies intact and stops matter from passing through itself. More importantly, they can accelerate objects of different masses by pushing on them, or applying an electric force to charged test bodies, so they quickly discover that matter has inertia, measured by its mass. In this way, they are able to discover Newton’s laws of mechanics. In addition, their experiments with electromagnetism and light eventually lead them to upgrade their picture of space-time, and their Newtonian mechanics is replaced by special relativistic mechanics and Maxwell’s equations for the electromagnetic field.

So far, so good! Except that, because they do not observe any orbiting planets or moving gravitating bodies (their own bodies being too light to produce any noticible attractive forces), they still have not reproduced Newtonian gravity. They know that there is a static field permeating space-time, called the gravitational field, that seems to be fixed to the frame of the box — but they have no reason to think that this gravitational force originates from matter. Indeed, there are two philosophical schools of thought on this. The first group holds that the gravitational field is to be thought of analogously to the electromagnetic field, and is therefore sourced by special “gravitational charges”. It was originally claimed that the material of the box itself carries gravitational charge, but scrapings of the material from the box revealed it to be the same kind of matter from which the aliens themselves were composed (let’s say Carbon) and the scrapings themselves seemed not to produce any gravitational fields, even when collected together in large amounts of several kilograms (a truly humungous weight to the minds of the aliens, whose entire population combined would only weigh ten kilograms). Some aliens pointed out that the gravitational charge of Carbon might be extremely weak, and since the mass of the entire box was likely to be many orders of magnitude larger than anything they had experienced before, it is possible that its cumulative charge would be enough to produce the field. However, these aliens were criticised for making ad-hoc modifications to their theory to avoid its obvious refutation by the kilograms-of-Carbon experiments. If gravity is analogous to the electromagnetic force — they were asked with a sneer — then why should it be so much weaker than electromagnetism? It seemed rather too convenient.

Some people suggested that the true gravitational charge was not Carbon, but some other material that coated the outside of the box. However, these people were derided even more severely than were the Carbon Gravitists (as they had become known). Instead, the popular scientific consensus shifted to a modern idea in which the gravitational force was considered to be a special kind of force field that simply had no source charges. It was a God-given field whose origin and patterns were not to be questioned but simply accepted, much like the very existence of the Great Box itself. This following gained great support when someone made a great discovery: the gravitational force could be regarded as the very geometry of spacetime itself.

The motivation for this was the peculiar observation, long known but never explained, that massive bodies always had the same acceleration in the gravitational field regardless of their different masses. A single alien falling towards one of the gravitating walls of the box would keep speed perfectly with a group of a hundred Aliens tied together, despite their clearly different masses. This dealt a crushing blow to the remnants of the Carbon Gravitists, for it implied that the gravitational charge of matter was exactly proportional to its inertial mass. This coincidence had no precedent in electromagnetism, where it was known that bodies of the same mass could have very different electric charges.

Under the new school of thought, the gravitational force was reinterpreted as the background geometry of space-time inside the box, which specified the inertial trajectories of all massive bodies. Hence, the gravitational force was not a force at all, so it was meaningless to ascribe a “gravitational charge” to matter. Tensor calculus was developed as a natural extension of special relativity, and the aliens derived the geodesic equation describing the motion of matter in a fixed curved space-time metric. The metric of the box was mapped out with high precision, and all questions about the universe seemed to have been settled.

Well, almost all. Some troublesome philosophers continued to insist that there should be some kind of connection between space-time geometry and matter. They wanted more than just the well-known description of how geometry caused matter to move: they tried to argue that matter should also tell space-time how to curve.

“Our entire population combined only weighs a fraction of the mass of the box. What would happen if there were more matter available to us? What if we did the Carbon-kilogram experiment again, but with 100 kilograms? Or a million? Surely the presence of such a large amount of matter would have an effect on space-time itself?”

But these philosophers were just laughed at. Why should any amount of matter affect the eternal and never-changing space-time geometry? Even if the Great Box itself were removed, the prevailing thought was that the gravitational field would remain, fixed as it was in space-time and not to any material source. So they all lived happily ever after, in blissful ignorance of the gravitational constant G, planetary orbits, and other such fantasies.

***

Did you find this fairytale disturbing? I did. It illustrates what I think is an under-appreciated uncomfortable feature of our best theories of gravity: they all take the fact that matter generates gravity as a premise, without justification apart from empirical observation. There’s nothing strictly wrong with this — we do essentially the same thing in special relativity when we take the speed of light to be constant regardless of the motion of its source, historically an empirically determined fact (and one that was found quite surprising).

However, there is a slight difference: one can in principle argue that the speed of light should be reference-frame independent from philosophical grounds, without appealing to empirical observations. Roughly, the relativity principle states that the laws of physics should be the same in all frames of motion, and from among the laws of physics we can include the non-relativistic equations of the electromagnetic field, from which the constant speed of light can be derived from the electric and magnetic constants of the vacuum. As far as I know, there is no similar philosophical grounding for the connection between matter and geometry as embodied by the gravitational constant, and hence no compelling reason for our hypothetical aliens to ever believe that matter is the source of space-time geometry.

Could it be that there is an essential piece missing from our accounts of the connection between matter and space-time? Or are our aliens are doomed by their unfortunately contrived situation, never to deduce the complete laws of the universe?

Searching for an invisible reality

Imagine that I am showing you a cube, and the face I am showing you is red. Now suppose I rotate it so the face is no longer visible. Do you think it is still red? Of course you do. And if I put a ball inside a box, do you still think the ball exists, even when you can’t see it? When did we get such faith in the existence of things that we can’t see? Probably from the age of around a few months old, according to research on developmental psychology. Babies younger than a few months appear unable to deduce the continued existence of an object hidden from sight, even if they observe the object while it is being hidden; babies lack a sense of “object permanence“. As we get older, we learn to believe in the existence of things that we can’t directly see. True, we don’t all believe in God, but most of us believe that our feet are still there after we put our shoes on.

In fact, scientific progress has gradually been acclimatising us to the real existence of things that we can’t directly see. It is all too easy to forget that, before Einstein blew our minds with general relativity, he first had to get humanity on board with a more basic idea: atoms. That’s right, the idea that things were made up of atoms was still quite controversial at the time that Einstein published his groundbreaking work on Brownian motion, supporting the idea that things are made of tiny particles. Forgetting this contribution of Einstein is a bit like thanking your math teacher for teaching you advanced calculus, while forgetting to mention that moments earlier he rescued you from the jungle, gave you a bath and taught you how to read and write.

Atoms, along with germs, the electromagnetic field, and extra-marital affairs are just one of those things that we accept as being real, even though we typically can’t see them without the aid of microscopes or private investigators. This trained and inbuilt tendency to believe in the persistence of objects and properties even when we can’t see them partially explains why quantum mechanics has been causing generations of theoretical physicists to have mental breakdowns and revert to childhood. You see, quantum mechanics tells us that the properties of some objects just don’t seem to exist until you look at them.

To explain what I mean, imagine that cube again. Suppose that we label the edges of the cube from one to eight, and we play this little game: you tell me which edge of the cube you want to look at, and I show you that edge of the cube, with its two adjacent faces. Now, imagine that no matter which edge you choose to look at, you always see one face that is red and the other face blue. While this might not be surprising to a small baby, it might occur to you after a moment’s thought that there is no possible way to paint a normal cube with two colours such that every edge connects faces of different colours. It is an impossible cube!

The only way an adult could make sense of this phenomenon would be to try and imagine the faces of the cube changing colour when they are not being observed, perhaps using some kind of hidden mechanism. But to an infant that is not bounded by silly ideas of object permanence, there is nothing particularly strange about this cube. It doesn’t make sense to the child to ask what the colour is of parts of the cube that they cannot see. They don’t exist.

Of course, while it makes a cute picture (the wisdom of children and all that), we should not pretend that the child’s lack of object permanence represents actual wisdom. It is no help to anyone to subscribe to a philosophy that physical properties pop in and out of existence willy-nilly, without any rules connecting them. Indeed, it is rather fortunate that we do believe in the reality of things not visible to the eye, or else sanitation and modern medicine might not have arisen (then again, nor would the atom bomb). But it is interesting that the path of wisdom seems to lead us into a world that looks more like a child’s wonderland than the dull realm of the senses. The cube I just described is not just a loose analogy, but can in fact be simulated using real quantum particles, like electrons, in the laboratory. Measuring which way the electron spins in a magnetic field is just like observing the colours on the faces of the impossible cube.

How do we then progress to a `childlike wisdom’ in this confusing universe of impossible electrons, without completely reverting back to childhood? Perhaps the trick is to remember that properties do not belong to objects, but to the relationships between objects. In order to measure the colour of the cube, we must shine light on it and collect the reflected light. This exchange of light crosses the boundary between the observer and the system — it connects us to the cube in an intimate way. Perhaps the nature of this connection is such that we cannot say what the colours of the cube’s faces are without also saying whether the observer is bound to it from one angle, or another angle, by the light.

This trick, of shifting our attention from properties of objects to properties of relations, is exactly what happens in relativity. There, we cannot ask how fast a car is moving, but only how fast it is moving relative to our own car, or to the road, or to some other object or observer. Nor can we ask what time it is — it is different times for different observers, and we can only measure time as a relative property of a system to a particular clock. This latter observation inspired Salvador Dali to paint `The Persistence of Memory’, his famous painting of the melting clocks:

According to Dali, someone once asked him why his clocks were limp, to which he replied:
“Limp or hard — that is not important. The important thing is that they keep the right time.”

If the clocks are all melting, how are we to know which one keeps the right time? Dali’s enigmatic and characteristically flippant answer makes sense if we allow the clocks to all be right, relative to their separate conditions of melting. If we could un-melt one clock and re-melt it into the same shape as another, we should expect their times to match — similarly, relativistic observers need not keep the same time, but should they transform themselves into the same frame of reference, their clocks must tick together. The `right’ time is defined by the condition that all the different times agree with each other under the right circumstances, namely, when the observers coincide.

The same insight is still waiting to happen in quantum mechanics. Somehow, deep down, we all know that the properties we should be talking about are not the ever-shifting colours of the faces of the cube, the spins of the electrons, nor the abstract wave-functions we write down, which seem to jump around as we measure them from one angle to the next. What we seek is a hidden structure that lies behind the consistent relationships between observers and objects. What is it that makes the outcome of one measurement always match up with the outcome of another, far away in space and time? When two observers measure different parts of the same ever-shifting and melting system, they must still agree on the probabilities of certain events when they come together again later on. Maybe, if we can see quantum systems through a child’s eyes, we will have a chance of glimpsing the overarching structure that keeps the relations between objects marching in lock-step, even as the individual properties of objects themselves dissolve away. But for the moment we are still mesmerised by those spinning faces of the cube, frustratingly unable to see past them, wondering if they are still really there every time they flicker in and out of our view.

Why Quantum Gravity needs Operationalism: Part 2

(Update: My colleagues pointed out that Wittgenstein was one of the greatest philosophers of the 20th century and I should not make fun of him, and anyway he was only very loosely associated with the Vienna circle. All well and true — but he was at least partly responsible for the idea that got the Vienna Circle onto Verificationism, and all of you pedants can go look at the references if you don’t believe me.)

“Where neither confirmation nor refutation is possible, science is not concerned.”    — Mach

Some physicists give philosophy a bad rap. I like to remind them that all the great figures in physics had a keen interest in philosophy, and were strongly influenced by the work of philosophers. Einstein made contributions to philosophy as well as physics, as did Ernst Mach, whose philosophical work had a strong influence on Einstein in formulating his General Theory of Relativity. In his own attitude to philosophy, Einstein was a self-described “epistemological opportunist” [1]. (Epistemology is, broadly speaking, the philosophy of knowledge and how it is acquired.) But philosophy sometimes gets in the way of progress, as explained in the following story.

A physicist was skipping along one day when he came upon a philosopher, standing rigid in the forest. “Why standeth you thus?” he inquired.

“I am troubled by a paradox!” said the philosopher. “How is it that things can move from place to place?”

“What do you mean? I moved here by skipping, didn’t I?”

“Yes, sure. But I cannot logically explain why the world allows it to be so. You see, a philosopher named Zeno argued that in order to traverse any finite distance, one would have to first traverse an infinite number of partitions of that distance. But how can one make sense of completing an infinite number of tasks in a finite amount of time?”

“Well dang,” said the physicist “that’s an interesting question. But wait! Could it be that space and time are actually divided up into a finite number of tiny chunks that cannot be sub-divided further? What an idea!”

“Ah! Perhaps,” says the philosopher, “but what if the world is indeed a continuum? Then we are truly stuck.”

At that moment, a mathematician who had been dozing in a tree fell out and landed with a great commotion.

“Terribly sorry! Couldn’t help but overhear,” he said. “In fact I do believe it is conceptually possible for an infinite number of things to add up to a finite quantity. Why, this gives me a great idea for calculating the area under curves. Thank you so much, I’d better get to it!”

“Yes, yes we must dash at once! There’s work to do!” agreed the physicist.

“But wait!” cried the philosopher, “what if time is merely an illusion? And what is the connection of abstract mathematics to the physical world? We have to work that out first!”

But the other two had already disappeared, leaving the philosopher in his forest to ponder his way down deeper and ever more complex rabbit-holes of thought.

***

Philosophy is valuable for pointing us in the right direction and helping us to think clearly. Sometimes philosophy can reveal a problem where nobody thought there was one, and this can lead to a new insight. Sometimes philosophy can identify and cure fallacies in reasoning. In solving a problem, it can highlight alternative solutions that might not have been noticed otherwise. But ultimately, physicists only tend to turn to philosophy when they have run out of ideas, and most of the time the connection of philosophy to practical matters seems tenuous at best. If philosophers have a weakness, it is only that they tend to think too much, whereas a physicist only thinks as hard as he needs to in order to get results.

After that brief detour, we are ready to return to our hero — physicist Percy Bridgman — and witness his own personal fling and falling-out with philosophy. In a previous post, we introduced Bridgman’s idea of operationalism. Recall that Bridgman emphasized that a physical quantity such as `length’ or `temperature’ should always be attached to some clear notion of how to measure that quantity in an experiment. It is not much of a leap from there to say that a concept is only meaningful if it comes equipped with instructions of how to measure it physically.

Although Bridgman was a physicist, his idea quickly caught on amongst philosophers, who saw in it the potential for a more general theory of meaning. But Bridgman quickly became disillusioned with the direction the philosophers were taking as it became increasingly clear that operationalism could not stand up to the demanding expectations set by the philosophers.

The main culprits were a group of philosophers called the Vienna Circle [2]. Following an idea of Ludwig Wittgenstein, these philosophers attempted to define concepts as meaningful only if they could somehow be verified in principle, an approach that became known as Verificationism. Verificationism was a major theme of the school of thought called `logical empiricism’ (aka logical positivism), the variants of which are embodied in the combined work of philosophers in the Vienna Circle, notably Reichenbach, Carnap and Schlick, as well as members outside the group, like the Berlin Society.

At that time, Bridgman’s operationalism was closely paralleled by the ideas of the Verificationists. This was unfortunate because around the middle of the 20th century it became increasingly apparent that there were big philosophical problems with this idea. On the physics side of things, the philosophers realized that there could be meaningful concepts that could not be directly verified. Einstein pointed out that we cannot measure the electric field inside a solid body, yet it is still meaningful to define the field at all points in space:

“We find that such an electrical continuum is always applicable only for the representation of electrical states of affairs in the interior of ponderable bodies. Here too we define the vector of electric field strength as the vector of the mechanical force exerted on the unit of positive electric quantity inside a body. But the force so defined is no longer directly accessible to experiments. It is one part of a theoretical construction that can be correct or false, i.e., consistent or not consistent with experience, only as a whole.” [1]

Incidentally, Einstein got this point of view from a philosopher, Duhem, who argued that isolated parts of a theory are do not stand as meaningful on their own, but only when taken together as a whole can they be matched with empirical data. It therefore does not always make sense to isolate  some apparently metaphysical aspect of a theory and criticize it as not being verifiable. In a sense, the verifiability of an abstract quantity like the electric field hinges on its placement within a larger theoretical framework that extends to the devices used to measure the field.

In addition, the Verificationists began to fall apart over some rather technical philosophical points. It went something like this:

Wittgenstein: “A proposition is meaningful if and only if it is conceivable for the proposition to be completely verified!”

Others: “What about the statement `All dogs are brown’? I can’t very well check that all dogs are brown can I? Most of the dogs who ever lived are long dead, for a start.”

Wittgenstein: “Err…”

Others: “And what about this guy Karl Popper? He says nothing can ever be completely verified. Our theories are always wrong, they just get less wrong with time.”

Wittgenstein: *cough* *cough* I have to go now. (runs away).

Carnap: Look, we don’t have to take such a hard line. Statements like `All dogs are brown’ are still meaningful, even though they can’t be completely verified.

Schlick: No, no, you’ve got it wrong! Statements like `All dogs are brown’ are meaningless! They simply serve to guide us towards other statements that do have meaning.

Quine: No, you guys are missing a much worse problem with your definition: how do you determine which statements actually require verification (like `The cat sat on the mat’), and which ones are just true by definition (`All bachelors are unmarried’)? I can show that there is no consistent way to separate the two kinds of statement.

So you can see how the philosophers tend to get carried away. And where was poor old Percy Bridgman during all this? He was backed into a corner, with people prodding his chest and shouting at him:

Gillies: “How do you tell if a measurement method is valid? If there is nothing more to a concept than its method of measurement, then every method of measurement is automatically valid!”

Bridgman: “Well, yes, I suppose…”

Positivists: “And isn’t it true that even if we all agree to use a single measurement of length, this does not come close to exhausting what we mean by the word length? How disappointing.”

Bridgman: “Now wait a minute –”

Margenau: “And just what the deuce do you mean by `operations’ anyhow?”

Bridgman: “Well, I … hey, aren’t you a physicist? You should be on my side!”

(Margenau discreetly melts into the crowd)

To cut a long story short, by the time Quine was stomping on the ashes of what once was logical empiricism, Bridgman’s operationalism had suffered a similar fate, leaving Bridgman battered and bloody on the sidelines wondering where he went wrong:

“To me now it seems incomprehensible that I should ever have thought it within my powers … to analyze so thoroughly the functioning of our thinking apparatus that I could confidently expect to exhaust the subject and eliminate the possibility of a bright new idea against which I would be defenseless.”

To console himself, Bridgman retreated to his laboratory where he at least knew what things were, and could spend hours hand-drilling holes in blocks of steel without having to waste his time arguing about it. Sometimes the positivists would prod him, saying:

“Bridgman! Hey Bridgman! If I measure the height of the Eiffel tower, does that count as an operation, or do you have to perform every experiment yourself?” to which Bridgman would narrow his eyes and mutter: “I don’t trust any experimental results except the ones I perform myself. Now leave me alone!”

Needless to say, Bridgman’s defiantly anti-social attitude to science did not help improve the standing of operationalism among philosophers or physicists; few people were prepared to agree that every experiment has to be verified by an individual for him or herself. Nevertheless, Bridgman remained a heroic figure and a defender of the scientific method as the best way to cope with an otherwise incomprehensible and overwhelming universe. Bridgman’s stubborn attitude of self-reliance was powerfully displayed in his final act: he committed suicide by gunshot wound after being diagnosed with metastatic cancer. In his suicide note, he wrote [3]:

“It isn’t decent for society to make a man do this thing himself. Probably this is the last day I will be able to do it myself.”

Bridgman’s original conception of operationalism continues to resonate with physicists to this very day. In the end he was forced to admit that it did not constitute a rigorous philosophical doctrine of meaning, and he retracted some of his initially over-optimistic statements. However, he never gave up the more pragmatic point of view that an operationalist attitude can be beneficial to the practicing scientist. Towards the end of his life, he maintained that:

“…[T]here is nothing absolute or final about an operational analysis […]. So far as any dogma is involved here at all, it is merely the conviction that it is better, because it takes us further, to analyze into doings or happenings rather than into objects or entities.”

[1]  See the SEP entry on Einstein’s philosophy: http://plato.stanford.edu/entries/einstein-philscience/

[2] SEP entry on the Vienna Circle: http://plato.stanford.edu/entries/vienna-circle/

[3] Sherwin B Nuland, “How We Die: Reflections on Life’s Final Chapter” Random House 1995

Is physics in a crisis?

We live in very interesting times, especially if you are a theoretical physicist like me. To understand what kind of time we are living in physics-wise, it will be helpful to review some ideas of Thomas Kuhn, a famous philosopher of science. Kuhn described science as proceeding through a series of paradigms. A `paradigm’ is a sort of established framework in which scientists work to solve problems using an agreed-upon set of tools. The paradigm provides both the puzzles to be solved and the tools to solve them. Over time, scientists discover that the tools of the paradigm cannot solve every puzzle. The problems that lie beyond the reach of a paradigm are called anomalies. When enough serious anomalies are discovered, scientists begin to lose confidence in the existing paradigm and a crisis occurs. Historically, each crisis has been resolved by a subsequent scientific revolution, in which the old paradigm was replaced by a new paradigm that is capable of resolving the anomalies [1].

Interestingly, although the new paradigm solves more problems than the old paradigm, it also represents a complete change in perspective, so that even those problems that were solved by the old paradigm have to be `re-solved’ by the new paradigm, from a completely new point of view. As a result, there might be the odd puzzle that was solved by the old paradigm but suddenly cannot be solved by the new paradigm! This phenomenon is known as `Kuhn-loss’. The new paradigm is successful so long as it solves more important puzzles than the ones it loses through Kuhn-loss. I mention this only to illustrate how significant a change in paradigm is from Kuhn’s point of view: it is not merely a period of accelerated science, but a complete reworking of how scientists see the world.

We are currently in a period of crisis. Some physicists might disagree with me, but I think one can make a strong case that the paradigm that has taken us this far is showing cracks. In this post, I won’t directly compare current events to Kuhn’s description of a crisis, nor will I spend effort trying to define what the present paradigm is. For the moment I will content myself by pointing to some (just a few!) of the major puzzles that are facing us, and explain why they may represent `anomalies’ that require a new paradigm in order to solve them [2].

Dark matter / energy: One of the best-known puzzles of our time is the mystery of dark matter and dark energy in cosmology. Briefly, the matter that we can see in the universe (galaxies, nebulae and so on) is moving around as though it is being pushed and pulled by gravitational forces that have no visible source. In fact, there seems to be 95% more `stuff’ in the universe that we can’t actually see directly – we can only deduce its presence by its gravitational interactions with visible matter. The fact that we don’t know what this stuff is has been called the most embarrassing problem in physics for good reason: if somebody asks me what kind of matter and energy there is in the universe, I have to admit that, for the most part, I have no freaking idea.

Quantum gravity: Going by Kuhn’s picture of science, the key tool of the present paradigm is the Standard Model (SM) of particle physics. This model is impressively accurate down to really tiny scales and has been spectacularly confirmed time and time again in the world’s big particle accelerators, right up to the recent discovery of the Higgs Boson at the Large Hadron Collider (LHC). However, a major limitation of the Standard Model is that it does not tell us how gravity fits into the picture. While we have brought electromagnetism and the nuclear forces up to date with quantum mechanics, our theory of gravity is still straggling behind by over a hundred years. All the other forces have been given a quantum makeover, but gravity remains the shy stepsister, cloaked in a classical veil. Despite some pioneering attempts to get behind that veil, most notably String Theory and Loop Quantum Gravity, there is still no agreement among the community about which approach is correct or whether we have to try something else entirely [3].

Quantum foundations: It is often said that nobody understands quantum mechanics. This would be very worrying if it were true, since much of today’s technology is based on it! So what is the situation really? Well, obviously we understand the theory well enough to use it in practical applications. The trouble is more on the philosophical side: physicists can’t agree on why quantum mechanics works so well. In fact, we still can’t agree on why the universe should be quantum mechanical in the first place! John Wheeler’s famous question `why the quantum?’ still keeps many of us awake at night. There is an ongoing body of research on quantum foundations, whose goal is to improve our understanding of quantum mechanics to the point where most of us can agree on a single interpretation. This interpretation (it is hoped) would reveal quantum mechanics in such a way that nearly every physicist will reflexively slap their forehead and declare `of course! It had to be that way’! The interpretation should be so compelling that classical physics will look absurd by comparison and quantum mechanics will be the most natural way to describe the world.

As an example, since Einstein, the gravitational force is now widely interpreted as the curvature of space and time. However, technically it is possible to explain gravity in terms of fields operating in flat spacetime, in a way that agrees with current experimental data – yet if you ask any physicist what gravity is, nearly all of them will say `the curvature of space-time due to matter’. By contrast, if you ask them what the wave function of quantum mechanics is, you will get all kinds of different answers, and probably an invitation to a conference on foundations where such matters are still being hotly debated. Whereas curved space-time seems like an elegant, simple and compelling way of visualizing gravity, we have no similarly compelling paradigm for visualizing quantum mechanics.

***

One of the tasks a physicist faces during a crisis is to identify which anomalies deserve our attention and which ones are less important. This decision is guided by one’s intuitions and one’s chosen philosophy, hence a physicist must embrace some philosophy in order to make progress. For my part, I am most interested in the latter two anomalies: quantum gravity and quantum foundations. I think that the two are deeply connected. Since the regime of quantum gravity is still far from being accessible to experiments, the success of a theory of quantum gravity will be decided by the intuitive appeal of the physical principles on which it is based, as well as its elegance and explanatory power. We cannot hope to meet these demands all the way down at the level of quantum gravity (the Planck scale) if we still can’t do it up here on our home turf for quantum mechanics. Indeed, it is embarrassing that we cannot claim to have such a compelling picture of quantum mechanics, given that we have so much experimental data to guide us!

In upcoming blog posts I intend to elaborate on quantum gravity and quantum foundations and their possible connection to one another. I will also present my own ideas about how we should try to resolve the connected anomalies, using a philosophy based on a modern revival of operationalism and ideas from the exciting new field of quantum information. Stay tuned!

[1] This is a very rough version of Kuhn’s picture of scientific progress. The reader is encouraged to read the entry on Thomas Kuhn in the Stanford Encyclopedia of Philosophy: http://plato.stanford.edu/entries/thomas-kuhn/ . The less lazy reader is referred to Kuhn’s seminal work The Structure of Scientific Revolutions, University of Chicago Press, 2nd ed. (1970).

[2] There are of course far more anomalies in physics than the three listed here, although many of them can be linked to the same broad categories. For a more thorough list, see John Baez’s `Open Questions in Physics’: http://math.ucr.edu/home/baez/physics/General/open_questions.html .

[3] Some people have gone as far as to argue that String Theory is a failure. As an ignoramus, my own stance on this is more cautious, but that is a topic for another blog post.