Tag Archives: Physics

A meditation on physical units: Part 1

[Preface: A while back, Michael Raymer, a professor at the University of Oregon, drew my attention to a curious paper by Craig Holt, who tragically passed away in 2014 [1]. Michael wrote:
“Dear Jacques … I would be very interested in knowing your opinion of this paper,
since Craig was not a professional academic, and had little community in
which to promote the ideas. He was one of the most brilliant PhD students
in my graduate classes back in the 1970s, turned down an opportunity to
interview for a position with John Wheeler, worked in industry until age
50 when he retired in order to spend the rest of his time in self study.
In his paper he takes a Machian view, emphasizing the relational nature of
all physical quantities even in classical physics. I can’t vouch for the
technical correctness of all of his results, but I am sure they are
inspiring.”

The paper makes for an interesting read because Holt, unencumbered by contemporary fashions, freely questions some standard assumptions about the meaning of `mass’ in physics. Probably because it was a work in progress, Craig’s paper is missing some of the niceties of a more polished academic work, like good referencing and a thoroughly researched introduction that places the work in context (the most notable omission is the lack of background material on dimensional analysis, which I will talk about in this post). Despite its rough edges, Craig’s paper led me down quite an interesting rabbit-hole, of which I hope to give you a glimpse. This post covers some background concepts; I’ll mention Craig’s contribution in a follow-up post. ]

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Imagine you have just woken up after a very bad hangover. You retain your basic faculties, such as the ability to reason and speak, but you have forgotten everything about the world in which you live. Not just your name and address, but your whole life history, family and friends, and entire education are lost to the epic blackout. Using pure thought, you are nevertheless able to deduce some facts about the world, such as the fact that you were probably drinking Tequila last night.

RM_hangover
The first thing you notice about the world around you is that it can be separated into objects distinct from yourself. These objects all possess properties: they have colour, weight, smell, texture. For instance, the leftover pizza is off-yellow, smells like sardines and sticks to your face (you run to the bathroom).

While bending over the toilet for an extended period of time, you notice that some properties can be easily measured, while others are more intangible. The toilet seems to be less white than the sink, and the sink less white than the curtains. But how much less? You cannot seem to put a number on it. On the other hand, you know from the ticking of the clock on the wall that you have spent 37 seconds thinking about it, which is exactly 14 seconds more than the time you spent thinking about calling a doctor.

You can measure exactly how much you weigh on the bathroom scale. You can also see how disheveled you look in the mirror. Unlike your weight, you have no idea how to quantify the amount of your disheveled-ness. You can say for sure that you are less disheveled than Johnny Depp after sleeping under a bridge, but beyond that, you can’t really put a number on it. Properties like time, weight and blood-alcohol content can be quantified, while other properties like squishiness, smelliness and dishevelled-ness are not easily converted into numbers.

You have rediscovered one of the first basic truths about the world: all that we know comes from our experience, and the objects of our experience can only be compared to other objects of experience. Some of those comparisons can be numerical, allowing us to say how much more or less of something one object has than another. These cases are the beginning of scientific inquiry: if you can put a number on it, then you can do science with it.

Rulers, stopwatches, compasses, bathroom scales — these are used as reference objects for measuring the `muchness’ of certain properties, namely, length, duration, angle, and weight. Looking in your wallet, you discover that you have exactly 5 dollars of cash, a receipt from a taxi for 30 dollars, and you are exactly 24 years old since yesterday night.

You reflect on the meaning of time. A year means the time it takes the Earth to go around the Sun, or approximately 365 and a quarter days. A day is the time it takes for the Earth to spin once on its axis. You remember your school teacher saying that all units of time are defined in terms of seconds, and one second is defined as 9192631770 oscillations of the light emitted by a Caesium atom. Why exactly 9192631770, you wonder? What if we just said 2 oscillations? A quick calculation shows that this would make you about 110 billion years old according to your new measure of time. Or what about switching to dog years, which are 7 per human year? That would make you 168 dog years old. You wouldn’t feel any different — you would just be having a lot more birthday parties. Given the events of last night, that seems like a bad idea.

You are twice as old as your cousin, and that is true in dog years, cat years, or clown years [2]. Similarly, you could measure your height in inches, centimeters, or stacked shot-glasses — but even though you might be 800 rice-crackers tall, you still won’t be able to reach the aspirin in the top shelf of the cupboard. Similarly, counting all your money in cents instead of dollars will make it a bigger number, but won’t actually make you richer. These are all examples of passive transformations of units, where you imagine measuring something using one set of units instead of another. Passive transformations change nothing in reality: they are all in your head. Changing the labels on objects clearly cannot change the physical relationships between them.

Things get interesting when we consider active transformations. If a passive transformation is like saying the length of your coffee table is 100 times larger when measured in cm than when measured in meters, then an active transformation would be if someone actually replaced your coffee table with a table 100 times bigger. Now, obviously you would notice the difference because the table wouldn’t fit in your apartment anymore. But imagine that someone, in addition to replacing the coffee table, also replaced your entire apartment and everything in it with scaled-up models 100 times the size. And imagine that you also grew to into a giant 100 times your original size while you were sleeping. Then when you woke up, as a giant inside a giant apartment with a giant coffee table, would you realise anything had changed? And if you made yourself a giant cup of coffee, would it make your giant hangover go away?

Kafka
Or if you woke up as a giant bug?

We now come to one of the deepest principles of physics, called Bridgman’s Principle of absolute significance of relative magnitude, named for our old friend Percy Bridgman. The Principle says that only relative quantities can enter into the laws of physics. This means that, whatever experiments I do and whatever measurements I perform, I can only obtain information about the relative sizes of quantities: the length of the coffee table relative to my ruler, or the mass of the table relative to the mass of my body, etc. According to this principle, actively changing the absolute values of some quantity by the same proportion for all objects should not affect the outcomes of any experiments we could perform.

To get a feeling for what the principle means, imagine you are a primitive scientist. You notice that fruit hanging from trees tends to bob up and down in the wind, but the heavier fruits seems to bounce more slowly than the lighter fruits (for those readers who are physics students, I’m talking about a mass on a spring here). You decide to discover the law that relates the frequency of bobbing motion to the mass of the fruit. You fill a sack with some pebbles (carefully chosen to all have the same weight) and hang it from a tree branch. You can measure the mass of the sack by counting the number of pebbles in it, but you still need a way to measure the frequency of the bobbing. Nearby you hear the sound of water dripping from a leaf into a pond. You decide to measure the frequency by how many times the sack bobs up and down in between drips of water. Now you are ready to do your experiment.

You measure the bobbing frequency of the sack for many different masses, and record the results by drawing in the dirt with a stick. After analysing your data, you discover that the frequency f (in oscillations per water drop) is related to the mass m (in pebbles) by a simple formula:

HookeSpring
where k stands for a particular number, say 16.8. But what does this number really mean?

Unbeknownst to you, a clever monkey was watching you from the bushes while you did the experiment. After you retire to your cave to sleep, the monkey comes out to play a trick on you. He carefully replaces each one of your pebbles with a heavier pebble of the same size and appearance, and makes sure that all of the heavier pebbles are the same weight as each other. He takes away the original pebbles and hides them. The next day, you repeat the experiment in exactly the same way, but now you discover that the constant k has changed from yesterday’s value of 16.8 to the new value of 11.2. Does this mean that the law of nature that governs the bobbing of things hanging from the tree has changed overnight? Or should you decide that the law is the same, but that the units that you used to measure frequency and mass have changed?

You decide to apply Bridgman’s Principle. The principle says that if (say) all the masses in the experiment were changed by the same proportion, then the laws of physics would not allow us to see any difference, provided we used the same measuring units. Since you do see a difference, Bridgman’s Principle says that it must be the units (and not the law itself) that has changed. `These must be different pebbles’ you say to yourself, and you mark them by scratching an X onto them. You go out looking for some other pebbles and eventually you find a new set of pebbles which give you the right value of 16.8 when you perform the experiment. `These must be the same kind of pebbles that I used in the original experiment’ you say to yourself, and you scratch an O on them so that you won’t lose them again. Ha! You have outsmarted the monkey.

Larson_rocks

Notice that as long as you use the right value for k — which depends on whether you measure the mass using X or O pebbles — then the abstract equation (1) remains true. In physics language, you are interpreting k as a dimensional constant, having the dimensions of  frequency times √mass. This means that if you use different units for measuring frequency or mass, the numerical value of k has to change in order to preserve the law. Notice also that the dimensions of k are chosen so that equation (1) has the same dimensions on each side of the equals sign. This is called a dimensionally homogeneous equation. Bridgman’s Principle can be rephrased as saying that all physical laws must be described by dimensionally homogeneous equations.

Bridgman’s Principle is useful because it allows us to start with a law expressed in particular units, in this case `oscillations per water-drop’ and `O-pebbles’, and then infer that the law holds for any units. Even though the numerical value of k changes when we change units, it remains the same in any fixed choice of units, so it represents a physical constant of nature.

The alternative is to insist that our units are the same as before (the pebbles look identical after all). That means that the change in k implies a change in the law itself, for instance, it implies that the same mass hanging from the tree today will bob up and down more slowly than it did yesterday. In our example, it turns out that Bridgman’s Principle leads us to the correct conclusion: that some tricky monkey must have switched our pebbles. But can the principle ever fail? What if physical laws really do change?

Suppose that after returning to your cave, the tricky monkey decides to have another go at fooling you. He climbs up the tree and whispers into its leaves: `Do you know why that primitive scientist is always hanging things from your branch? She is testing how strong you are! Make your branches as stiff and strong as you can tomorrow, and she will reward you with water from the pond’.

The next day, you perform the experiment a third time — being sure to use your `O-pebbles’ this time — and you discover again that the value of k seems to have changed. It now takes many more pebbles to achieve a given frequency than it did on the first day. Using Bridgman’s Principle, you again decide that something must be wrong with your measuring units. Maybe this time it is the dripping water that is wrong and needs to be adjusted, or maybe you have confidence in the regularity of the water drip and conclude that the `O-pebbles’ have somehow become too light. Perhaps, you conjecture, they were replaced by the tricky monkey again? So you throw them out and go searching for some heavier pebbles. You find some that give you the right value of k=16.8, and conclude that these are the real `O-pebbles’.

The difference is that this time, you were tricked! In fact the pebbles you threw out were the real `O-pebbles’. The change in k came from the background conditions of the experiment, namely the stiffness in the tree branches, which you did not consider as a physical variable. Hence, in a sense, the law that relates bobbing frequency to mass (for this tree) has indeed changed [3].

You thought that the change in the constant k was caused by using the wrong measuring units, but in fact it was due to a change in the physical constant k itself. This is an example of a scenario where a physical constant turns out not to be constant after all. If we simply assume Bridgman’s Principle to be true without carefully checking whether it is justified, then it is harder to discover situations in which the physical constants themselves are changing. So, Bridgman’s Principle can be thought of as the assumption that the values of physical constants (expressed in some fixed units) don’t change over time. If we are sure that the laws of physics are constant, then we can use the Principle to detect changes or inaccuracies in our measuring devices that define the physical units — i.e. we can leverage the laws of physics to improve the accuracy of our measuring devices.

We can’t always trust our measuring units, but the monkey also showed us that we can’t always trust the laws of physics. After all, scientific progress depends on occasionally throwing out old laws and replacing them with more accurate ones. In our example, a new law that includes the tree-branch stiffness as a variable would be the obvious next step.

One of the more artistic aspects of the scientific method is knowing when to trust your measuring devices, and when to trust the laws of physics [4]. Progress is made by `bootstrapping’ from one to the other: first we trust our units and use them to discover a physical law, and then we trust in the physical law and use it to define better units, and so on. It sounds like a circular process, but actually it represents the gradual refinement of knowledge, through increasingly smaller adjustments from different angles. Imagine trying to balance a scale by placing handfuls of sand on each side. At first you just dump about a handful on each side and see which is heavier. Then you add a smaller amount to the lighter side until it becomes heavier. Then you add an even smaller amount to the other side until it becomes heavier, and so on, until the scale is almost perfectly balanced. In a similar way, switching back and forth between physical laws and measurement units actually results in both the laws and measuring instruments becoming more accurate over time.

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[1] It is a shame that Craig’s work remains incomplete, because I think physicists could benefit from a re-examination of the principles of dimensional analysis. Simplified dimensional arguments are sometimes invoked in the literature on quantum gravity without due consideration for their meaning.

[2] Clowns have several birthdays a week, but they aren’t allowed to get drunk at them, which kind of defeats the purpose if you ask me.

[3] If you are uncomfortable with treating the branch stiffness as part of the physical law, imagine instead that the strength of gravity actually becomes weaker overnight.

[4] This is related to a deep result in the philosophy of science called the Duhem-Quine Thesis.
Quoth Duhem: `If the predicted phenomenon is not produced, not only is the questioned proposition put into doubt, but also the whole theoretical scaffolding used by the physicist’.

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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.

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

Why does matter curve space and time?

This is one of those questions that has always bugged me.
black-hole
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?

Skin Deep, by Xetobyte
Image Credit: Xetobyte

 

Stop whining and accept these axioms.

One of the stated goals of quantum foundations is to find a set of intuitive physical principles, that can be stated in plain language, from which the essential structure of quantum mechanics can be derived.

So what exactly is wrong with the axioms proposed by Chiribella et. al. in arXiv:1011.6451 ? Loosely speaking, the principles state that information should be localised in space and time, that systems should be able to encode information about each other, and that every process should in principle be reversible, so that information is conserved. The axioms can all be explained using ordinary language, as demonstrated in the sister paper arXiv:1209.5533. They all pertain directly to the elements of human experience, namely, what real experimenters ought to be able to do with the systems in their laboratories. And they all seem quite reasonable, so that it is easy to accept their truth. This is essential, because it means that the apparently counter intuitive behaviour of QM is directly derivable from intuitive principles, much as the counter intuitive aspects of special relativity follow as logical consequences of its two intuitive axioms, the constancy of the speed of light and the relativity principle. Given these features, maybe we can finally say that quantum mechanics makes sense: it is the only way that the laws of physics can lead to a sensible model of information storage and communication!

Let me run through the axioms briefly (note to the wise: I take the `causality’ axiom as implicit, and I’ve changed some of the names to make them sound nicer). I’ll assume the reader is familiar with the distinction between pure states and mixed states, but here is a brief summary. Roughly, a pure state describes a system about which you have maximum information, whereas a mixed state can be interpreted as uncertainty about which pure state the system is really in. Importantly, a pure state does not need to determine the outcomes to every measurement that could be performed on it: even though it contains maximal information about the state, it might only specify the probabilities of what will happen in any given experiment. This is what we mean when we say a theory is `probabilistic’.

First axiom (Distinguishability): if there is a mixed state, for which there is at least one pure state that it cannot possibly be with any probability, then the mixed state must be perfectly distinguishable from some other state (presumably, the aforementioned one). It is hard to imagine how this rule could fail: if I have a bag that contains either a spider or a fly with some probability, I should have no problem distinguishing it from a bag that contains a snake. On the other hand, I can’t so easily tell it apart from another bag that simply contains a fly (at least not in a single trial of the experiment).

Second axiom (Compression): If a system contains any redundant information or `extra space’, it should be possible to encode it in a smaller system such that the information can be perfectly retrieved. For example, suppose I have a badly edited book containing multiple copies of some pages, and a few blank pages at the end. I should be able to store all of the information written in the book in a much smaller book, without losing any information, just by removing the redundant copies and blank pages. Moreover, I should be able to recover the original book by copying pages and adding blank pages as needed. This seems like a pretty intuitive and essential feature of the way information is encoded in physical systems.

Third axiom (Locality of information): If I have a joint system (say, of two particles) that can be in one of two different states, then I should be able to distinguish the two different states over many trials, by performing only local measurements on each individual particle and using classical communication. For example, we allow the local measurements performed on one particle to depend on the outcomes of the local measurements on the other particle. On the other hand, we do not need to make use of any other shared resources (like a second set of correlated particles) in order to distinguish the states. I must admit, out of all the axioms, this one seems the hardest to justify intuitively. What indeed is so special about local operations and classical communication that it should be sufficient to tell different states apart? Why can’t we imagine a world in which the only way to distinguish two states of a joint system is to make use of some other joint system? But let us put this issue aside for the moment.

Fourth axiom (Locality of ignorance): If I have two particles in a joint state that is pure (i.e. I have maximal information about it) and if I measure one of them and find it in a pure state, the axiom states that the other particle must also be in a pure state. This makes sense: if I do a measurement on one subsystem of a pure state that results in still having maximal information about that subsystem, I should not lose any information about the other subsystems during the process. Learning new information about one part of a system should not make me more ignorant of the other parts.

So far, all of the axioms described above are satisfied by classical and quantum information theory. Therefore, at the very least, if any of these axioms do not seem intuitive, it is only because we have not sufficiently well developed our intuitions about classical physics, so it cannot really be taken as a fault of the axioms themselves (which is why I am not so concerned about the detailed justification for axiom 3). The interesting axiom is the last one, `purification’, which holds in quantum physics but not in probabilistic classical physics.

Fifth axiom (Conservation of information) [aka the purification postulate]: Every mixed state of a system can be obtained by starting with several systems in a joint pure state, and then discarding or ignoring all except for the system in question. Thus, the mixedness of any state can be interpreted as ignorance of some other correlated states. Furthermore, we require that the purification be essentially unique: all possible pure states of the total set of systems that do the job must be convertible into one another by reversible transformations.

As stated above, it is not so clear why this property should hold in the world. However, it makes more sense if we consider one of its consequences: every irreversible, probabilistic process can be obtained from a reversible process involving additional systems, which are then ignored. In the same way that statistical mechanics allows us to imagine that we could un-scramble an egg, if only we had complete information about its individual atoms and the power to re-arrange them, the purification postulate says that everything that occurs in nature can be un-done in principle, if we have sufficient resources and information. Another way of stating this is that the loss of information that occurs in a probabilistic process is only apparent: in principle the information is conserved somewhere in the universe and is never lost, even though we might not have direct access to it. The `missing information’ in a mixed state is never lost forever, but can always be accessed by some observer, at least in principle.

It is curious that probabilistic classical physics does not obey this property. Surely it seems reasonable to expect that one could construct a probabilistic classical theory in which information is ultimately conserved! In fact, if one attempts this, one arrives at a theory of deterministic classical physics. In such a theory, having maximal knowledge of a state (i.e. the state is pure) further implies that one can perfectly predict the outcome of any measurement on the state, but this means the theory is no longer probabilistic. Indeed, for a classical theory to be probabilistic in the sense that we have defined the term, it necessarily allows processes in which information is irretrievably lost, violating the spirit of the purification postulate.

In conclusion, I’d say this is pretty close to the mystical “Zing” that we were looking for: quantum mechanics is the only reasonable theory in which processes can be inherently probabilistic while at the same time conserving information.

The cracked mirror

“I know who I WAS when I got up this morning, but I think I must have been changed several times since then.”
— Alice Through the Looking-Glass

Magritte - La Reproduction Interdite
Magritte – La Reproduction Interdite

Professor Lee Tsung gripped the edge of the sink and stared into the eyes of her reflection. In the Physics department’s toilets, all was silent, except for the dripping of a single tap, and her terse breathing. Finally, the door swung open and someone else entered, breaking the spell. The intruder was momentarily baffled by the end of a phrase that Lee whispered to herself on her way out. Something about her eyes being switched.

“I’m a mess,” she confessed later to Yang Chen, her friend and colleague in the particle physics department. Both women had been offered jobs at the American Institute of Particle Physics at the same time, and had become close friends and collaborators in their work on extensions to the Standard Model. Lee Tsung’s ambition and penetrating vision had overflowed into her personal life. It infiltrated her mannerisms, giving her nervous ticks, fiery and unstable relationships and a series of dramatic break-downs and comebacks that littered her increasingly illustrious career. Chen was the antidote to Lee’s anxious and hyperactive working style; calm, meditative and thorough, her students’ biggest complaint was that she was boring. But united by a common goal, the two scientists had worked perfectly together to uncover some of the deepest secrets of nature, pioneering the field of research on neutrino oscillations and being heavily involved with experimentalists and theoreticians in the recently successful hunt for the Higgs Boson.

“I have to quit physics. I can’t look at another textbook. I don’t dare.”

Chen was visibly shocked. In all of the ups and downs she had experienced with Tsung, the idea of quitting physics altogether had never arisen.

“What’s going on? What happened?”

Lee fixed her friend with a two-colour gaze. Her eyes, normally hidden in brooding black shadows beneath her eyebrows, now reflected the dim light of the university cafe. One eye was green and the other brown.

“You’ll think I’m crazy.”

“I already do. You’ve got nothing to lose.”

Lee studied her friend a moment longer, then sighed in resignation.

“Well if I don’t tell you, I suppose I’ll go mad anyway. But before I tell you, you have to promise me something. Promise me that you won’t tell me, not even drop a hint, which way the bias went in the Wu experiment.”

“What, you mean the parity violation experiment?”

“Don’t even talk about it! It is too dangerous. You might let something slip. I don’t want to know anything about their result.”

“But you already know the result — you lectured on particle theory back when you were an associate professor.”

“Shush already! Just listen. Last night I was working late at the cyclotron. Nothing to do with the machine itself, I was just hanging out in the lab trying to finish these damn calculations — that blasted theoretical paper on symmetry breaking. Anyway, I could barely keep my eyes open. You know how the craziest ideas always come just when you are dozing off to sleep? Well, I had one of those, and it was, –” Lee broke off to give a short laugh, “– well, it was as crazy as they come. I was thinking, isn’t it weird that the string theorists tell us every particle has a heavier super-partner, so that their calculations balance out. Well, why don’t we do the same thing for parity?”

“You lost me already.”

“You know, what if there is another universe that exists, identical to ours in every way — except that it is flipped. Into its mirror image.”

“Like in Alice through the looking-glass?”

“Exactly. In theory, there is nothing against having matter that is ordinary in every respect, except with left and right handedness reversed. The only question would be, if such a mirror-image universe existed, where is it? So I did some back-of-the-envelope calculations and found out that the coupling between mirror-matter and ordinary matter would be extremely weak. The two worlds could co-exist side by side, and we wouldn’t even know!”

Chen stirred her coffee, looking almost bored, but she didn’t drink it for a full minute. In any case, it didn’t need stirring — there was no sugar in it. Lee could almost see her friend’s mind working. At last she said:

“That’s pretty unlikely. We have some really sensitive instruments downstairs, and some really high energies. Are you telling me even they wouldn’t be able to pick something up?”

Lee’s eyes glittered with excitement.

“Exactly! That’s what I thought. It turns out that, with just a small modification of the collider experiment — the one we’re running right this minute — we could instantiate a reaction between our universe and the mirror universe. We could even exchange a substantial amount of matter between the two worlds!”

Chen’s looked up sharply.

“Lee,” she said, “Please tell me you didn’t already do it.”

Lee shrugged guiltily.

“It only cost them a few hours of data. Nobody will care – they’ll assume the diversion of the beam was due to a mistake by one of the grad students. But it worked Chen! I opened up the mirror world.”

“That’s great! You’ll be famous!”

But Lee stared down at her fingers, the nails chewed raw, and said nothing.

“That’s a Nobel prize right there! Why are you freaking out?”

“Just wait. We’re about to get to the really weird part,” said Lee.

“At first I thought the experiment wasn’t working. I had expected to see a definite interaction region, generating all kinds of particles. But I guess I hadn’t really worked out the details of what to expect. Nothing seemed to be happening to the beam. I was puzzled for a few seconds. But then there was a weird change in the light of the whole building – it seemed to get slightly brighter. And everything doubled — even the humming of the machine seemed to get twice as loud. And the numbers coming up were really bizarre. I started seeing not just the normal data stream, but additional characters superimposed on top. I don’t know that much about the displays we have, but I’m pretty sure they can’t make figures like that.”

“What do you mean?”

“They were backwards. You know, like when you try to read a book in the mirror. When I looked at the clock on the wall, it had six hands, and the two second-hands were ticking in opposite directions. The three wrong hands seemed to flicker in and out of existence, along with the extra light and sound that was coming through. ”

“Wait a second,” said Chen breathlessly, “you’re saying the interaction region encompassed the whole building?”

“Yes. Well, at least the lab and most of the surrounding infrastructure. I don’t know if it extended outside. Nobody would have noticed, I think. It was 3am.”

Chen exhaled and leaned back in her chair.

“Wow. Okay, that does sound pretty nuts. In fact, it sounds just like a crazy dream. Have you seen a therapist?”

“It felt pretty real to me. And it gets crazier. I got this overwhelming sense of dread. Fear, like you can’t imagine. I couldn’t figure out where it was coming from, and then I realised that my PC screen had gone dark, and I could see my own reflection in it.”

She swallowed.

“Not just everything in the room, but me too — I was also doubled up. There were two versions of me coexisting at once. One of them was facing me, but the other, sitting in the same place — I could only see the back of her head. I don’t know why I felt so afraid. But I did.”

“But if the two worlds were really superimposed on each other like you said, and the interaction region was so large, than the coupling must have still been very weak. Probably mostly electromagnetic. So it would have ended the party pretty fast, right? And with a very low rate of matter exchange.”

“Yes, that’s what I expected too. But it didn’t happen. The double-images persisted for at least a minute. It seemed like forever, just me sitting there staring at the back of my own head bizarrely superimposed on my face. I kept wondering, if I were in the other world, would I also just be sitting here? But it was the strangest thing … it was quiet enough that I could hear us both breathing. Her and me — or me and me, I suppose. But I could also hear buttons being pressed at the console, very slowly and softly. I recognised the `click’ they made. It was unmistakable. I swear she had an arm up somewhere where I couldn’t see in the reflection, controlling the beam.”

“Wait. What does that mean? What are you saying?”

Lee leaned forward, almost hesitating to speak. When she did, it was in a low voice, uncharacteristic of her.

“Don’t play dumb Chen. I’m saying, maybe that interaction was exactly as strong as I expected. But maybe all the matter exchange was happening at a single location. It’s against protocol, but I know that in principle we can localise the beam almost anywhere within the facility … including the console where I was sitting.”

“You think your mirror-self was focusing the interaction on herself? On you? Swapping your matter with hers between the two universes?”

“Well, I don’t know really – I sort of blacked out. I woke up after 5am, slumped at the desk by the beam controls, drooling like a baby. First thing I did was look at the clock. The second hand was moving clockwise, like always. I checked every document I could find, it was all written left to right. I still have the birthmark on my left hand, not the right. You can verify that.”

Lee held up her hand. Chen said:

“So, everything’s fine then! You’re not in the mirror world. You’re in the real world. I’m the real me, you’re the real you. And you’ll be famous for discovering mirror matter!”

Lee shook her head.

“There’s more. I was looking at myself in the mirror just before I called you today. Staring at my eyes. Of course, as you might guess, the left one was still brown and the right one was still green, as it always was. But a thought occurred to me. These eyes being examined — they themselves are the examiners. The world looks the right way around, alright, but what if I’m seeing it through mirrored eyes? Sure, when you look in the mirror everything looks flipped left and right from your perspective. But what if your perspective also gets flipped?”

“You mean, if a mirror image reads a book, does it look backwards to her?”

“Exactly. You look at your reflection and you see its left and right hands are switched. But if you point to the hand that you think is your right hand, the image points to its left hand. The image perceives it’s left hand as its right hand. It looks at you, and from its perspective, you are the one who has got it wrong. The mirror image can’t tell that it is a mirror image.”

Chen was silent.

“Imagine that, next time you wake up, you have a fifty-fifty chance of waking up as your own mirror image, in the mirror universe. Could you leave any kind of trace or signal for yourself that you could use to tell if it happened or not? You can try to use books, clocks, birthmarks or even tattoo yourself with big signs saying `left hand’ and `right hand’ — but it won’t do any good, because the switch is always compensated by your own switch in perspective. You lose your reference point.”

“Come on. There has to be some way to tell. Gyroscopes? Spinning stars? Light polarisation?”

Lee shook her head.

“Not quite. We know that classical physics is parity invariant. Newton’s equations, even electromagnetism, all invariant under flipping left and right. Think more fundamental. More modern.”

Chen sucked on the end of her spoon, frowning at the ceiling of the cafe. She still hadn’t touched her coffee. Then she gasped:

“Beta decay! Weak interactions violate parity! You could just dig up the paper by Wu and check whether the direction of emission was — mmf!”

Lee lunged over the table, upsetting a glass of water, to block Chen’s mouth forcibly with her hand.

“Sorry!” Chen whispered breathlessly. Lee glared at her.

“I told you! I don’t want to know which way those experiments came out.”

There was a pause as a waiter came to mop up the spill, glancing nervously at the two women before moving on.

“But why not?” said Chen when he was gone.

“It will resolve your question once and for all. In fact, –” she rummaged around in her bag, “I have my lecture notes here that I prepared for the particle physics course. It’s on page 68 … or maybe 69. One of those.”

She carefully placed the paper on the table, her lips pursed to prove to Lee that she wasn’t going to accidentally mention the answer. Lee took the paper and placed her coffee cup solidly on top.

“You have to understand,” said Lee, “what it would mean if I was right. If I find out that the direction of parity violation in this universe is different to what it is in my memory, that means that I live in the wrong world. Could I live with that knowledge?”

Chen shrugged.

“Why not? You said everything is the same between the worlds, right? Who cares if your left hand turned into your right?”

“Yes. That’s the point. Doesn’t it all seem rather convenient? That the mirror world should exactly match our universe, in all details, apart from things like the direction of beta decay. Don’t forget, we are talking about physics here. Simply reversing the handedness of matter doesn’t say anything about what kind of world is constructed out of it. In all probability, I should have coupled through to just empty space — after all, most of the universe is empty space. Why should the orbits of the two Earth’s match up so precisely, and their rotations, right down to the location of my laboratory? Think about it Chen. What kind of powerful force could arrange everything just so that, if one person should find a way to open up a gateway between the worlds, it would be possible to switch her with her mirror copy, and she wouldn’t notice a thing?”

“I don’t know, Lee!” said Chen, now visibly exasperated.

Lee slumped in her chair.

“I don’t know either,” she said at last.

“That’s the thing that bothers me. Maybe there really is a perfectly good reason why there should be another copy of Earth in the mirror universe, and another copy of me. But why would the people on the other side try to hide it? It is like they were waiting for it. Like they didn’t want me to know the difference. So that I wouldn’t try to go back after the switch was made. But if that’s true, then who — or what — took my place?”

Chen held her friend’s hand tight.

“Okay. I believe you. But please listen to me. It might seem like a fifty-fifty chance whether you are in the real world or the mirror world. But that’s not how probability works. Taking into account human psychology, you have to admit, it’s far more likely that you are suffering from delusions. I beg you, read the results of the Wu experiment. Set your mind at rest. The odds aren’t even — they’re a billion to one against. Do it right now, and end this.”

Lee looked at the document in front of her. She sighed. What was worse, knowing or not knowing? She leafed over to page 68.

“Hmm.”

Chen waited eagerly.

“Just preliminaries.”

“Must be the next page!”

Chen nearly tore the page while turning it, and pointed to the relevant paragraph.

“Look. That’s where I describe the set-up.”

Lee was looking curiously at her friend.

“What? Don’t you want to know?”

“I don’t know. Why are you so eager to show me? Is this part of the plan?”

Chen was caught off guard.

“What plan? Come on, Lee. I just want you to stop acting crazy so we can go back to how things were before.”

Lee held Chen’s eyes a moment longer, then finally looked down at the page.

“Okay. From what I remember, the electrons were biased parallel to the direction of current through the coil.”

She skimmed through the paragraph with her fingertip and then froze. For a moment, she seemed unable to lift her head, and when she did, her eyes held a peculiar expression.

“Chen…” she said, and her voice barely came out, “this says the bias was against the current.”

A strange blank stare had come over Chen’s face.

“Who … what are you?” said Lee. Her voice rose and her eyes flickered over the people around her in the cafe:

“Why did you do this? What world is this?”

She stood up and her chair scraped backwards and almost toppled. At the sound, Chen’s peculiar paralysis seemed to break. She held up both her hands.

“Woah woah woah. Calm down.”

“What! Explain to me what the hell is going on!”

“Listen to me,” said Chen urgently, “what charge convention were you using?”

Lee stared, speechless. Chen blustered on:

“I know you like to be unconventional. I remember you often saying that sometimes you define current as being in the direction of positive charge, just to keep your students on their toes. If so, then your memory of the result would be that the electrons were emitted parallel to positive current — which means against the actual flow of electrons. Just like it says in my notes.”

Lee stood still for a full ten seconds, and the entire cafe had gone quiet, waiting for a scene to break out. But after what seemed like an eternity, she fell back into her seat and buried her face in her arms.

“I can’t remember.”

And all the while, as Chen tried to console her, as Lee slowly came to terms with the fact that with the one escaped memory of that lecture she had given, ten years ago, where she may or may not have used an unconventional definition of electric current, another memory kept returning to her. It was a memory, not form ten years ago, but in fact from that very same day, after she had woken up — from what might have been a dream — and staggered down to the bathroom to stare at herself so long in the mirror. The memory of what might have been an involuntary twitch of the eye of her reflection. Nothing to notice at the time, but on reflection, now that she thought about it, it seemed almost, unmistakably: a suppressed wink.

Death to Powerpoint!

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

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

The Far Side

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

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

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

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

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

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

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

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

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

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