On the Importance of Phenomenology

Quantum gravity has the potential to revolutionize our understanding of space, time, and matter and with it redefine our own place in the world. While my main interest is in finding the fundamental theory, I work on the phenomenology of quantum gravity because there is a need for it. The quest for a theory of quantum gravity is more than 75 years old, and though a lot has been learned along the way we are still waiting for a theory of quantum gravity that is connected to and confirmed by data. There is no way around phenomenology one way or the other; it is the necessary connection between theory and experiment. Here I want to reflect on the role phenomenological models have played in the history of physics and why they play an important role also in our search for a theory of quantum gravity.

If you know one thing about theoretical physics, it's Albert Einstein's name. While Einstein was inspired and guided by his contemporaries, both in theory as well as in experiment, his achievements are remarkable examples for the power of pure thought combined with mathematics. Einstein is not the only example; Dirac's equation that describes relativistic particles with spin 1/2 is another case where an axiomatic approach lead to predictions that were later confirmed by experiment, leaving us in awe of genius and the beauty of equations.

In the history of science these examples are however rare, and it is exactly because of their rarity that they impress us. An axiomatic approach towards the reconciliation of general relativity and quantum mechanics will, I am sure, if pursued vigorously, eventually lead to success. But the question remains if pure thought is sufficient to find the right starting point, for there might be more than one, some of which leading to theories incompatible with observations. And an axiomatic top-down approach brings with it a heavy load of developing mathematical tools along the way, detours to insight that can take a long time. In the history of science, physicists have often taken the freedom to go ahead and write down phenomenological models that were indeed not justified by any solid basis. And while rightfully met with skepticism, again and again they have been successful with it, thereby helping along the development of more and more fundamental theories.

The above mentioned example of Dirac's equation an instructive one. In the non-relativistic limit, Dirac's equation in the presence of an electromagnetic field reduces to the Pauli-equation which describes the coupling of electrons to electromagnetic fields with a gyromagnetic ratio of 2. It was derived by Dirac from his equation in 1928, but already in 1925 two Dutch graduate students, Samuel Goudsmit and Georg Uhlenbeg, had used a phenomenological model to describe the structure of atoms and the response of ions to magnetic fields. Their model did not make much sense since, classically, the gyromagnetic ratio should be one. Naturally, many physicists were not convinced by the model and Pauli even advised the students not to publish it. Yet, it described experiments well and Dirac's later derivation of their model from his equation served to document the validity of Dirac's theory.

Another example is Pauli's exclusion principle, according to which no two fermions can occupy the same state. It was postulated and used since 1925, among other things to explain the Zeeman effect. Yet it was not until the development of quantum field theory and an understanding of the properties of multi-particle states in 1940 that a derivation was achieved.

Coulomb's law, Ampere's law and Biot-Savart's law can be derived from Maxwell's equations, but they were known and in use long before that, significantly contributing to the development of the full theory of electrodynamics. Fermi's theory we know today is an approximation of the electroweak gauge theory, but was in use long before that, teaching us lessons in renormalizability. The Rahleigh-Jeans law and Wien's law for the spectrum of thermal radiation were combined in Planck's law. In 1900, Planck constructed a derivation for this radiation spectrum based on the, back then unfounded, assumption that the energy of photons is quantized and proportional to the frequency. It predated Einstein's explanation for the photoelectric effect by 5 years. The constant of proportionality that Planck introduced is now called Planck's constant and it was the starting shot for quantum mechanics.

Due to the difficulty to analytically describe the formation of bound states in Quantum Chromodynamics (QCD is asymptotically free, ie it's easier to deal with it the higher the energy) still today most of the models used are phenomenological and many predate the development of QCD. There is for example the the Nambu-Jona-Lasinio model, the Gell-Mann-Levy model or the String-Lund model, all of which have significantly contributed to our understanding of the structure of elementary matter.

One could at this point speculate which present day phenomenological models will turn out to have lead the way towards the now searched-for theory describing the fundamentals of space and time. It springs to mind String cosmology and Loop Quantum Cosmology, searches for deviations from Lorentz-invariance, extra dimensions, or signatures of space-time discreteness. The models currently in use are not derived from a fundamental theory. Instead, they aim to incorporate and allow tests for specific features the fundamental theory might have, like additional dimensions or modified Lorentz-invariance. But these models, even if they turn out to be incompatible with experiment, are guides on our search for the correct theory. Guides that, after 75 years, we have good use for.

Interna

Lara and Gloria are now five months old. They have made a lot of progress in coordinating their movements. They can now grab and hold things, including other peoples' noses and glasses, and they try to hold their bottles and spoons. We've bought some first picture books and they look with big eyes at the images while Stefan and I practice Swedish vocabulary: En elefant, två körsbär, tre ballonger, fyra muffins... Yesterday, Gloria rolled over for the first time.

Stefan makes an admirable stay-at-home daddy, who has even taken on the pretty much futile task of folding my T-shirts and pairing my socks. I meanwhile am back sitting in seminars, talking physics over coffee, sorting though piles of papers. Unfortunately, I still seem to spend a lot of time on the phone with the social insurance who still hasn't paid a single cent of my parental benefits. It turned out that they mistakenly believed I had moved out of country. The good news of the week is that I received a letter confirming I am indeed still insured with them and hope now things will finally be sorted out. It's about time since my account balance has been monotonically decreasing since October and the pain at the pump is substantial.

If you're a parent it is almost unavoidable that friends send you all sorts of baby-related information. Here are some of the more interesting articles that I came across: If your baby sleeps more than usual, expect a growth spurt, Statistically, mothers of twins live longer than other moms (it's a correlation, not a causation), for women with jobs that require a high skill level, having children significantly reduces their average lifetime income, and Nature Jobs reports that the gender divide in physics spans the globe:

"Balancing motherhood and work continues to be the biggest career challenge for women. Carola Meyer, an investigator at the Peter Grünberg Institute in Jülich, Germany, and vice speaker of the German Physical Society's gender-equality working group, says that although institutes and funding bodies provide career breaks for people who wish to have children, such schemes don't necessarily ease the balancing act. Women hold 17% of the 42 positions at her institute — a relatively large proportion, says Meyer. Yet all are under 40 and have no children. Those who want to rise within the scientific community can't consider having children until they are established, she says."

That stinks like a self-fulfilling prophecy. Let me clean up the stink by a quotation from the (otherwise cute but unremarkable) movie "Little Miss Sunshine" (that I watched on a flight on the way to some conference):

"Do what you love, and fuck the rest."

The cube of physical theories

Stefan has a lot of books. And most of them are about physics. The other day I picked a random book and opened a random page and saw myself faced with the "cube de théories physiques" (the cube of physical theories) in the book "De l'importance d'être une constante" by Jean-Philippe Uzan and Bénédicte Leclercq. You find a nice, though very French, illustration of that cube here. There is also an English translation of that book ("The natural laws of the universe: understanding fundamental constants") which has an English, though somewhat unsightly version of the cube on page 57. For your convenience, I've redrawn the illustration:



It shows a coordinate system with three axis that depict the values of three fundamental constants, G, ℏ, and 1/c – the coupling constant of gravity, Planck's constant and the inverse of the speed of light. To our best present knowledge these constants are indeed constant, but you can imagine varying them and ask what happens to the theory then. In many cases this corresponds to some physical limit. For example, if your theory contains terms in v/c, where v is velocity, then the limit of velocities small compared to c (i.e. non-relativistic) formally corresponds to taking c to infinity, ie 1/c to zero.

The cube seems to go back to Gamow, Ivanenko and Landau about a century ago, who allegedly cooked it up for a paper to impress a girl. It was rediscovered about 50 years later by some Russian guy named Okun, and then again by the Frenchmen who wrote above mentioned book. You can find here (PDF) a translation of the original paper by Gamow, Ivanenko and Landau, together with a comment by Okun.

You'd surprise me if you've seen that cube before. It is certainly not a particularly deep illustration, but it's inspirational and it gives you food for thought.

My trouble with popular physics books, though, is that in some cases you better not think about what you read because you might get terribly confused. That's what happened to me in this case.

To begin with it isn't clear to me what, physically, corresponds to varying G which is essentially the strength by which matter deforms the background geometry. It would seem more illustrative to e.g. take a constant with dimension of an energy density, so one could think of varying it as considering higher and lower energy densities. And taking the limit G to zero does decouple all the matter but doesn't actually give Special Relativity. Special Relativity is the limit of the vanishing of the curvature tensor or, equivalently, that of flat Minkowski space. Yet General Relativity has nontrivial vacuum solutions even in the absence of matter. These are Ricci-flat, but the curvature tensor doesn't necessarily also vanish. So there's something fishy about the front, lower left corner.

Also, it is to some degree of course a question of terminology, but what is usually referred to as the Newtonian limit of General Relativity is not the limit of velocities small compared to the speed of light. Instead, it is the limit of small distortions to the background, so there's something fishy about the back, upper left corner too.

What the nonzero value of all of these constants in the top, upper left corner has to do with a unification of all particle interactions is entirely unclear to me, and what the non-relativistic limit of that theory is good for I don't really know, though it arguably exists.

There is also the question whether taking these limits does actually commute, or if not approaching a corner does depend on the direction one is coming from. You can for example reach the corner with G and ℏ equal zero while keeping the ratio (the Planck mass) fixed. Or you can let them go to zero at a different pace so that the ratio goes to zero or infinity. It seems to me the difference should play a role, yet the diagram makes no distinction.

All together, the "cube of theories" is a very appealing representation. But do not wonder if it confuses you – it has to be taken with a large grain of salt.

Interna

So we've made it to Stockholm, but presently life is chaos. The plan was that I drive the household to Sweden by car and Stefan and the babies take a flight two days later so I can pick them up at the Arlanda airport. During packing however, we noticed the car was leaking oil and thought it was a good idea to have this checked in advance of a 1,500 km trip. Turned out the oil belongs to the servo steering and some broken hose would have to be replaced. I'm driving a Saab and the missing part had to be shipped from Sweden. By the time I wanted to leave, the hose was nowhere in sight. The mechanic advised us not to take longer trips. A cheerful Saab dealer however said not to worry, Autobahn is mostly straight driving anyway and who cares about the steering. I got a paper with the number of the broken part and a bottle of oil and he wished me good luck.

To his credit, I made it to Stockholm without problems. Problems started upon arrival. You see, I am living in a one bedroom apartment that's just about large enough for one person. The issue isn't so much lacking space as a lot of bulky, not to mention ugly, furniture of my landlord's wife that I can neither trow away nor sell nor move to the basement because the basement is full with her stuff too. The apartment has a second bedroom that the landlord told me last year he'd move out so we can use it as a nursery. Apparently he changed his mind about this some months ago and didn't bother telling me. The result is that now the four of us live in a clogged one bedroom apartment. One can't turn around without knocking something over and just hope that it doesn't hit a baby.

The internet wasn't working because the account hadn't been used for several months. The contract runs on my landlord's name and the company wouldn't give me the password. I tried to clean the apartment upon which my landlord's 20+ years old vacuum cleaner died with a small poof and a little black cloud and blowing a fuse. I sorted through a huge pile of mail that while consisting mostly of advertisement contains some serious looking påminnelse, and I know just enough Swedish to understand this means I should have done something long ago. I bought a new vacuum cleaner on the way to the airport.

The babies' first flight went well though Stefan reports Lufthansa staff wasn't very helpful. Since the baby seats don't fit on the baggage carts, he actually had to carry both babies and two bags to the gate. The apartment complex I live is gated and when we came back the gate was open. I dropped Stefan, the babies and the vacuum cleaner in front of the door and then found the gate locked on the way out. I noticed then that the key my landlord gave me didn't fit. I jumped upon the next person that came along, but she didn't speak English. After a considerable amount of time, I finally managed to find someone to let me out just to notice that I couldn't park the car in the garage because they were doing some repair. Stefan later found out that I did have a key to the gate, just that my landlord mixed up the labels and the key to the gate was labelled with 'basement.'

Inspecting the fuse box, Stefan reported he'd last seen these things in the late 70s. We spent a full hour searching for spare fuses and found them on the fuse box. Stefan drove to IKEA to get beds for the babies. I noticed that while they do sell in Sweden the formula we're using, they have different labels. Last time I tried to give Lara a different formula she actually refused to drink it, so I meant to call customer service. Just that, without internet, I couldn't find out the number. I had to call my mother to look it up. The winner of the day is the Hipp customer service that actually has human beings taking calls, and a friendly woman answered my question before I had even finished it. (The German A1 milk is the Swedish E2.) The German mobile phone company sends a warning about my roaming fees exceeding EUR 100 this month. A stressed daddy doesn't properly fit the diaper and Lara pees all over her cloths.

Between humoring the babies, changing diapers and noticing we have no diaper pail, unpacking my boxes and trying to fix a leaking tap, I called the social insurance to ask them for the umpteenth time why I still haven't received my parental benefits. A very confused sounding women told me that might be because I'm not registered with them anymore. Didn't I move out of country? (I think the next generation of cellphones should come with a little plastic pad to sink teeth into. Some of our baby toys have them too.) Having convinced her that I actually still live and work in Sweden, she said, well, but my husband doesn't. So they'll have to wait what the Germans do about his benefits. Just that the Germans tell us they're waiting for the Swedes to decide about my benefits. I must have left some impression on the women because she put something in my file that prompted somebody to call me back within 3 hours and assure me they're working on the case. But I estimate chances I'll have any money incoming to my bank account in the near future are slim.

Tried to take the babies for a walk. The twin stroller doesn't fit through the apartment door.

Late May in Sweden the days are very long. Being used to sleeping in the dark, the babies and me were up at 4am, hoping this day won't be quite as messy. Despite the mess, I'm looking forward to going back to work on Monday. Oh, and I wrote a paper. On the foundations of quantum mechanics, no really. I'll upload it sometime next week.

Basically, this is just to explain why I haven't done any substantial blogging for a while. But at least the internet connection is working again. Have to go change diapers now...

Filter bubbles

Our democracies rely on informed decision making. The internet is an asset when it comes to sharing of information, but as with any tool it needs to be used properly for the desired effect. The problem today is that we have too much available information and in order to make any sort of decision - and in order to find time to eat and sleep - we need to filter this information. From an evolutionary perspective, this is not a new problem in that our brains constantly filter information and only process the most relevant parts. That has advantages and disadvantages. What is new about the filtering we need for online information is that the filters are designed by some software engineers rather than by Nature, and they haven't proven their usefulness during thousands of years.

The risks that come with the filtering of information are a returning theme on this blog. In my post The Spirits that We Called I argued that the right filtering of information is crucial because people don't make a lot of effort questioning the order or relevance of information. If it doesn't come "cheaply," in the sense of it not requiring time and effort, it's likely to have low impact, thus the importance of search engines and social networks for democracy. From an evolutionary perspective the limiting of time spent on information gathering is just a careful dealing with resources and not irrational at all. That has always been the case, but the internet vastly centralizes provision of information and amplifies its impact at the same time. The consequence to draw, as I argued in my post Can Technology make us happy?, is that we should be very careful with designing information structure and filters. Do we really get the information that we need? One of the biggest problems, I think, is The Illusion of Knowledge that leads people to believe they have all the relevant information already.

Some days ago I saw the below TED talk by Eli Pariser, who makes this point extremely well. If you have ten minutes of time, they are well spend on the below video.

On the measurement of happiness

You might think it's the individual's pursuit of happiness that is the driving force behind our societies' dynamics, the progress as well as the regress. At least I thought that for a long time. And then, some years back, during a talk by Stuart Kauffman, it occurred to me this doesn't make sense and, worse, it's actually not true.

It doesn't make sense because from an evolutionary perspective the driving force is survival. It just happens to be beneficial for your survival if you're happy about actions that eventually produce healthy offspring. But if you think about happiness as some biochemical reaction it's not an end unto itself: For keeping your body supplied with energy it's actually irrelevant if you like eating. The reward circuit that triggers dopamine release is just a handy neurological tool to memorize the dos and don'ts. And you don't have to look far to figure that people don't make decisions to optimize happiness in the first place. There are, just to pick one example, many studies showing vicinity to nature (forest, parks, beach etc) improves not only people's self-declared happiness but also their health and life-expectancy. Yet, most people live in cities and spend their time indoors. Why?

In the wealthier nations on the planet, word has it that money doesn't make happy and even politicians and economists have come around to seeing that the GDP is far from measuring well-being. British Prime Minister David Cameron has set out to measure the Brits mood by means of a national happiness index, the French too have created a Commission to assess happiness, and residents of Somerville have recently been asked to fill out a questionnaire about their life satisfaction. We will certainly see more efforts into this direction. But this left me wondering. What quantity it that the Brits, the French, the Americans aim to optimize here? And do we really want that?

I'm not an economist, but I know so much as that the question how to optimize collective happiness is not new to economists. If you want to determine the "national well-being" you inevitably have to sum, or aggregate in other ways, different people's happiness. Yours and mine and that of my babies. And do they all count the same? How does your happiness compare to mine? How many ways are there to aggregate, and which one is the right? How do you, objectively, measure it? Can you at all?

People have tried, and are trying, seriously, to determine the amount of happiness as a neurological reaction, a red on an fMRI or a peak in a hormone level with the aim to eventually determine a 'true' value of stuff essentially. Yet 100 years ago most economists abandoned an inter-individually comparable happiness in favor of a measure of preferences that cannot and, interestingly, doesn't have to be compared between you and me. They call it the utility function.

The utility function works well on an individual level, but leaves an ambiguity among different possible optima as to which is the collectively preferable one. The aggregation would necessitate a 'social welfare function' which is basically the weight for everybodies' happiness in order to sum it up and it is ambiguous - call it the measurement problem of economy. Lacking a rationale for one particular choice, for the hard-core neo-conservative it's a capital DONT. And, from a theoretical basis, a justified one. But all these attempts to measure happiness then bring us back to this century-old question: What do we want? And what's the rationale for it?

To illustrate the problem, consider you are redistributing money from the rich to the poor. You do it on the premise that taking $10 away from a billionaire will decrease his happiness less than it will raise the happiness of a starving child in Africa. But how do you know if you can't compare their happiness? And if you would indeed measure their brain activity should the ability to produce high dopamine levels, that is to some extent genetic and age dependent, affect your decision?

In all this discussion, nobody ever questions that it is actually happiness that we want. But beware the self-evident assumptions for I am here to disagree. So I argue what we are really pursuing both individually and collectively is not happiness, it is the maximization of possibilities. Money doesn't make happy. It opens possibilities. You don't move to the city because it makes you happy, but because it opens doors, increases the number of available mates, and enriches your nightlife. The relevant point is that the number of possibilities is not weighted. It's just a number. You can add it and you can compare it. So here's the rationale for giving the tenner to the starving child. The billionaires' options are hardly affected. Yet the money has a large impact on the child's health and education. It opens a large number of future possibilities, more than it closes for the billionaire.

You can find a writeup of my thoughts on the Social Science Research Network (that's the humanists' arXiv):

On the Problem of Measuring Happiness
http://ssrn.com/abstract=1754423

Hello from Perimeter Institute

Sorry for the silence. I seem to have caught a stomach bug on the trip to Canada and spent the better half of the week commuting between bed and bathroom. I'll call it the Air Canada diet. Nothing quite like it to get rid of that excess pregnancy weight.

The construction at Perimeter Institute has been progressing well. The new part of the building is supposed to be finished sometime early fall or so, and I hear they're still on schedule. (See here for the photos from last year.)




The main entrance to the building is well hidden between fences, walls, and various dangerous looking machinery. Its location seems to be changing by the day like some secret code. The reception has been replaced by a study area, the bistro is now in the lobby, and staff features some new, unfamiliar faces. Still, after the last year's many changes in my life, it is comforting to come back and find things are still like they've always been. People are still talking about spin foams and black holes and their favorite interpretation of quantum mechanics. They still drink too much coffee and on your way to Starbucks on a Sunday morning you might run into the director. Waterloo is really a small town and the physicists' universe is expanding while they're orbiting around the center of their own gravity.