Are the laws of nature beautiful?

Physicists like to talk about the beauty and elegance of theories, books have been written about the beautiful equations, and the internet, being the internet, offers a selection of various lists that are just a Google search away.

Max Tegmark famously believes all math is equally real, but most physicists are pickier. Garrett Lisi may be the most outspoken example who likes to say that the mathematics of reality has to be beautiful. Now Garrett’s idea of beautiful is a large root diagram which may not be everybody’s first choice, but symmetry is a common ingredient to beauty.

Physicists also like to speak about simplicity, but simplicity isn’t useful as an absolute criterion. The laws of nature would be much simpler if there was no matter or if symmetries were never broken or if the universe was two dimensional. But this just isn’t our reality. As Einstein said, things should be made as simple as possible but not any simpler, and that limits the use of simplicity as guiding principle. When simplicity reaches its limits, physicists call upon beauty.

Personally, I value interesting over beautiful. Symmetry and order is to art what harmony and repetition is to music – it’s bland in excess. But more importantly, there is no reason why the sense of beauty that humans have developed during evolution should have any relevance for the fundamental laws of nature. Using beauty as guide is even worse than appealing to naturalness. Naturalness, like beauty, is a requirement based on experience, not on logic, but at least naturalness can be quantified while beauty is subjective, and malleable in addition.

Frank Wilczek has an interesting transcript of a talk about “Quantum Beauty” online in which he writes

“The Standard Model is a very powerful, very compact framework. It would be difficult... to exaggerate.. its beauty.”

He then goes on to explain why this is an exaggeration. The Standard Model really isn’t all that beautiful as with all these generations and families of particles and let’s not even mention Yukawa couplings. Frank thinks a grand unification would be much more beautiful, especially when supersymmetric:

“If [SUSY’s new particles] exist, and are light enough to do the job, they will be produced and detected at [the] new Large Hadron Collider – a fantastic undertaking at the CERN laboratory, near Geneva, just now coming into operation. There will be a trial by fire. Will the particles SUSY requires reveal themselves? If not, we will have the satisfaction of knowing we have done our job, according to Popper, by producing a falsifiable theory and showing that it is false.”

Particle physicists who have wasted their time working out SUSY cross-sections don’t seem to be very “satisfied” with the LHC no-show. In fact they seem to be insulted because nature didn’t obey their beauty demands. In a recent cover story for Scientific American Joseph Lykken and Maria Spiropulu wrote:

“It is not an exaggeration to say that most of the world’s particle physicists believe that supersymmetry must be true.”

That is another exaggeration of course, a cognitive bias known as the “false-consensus effect”. People tend to think that others share their opinion, but let’s not dwell on the sociological issues this raises. Yes, symmetry and unification has historically been very successful and these are good reasons to try to use it as a guide. But is it sufficient reason for a scientist to believe that it must be true? Is this something a scientist should ever believe?

Somewhere along the line theoretical physicists have mistaken their success in describing the natural world for evidence that they must be able to recognize truth by beauty, that introspection suffices to reveal the laws of nature. It’s not like it’s only particle physicists. Lee Smolin likes to speak about the “ring of truth” that the theory of quantum gravity must have. He hasn’t yet heard that ring. String theorists on the other hand have heard that bell of truth ringing for some decades and, ach, aren’t these Calabi-Yaus oh-so beautiful and these theorems so elegant etc. pp. One ring to rule them all.

But relying on beauty as a guide leads nowhere because understanding changes our perception of beauty. Many people seem to be afraid of science because they believe understanding will diminish their perception of beauty, but in the end understanding most often contributes to beauty. However, there seems to be an uncanny valley of understanding: When you start learning, it first gets messy and confused and ugly, and only after some effort do you come to see the beauty. But spend enough time with something, anything really, and in most cases it will become interesting and eventually you almost always find beauty.

If you don’t know what I mean, watch this classic music critic going off on 12 tone music. [Video embedding didn't work, sorry for the ad.]

Chances are, if you listen to that sufficiently often you’ll stop hearing cacophony and also start thinking of it as “delicate” and “emancipating”. The student who goes on about the beauty of broken supersymmetry with all its 105 parameters and scatter plots went down that very same road.

There are limits to what humans can find beautiful, understanding or not. I have for example a phopia of certain patterns which, if you believe Google, is very common. Much of it is probably due to the appearance of some diseases, parasites, poisonous plants and so on, ie, it clearly has an evolutionary origin. So what if space-time foam looks like a skin disease and quantum gravity is ugly as gooseshit? Do we have any reason to believe that our brains should have developed so as to appreciate the beauty of something none of our ancestors could possibly ever have seen?

The laws of nature that you often find listed among the “most beautiful equations” derive much of their beauty not from structure but from meaning. The laws of black hole thermodynamics would be utterly unremarkable without the physical interpretation. In fact, equations in and by themselves are unremarkable generally – it is only the context, the definition of the quantities that are put in relation by the equation that make an equation valuable. X=Y isn’t just one equation. Unless I tell you what X and Y are, this is every equation.

So, are the laws of nature beautiful? You can bet that whatever law of nature wins a Nobel prize will be called “beautiful” by the next generation of physicists who spend their life studying it. Should we use “beauty” as a requirement to construct a scientific theory? That, I’m afraid, would be too simple to be true.

The Firewall Song

Yes, I've been singing again... Enjoy and have a nice weekend :o)

Book Review: “The Cosmic Cocktail” by Katherine Freese

The Cosmic Cocktail: Three Parts Dark Matter
Katherine Freese
Princeton University Press (May 4, 2014)

Katherine Freese’s “Cosmic Cocktail” lays out the current evidence for dark matter and dark energy, and the status of the relevant experiments. The book excels in the chapter about indirect and direct detection of WIMPs, a class of particles that constitutes the presently best motivated and most popular dark matter candidates. “The Cosmic Cocktail” is is Freese’s first popular science book.

Freese is a specialist in the area of astroparticle physics, and she explains the experimental status for WIMP detection clearly, not leaving out the subtleties in the data interpretation. She integrates her own contributions to the field where appropriate; the balance between her own work and that of others is well met throughout the book.

The book also covers dark energy, and while this part is informative and covers the basics, it is nowhere near as detailed as that about dark matter detection. Along the way to the very recent developments, “The Cosmic Cocktail” introduces the reader to the concepts necessary to understand the physics and relevance of the matter composition of the universe. In the first chapters, Freese explains the time-evolution of the universe, structure formation, the evolution of stars, and the essentials of particle physics necessary to understand matter in the early universe. She adds some historical facts, but the scientific history of the field is not the main theme of the book.

Freese follows the advice to first say what you want to tell them, then tell them, then tell them what you just told them. She regularly reminds the reader of what was explained in earlier chapters, and repeats explanations frequently throughout the book. While this makes it easy to follow the explanations, the alert reader might find the presumed inattention somewhat annoying. The measure of electron volts, for example, is explained at least four times. Several sentences are repeated almost verbatim in various places, for example that “eventually galaxies formed… these galaxies then merged to make clusters and superclusters…” (p. 31) “…eventually this merger lead to the formation of galaxies and clusters of galaxies...” (p. 51) or “Because neutrons are slightly heavier than protons, protons are the more stable of the objects...” (p. 70), “neutrons are a tiny bit heavier than protons… Because protons are lighter, they are the more stable of the two particles.” (p. 76), “Inflation is a period of exponential expansion just after the Big Bang”. “inflationary cosmology… an early accelerating period of the history of the Universe” (p. 202), and so on.

The topics covered in the book are timely, but do not all contribute to the theme of the book, the “cosmic cocktail”. Freese narrates for example the relevance and discovery of the Higgs and the construction details of the four LHC detectors, but does only mention the inflaton in one sentence while inflation itself is explained in two sentences (plus two sentences in an endnote). She covers the OPERA anomaly of faster-than-light neutrino (yes, including the joke about the neutrino entering a bar) and in this context mentions that faster-than-light travel implies violations of causality, confusing readers not familiar with Special Relativity. On the other hand, she does not even name the Tully-Fisher relation, and dedicates only half a sentence to baryon acoustic oscillations.

The book contains some factual errors (3 kilometers are not 5 miles (p. 92), the radius of the Sun is not 10,000 kilometers (p. 95), Hawking radiation is not caused by quantum fluctuations of space-time (p.98), the HESS experiment is not in Europe (p. 170), the possible vacua in the string theory landscape do not all have a different cosmological constant (p. 201)). Several explanations are expressed in unfortunate phrases, eg: “[T]he mass of all galaxies, including our own Milky Way, must be made of dark matter.” (p. 20) All its mass? “Imagine drawing a circle around the [gravitational lens]; the light could pass through any point on that circle.” (p. 22). Circle in which plane?

The metaphors and analogies used by Freese’s are common in the popular science literature: The universe is an expanding balloon or a raisin bread, the Higgs field is “a crowded room of dancing people” or some kind of molasses (p.116). Some explanations are vague “The multiverse perspective is strengthened by theories of inflationary cosmology” (which?) others are misleading, eg, the reader may be left with the idea that Casimir energy causes cosmic acceleration (p. 196) or that “Only with a flat geometry can the universe grow old enough to create the conditions for life to exist.” (p. 44). One has to be very careful (and check the endnote) to extract that she means the spatial geometry has to be almost flat. Redshift at the black hole horizon is often illustrated with somebody sending light signals while falling through the horizon. Freese instead uses sound waves, which adds confusion because sounds needs a medium to travel.

These are minor shortcomings, but they do limit the target group that will benefit from the book. The reader who brings no background knowledge in cosmology and particle physics I am afraid will inevitably stumble at various places.

Freese’s writing style is very individual and breaks with the smooth – some may find too smooth – style that has come to dominate the popular science literature. It takes some getting used to her occasionally quite abrupt changes of narrative direction in the first chapters, but the later chapters are more fluently written. Freese interweaves anecdotes from her personal life with the scientific explanations. Some anecdotes document academic life, others seem to serve no particular purpose other than breaking up the text. The book comes with a light dose of humor that shows mostly in the figures, which contain a skull to illustrate the ‘Death of MACHO’s’, a penguin, and a blurry photo of a potted plant.

The topic of dark energy and dark matter has of course been covered in many books, one may mention Dan Hooper’s “Dark Cosmos” (Smithsonian Books, 2006) and Evalyn Gates “Einstein’s Telescope” (WW Norton, 2009). These two books are meanwhile somewhat out-of-date because the field has developed so quickly, making Freese’s book a relevant update. Both Gates’ and Hooper’s book are more easily accessible and have a smoother narrative than “The Cosmic Cocktail”. Freese demands more of the reader but also gets across more scientific facts.

I counted more than a dozen instances of the word “exciting” throughout the book. I agree that these are indeed exciting times for cosmology and astroparticle physics. Freese’s book is a valuable, non-technical and yet up-to-date review, especially on the topic of dark matter detection.

[Disclaimer: Free review copy. Page numbers in the final version might slightly differ.]

What is direct evidence and does the BICEP2 measurement prove that gravity must be quantized?

Fast track to wisdom: Direct evidence is relative and no, BICEP doesn’t prove that gravity must be quantized.

In the media storm following the BICEP announcement that they had measured the polarization of the cosmic microwave background due to gravitational waves, Chao-Lin Kuo, member of the BICEP team was widely quoted with saying:

“This is the first direct image of gravitational waves across the primordial sky.”

As of lately, it’s been debated whether BICEP has signals from the early universe at all, or whether their signal is mostly produced by matter in our own galaxy that hasn’t been properly accounted for. This isn’t my area of research and I don’t know the details of their data analysis. Let me just say that this kind of discussion is perfectly normal to have when data are young. Whether or not they actually have seen what they claimed, it is worthwhile to sort out exactly what it would mean if the BICEP claims correct, and that is the purpose of this post.

The BICEP2 results have variously been reported as the first direct evidence of cosmic inflation, direct proof of the theory of inflation, indirect evidence for the existence of gravitational waves, the first indirect detection of the gravitational wave background [emphasis theirs],the most direct evidence of Albert Einstein’s last major unconfirmed prediction, and evidence for the first detection of gravitational waves in the initial moments of the universe.

Confused already?

What is a direct measurement?

A direct measurement of a quantity X is if your detector measures quantity X.

One can now have a philosophical discussion about whether not human senses should account for as the actual detector. Then all measurements with external devices are indirect because they are inferred from secondary measurements, for example the reading off a display. However, for what physicists are concerned the reading of the detector by a human is irrelevant, so if you want to have this discussion, you can have it without me.

An indirect measurement is if your detector measures Y and you use a relation between X and Y to obtain X.

A Geiger-counter counts highly energetic particles as directly as it gets, but once you start thinking about it, you’ll note that we rarely measure anything directly. A common household thermometer for example does not actually measure temperature, it measures volume. A GPS device does not actually measure position, it measures the delay between signals received from different satellites and infers the position from that. Your microphone doesn’t actually measure decibel, it measures voltage. And so on.

One problem in distinguishing between direct and indirect measurements is that it’s not always so clear what is or isn’t part of the detector. Is the water in the Kamiokande tank part of the detector, or is the measurement only made in the photodetectors sourrounding the water? And is the Antarctic part of the IceCube detector?

The other problem is that in many cases scientists do not talk about quantities, they talk about concepts, ideas, hypotheses, or models. And that’s where things become murky.

What is direct evidence?

There is no clear definition for this.

You might want to extend the definition of a direct measurement to direct evidence, but this most often does not work. If you are talking about direct evidence for a particle, you can ask for the particle to hit the detector for it to be direct evidence. (Again, I am leaving aside that most detectors will amplify and process the signal before it is read out by a human because commonly the detector and data analysis are discussed separately.)

However, if you are measuring something like a symmetry violation or a decay time, then your measurement would always be indirect. What is commonly known as “direct” CP violation for example would then also be an indirect measurement since the CP violation is inferred from decay products.

In practice whether some evidence is called direct or indirect is a relative statement about the amount of assumptions that you had to use to extract the evidence. Evidence is indirect if you can think of a more direct way to make the measurement. There is some ambiguity in this which comes from the question whether the ‘more direct measurement’ must be possible in practice or in principle, but this is a problem that only people in quantum gravity and quantum foundations spend sleepless nights over...

BICEP2 is direct evidence for what?

BICEP2 has directly measured the polarization of CMB photons. Making certain assumptions about the evolution of the universe (and after subtracting the galactic foreground) this is indirect evidence for the presence of gravitational waves in the early universe, also called the relic gravitational wave background.

Direct measurement of gravitational waves is believed to be possible with gravitational wave detectors that basically measure how space-time periodically contracts and expands. The slowing down of the rotation period in pulsar systems is also indirect evidence for gravitational waves, which according to Einstein’s theory of General Relativity should carry away energy from the system. This evidence gave rise to a Nobel Prize in 1993.

Evidence for inflation comes from the presence of the gravitational wave background in the (allegedly) observed range. How can this evidence for inflation plausibly be called “direct” if it is inferred from a measurement of gravitational waves that was already indirect? That’s because we do not presently know of any evidence for inflation that would be more direct than this. Maybe one day somebody will devise a way to measure the inflaton directly in a detector, but I’m not even sure a thought experiment can do that. Until then, I think it is fair to call this direct evidence.

One should not mistake evidence for proof. We will never prove any model correct. We only collect support for it. Evidence – theoretical or experimental – is such support.

Now what about BICEP and quantum gravity?

Let us be clear that most people working on quantum gravity mean the UV-completion of the theory when they use the word ‘quantum gravity’. The BICEP2 data has the potential to rule out some models derived from these UV-completions, for example variants of string cosmology or loop quantum cosmology, and many researchers are presently very active in deriving the constraints. However, the more immediate question raised by the BICEP2 data is about the perturbative quantization of quantum gravity, that is the question whether the CMB polarization is evidence not only for classical gravitational waves, but for gravitons, the quanta of the gravitational field.

Since the evidence for gravitational waves was indirect already, the evidence for gravitons would also be indirect, though this brings up the above mentioned caveat about whether a direct detection must not only be theoretically possible, but actually be practically feasible. Direct detection of gravitons is widely believed to be not feasible.

There have been claims by Krauss and Wilzcek (which we discussed earlier here) and a 2012 paper by Ashoorioon, Dev, and Mazumdar that argues that, yes, the gravitational wave background is evidence for the quantization of gravity. The arguments in a nutshell say that quantum fluctuations of space-time are the only way the observed fluctuations could have been large enough to produce the measured spectrum.

The problems with the existing arguments is that they do not carefully track the assumptions that go into it. They do for example make assumptions about the coupling between gravity and matter fields being the usual coupling. That is plausible of course, but these are couplings at energy densities higher than we have ever tested. They also assume, rather trivially, that space-time exists to begin with. If one has a scenario in which space-time comes into being by some type of geometric phase transition, as is being suggested in some approaches to quantum gravity, one might have an entirely different mechanism for producing fluctuations. Many emergent and induced gravity approaches to quantum gravity tend not to have gravitons, which raises the question of whether these approaches could be ruled out with the BICEP data. Alas, I am not aware of any prediction for the gravitational wave background coming from these approaches, so clearly there is a knowledge gap here.

What we would need to make the case that gravity must have been perturbatively quantized in the early universe is a cosmic version of Bell’s theorem. An argument that demonstrates that no classical version of gravity would have been able to produce the observations. The power of Bell’s inequality is not in proving quantum mechanics right - this is not possible. The power of of Bell’s inequality (or measuring violations thereof respectively) is in showing that a local classical, ie “old fashioned”, theory can not account for the observations and something has to give. The present arguments about the CMB polarization are not (yet) that stringent.

This means that the BICEP2 result is strong support for the quantization of gravity, but it does not presently rule out the option that gravity is entirely classical. Though, as we discussed earlier, this option is hard to make sense of theoretically, it is infuriatingly difficult to get rid of experimentally.

Summary

The BICEP2 data, if it holds up to scrutiny, is indirect evidence for the relic gravitational wave background. It is not the first indirect evidence for gravitational waves, but the first indirect evidence for this gravitational wave background that was created in the early universe. I think it is fair to say that it is direct evidence for inflation, but the terminology is somewhat ambiguous. It is indirect evidence for the perturbative quantization of gravity, but cannot presently rule out the option that gravity was never quantized at all.

10 Things I wish I had known 20 years ago – Science Edition

The blogosphere thrives with advice for your younger self. Leaving aside lottery numbers and such, the older selves know this haircut was a really bad idea, you’ll eternally regret cheating on the nice guy, and you will never be that young again. This made me wonder which scientific knowledge I wish I had had already as a teenager. Leaving aside the scientific equivalent of sending lottery numbers back in time and recommend, say, that I have a close look at those type Ia supernovae, here’s my top 10:

1. The fundamental theorems of welfare economics and Arrow’s impossibility theorem.
   
   I was absolutely disinterested in economics and sociology as a teenager. After reading some books on microeconomics, welfare economics, and social choice theory, the world made dramatically more sense to me. That’s how the hamster wheel works, and that’s the root of most of the quarrels in politics. Now my problem is that I don’t understand why most people don’t understand this...
   
   
2. Exoplanets!
   
   Are much more common than anybody expected when I was a teenager. This has really changed the way I perceive our place in the universe, and I guess that this topic gets so much coverage in the media because this is the case for many people.
   
   
3. Medicine is not a science.
   
   I was only after I read about the ‘recent’ field of ‘evidence based medicine’ that I realized I had falsely assumed medical practice is rooted in scientific evidence. Truth is, for the most part it’s not. Medicine isn’t a science, it’s a handcraft, and this is only slowly changing. You are well advised to check the literature for yourself.
   
   
4. Most drugs are not tested on women.
   
   Pharma companies often don’t test drugs on women because changing hormone levels make it more difficult to find statistically significant effects. The result is that little is known about how the female body reacts differently to drugs than the male body. In many cases the recommended doses of certain medicines tend to be way too high for me, and had I known this earlier I would have trusted my body, not the label.
   
   
5. Capsaicin isn’t water soluble.
   
   The stuff that makes Chili spicy doesn’t wash off with water, it takes alcohol or fat to get it off your tongue. Yes, this did make my life much better...
   
   
6. Genetics.
   
   I wish I had known back then what I know today about genetic predispositions, eg that introversion, pain tolerance, response to training, and body odor have genetic factors, and I wish I had had a chance to have my DNA sampled 20 years ago.
   
   The default assumption that I, and I think most people, bring is that other people’s experiences are similar to our own. It never occurred to me, for example, that the other kids weren’t overdramatizing, they were really hurting more. Just by looking at my daughters I would bet that Lara got my pain tolerance while Gloria didn’t, and I can tell that Lara doesn’t mean to hurt Gloria, she just doesn’t believe it hurts as much as Gloria screams. And after reading Cain’s book that covers the correlation between introversion and a neurological trait called ‘high sensitivity’ I could finally stop wondering what is wrong with me.
   
   
7. You probably have no free will, but it’s no reason to worry.
   
   Took me two decades to wrap my mind around this. Tough one.
   
   
8. Most people talk to themselves.
   
   Psychologists call it the ‘internal monologue’. How was I supposed to know that pretty much everybody does that?
   
   
9. Adaptive Systems.
   
   Adaptive systems are basically a generalization of the process of mutation and natural selection. This was really helpful to understand much of the changes in institutions and organizations, and all the talk about incentives. It also reveals that many of our problems stem from our inability to adapt. This is basically what gave rise to my this year’s FQXi essay.
   
   
10. That guy really smells good.
    
    It was long believed that humans do not detect pheromones because the respective nerve is missing. Alas, MRI imaging settled the dispute in the 90s. The nerve, now called 'Cranial Nerve Zero' does exist. But note that while both, the olfactory and the zero nerve, end in the nostrils, the olfactory nerve does not detect pheromones and the nerves wire to different areas of the brain. Exactly what influence pheromones have on humans is still an active subject of study.

Nordita's Science Writers Workshop on Quantum Theory: Apply Now

Yes! We will have another science writers workshop at Nordita, after last year's workshop was as enjoyable as it was interesting, and we received numerous encouragements to continue with our efforts in science communication. So George and I, we have teamed up again and decided that after astrophysics and cosmology, this time we will focus on all things quantum. We got financial support from FQXi and the Fetzer Franklin Fund, and are well along with the organization.

I am particularly excited that Chad Orzel, he who teaches physics to his dog and preaches physics at Uncertain Principles, will join us and give a lecture. Which is not to say that the rest of the lecturers are any less interesting! We got everything covered from atom interferometry and quantum computing, over tests of the foundations of quantum mechanics to topological insulators and the gauge-gravity duality - and more.

You can find the full list on the workshop website and the purpose of this post is to let you know that you can now apply to join our meeting. The number of participants is strictly limited due to space restrictions and fire regulations, but we do have some spaces left. If you are a science writer who covers physics, and quantum stuff crosses your way every other day, then this workshop is for you. Just fill in the webform and tell us a few words about who you are and what you do and we will get back to you.

A Thousand Words

Have you noticed that paragraphs have gotten shorter?

We are reading more and more text displayed on screens, in landscape rather than portrait, or on tiny handheld devices. This hasn’t only affected the layout and typesetting, it has altered the way we write.

Short paragraphs and lists are now often used to break up blocks of text, and so are images. There is hardly any writing on the internet not decorated with an image. Besides reasons of layout there is the image grab of sharing apps that insists you need to have a picture. If none is provided this often comes out to be some advertisement or a commenter’s avatar. Adding a default image avoids this.

A picture, as they say, is worth a thousand words, but these thousand words are specifics that are often uncalled for, in the best case distracting in the worst case misleading. Think of “scientist” or “academia”. What image to pick that will not propagate a stereotype or single out a discipline? You may want to use a female scientist just to avoid criticism, but then isn’t your image misleading? And to make sure everybody understand she’s a s-c-i-e-n-t-i-s-t, even though she’s got lipstick on, you need a visual identification marker, a lab coat maybe, or a microscope, or at least a blackboard with equations. And now you’ve got a Latino woman in a lab coat looking into a microscope when all you meant was “scientist”.

FQXi launched a video contest “Show Me the Physics!” and in the accompanying visualization you’ll find me representing “scientist”, think bubble included (0:22). I’m very flattered that I’ve been promoted to a stereotype killer. Do you feel aptly represented? (Really, do not take pictures of yourself within 5 minutes of waking up. You never know, they might end up being your most popular ones.)

But if a picture adds a thousand words worth of detail, then a word calls upon a thousand pictures. The word is a generalization and abstraction that encompasses whole classes.

When my two year old daughter had spaghetti the first time, she excitedly proclaimed “Hair!” Humans are by nature good at classification, generalization and abstraction and this expresses in our language. That’s why we understand metaphors and analogies, and that’s where much of our humor roots.

This generalization is why we are so good at recognizing patterns, devising theories and, yes, at building stereotypes. Show me an image that captures all the richness, all the associations, all the analogies and connotations that come with the words “life” or “hope” or “yesterday”.

What are we doing then by drowning readers in unwanted and often unnecessary information? Sometimes I wonder if not the well-intended image works against the writer’s intent of making the text more accessible.

I love music, almost all kinds, but if anyhow possible I avoid music videos. I actually don’t want to know how the band looks like and I don’t want to know their interpretation of the lyrics. I want to make up my own story. Images are powerful. They stick. This video ruined David Ghetta’s Titanium for me.

This made me wonder if not this fear of the abstract, the word all by itself, is the same fear that leads science writers to shy away from equations. If a word calls upon a thousand images, an equation calls upon a thousand words. Think of exponential growth, or the wave equation, or the second law of thermodynamics. Did you just think of stirring milk into your coffee? Verbal explanations add details that are as uncalled for and can be as misleading as adding an image to illustrate a word. An analogy, a metaphor or a witty example does not convey what makes these equations so relevant: Their broad applicability and the ability to describe very diverse phenomena.

Recall these word problems from 8th class? The verbal description is supposed to make the math more accessible, but finding the equation is the real challenge. Science isn’t so much about solving equations. It’s about finding the equations to begin with. It’s about finding the underlying laws amidst all the clutter, the laws that are worth a thousand words.

Sometimes I wonder if I’d not rather be an abstract “scientist” for you, instead of a married middle-European mother of two, and I wonder what are the thousand words that my profile image speaks to you. And I fear that, by adding all these visual details, we are limiting the reader’s ability to extract and appreciate abstract ideas, that by adding all these verbal details to science writing, we are ultimately limiting the reader’s ability to appreciate science - in all its abstract glory. Hear my words...

Consciousness and Physics from Scratch

Brain in a squeezed state [Source]

Max Tegmark’s claim that we are all mathematical structures taught me an important lesson: Do not take photos of yourself within 5 minutes of waking up. Since he has influenced my thinking so thoroughly, his newest paper on the physical basis of consciousness was mandatory reading.

Titled “Consciousness as a state of matter”, the paper scores at 30 pages in 10 pt font. The argument has some gaps that are filled with conjectures, but it is an interesting attempt to quantify and formalize the slippery notion of consciousness. I’ll not claim I understood it all, but my below summary should convey the general idea.

The title of Tegmark’s paper is somewhat misleading because except for the rather vague introduction, the idea that consciousness is a “state of matter” is not rigorously pursued. In fact the original title “Space, consciousness and the quantum factorization problem” would have been much more informative if less catchy. I recommend that before you upload your LaTeX file to the arXiv you remove all comments, including discarded title options.

Tegmark’s paper actually tackles two different problems. One is the question what properties a conscious system has and how to formalize them. The other is the question of how to identify macroscopic and mostly classical objects from a fundamental Hamiltonian and wavefunction that describes presumably everything. At least that is my reading of what Tegmark calls the “physics-from-scratch problem” though this left me to wonder where the rest of the mathematical universe has gone. Maybe I should have taken the blue pill.

So let us look at the question of consciousness first.

1. Consciousness

Tegmark builds on defining qualities for consciousness suggested by Giulio Tononi (never heard of him) according to which a conscious system needs to be able to a) store large amounts of information, and b) the information must be “integrated into a unified whole”. I’ll add my comments later, let me just say that though I don’t think these are very useful criteria, at least they are criteria. He later adds three more criteria c) dynamics (time-dependence), d) independence (dynamics is dominated by ‘forces from within’) and e) utility (records mainly information that is useful for it). The latter inches quite close to adaptive systems.

Tegmark then goes on to express the two criteria of information and integration in mathematical form and tries to derive conclusions about the conscious system from this. The approach that he uses is that he assumes the system is fundamentally a quantum system described by a Hamiltonian and a density matrix, and he performs various operations on the Hamiltonian that are supposed to bring it into a form where it is an ‘integrated whole’. For this, he essentially looks for a minimum of shared information between two subsystems under arbitrary unitary transformations. These subsystems are not local in any way, they are generic divisions of the Hilbert space.

He finds that arbitrary unitary transformations can dramatically lower the integrated information in a quantum system, basically by reducing entanglement between any two subsystems. Tegmarks uses a particular conjecture about the eigenvalues of the density matrix to make this point, and while the details may depend on this conjecture I don’t think this will be news for the folks in quantum information. It is basically the idea that Verlinde and Verlinde used in their solution to the firewall paradox, the same idea that I later used in my paper, that unitary operations can ‘disentangle’ subsystems. Tegmark concludes then that we have an “integration paradox […] No matter how large a quantum system we create, its state can never contain more than about a quarter of a bit of integrated information.”

A quarter of a bit is not much and if you can still follow my elaboration it’s probably not enough to explain your brain’s workings, so the criterion of integration does not seem particularly useful. Tegmark thus goes on to amend it by taking into account dynamics, ie the requirement to process information.

Comments: I don’t find it very plausible to require that the degree of integration a system possesses must be found by minimizing over all unitary transformations. Tegmark only acts with these transformation on the density matrix, so I am not sure whether the transformation is supposed to be an actual operation or whether it also should act on the Hamiltonian. In the latter case doing the transformation wouldn’t make a difference to observables, so why look for the minimum? Tegmark unfortunately doesn’t discuss observables at all. In the former case, if the unitary transformation is an actual change to the system then I think one should consider these different systems and again I don’t see why one should look for the minimum.

In any case, let us go on to the next point then, taking into account the dynamics. For this Tegmark now aims at finding a basis in the Hilbert space that minimizes the interaction terms in the Hamiltonian, thus maximizing what he calls separability. This leads to the second topic of the paper.

2. Physics from Scratch

Tegmark interprets the “physics-from-scratch problem” as the question how to identify subsystems of the whole Hilbert space that can be separated as well as possible. These subsystems I believe are eventually supposed to give rise to the neatly separated (and almost classical) objects we experience, not to mention our own brains. He thus sets out to find a basis in which the interaction Hamiltonian between subspaces is minimized.

After another conjecture, this time about the energy eigenvalues of the Hamiltonian, he however finds that the minimal interaction Hamiltonian will always commute with the Hamiltonian of the subsystem, so there isn’t only little energy exchange, but actually none which then creates another paradox: “If we decompose our universe into maximally independent objects, then all change grinds to a halt.” This he finds does not describe reality and concludes “We have tried to understand the emergence of our observed semiclassical world, with its hierarchy of moving objects, by decomposing the world into maximally independent parts, but our attempts have failed dismally, producing merely a timeless world reminiscent of heat death.”

Then he goes on to weaken these requirements.

Comments: Recall that in Tegmark’s reading the physics-from-scratch problem includes the emergence of space and time. If that is so, I know neither what time nor what energy is supposed to mean and I have no clue how to interpret the equations. That there are unitary transformations which lead to a seemingly “timeless” picture is clear because one can shuffle the time-evolution from the wave-function into the operators. That of course does not affect observables, which brings me back to my earlier remark that it doesn’t seem very useful to try to quantify operators when no attention is paid to their expectation values.

Before reading Tegmark’s paper, I would have envisioned the physics-from-scratch procedure as follows. First you need to identify space and time from your Hamiltonian. Space and time are roughly the degrees of freedom that make the rest look as local as possible. Once you have that, you should be able to write down the Hamiltonian in a series of local, or almost local, operators of various dimensions. You need to define a vacuum state, then you can start building your Fock space. The rest is basically effective field theory. That, needless to say, is all “in principle”, not that anybody could do this in practice.

Just why the world we observe contains large things that are almost classical is probably not a question we can answer by looking at the properties of Hilbert-space decompositions in general, but it depends on the specific Hamiltonian. If we didn’t have confinement and if we didn’t have gravity our universe might just be a quantum soup.

After reading Tegmark’s paper, I am even more convinced that locality is a key requirement for the physics-from-scratch problem. Tegmark has some comments on this towards the end of the paper, but believes this requirement to be in conflict with the idea that space-time is emergent. I don’t think so, I think locality is what identifies space-time. Given that the objects that Tegmark wants to identify in the physics-from-scratch procedure are in practice very localized, I’d have expected this to be paid more attention to.

3. Summary

Having said that I don’t think Tegmark’s is a promising approach to the physics-from-scratch problem, let me come back to the topic of consciousness and the main premise that consciousness has to fulfill the above listed five criteria.

To begin with, these criteria I think are in the best case necessary but not sufficient criteria that you may want to look for in some system.

The problem is that “consciousness” is not in and by itself a thing, and it isn’t a state of something either. Consciousness is a noun that is shorthand for a verb much like, for example, the word “leadership”. Leadership isn’t a thing and it isn’t a property, it’s a relation. It’s somebody leading somebody. Consciousness too isn’t a thing, it’s a relation. It’s A being consciously aware of B. (Depending on whether you also want self-awareness B can be identical to A.) We call A conscious if we have evidence it is aware of many B’s. Just how many B’s you want is pretty arbitrary, I think it’s a sliding scale (just think about anesthesia or sleepwalking) and there is no sharp line where something becomes conscious.

Having said that, while I think Tegmark’s paper has some flaws, it is interesting and it provides a mathematical basis for further investigation. With some refinements of the criteria he has applied this can become a very fruitful approach to the physical basis of consciousness. All over the world neuroscientists are presently trying to build and program artificial brains. I am sure this mathematical approach with the possibility of quantification will one day become highly relevant to the study of artificial intelligence. It is a very courageous paper that pushes the boundaries of our knowledge and I hope that it will be influential. I really want to understand consciousness better, and for me the only proper way of understanding is by way of maths.

So what did I learn from this paper? I learned that you should not read papers about the physical basis of consciousness within five minutes of waking up. You might spend the rest of the day staring at your hand, in amazement of the fact that you have a hand, two of them even, and are able to stare, not to mention being able to think about staring. If you’ve stopped staring at your hand, let me know what you think about Tegmark’s idea.

FQXi essay contest 2014: How Should Humanity Steer the Future?

This year’s essay contest of the Foundational Questions Institute “How Should Humanity Steer the Future?” broaches a question that is fundamental indeed, fundamental not for quantum gravity but for the future of mankind. I suspect the topic selection has been influenced by the contest being “presented in partnership with” (which I translate into “sponsored by”) not only the John Templeton foundation and Scientific American, but also a philanthropic organization called the “Gruber Foundation” (which I had never heard of before) and Jaan Tallinn.

Tallinn is no unknown, he is one of the developers of Skype and when I type his name into Google the auto completion is “net worth”. I met him at the 2011 FQXi conference where he gave a little speech about his worries that artificial intelligence will turn into a threat to humans. I wrote back then a blogpost explaining that I don’t share this particular worry. However, I recall Tallinn’s speech vividly, not because it was so well delivered (in fact, he seemed to be reading off his phone), but because he was so very sincere about it. Most people’s standard reaction in the face of threats to the future of mankind is cynicism or sarcasm, essentially a vocal shoulder shrug, whereas Tallinn seems to have spent quite some time thinking about this. And well, somebody really should be thinking about this...

And so I appreciate the topic of this year’s essay contest has a social dimension, not only because it gets tiresome to always circle the same question of where the next breakthrough in theoretical physics will be and the always same answers (let me guess, it’s what you work on), but also because it gives me an outlet for my interests besides quantum gravity. I have always been fascinated by the complex dynamics of systems that are driven by the individual actions of many humans because this reaches out to the larger question of where life on planet Earth is going and why and what all of this is good for.

If somebody asks you how humanity should steer the future, a modest reply isn’t really an option, so I have submitted my five step plan to save the world. Well, at least you can’t blame me for not having a vision. The executive summary is that we will only be able to steer at all if we have a way to collectively react to large scale behavior and long-term trends of global systems, and this can only happen if we are able to make informed decisions intuitively, quickly and without much thinking.

A steering wheel like this might not be sufficient to avoid running into obstacles, but it is definitely necessary, so that is what we have to start with.

The trends that we need to react to are those of global and multi-leveled systems, including economic, social, ecological and politic systems, as well as various infrastructure networks. Presently, we basically fail to act when problems appear. While the problems arise from the interaction of many people and their environment, it is still the individual that has to make decisions. But the individual presently cannot tell how their own action works towards their goals on long distance or time scales. To enable them to make good decisions, the information about the whole system has to be routed back to the individual. But that feedback loop doesn’t presently exist.

In principle it would be possible today, but the process is presently far too difficult. The vast majority of people do not have the time and energy to collect the necessary information and make decisions based on it. It doesn’t help to write essays about what we ‘should’ do. People will only act if it’s really simple to do and of immediate relevance for them. Thus my suggestion is to create individual ‘priority maps’ that chart personal values and provide people with intuitive feedback for how well a decision matches with their priorities.

A simple example. Suppose you train some software to tell what kind of images you find aesthetically pleasing and what you dislike. You now have various parameters, say colors, shapes, symmetries, composition and so on. You then fill out a questionnaire about preferences for political values. Now rather than long explanations which candidate says what, you get an image that represents how good the match is by converting the match in political values to parameters in an image. You pick the image you like best and are done. The point is that you are being spared having to look into the information yourself, you only get to see the summary that encodes whether voting for that person would work towards what you regard important.

Oh, I hear you say, but that vastly oversimplifies matters. Indeed, that is exactly the point. Oversimplification is the only way we’ll manage to overcome our present inability to act.

If mankind is to be successful in the long run, we have to evolve to anticipate and react to interrelated global trends in systems of billions of people. Natural selection might do this, but it would take too much time. The priority maps are a technological shortcut to emulate an advanced species that is ‘fit’ in the Darwinian sense, fit to adapt to its changing environment. I envision this to become a brain extension one day.

I had a runner up to this essay contribution, which was an argument that research in quantum gravity will be relevant for quantum computing, interstellar travel and technological progress in general. But it would have been a quite impractical speculation (not to mention a self-advertisement of my work on superdeterminism, superluminal information exchange and antigravity). In my mind of course it’s all related – the laws of physics are what eventually drive the evolution of consciousness and also of our species. But I decided to stick with a proposal that I think is indeed realizable today and that would go a long way to enable humanity to steer the future.

I encourage you to check out the essays which cover a large variety of ideas. Some of the contributions seem to be very bent towards the aim of making a philosophical case for some understanding of natural law rather than the other, or to find parallels to unsolved problems in physics, but this seems quite a stretch to me. However, I am sure you will find something of interest there. At the very least it will give you some new things to worry about...

Academia isn’t what I expected

The Ivory Tower from
The Neverending Story. [Source]

Talking to the students at the Sussex school let me realize how straight-forward it is today to get a realistic impression of what research in this field looks like. Blogs are a good source of information about scientist’s daily life and duties, and it has also become so much easier to find and make contact with people in the field, either using social networks or joining dedicated mentoring programs.

Before I myself got an office at a physics institute I only had a vague idea of what people did there. Absent the lauded ‘role models’ my mental image of academic research formed mostly by reading biographies of the heroes of General Relativity and Quantum Mechanics, plus a stack of popular science books. The latter didn’t contain much about the average researcher’s daily tasks, and to the extent that the former captured university life, it was life in the first half of the 20nd century.

I expected some things to have changed during 50 years, notably in technological advances and the ease of travel, publishing, and communication. I finished high school in ’95, so the biggest changes were yet to come. I also knew that disciplines had drifted apart, that philosophy and physics were mostly going separate ways now, and that the days in which a physicist could also be a chemist could also be an artist were long gone. It was clear that academia had generally grown, become more organized and institutionalized, and closer linked to industrial research and applications. I had heard that applying for money was a big part of the game. Those were the days.

But my expectations were wrong in many other ways. 20 years, 9 moves and 6 jobs later, here’s the contrast of what I believed theoretical physics would be like to reality:

1. Specialization
   
   While I knew that interdisciplinarity had given in to specialization I thought that theoretical physicists would be in close connection to the experimentalists, that they would frequently discuss experiments that might be interesting to develop, or data that required explanation. I also expected theoretical physicists to work closely together with mathematicians, because in the history of physics the mathematics has often been developed alongside the physics. In both cases the reality is an almost complete disconnect. The exchange takes place mostly through published literature or especially dedicated meetings or initiatives.
   
   
2. Disconnect
   
   I expected a much larger general intellectual curiosity and social responsibility in academia. Instead I found that most researchers are very focused on their own work and nothing but their own work. Not only do institutes rarely if ever have organized public engagement or events that are not closely related to the local research, it’s also that most individual researchers are not interested. In most cases, they plainly don’t have the time to think about anything than their next paper. That disconnect is the root of complaints like Nicholas Kristof’s recent Op-Ed, where calls upon academics: “[P]rofessors, don’t cloister yourselves like medieval monks — we need you!”
   
   
3. The Machinery
   
   My biggest reality shock was how much of research has turned into manufacturing, into the production of PhDs and papers, papers that are necessary for the next grant, which is necessary to pay the next students, who will write the next papers, iterate. This unromantic hamster wheel still shocks me. It has its good side too though: The standardization of research procedures limits the risks of the individual. If you know how to play along, and are willing to, you have good chances that you can stay. The disadvantage is though that this can force students and postdocs to work on topics they are not actually interested in, and that turns off many bright and creative people.
   
   
4. Nonlocality
   
   I did not anticipate just how frequent travel and moves are necessary these days. If I had known about this in advance, I think I would have left academia after my diploma. But so I just slipped into it. Luckily I had a very patient boyfriend who turned husband who turned father of my children.
   
   
5. The 2nd family
   
   The specialization, the single-mindedness, the pressure and, most of all, the loss of friends due to frequent moves create close ties among those who are together in the same boat. It’s a mutual understanding, the nod of been-there-done-that, the sympathy with your own problems that make your colleagues and officemates, driftwood as they often are, a second family. In all these years I have felt welcome at every single institute that I have visited. The books hadn’t told me about this.
   
   

Experience, as they say, is what you get when you were expecting something else. By and large, I enjoy my job. Most of the time anyway.

My lectures at the Sussex school went well, except that the combination of a recent cold and several hours of speaking stressed my voice box to the point of total failure. Yesterday I could only whisper. Today I get out some freak sounds below C2 but that’s pretty much it. It would be funny if it wasn’t so painful.

You can find the slides of my lectures here and the guide to further reading here. I hope they live up to your expectations :)

Away note

I will be traveling the rest of the week to give a lecture at the Sussex graduate school "From Classical to Quantum GR", so not much will happen on this blog. For the school, we were asked for discussion topics related to our lectures, below are my suggestions. Leave your thoughts in the comments, additional suggestions for topics are also welcome.

• Is it socially responsible to spend money on quantum gravity research? Don't we have better things to do? How could mankind possibly benefit from quantum gravity?
• Can we make any progress on the theory of quantum gravity without connection to experiment? Should we think at all about theories of quantum gravity that do not produce testable predictions? How much time do we grant researchers to come up with predictions?
• What is your favorite approach towards quantum gravity? Why? Should you have a favorite approach at all?
• Is our problem maybe not with the quantization of gravity but with the foundations of quantum mechanics and the process of quantization?
• How plausible is it that gravity remains classical while all the other forces are quantized? Could gravity be neither classical nor quantized?
• How convinced are you that the Planck length is at 10^-33cm? Do you think it is plausible that it is lower? Should we continue looking for it?
• What do you think is the most promising area to look for quantum gravitational effects and why?
• Do you think that gravity can be successfully quantized without paying attention to unification?

Lara and Gloria say hello and wish you a happy Easter :o)

The Problem of Now

[Image Source]

Einstein’s greatest blunder wasn’t the cosmological constant, and neither was it his conviction that god doesn’t throw dice. No, his greatest blunder was to speak to a philosopher named Carnap about the Now, with a capital.

“The problem of Now”, Carnap wrote in 1963, “worried Einstein seriously. He explained that the experience of the Now means something special for men, something different from the past and the future, but that this important difference does not and cannot occur within physics”

I call it Einstein’s greatest blunder because, unlike the cosmological constant and indeterminism, philosophers, and some physicists too, are still confused about this alleged “Problem of Now”.

The problem is often presented like this. Most of us experience a present moment, which is a special moment in time, unlike the past and unlike the future. If you write down the equations governing the motion of some particle through space, then this particle is described, mathematically, by a function. In the simplest case this is a curve in space-time, meaning the function is a map from the real numbers to a four-dimensional manifold. The particle changes its location with time. But regardless of whether you use an external definition of time (some coordinate system) or an internal definition (such as the length of the curve), every single instant on that curve is just some point in space-time. Which one, then, is “now”?

You could argue rightfully that as long as there’s just one particle moving on a straight line, nothing is happening, and so it’s not very surprising that no notion of change appears in the mathematical description. If the particle would scatter on some other particle, or take a sudden turn, then these instances can be identified as events in space-time. Alas, that still doesn’t tell you whether they happen to the particle “now” or at some other time.

Now what?

The cause for this problem is often assigned to the timeless-ness of mathematics itself. Mathematics deals in its core with truth values and the very point of using math to describe nature is that these truths do not change. Lee Smolin has written a whole book about the problem with the timeless math, you can read my review here.

It may or may not be that mathematics is able to describe all of our reality, but to solve the problem of now, excuse the heresy, you do not need to abandon a mathematical description of physical law. All you have to do is realize that the human experience of now is subjective. It can perfectly well be described by math, it’s just that humans are not elementary particles.

The decisive ability that allows us to experience the present moment as being unlike other moments is that we have a memory. We have a memory of events in the past, an imperfect one, and we do not have memory of events in the future. Memory is not in and by itself tied to consciousness, it is tied to the increase of entropy, or the arrow of time if you wish. Many materials show memory; every system with a path dependence like eg hysteresis does. If you get a perm the molecule chains in your hair remember the bonds, not your brain.

Memory has nothing to do with consciousness in particular which is good because it makes it much easier to find the flaw in the argument leading to the problem of now.

If we want to describe systems with memory we need at the very least two time parameters: t to parameterize the location of the particle and τ to parameterize the strength of memory of other times depending on its present location. This means there is a function f(t,τ) that encodes how strong is the memory of time τ at moment t. You need, in other words, at the very least a two-point function, a plain particle trajectory will not do.

That we experience a “now” means that the strength of memory peaks when both time parameters are identical, ie t-τ = 0. That we do not have any memory of the future means that the function vanishes when τ > t. For the past it must decay somehow, but the details don’t matter. This construction is already sufficient to explain why we have the subjective experience of the present moment being special. And it wasn’t that difficult, was it?

The origin of the problem is not in the mathematics, but in the failure to distinguish subjective experience of physical existence from objective truth. Einstein spoke about “the experience of the Now [that] means something special for men”. Yes, it means something special for men. This does not mean however, and does not necessitate, that there is a present moment which is objectively special in the mathematical description. In the above construction all moments are special in the same way, but in every moment that very moment is perceived as special. This is perfectly compatible with both our experience and the block universe of general relativity. So Einstein should not have worried.

I have a more detailed explanation of this argument – including a cartoon! – in a post from 2008. I was reminded of this now because Mermin had a comment in the recent issue of Nature magazine about the problem of now.

Physics: QBism puts the scientist back into science
A participatory view of science resolves quantum paradoxes and finds room in classical physics for 'the Now', says N. David Mermin.

In his piece, Mermin elaborates on qbism, a subjective interpretation of quantum mechanics. I was destined to dislike this just because it’s a waste of time and paper to write about non-existent problems. Amazingly however, Mermin uses the subjectiveness of qbism to arrive at the right conclusion, namely that the problem of the now does not exist because our experiences are by its very nature subjective. However, he fails to point out that you don’t need to buy into fancy interpretations of quantum mechanics for this. All you have to do is watch your hair recall sulphur bonds.

The summary, please forgive me, is that Einstein was wrong and Mermin is right, but for the wrong reaons. It is possible to describe the human experience of the present moment with the “timeless” mathematics that we presently use for physical laws, it isn’t even difficult and you don’t have to give up the standard interpretation of quantum mechanics for this. There is no problem of Now and there is no problem with Tegmark’s mathematical universe either.

And Lee Smolin, well, he is neither wrong nor right, he just has a shaky motivation for his cosmological philosophy. It is correct, as he argues, that mathematics doesn’t objectively describe a present moment. However, it’s a non sequitur that the current approach to physics has reached its limits because this timeless math doesn’t constitute a conflict with our experience. observation.

Most people get a general feeling of uneasiness when they first realize that the block universe implies all the past and all the future is equally real as the present moment, that even though we experience the present moment as special, it is only subjectively so. But if you can combat your uneasiness for long enough, you might come to see the beauty in eternal mathematical truths that transcend the passage of time. We always have been, and always will be, children of the universe.

Book review: “The Theoretical Minimum – Quantum Mechanics” By Susskind and Friedman

Quantum Mechanics: The Theoretical Minimum
What You Need to Know to Start Doing Physics
By Leonard Susskind, Art Friedman
Basic Books (February 25, 2014)

This book is the second volume in a series that we can expect to be continued. The first part covered Classical Mechanics. You can read my review here.

The volume on quantum mechanics seems to have come into being much like the first, Leonard Susskind teamed up with Art Friedman, a data consultant whose role I envision being to say “Wait, wait, wait” whenever the professor’s pace gets too fast. The result is an introduction to quantum mechanics like I haven’t seen before.

The ‘Theoretical Minimum’ focuses, as its name promises, on the absolute minimum and aims at being accessible with no previous knowledge other than the first volume. The necessary math is provided along the way in separate interludes that can be skipped. The book begins with explaining state vectors and operators, the bra-ket notation, then moves on to measurements, entanglement and time-evolution. It uses the concrete example of spin-states and works its way up to Bell’s theorem, which however isn’t explicitly derived, just captured verbally. However, everybody who has made it through Susskind’s book should be able to then understand Bell’s theorem. It is only in the last chapters that the general wave-function for particles and the Schrödinger equation make an appearance. The uncertainty principle is derived and path integrals are very briefly introduced. The book ends with a discussion of the harmonic oscillator, clearly building up towards quantum field theory there.

I find the approach to quantum mechanics in this book valuable for several reasons. First, it gives a prominent role to entanglement and density matrices, pure and mixed states, Alice and Bob and traces over subspaces. The book thus provides you with the ‘minimal’ equipment you need to understand what all the fuzz with quantum optics, quantum computing, and black hole evaporation is about. Second, it doesn’t dismiss philosophical questions about the interpretation of quantum mechanics but also doesn’t give these very prominent space. They are acknowledged, but then it gets back to the physics. Third, the book is very careful in pointing out common misunderstandings or alternative notations, thus preventing much potential confusion.

The decision to go from classical mechanics straight to quantum mechanics has its disadvantages though. Normally the student encounters Electrodynamics and Special Relativity in between, but if you want to read Susskind’s lectures as self-contained introductions, the author now doesn’t have much to work with. This time-ordering problem means that every once in a while a reference to Electrodynamics or Special Relativity is bound to confuse the reader who really doesn’t know anything besides this lecture series.

It also must be said that the book, due to its emphasis on minimalism, will strike some readers as entirely disconnected from history and experiment. Not even the double-slit, the ultraviolet catastrophe, the hydrogen atom or the photoelectric effect made it into the book. This might not be for everybody. Again however, if you’ve made it through the book you are then in a good position to read up on these topics elsewhere. My only real complaint is that Ehrenfest’s name doesn’t appear together with his theorem.

The book isn’t written like your typical textbook. It has fairly long passages that offer a lot of explanation around the equations, and the chapters are introduced with brief dialogues between fictitious characters. I don’t find these dialogues particularly witty, but at least the humor isn’t as nauseating as that in Goldberg’s book.

All together, the “Theoretical Minimum” achieves what it promises. If you want to make the step from popular science literature to textbooks and the general scientific literature, then this book series is a must-read. If you can’t make your way through abstract mathematical discussions and prefer a close connection to example and history, you might however find it hard to get through this book.

I am certainly looking forward to the next volume.

(Disclaimer: Free review copy.)

Will the social sciences ever become hard sciences?

The term “hard science” as opposed to “soft science” has no clear definition. But roughly speaking, the less the predictive power and the smaller the statistical significance, the softer the science. Physics, without doubt, is the hard core of the sciences, followed by the other natural sciences and the life sciences. The higher the complexity of the systems a research area is dealing with, the softer it tends to be. The social sciences are at the soft end of the spectrum.

To me the very purpose of research is making science increasingly harder. If you don’t want to improve on predictive power, what’s the point of science to begin with? The social sciences are soft mainly because data that quantifies the behavior of social, political, and economic systems is hard to come by: it’s huge amounts, difficult to obtain and even more difficult to handle. Historically, these research areas therefore worked with narratives relating plausible causal relations. Needless to say, as computing power skyrockets, increasingly larger data sets can be handled. So the social sciences are finally on the track to become useful. Or so you’d think if you’re a physicist.

But interestingly, there is a large opposition to this trend of hardening the social sciences, and this opposition is particularly pronounced towards physicists who take their knowledge to work on data about social systems. You can see this opposition in the comment section to every popular science article on the topic. “Social engineering!” they will yell accusingly.

It isn’t so surprising that social scientists themselves are unhappy because the boat of inadequate skills is sinking in the data sea and physics envy won’t keep it afloat. More interesting than the paddling social scientists is the public opposition to the idea that the behavior of social systems can be modeled, understood, and predicted. This opposition is an echo of the desperate belief in free will that ignores all evidence to the contrary. The desperation in both cases is based on unfounded fears, but unfortunately it results in a forward defense.

And so the world is full with people who argue that they must have free will because they believe they have free will, the ultimate confirmation bias. And when it comes to social systems they’ll snort at the physicists “People are not elementary particles”. That worries me, worries me more than their clinging to the belief in free will, because the only way we can solve the problems that mankind faces today – the global problems in highly connected and multi-layered political, social, economic and ecological networks – is to better understand and learn how to improve the systems that govern our lives.

That people are not elementary particles is not a particularly deep insight, but it collects several valid points of criticism:

1. People are too difficult. You can’t predict them.
   
   Humans are made of a many elementary particles and even though you don’t have to know the exact motion of every single one of these particles, a person still has an awful lot of degrees of freedom and needs to be described by a lot of parameters. That’s a complicated way of saying people can do more things than electrons, and it isn’t always clear exactly why they do what they do.
   
   That is correct of course, but this objection fails to take into account that not all possible courses of action are always relevant. If it was true that people have too many possible ways to act to gather any useful knowledge about their behavior our world would be entirely dysfunctional. Our societies work only because people are to a large degree predictable.
   
   If you go shopping you expect certain behaviors of other people. You expect them to be dressed, you expect them to walk forwards, you expect them to read labels and put things into a cart. There, I’ve made a prediction about human behavior! Yawn, you say, I could have told you that. Sure you could, because making predictions about other people’s behavior is pretty much what we do all day. Modeling social systems is just a scientific version of this.
   
   This objection that people are just too complicated is also weak because, as a matter of fact, humans can and have been modeled with quite simple systems. This is particularly effective in situations when intuitive reaction trumps conscious deliberation. Existing examples are traffic flows or the density of crowds when they have to pass through narrow passages.
   
   So, yes, people are difficult and they can do strange things, more things than any model can presently capture. But modeling a system is always an oversimplification. The only way to find out whether that simplification works is to actually test it with data.
   
   
2. People have free will. You cannot predict what they will do.
   
   To begin with it is highly questionable that people have free will. But leaving this aside for a moment, this objection confuses the predictability of individual behavior with the statistical trend of large numbers of people. Maybe you don’t feel like going to work tomorrow, but most people will go. Maybe you like to take walks in the pouring rain, but most people don’t. The existence of free will is in no conflict with discovering correlations between certain types of behavior or preferences in groups. It’s the same difference that doesn’t allow you to tell when your children will speak the first word or make the first step, but that almost certainly by the age of three they’ll have mastered it.
   
   
3. People can understand the models and this knowledge makes predictions useless.
   
   This objection always stuns me. If that was true, why then isn’t obesity cured by telling people it will remain a problem? Why are the highways still clogged at 5pm if I predict they will be clogged? Why will people drink more beer if it’s free even though they know it’s free to make them drink more? Because the fact that a prediction exists in most cases doesn’t constitute any good reason to change behavior. I can predict that you will almost certainly still be alive when you finish reading this blogpost because I know this prediction is exceedingly unlikely to make you want to prove it wrong.
   
   Yes, there are cases when people’s knowledge of a prediction changes their behavior – self-fulfilling prophecies are the best-known examples of this. But this is the exception rather than the rule. In an earlier blogpost, I referred to this as societal fixed points. These are configurations in which the backreaction of the model into the system does not change the prediction. The simplest example is a model whose predictions few people know or care about.
   
   
4. Effects don’t scale and don’t transfer.
   
   This objection is the most subtle one. It posits that the social sciences aren’t really sciences until you can do and reproduce the outcome of “experiments”, which may be designed or naturally occurring. The typical social experiment that lends itself to analysis will be in relatively small and well-controlled communities (say, testing the implementation of a new policy). But then you have to extrapolate from this how the results will be in larger and potentially very different communities. Increasing the size of the system might bring in entirely new effects that you didn’t even know of (doesn’t scale), and there are a lot of cultural variables that your experimental outcome might have depended on that you didn’t know of and thus cannot adjust for (doesn’t transfer). As a consequence, repeating the experiment elsewhere will not reproduce the outcome.
   
   Indeed, this is likely to happen and I think it is the major challenge in this type of research. For complex relations it will take a long time to identify the relevant environmental parameters and to learn how to account for their variation. The more parameters there are and the more relevant they are, the less the predictive value of a model will be. If there are too many parameters that have to be accounted for it basically means doing experiments is the only thing we can ever do. It seems plausible to me, even likely, that there are types of social behavior that fall into this category, and that will leave us with questions that we just cannot answer.
   
   However, whether or not a certain trend can or cannot be modeled we will only know by trying. We know that there are cases where it can be done. Geoffry West’s city theory I find a beautiful example where quite simple laws can be found in the midst of all these cultural and contextual differences.

In summary.

The social sciences will never be as “hard” as the natural sciences because there is much more variation among people than among particles and among cities than among molecules. But the social sciences have become harder already and there is no reason why this trend shouldn’t continue. I certainly hope it will continue because we need this knowledge to collectively solve the problems we have collectively created.

Do we live in a hologram? Really??

Physicists fly high on the idea that our three-dimensional world is actually two-dimensional, that we live in a hologram, and that we’re all projections on the boundary of space. Or something like this you’ve probably read somewhere. It’s been all over the pop science news ever since string theorists sang the Maldacena. Two weeks ago Scientific American produced this “Instant Egghead” video which is a condensed mashup of all the articles I’ve endured on the topic:

The second most confusing thing about this video is the hook “Many physicist now believe that reality is not, in fact, 3-dimensional.”

To begin with, physicists haven’t believed this since Minkowski doomed space and time to “fade away into mere shadows”. Moyer in his video apparently refers only to space when he says “reality.” That’s forgiveable. I am more disturbed by the word “reality” that always creeps up in this context. Last year I was at a workshop that mixed physicists with philosophers. Inevitably, upon mentioning the gauge-gravity duality, some philosopher would ask, well, how many dimensions then do we really live in? Really? I have some explanations for you about what this really means.

Q: Do we really live in a hologram?

A: What is “real” anyway?

Q: Having a bad day, yes?

A: Yes. How am I supposed to answer a question when I don’t know what it means?

Q: Let me be more precise then. Do we live in a hologram as really as, say, we live on planet Earth?

A: Thank you, much better. The holographic principle is a conjecture. It has zero experimental evidence. String theorists believe in it because their theory supports a specific version of holography, and in some interpretations black hole thermodynamics hints at it too. Be that as it may, we don’t know whether it is the correct description of nature.

Q: So if the holographic principle was the correct description of nature, would we live in a hologram as really as we live on planet Earth?

A: The holographic principle is a mathematical statement about the theories that describe nature. There’s a several thousand years long debate about whether or not math is as real as that apple tree in your back yard. This isn’t a question about holography in particular, you could also ask that question also in general relativity: Do we really live in a metric manifold of dimension four and Lorentzian signature?

Q: Well, do we?

A: On most days I think of the math of our theories as machinery that allows us to describe nature but is not itself nature. On the remaining days I’m not sure what reality is and have a lot of sympathy for Platonism. Make your pick.

Q: So if the holographic principle was true, would we live in a hologram as really as we previously thought we live in the space-time of Einstein’s theory of General Relativity?

A: A hologram is an image on a 2-dimensional surface that allows one to reconstruct a 3-dimensional image. One shouldn’t take the nomenclature “holographic principle” too seriously. To begin with actual holograms are never 2-dimensional in the mathematical sense; they have a finite width. After all they’re made of atoms and stuff. They also do not perfectly recreate the 3-dimensional image because they have a resolution limit which comes from the wavelength of the light used to take (and reconstruct) the image. A hologram is basically a Fourier transformation. If that doesn’t tell you anything, suffices to say this isn’t the same mathematics as that behind the holographic principle.

Q: I keep hearing that the holographic principle says the information of a volume can be encoded on the boundary. What’s the big deal with that? If I get a parcel with a customs declaration, information about the volume is also encoded on the boundary.

A: That statement about the encoding of information is sloppy wording. You have to take into account the resolution that you want to achieve. You are right of course in that there’s no problem in writing down the information about some volume and printing it on some surface (or a string for that matter). The point is that the larger the volume the smaller you’ll have to print.

Here’s an example. Take a square made out of N² smaller squares and think of each of them as one bit. They’re either black or white. There are 2^N2 different patterns of black and white. In analogy, the square is a box full of matter in our universe and the colors are information about the particles in the inside.

Now you want to encode the information about the pattern of that square on the boundary using pieces of the same length as the sidelength of the smaller squares. See image below for N=3. On the left is the division of the square and the boundary, on the right is one way these could encode information.

There’s 4N of these boundary pieces and 2^4N different patterns for them. If N is larger than 4, there are more ways the square can be colored than you have different patterns for the boundary. This means you cannot uniquely encode the information about the volume on the boundary.

The holographic principle says that this isn’t so. It says yes, you can always encode the volume on the boundary. Now this means, basically, that some of the patterns for the squares can’t happen.

Q: That’s pretty disturbing. Does this mean I can’t pack a parcel in as many ways as I want to?

A: In principle, yes. In practice the things we deal with, even the smallest ones we can presently handle in laboratories, are still far above the resolution limit. They are very large chunks compared to the little squares I have drawn above. There is thus no problem encoding all that we can do to them on the boundary.

Q: What then is the typical size of these pieces?

A: They’re thought to be at the Planck scale, that’s about 10^-33 cm. You should not however take the example with the box too seriously. That is just an illustration to explain the scaling of the number of different configurations with the system size. The theory on the surface looks entirely different than the theory in the volume.

Q: Can you reach this resolution limit with an actual hologram?

A: No you can’t. If you’d use photons with a sufficiently high energy, you’d just blast away the sample of whatever image you wanted to take. However, if you loosely interpret the result of such a high energy blast as a hologram, albeit one that’s very difficult to reconstruct, you would eventually notice these limitations and be able to test the underlying theory.

Q: Let me come back to my question then, do we live in the volume or on the boundary?

A: Well, the holographic principle is quite a vague idea. It has a concrete realization in the gauge-gravity correspondence that was discovered in string theory. In this case one knows very well how the volume is related to the boundary and has theories that describe each. These both descriptions are identical. They are said to be “dual” and both equally “real” if you wish. They are just different ways of describing the same thing. In fact, depending on what system you describe, we are living on the boundary of a higher-dimensional space rather than in a volume with a lower dimensional surface.

Q: If they’re the same why then do we think we live in 3 dimensions and not in 2? Or 4?

A: Depends on what you mean with dimension. One way to measure the dimensionality is, roughly speaking, to count the number of ways a particle can get lost if it moves randomly away from a point. The result then depends on what particle you use for the measurement. The particles we deal with will move in 3 dimensions, at least on the distance scales that we typically measure. That’s why we think, feel, and move like we live in 3 dimensions, and nothing wrong with that. The type of particles (or fields) you would have in the dual theories do not correspond to the ones we are used to. And if you ask a string theorist, we live in 11 dimensions one way or the other.

Q: I can see then why it is confusing to vaguely ask what dimension “reality” has. But what is the most confusing thing about Moyer’s video?

A: The reflection on his glasses.

Q: Still having a bad day?

A: It’s this time of the month.

Q: Okay, then let me summarize what I think I learned here. The holographic principle is an unproved conjecture supported by string theory and black hole physics. It has a concrete theoretical formalization in the gauge-gravity correspondence. There, it identifies a theory in a volume with a theory on the boundary of that volume in a mathematically rigorous way. These theories are both equally real. How “real” that is depends on how real you believe math to be to begin with. It is only surprising that information can always be encoded on the boundary of a volum if you request to maintain the resolution, but then it is quite a mindboggling idea indeed. If one defines the number of dimensions in a suitable way that matches our intuition, we live in 3 spatial dimensions as we always thought we do, though experimental tests in extreme regimes may one day reveal that fundamentally our theories can be rewritten to spaces with different numbers of dimensions. Did I get that right?

A: You’re so awesomely attentive.

Q: Any plans on getting a dog?

A: No, I have interesting conversations with my plants.