Sunday, February 28, 2010

Yes, We Can't

Elementary logic is arguably the most basic ingredient to fruitful argumentation. Nevertheless, you don't have to look far in the world wide web to figure most people have one or the other problem with it. I blame English grammar for it.

For example, in classical logic a double negation of a statement is equivalent to the statement itself. Ergo, "We can visit my parents," means the same as "We can not not visit my parents," which however means we have to visit them. Thus, we have to visit my parents whenever we can. But what's even better is that "I could care less" actually means "I couldn't care less." According to that logic "Yes, we can!" means the same as "Yes, we can't!" This clearly has extraordinary explanatory power when it comes to American politics. And let's not even get started on issues like boxing rings that are actually square, and that one fills in a form by filling it out, and so on.

Another logic relation that people often stumble over is that "From A follows B" is equivalent to "From not B follows not A" and not to "From not A follows not B," which would be equivalent to "From B follows A." Consequently, if you hypothesize that "All of reality is mathematics" it does not follow "All of mathematics is real." Neither does "All of mathematics is real" mean that "All what's real is mathematics."

Then, let's have a look at what it means for an argument to be circular. A circular argument is not necessarily wrong, it just doesn't have explanatory power. Consider you ask an alcoholic why he drinks: "I drink to forget," he tells you. "Well, what do you want to forget?" you ask. "That I drink." We laugh about that exactly because it doesn't explain anything. You could just as well not drink and not forget that you don't drink. However, there is nothing logically wrong with his explanation. Circular arguments are very common mistakes in proofs, when you accidentally make an assumption that already implies the outcome. For example, if you want to show free will exists, you better not use free will as an assumption in your argument.

Finally, let me expand on one of the few enlightened comments to our recent post, made by Neil B on what it means for something to be tautologically true: "if we thought everything that could be logically inferred directly was superfluous to state, then the entire body of what is analytically derivable from given evidence should just remain unsaid." In fact the value of logical conclusion is subjective. If it follows from the assumptions (or axioms) the question whether or not you find something "tautologially true" depends on how difficult it is for you to understand the conclusion. Given the standard model lagrangian, next-to-next-to-next-to leading order contributions to the top quark pair production are at least to me not obvious. Given the Maxwell equations, the continuity equation is "tautologically true." But that might not be obvious to everybody. Or maybe it might not not be not obvious. Now I'm confused. No, I'm not. Wait....

Thursday, February 25, 2010

The Stephen Hawking Centre

Last year, I told you about Perimeter Institute's expansion. According to their 5 year plan (which you can download here) the "recruitment goal is approximately 25 Faculty members (11 at present) and 25 Associate Faculty members (11 at present)." The number of postdocs is supposed to increase to 45-50. Needless to say, they only hire "the world’s most promising Postdoctoral Researchers, seeking out independent-minded individuals and encourag[e] them to pursue unorthodox, “riskier” research." Cough. Let's not forget however that these postdocs just "generat[e] a flow-through of the most promising talent." In other words, if you integrate them over a closed surface, you get zilch. The 5-year plan contains many more nice words, together with a detailed explanation how "the whole" will be "far greater than the sum of its parts," and how this master-plan relates to the root-system of of E8 (see diagram).

In any case, the original estimate for the Institute's space requirements had a factor 2 or so missing. Is what happens when the parts don't sum. By now, the box is full, students sit in the corners on the corridors and thus the building will be expanded by the "Stephen Hawking Centre." (Not a typo but a tribute to the Queen.) Speaking of Stephen Hawking, I'm presently sitting in my old office which, so I'm told will be used for Hawking's assistant during his visit, while he himself will get the corner office, directly below Lee's. Some great man stocking going on here. But more great men have to be stocked, so architects were consulted how to extend the building without ruining its looks. Here's what they came up with:

(That's where you're supposed to ooh and aaah.) Pretty, hum? I actually like it better than the original design, it looks more dynamic and less intimidating. It wasn't easy to come up with a feasible expansion due to various environmental constraints. What you see in the picture is the (new) main entrance and the East and North side of the building. (The lake is to the right.) The new part is being built around the old one. In reality it presently looks like this (click to enlarge):

I'm curious how it will look when finished. Inside the building, the ongoing construction is hardly noticeable. Except that the stair that I used to take to get to my office is gone, which I keep forgetting and then find myself standing in front of a wall wondering what's going on.

Monday, February 22, 2010


I'll be visiting Perimeter Institute the coming three weeks. If I manage to get to Toronto that is. I'm flying with Lufthansa, but Lufthansa decided they'll go on strike, starting today. According to newspaper reports two thirds of their flights were cancelled, mine among them. I managed to rebook on a partner airline, but since the flight is operated by Lufthansa, I'm still not entirely sure I'll actually make it to the other side of the ocean. Not to mention that the rebooking implies I'll have to get up in the middle of the night, which doesn't lift my mood. Reason for the strike is apparently that the labor union of pilots is afraid Lufthansa will increasingly outsource services and insists on having a say in the decisions which routes will remain for Lufthansa pilots. The employer says this request is "not negotiable." Sympathies for the pilots are limited though because it's a tremendously well-paid job. For what I am concerned, well, next time I'll fly Delta.

In any case I'll probably be stuck in transit for a while. Should I make it to Canada you'll get an update on the building construction at PI.

Some of our readers might enjoy having a look at our last week's colloquium by Jan de Boer, a string theorist from the University of Amsterdam, on "Holography, quantum gravity and black holes" (video and audio here.) I found his talk was somewhat too basic even for a colloquium, it would have been more suitable for a public lecture but it was well delivered and is very accessible indeed. You'll have to take this talk with a grain of salt though. I can basically see some of you'll have their hair stand up with statements like "string theory is right now the only consistent theoretical framework which contains both quantum mechanics and general relativity."Anyway, it will give you an idea why string theorists are excited about the AdS/CFT duality and what it's good for, see also these earlier posts, so forgive the man some overstatements.

Friday, February 19, 2010


I meant to just try it once, but then I couldn't stop. CAPITAL LETTERS! They were demanding immediate attention, captivating, impossible to ignore. I GOT STUCK IN CAPS LOCK. Now I'm on withdrawal. WITH OCCASIONAL RELAPSE. Therefore, today we'll talk about ADDICTIONS.

In the comments to a previous post, Steven remarked:
“[Chad Orzel] is a blog addict, by all accounts. Me too, I admit it, and I've only been blogging seriously for a few months! Christ, this stuff is more addictive that nicotine. Is there a 12-step program for blogging addicts, somewhere?

David Carr from the New York Times is quoted with saying:
“Sometimes I wonder whether I care [about my blog] to the point that I neglect other things, like, oh, my job. Tweaking the blog is seductive in a way that a print deadline never is. By the time I am done posting entries, moderating comments and making links, my, has the time flown. I probably should have made some phone calls about next week's column, but maybe I'll write about, ah, blogging instead.

And of course there's a self-help group called Bloggers Anonymous (Living with blog addiction? You are not alone!) This made me wonder what it actually means to be addicted. CAN ONE GET ADDICTED TO CAPITAL LETTERS? And am I addicted to my blog? Googling for “addicted to blogging” brings up a rather silly self-test (on which I score 57%, whatever that might mean) and a Dr. who wants to tell you you're seriously sick when “you recognize yourself in any of those:
  • I only blog on important topics - well, important topics to me.
  • I can stop blogging anytime I want. I just don’t want to stop. This is not hurting me or anyone else.
  • I am not addicted [...] Blogging isn’t a drug.
  • ...
And of course you are denying it! “Disbelief that it is possible to be addicted to blogging” is part of your problem. There is probably a book you can waste money on that will cure you. Okay, WAIT.

Let's clarify what we are talking about:

The Diagnostic and Statistical Manual of Mental Disorders” (DSM) doesn't talk about addiction at all, it distinguishes between substance dependence” and compulsive behaviour” (not to be confused with the obsessive-compulsive disorder). Substance dependence involves, well, a “substance” whose repeated abuse has averse effect on the health and/or ability to organize ones life, in med speech it “leads to clinically significant impairment or distress.” A compulsive behavior is basically a behavior which you can't stop even though you'd want to. Trying, trying, FAIL.

Typically, substance abuse is associated with mindaltering drugs while compulsive behavior is associated with self-control problems like gambling, overeating, or blogging. Addiction is colloquially meant to encompass both. There is however no clear demarcation line between substance abuse and compulsive behavior. Really, what is a substance?” Is a blogpost substance? Well, what is not substance? One can get quite metaphysical about that.

But besides that, as typical for psychological problems, exactly where a behavior starts being in need of professional help is not clearly defined either. You can find examples in your newspaper: nicotine addiction is meanwhile considered an illness, while it is under debate whether or not overeating is an actual disease or a bad habit. And then there's the Dr. who tells you your “internet addiction” needs treatment. Dear Abby, I obsessively check my BlackBerry every two minutes. Can I call in sick?

Okay, so I learned my Capslock disease is not a case of substance dependence, just a little compulsive behavior. I'LL GET OVER IT. I am also still in denial about my alleged blogging addiction. But now I'm concerned about something else. Is information a “substance” one can be dependent on? Steven later added to his above comment
“What is addictive about blogging? Hmm. Well, for me, it's knowledge. I can't get enough.”

Arguably, information is a mindaltering experience indeed: it can create knowledge. So to understand the risks let's have a look at the averse effects of addictions. The neurological basis for both substance dependence and compulsive behavior is the same and lies in what is known as

The Reward Circuit

Happiness and self-fulfilment are common goals in the game that is human life. However complex the rules of that game, eventually it is a neurobiological response in our brains that makes us feel happy or satisfied. Natural selection favored those who desired to achieve behavior that was beneficial for the survival of the individual and its kind. In the course of evolution, we were thus endowed with what neuroscientists call the “reward circuit.” The reward circuit becomes active if we do what is necessary or beneficial for survival - such as eating, learning, or having sex - and triggers a feeling of happiness by a complex release of chemicals.

But research has also shown the reward circuit is not only a direct response mechanism that leads to the production of endorphins responsible for happiness. It is coupled to the hippocampus, our learning and memory center, and the prefrontal cortex, relevant for our thinking and planning. This enables us to develop possibly quite elaborated tactics to trigger the reward mechanism.

And there are shortcuts to immediate happiness. Drugs like cocaine, speed, angel dust, heroine, morphine, alcohol and tobacco stimulate the reward system, and often provide greater pleasure than is normally the result of natural stimulation.

With repeated drug use, neurotransmitters in the brain develop a SUBSTANCE TOLERANCE, it then takes a larger dose to achieve the same effect. Simultaneously, the user becomes less receptive to natural stimuli and loses interest in activities other than obtaining the next dose. Changes in the brain metabolism cause WITHDRAWAL effects, which makes it hard to fall back into a previously stable and pleasant state. Our usually beneficial ability to learn from rewards and direct our actions towards this goal then leads to a planning of how to get the next kick. It becomes the center of interest, many users report a constant OBSESSION. The addict neglects primary survival needs. The result can be fatal.

A wrongly wired reward circuit thus leads us to learn behavior damaging for the physical and mental health. What makes this rewiring of the brain so dangerous is that knowledge of negative consequences is generally not sufficient to break out of the vicious cycle.

Addiction... thus characterized by: withdrawal symptoms, obsession with the next kick, substance tolerance, and is accompanied by physical changes in the brain's function. However, as far as the physical changes are concerned, it is also known that there are correlations between physiological and psychological changes in the brain, and the causation is not always clear. Thus, exactly when and why substance use turns into substance abuse in general remains fuzzy, though for some drugs the mechanisms are meanwhile well understood.

Knowing the working of the reward circuit also makes clear why many popular songs refer to love as an addiction: you can quite literally be Addicted to Love. Falling in love causes release of phenylethylalamine (a natural monoamine alkaloid that is also found in chocolate), which is responsible for the euphoric feeling, not to mention that it evidently sparks creativity. I hate myself for loving you, but how am I supposed to live without you? I can't get you out of my head! I try to say goodbye and I choke, I try to walk away and I stumble, I promise myself, No, I’m not gonna do this, but oops, I did it again. It's all chemistry, really. Thus, being in love comes with all the symptoms of an addiction: obsession, withdrawal symptoms, and finally substance tolerance, also known as marriage.

So, can one be addicted to blogging?

It still seems implausible to me that blogging makes for a sensible addiction, mostly because its behavioral meaning is vague and individually different. It is more plausible one or the other aspect of blogging is addictive. Being on top of news is likely one of them, fame is another. And to some extend blogging has elements of gambling too. Combine all that with the instant social glue of Web2.0, and you get a very sticky mess instead. The immediateness and global connectivity the internet offers can amplify these effects, but is there really something new about this?

Okay, so now that I've convinced myself I'm not an addict, I have a confession to make. I sometimes do get up in the middle of the night. Not to check my blog stats though, but to look up an equation. Last night I fell asleep on Jackson's Classical Electrodynamics. Clearly not healthy. I'm probably addicted to physics! Help! I always have some in my drawer. It's affecting my work life.

But at least I got over my little problem with the capital letters. Well. ALMOST :-)

PS: And of course I only blog on important topics. Well, important topics to me.

Tuesday, February 16, 2010

Endless Talking

Yesterday, I read that Chad Orzel decided he won't read any blogs for Lent. I'm not Catholic, so can't really relate to the religious aspect of the decision, but some of his remarks might resonate with you:

"[T]his is really part of a larger disillusionment with the medium as a whole that's been growing for the past several months [...] I'm coming to doubt the idea of blogs as a conversation medium [...] "conversation" implies something more than a series of alternating lectures. For a real conversation, you need some give and take-- each party needs to give the other's arguments serious consideration, and ideally, there should be some development, some evolution.

And more and more, I'm finding that this sort of conversation doesn't take place on or between blogs. People just trade position statements over and over and over.

The most obvious and direct example of this is the well known comment section phenomenon in which the latest commenter doesn't bother to read the 17 previous comments before posting the exact same thing that has already been said a dozen times.

I'm finding this more and more irritating as time goes by. I find myself walking around wanting to punch something, all because people on the Internet are pissing me off. And, you know, this isn't good."

Having met Chad, I can tell you the idea that he's walking around wanting to punch something really isn't good ;-) But more seriously, I consider myself a nice and peaceful person but even I can understand the sentiment. A sane comment to a provocative blogpost is like the drop on the hot stone.

For a while I was quite frequently commenting on blogs. But over the course of time I realized I'll have to make a choice: I either comment to what others write, or I take care of my own blog. I decided focusing on this blog. I read a bunch of other blogs, but rarely read the comment threads and even more rarely comment myself. Part of the reason is that a lot of what one finds in the blogosphere is very repetitive and I'm not patient enough for that. I don't want to comment without having read a post, but if it's not a topic that's currently in my mind, I have a tendency to only read partially and guess the rest. I have a quick finger on the scroll wheel. As a consequence, I'm exactly the kind of commenter I wouldn't want myself. On the other hand, there's people around who make excellent commenters - that's you! - and provide the glue in the blogosphere.

The other reason I'm rarely reading comments is that I realized most people just blog and comment for entertainment. It just isn't about conversation, it's not about learning or changing an opinion. It's to hang out with others, share good and bad news, comfort a friend, or pick a fight. And for some it's to show off. (Look how many comments I get! Look how many visitors I have!) Blogging makes their life interesting and relevant, it provides appreciation. It barely matters if what they write makes a lot of sense, as long as it sparks attention. (No comment.) Or in other words, the blogosphere is just a reflection of the real world. Maybe my "disillusionment" with communication in the blogosphere was limited because I find communication works generally badly. (I'm not weird! It's just that nobody understands me!)

So far about the disillusionment. Let me however mention something remarkable that occurred to me recently: The LHC has meanwhile seen the first collisions. They've been at collision energies higher than what has previously been reached in the lab. I haven't noticed a single newspaper proclaiming the world is going to end. I believe that one of the reasons for this silence is the outcry earlier scary stories caused on many science blogs, and that the tireless repetitions why these stories are scientifically unfounded eventually reminded editors of their responsibility.

It's not that conversation entirely doesn't work. It just works very slowly. It takes a lot of water drops to cool a hot stone. So keep on droppin'.

    "Walk in silence,
    Don't walk away, in silence.
    See the danger,
    Always danger,
    Endless talking,
    Life rebuilding,
    Don't walk away.

    Walk in silence,
    Don't turn away, in silence.
    Your confusion,
    My illusion,
    Worn like a mask of self-hate,
    Confronts and then dies.
    Don't walk away."

Sunday, February 14, 2010

Free Falling

My recent post on the black hole information loss problem drifted off into the basics of General Relativity, and I thought it would be worthwhile to repeat some essentials, most notably what "freely falling" means. To start with, we need the Equivalence Principle which we previously discussed here:
    The Equivalence Principle: Locally, the effects of gravitation (motion in a curved space) are the same as that of an accelerated observer in flat space.

The commonly used example is if you were standing in an elevator, you couldn't distinguish between the elevator being pulled up in constant acceleration (by, say, a flying pig) far away from any gravitating masses, or standing on the surface of a planet, being pulled down by gravity. Similarly, you couldn't distinguish between your elevator being not accelerated in empty space, and being freely falling in a gravitational field. That indeed was, so the story goes, what sparked Einstein's idea of the Equivalence principle:
    “For if one considers an observer in free fall, e.g. from the roof of a house, there exists for him during his fall no gravitational field---at least in his immediate vicinity.”~A.Einstein [via]

The easiest way to understand how the non-accelerated observer in Special Relativity becomes a freely falling observer in a curved background is to generalize Newton's first law: “In the absence of a force, a body either is at rest or moves in a straight line with constant speed.” (:-)) Now in a curved background, speaking of a “straight line” is not particularly meaningful. Instead, one uses curves of minimal length, so called “geodesics” which is the straight-forward generalization of the flat space's straight lines. The first law then turns into: In the absence of a force, a body moves on a geodesic. And that's what we mean by freely falling.

Doesn't sound too complicated, but there's one thing people tend to get confused about. If space-time is not flat, the motion on a geodesic describes the motion in a gravitational field already. It thus seems like there's a force acting on the body, isn't that what we've learned in high school, things falling from towers etc? No! That's exactly what we mean with “gravity is not a force.” Gravity is a property of space-time. You are “freely falling” as long as there's no force acting on you that pushes you off the geodesic.

Right now, sitting in a chair trying to figure out what I'm telling you, you are not freely falling. There's a force acting on you, which is a combination of the electromagnetic interaction and the Pauli exclusion principle that prohibits you from falling through the Earth. You are not moving on a geodesic. The guy who fell off the roof was moving on a geodesic - no force acting, no acceleration - until he hit the pavement. That's where he was accelerated, which corresponds to a force acting. That's what makes the confrontation with the pavement so unpleasant.

[If you know a little bit about the mathematics, the Equivalence Principle says one can always locally chose coordinates in which space-time is flat and you can get the first derivatives of the metric to vanish too. This means in particular that in this “freely falling” coordinate system, the Christoffel-symbols vanish. That is only possible because the Christoffel-symbols are not tensors. In this freely falling coordinate system, the equation of motion is just that the derivative of the momentum with respect to the proper time vanishes, i.e. it's the same as Special Relativity - the Equivalence Principle at work. You can actually start from there and, using covariance, obtain the equation of motion in all other coordinate systems.]

If you look outside the “local” surrounding mentioned in the Equivalence Principle you can however distinguish flat from curved space. You can do that for example by measuring the distance to nearby geodesics over time. The change of this distance gives you something called “geodesic deviation” which is related to the curvature tensor. Whether or not this geodesic deviation vanishes is a coordinate independent statement: A tensor that vanishes in one coordinate system does so in all coordinate systems. In your elevator this means if you measure very precisely you could figure out that in a gravitational field there's a slight difference between particles moving at the top and at the bottom of your elevator.

Okay, if you've made it till here, there's one question remaining: how do we get back the “gravitational force” that we're used to talk about? Well, you can go and define something like a force in a particular coordinate system, for example the coordinate system labeling distances to the Earth's surface (or, more conveniently, distance to its center). Using such a particular coordinate system allows to separate the terms in the geodesic equation between the time derivative of the momentum (dot p) and “everything else,” which you can then go and interpret as a “force.” Also known as “the Newtonian limit” for obvious reasons, this allows to identify a derivative of the metric tensor in Einstein's field equations with the Newtonian potential.

[You can find this derivation in any textbook on the topic, in Sean Carroll's lecture notes page 105/106 or in my master's thesis, page 28 (in German).]

Zero G flights make active use of the Equivalence Principle. Basically, when you're inside the plane you get the floor pulled away below your feet and are freely falling: there is no force acting on you. You don't need the plane for the fall. You need the plane to slowly push you off the geodesic again and prevent you from colliding with planet Earth. Not to mention that said planet has an atmosphere which, at some hundred miles per hour, causes quite some friction that would prevent actual geodesic motion. But if being a theoretical physicist has any advantage then it's to disregard friction on cue ;-)

Friday, February 12, 2010

350 years Royal Society

As Sabine has mentioned earlier today, this year is the 350th anniversary of the Royal Society, the british national academy of science. Going back to a gathering of a few men interested in "Experimental Philosophy" in London in November 1660, the Royal Society is one of the oldest scientific academies in the world.

Outside Britain, it may be best known for its 13th president, Sir Isaac Newton, and for the publication of the "Philosophical Transactions of the Royal Society", the oldest existing scientific journal in continuous publication.

The Royal Society has set up a special website, and a very nice interactive timeline dubbed "trailblazing", which allows a brief virtual journey through the history of science since the 1650s.

Moreover, there will be several commemorative publications free to access over the anniversary year 2010, for example a special issue of the "Philosophical Transactions A". It features articles not requiring the reader to be a specialist to gain understanding of the content, ranging in topics from "Geometry and physics" by Michael Atiyah, Robbert Dijkgraaf and Nigel Hitchin to "Flat-panel electronic displays" by Cyril Hilsum.

And, most important, the Royal Society Digital Journal Archive will free until 28 February 2010 (two more weeks left only, unfortunately). This means full access to all issues of the "Philosophical Transactions" starting back in 1665!

So, for example, we can read about

  • Isaac Newton presenting his "New Theory about Light and Colors", with the description of his experiments with prisms and the spectrum (1671, 6 3075-3087),

  • Benjamin Franklin reporting his experiments "concerning an Electrical Kite" (1751, 47 565-567),

  • John Michell discussing "the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light...", suggesting stars so massive that light cannot escape from them (1784, 74 35-57),

  • Henry Cavendish describing his "Experiments to Determine the Density of the Earth", or to measure Newton's gravitational constant with a torsion balance (1798, 88 469-526),

  • Alexander Volta reporting Galvani's experiments on electricity (the "frog" experiments - 1793, 83 10-44) and his own construction of the "Volta pile", the prototype of an electrical battery (1800, 90 403-431),

  • William Herschel discussing recent developments about "his" planet Uranus (1783, 73 1-3), reasoning "On the Construction of the Heavens" (1785, 75 213-266) and "the Nature and Construction of the Sun and Fixed Stars" (1795, 85 46-72), and describing his discovery of "Solar, and ... Terrestrial Rays that Occasion Heat", now known as infrared light (1800, 90 293-326),

  • Thomas Young arguing for the wave nature of light in "Outlines of Experiments and Inquiries Respecting Sound and Light" (1800, 90 106-150), and reporting the results of his interference experiments (1804, 94 1-16),

  • James Prescott Joule demonstrating the "Mechanical Equivalent of Heat" (1850, 140 61-82), and

  • James Clerk Maxwell introducing the principle of the RGB colour system in "On the Theory of Compound Colours" (1860, 150 57-84), presenting "A Dynamical Theory of the Electromagnetic Field" (1865, 155 459-512) and contributing to the "Dynamical Theory of Gases" (1867, 157 49-88).

More findings are welcome in the comments! Have a great reading weekend!

This and That

I'm presently stuck with what I've been working on lately. It's the really, really frustrating phase. Once you start looking into the details of an idea, problems occur to you that you previously weren't aware of. So then you have to rethink, read more papers, try differently. Sometimes it just doesn't work no matter what you try. One day it seems to work, the next day you figure out a mistake, then you find a better way, and that doesn't work either, and so on. Sigh.

But there's also good news from my work life: two of my recent papers "A model for non-singular black hole collapse and evaporation" with Leonardo Modesto and Isabeau Prémont-Schwarz, and "Conservative solutions to the black hole information problem" with Lee Smolin were just accepted for publication in PRD. So now we have to read the proofs. I like that part.

Besides that, I learned recently that the Royal Society has their 350th anniversary this year. They are celebrating the occasion with some open access special issues of the Philosophical Transactions, and they have an interactive timeline marking important papers, eg 1891 the proof that fingerprints are unique. One never stops learning. If you have an interest in the history of science, check this out.

Another news item is that the American Physical Society is giving blogging a try. They've called it "Physics Frontline" and according to their description cover "the latest scientific news, analysis and commentary on the intersection of physics with science policy issues, including innovation, education, energy, climate change, and nuclear policy." Despite presently 7 contributors, blogging is somewhat scarce there. Anyway, I think it's a good idea to provide commentary on science policy from people who actually know what they're talking about, and I thus hope to see somewhat more activity over there in the future.

Monday, February 08, 2010

Why, oh why, is the Psi called Psi?

I'm currently reading Sean Carroll's book "From Eternity to Here" and stumbled over this remark
In Newtonian mechanics, the space of states is called "phase space" for reasons that are pretty mysterious.

A mystery that hadn't occurred to me before, probably because the German word "Zustandsraum" means literally "state space," so no mystery there. Stefan and I were guessing Gibbs, who introduced the word, might have generalized the terminology from the harmonic oscillator where the location in phase space does indeed tell you the phase of the oscillation. (You find a nice applet depicting the phase-space diagram of the damped and undamped oscillator here).

In any case, this caused me to ponder what other words with funny origin physicists like to use. (Both funny ha-ha, and funny peculiar.) Why, for example, is the recombination in the early universe called recombination if there was no prior combination? Not that I was the first to ask that question. Sean offered the explanation that the word is borrowed from nuclear physics. But then why don't nuclear physicists call the fragmentation refragmentation?

There are more interesting nomenclatures though than presence or absence of prefixes.

A particularly well known oddity is the name "quarks" introduced by Gell-Mann, who couldn't decide how to spell the sound ducks make:
In 1963, when I assigned the name "quark" to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been "kwork". Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word "quark" in the phrase "Three quarks for Muster Mark". Since "quark" (meaning, for one thing, the cry of the gull) was clearly intended to rhyme with "Mark", as well as "bark" and other such words, I had to find an excuse to pronounce it as "kwork".
~M. Gell-Mann, The Quark and the Jaguar, via Wikipedia

Had Gell-Mann read a German dictionary instead of Joyce, he'd have noticed "Quark" is the German word for a milk product (often mistakenly translated as "cottage cheese" which is something entirely different). Besides this, "Quark" is a frequently used colloquial expression for nonsense.

But at least we know how that word came along. A mystery remained to me why the English adaption of the German word "Eigenvektor" came out to be "eigenvector." The German word "eigen" simply means "innate," and could easily have been translated.

A better example fo imaginative nomenclature is the Psi-particle (now known as J/Psi) whose cloud-chamber pictures frequently have the shape of a Psi (see picture above).

Then there is the "Penguin diagram", which owes its name to a lost bet and some illegal substances, and the "tadpole diagram" which once run risk of turning into a "spermion." Probably a good thing the tadpoles kept their name - just imagine what issues the anti-abortionists would have had with spermion cancellation.

In General Relativity, we have the conjecture of "cosmic censorship" to prevent us from seeing "naked singularities," and "wormholes" are already a classic. Cosmologists have further blessed us with MACHOs and WIMPs, acronyms for MAssive Compact Halo Object and Weakly Interacting Massive Particles respectively. Loop Quantum Gravity features a LOST theorem, after the last names of its authors. The large gap between the energy scale of currently known physics and the scale where grand unification is thought to occur is also known as "desert." We have a seesaw mechanism, play with Mexican hat potentials, have ghosts and talk about stop particles. There's a swiss cheese universe and neutron stars have pasta-antipasta layers with a spaghetti-phase. The most stupid nomenclature I so far have come up with is a "pullover". Yes, I know, not terribly original, but then I didn't expect a Nobelprize for it ;-)

Did I miss something? Leave it in the comments!

Sunday, February 07, 2010

Black Holes and Information Loss

Here is - finally! - the continuation of my previous posts on Causal Diagrams and The Causal Diagram of the Black Hole. Due to popular demand, this time we will discuss the black hole information loss paradox. I previously wrote about this topic here, where I also listed the most common solution attempts. I am not going to repeat this list of solution attempts, so please refer to the older post for that. I want to focus here instead on the causal diagram.


Last time, we finally arrived at the diagram of the evaporating black hole:

More precisely, it's a non-rotating uncharged black hole.

The most important features of this spacetime are that it has a (spacelike) singularity and an event horizon. The blue line indicates the surface of some collapsing matter configuration [1]. Let me remind you that since we've chosen radial coordinates, curves that pass through r=0 (where it is non-singular) look like they are reflected back. These segments of curves are also referred to as in- and outgoing in an obvious terminology.

Shown in the figure is v0, the last ray of light that passes through the collapsing matter and still manages to escape [2]. In the background depicted in the diagram, particle creation takes place at the horizon, which causes the black hole to lose mass. It then shrinks until it has finally completely evaporated, leaving behind nothing but thermal Hawking radiation [3].

Another important fact is that this spacetime is "asymptotically flat" or "asymptotically Minkowski," which means that at an infinite distance from the black hole spacetime is flat (flat as in "the curvature tensor vanishes"). This doesn't necessarily have to be the case (i.e. it could be asymptotically AdS instead), but it will make our discussion leaner. The reason for this asymptotic flatness is simply that in the beginning as well as in the end the matter is arbitrarily thinly dispersed.

To wrap up the summary, note that this diagram depicts a highly idealized situation. It's an evaporating black hole in an otherwise entirely empty spacetime. Realistic black holes are surrounded by matter and accrete mass, and occasionally Bob sends one of his Alices behind the horizon. But, as so often in physics, the uncluttered idealized version will help us understand the situation better without spoiling the conclusions.


To understand the black hole information loss problem you need one further ingredient, that's what physicists mean with time-evolution. Intuitively, it means that one specifies a system at one moment in time, known as "initial conditions" and from this determines the status of that system at any other time by the help of a differential equation [4]. The most basic example is throwing a ball. The initial conditions needed are the location and velocity at one moment. The equation you use is Newton's law (or something equivalent).

In General Relativity the situation is more complicated but conceptually similar. You specify the initial conditions of your matter configuration at one moment in time and use Einstein's field equations to determine what space-time and matter are doing at any other time [5]. The attentive reader might remark that already in Special Relativity "one moment in time" is ambiguous. Indeed, and this is also the case in General Relativity. Point is, you can use any "moment in time" for you initial conditions, as long as it's at one moment, but everywhere in space (this is not the only option, but the most commonly used one). We call that a "complete spacelike hypersurface." Complete means basically it doesn't have holes and no expandable boundaries.

Almost there now. In the below picture I've added two complete spacelike hypersurfaces denoted Σ1 and Σ2

Information Loss

The evolution of a quantum mechanical state is unitary. That means in particular it is time-reversible [6]. You can evolve the status of your system back and forth how you like. There are many ways to think about information, and when talking about the black hole evolution some people like to hang themselves up on the exact meaning of information. That's a very interesting topic, but we'll cut this discussion short because it's irrelevant to understand the problem. Consider you have an initial state and you evolve it into a final state. If your final state does not uniquely specify the initial state we'll consider this loss of information. It means you can't tell what happened.

Black hole evaporation causes a loss of information because the outgoing radiation depends only on the total mass. Once the black hole is evaporated, all states with the same initial mass are converted into the same endstate. There are many ways a system can be composed if you only know the total mass [7]. There's only one way it will look after evaporation. This process is thus not reversible: it is not possible to reconstruct the initial state from the final state. But if it's not reversible, it can't be unitary. And for beginners that's the problem: The formation and complete evaporation of the black hole seems to be incompatible with quantum mechanics. On the advanced level it's more complicated since we know the computation leading to Hawking radiation breaks down when quantum gravity becomes important. In this case the problem is that this quantum gravitational contribution doesn't help you to get enough information out.

There are several points that people tend to misunderstand about the problem already on the beginner's level, so let me mention some pitfalls. First, note that the problem is not that the information is inaccessible behind a horizon. There is no horizon in the endstate, look at the diagram. It's flat Minkowski space with infinitely thinly dispersed thermal radiation. Think of the black hole as a black box. You start with flat Minkowski space, something happens in between, you end with flat Minkowski space. Yet, this evolution cannot be described by quantum mechanics as we know it. Second, to lay out the problem I didn't have to refer to measurement at all. It's a fundamental incompatibility in the evolution, you don't solve that incompatibility by waving your hands and yelling "measurement problem." Third, we are talking about the microscopic laws. Yes, on macroscopic scales we do have an arrow of time and entropy tends to increase anyway, but the problem is to accommodate the black hole evolution with the fundamentals of quantum mechanics prior to coarse graining. Fourth, yes, it is possible to cover the the Schwarzschild geometry by what is known as "nice slices," hypersurfaces that avoid the singularity for any finite time. (You find some very good graphics for that here, on slide 10). That doesn't solve the problem either because no matter how you turn it, your black hole evaporates away and you'll finally have to face that all you have left at scri minus is thermal radiation.

If you want to argue that the problem is a thought-experiment and unobservable, please read my earlier post on Thoughts and Experiments. We have to pay attention to inconsistencies even if they are not observable since they document a gap in our knowledge. While troubelsome, they also offer us opportunities to improve our understanding of Nature, which is why physicists turn problems like this upside-down and inside-out.

The value of the causal diagram once again is that it captures a lot of physics in one simple picture. If you look at it one more time you can see the problem. At the singularity matter gets crushed to infinite density and absent non-local effects everything that crossed the horizon has to fall into the singularity. Recall that curves on 45° angles depict the trajectories light travels on. You'd have to be faster than light to avoid the singularity once you've passed the horizon. All information about the initial state that evolves into the singularity is thus not available on the final slice. And that's exactly what happens in the calculation. You have to finally let go of the part of the initial wave-function that vanished behind the horizon, because it cannot avoid the singularity.

Now what

This then opens the playground for solutions to the problem. You either have to get the information out before it hits the singularity or avoid that it crosses the horizon at all. Lee and I argued in our last year's paper (see previous post for details) that the easiest way to avoid hitting the singularity is if there is no singularity. This by itself doesn't mean information behind the horizon becomes accessible again for the observer outside the horizon. But if you recall, this wasn't the problem to begin with. The problem was to achieve compatibility with unitary evolution, and this doesn't require information to be accessible to everybody as long as it exists.

In any case, since the black evaporation is and will likely remain elusive to experiment, everybody has their favorite solution. String theorists like the idea that information never gets lost because the evolution of the black hole is equivalently described by a dual, unitary, theory formulated on the boundary of the space-time which has been shown to encode regions of the bulk both inside and outside the horizon. People working on other approaches to quantum gravity seem to favor the idea that the singularity is avoided and the information somehow makes it out of the horizon, though at least to me it's remained unclear how so. (I sometimes suspect they'll finally reinvent and adopt the string theory solution.) Scenarios with stable or quasi-stable remnants that keep information or slowly release it also occasionally reoccur, and then there's parallel- and baby universes and a long list of miscellaneous other. The idea that black holes can't be formed to begin with lies in a shadowy fringe-area and is not considered plausible by the vast majority of researchers in the field.

I personally am somewhat agnostic on the how of information release, but am certain it can eventually only be achieved if the singularity is avoided (in the sense explained in mentioned paper.)

So. *wiping sweat off forehead* If you still haven't enough let me know.

[1] Modulo the question where it hits the singularity, see comments to previous post, but that's not relevant for our purposes.
[2] To be more precise, since we have assumed spherical symmetry to be able to draw a 4 dimensional manifold, a point in the figure is actually a sphere, but this distinction isn't so relevant. One can decompose the solutions to the wave-equation in spherical harmonics as usual. We are then talking here only about the s-wave state. States with higher angular momentum have a more complicated behavior.
[3] In the upheaval around the alleged risk of black holes at the LHC, some people ridiculed the fact that Hawking's calculation does not "automatically" decrease the mass of the black hole but that energy conservation is "put in by hand." That is in fact true. But that in this calculation the radiation does not "automatically" carry away the mass of the black hole is an artifact of doing the analysis in a fixed background, which "by hand" prohibits the mass from changing. There is absolutely nothing wrong with the argument that taking into account the energy loss through radiation the mass is not in fact constant. This in turn does not render the calculation false, it merely sets limits to its accuracy, and Hawking's calculation can be shown to be an excellent approximation as long as the ratio of mass loss is small. It is only in the end stage of evaporation when quantum gravity is important that the mass loss becomes relevant for the properties of the emitted radiation. This phase is thus still a matter of discussion.
[4] Note that it is entirely irrelevant the "initial" conditions are indeed the beginning of the evolution from which you determine the past. You could equally well specify the state of your system in the future and evolve it into the past.
[5] Note that this means once you've specified an equation of state for the matter, General Relativity does not allow you to specify what you want the matter to do over the course of time.
[6] The reverse is not true. A reversible evolution is in general not also unitary.
[7] Even if it's spherically symmetric. You lose all information in the radial direction.

Friday, February 05, 2010

The LHC Proton Source

Yesterday, we had a very nice colloquium by Jonas Strandberg from the University of Michigan on "The startup of the LHC and the very first collisions in the ATLAS detector" (abstract and video here). If you have an hour time, watching the video is a good way to spend it. Here, I just want to pick out one image he showed because it got stuck in my head.

As you might know the protons the LHC is circulating are accelerated in various stages. From a duoplasmatron, they are first injected into a linear accelerator (up to 50 MeV), then in the first small circular accelerator, the Proton Synchroton Booster (50 MeV -> 1.4 GeV), then in the Proton Synchroton (1.4 GeV -> 26GeV) and then in the Super Proton Synchroton (26 GeV -> 450 GeV). Only after this are they injected into the LHC tunnel for the real kick (450 GeV -> 7 TeV).

[picture source]

But where do the protons come from? Rather banally, out of a bottle of hydrogen:

[picture source]

I find it amazing, the contrast between that hydrogen bottle and the mighty LHC complex necessary to accelerate the protons.

Tuesday, February 02, 2010

LaserFest 2010

This year, the laser will turn 50! On May 16, 1960, at the Hughes Research Laboratories in Malibu, California, Theodore Maiman realized for the first time "Light Amplification by Stimulated Emission of Radiation", using a tiny ruby crystal.

Actually, Maiman and his small group of coworkers was back then just one of several teams, all at industrial laboratories, intensely searching for ways to create laser beams. At the end of the year, the ruby laser was replicated and improved, and lasing was realized using other crystals, and helium-neon gas mixtures. So, it's just fair that the American Physical Society, the Optical Society, SPIE, and the IEEE Photonics Society have decided to organize a yearlong celebration of the 50th anniversary of the laser - that's LaserFest.

But in fact, the path to the laser had begun much earlier.

Berlin, 1916

In the summer of 1916, Albert Einstein took a break from general relativity and cosmology and tried to make sense, once more, of the riddle of the quantum. Specifically, he thought about ways to combine the recent ideas of Bohr on discrete energy levels in atoms with the Planck spectrum of blackbody radiation.

Atoms in thermal equilibrium with radiation can absorb radiation, thereby transiting to a state of higher energy, and they can drop from an excited state to a state with lower energy spontaneously, thereby emitting radiation. Could it be, so Einstein's idea, that atoms also will transit from an excited to a lower-energy state when they are hit by radiation with suitable energy?

Indeed, assuming a thermal Boltzmann distribution for the states of the atoms interacting with radiation, and equal rates for absorption on the one hand and spontaneous and stimulated emission – as the newly stipulated process came to be called – on the other hand, as one would expect for a thermal equilibrium between the atoms and radiation, Einstein could reproduce the Planck formula for the spectrum of blackbody radiation. "A splendid light has dawned on me about the absorption and emission of radiation," he wrote in a letter to his friend Michele Besso on August 11, 1916.

Einstein's "splendid light" of stimulated emission of radiation: An atom in a state with energy E2 is hit by a photon with energy = E2E1. This can trigger a transition of the atom to the lower energy level E1, accompanied with the emission of a photon with energy , in phase with the initial photon. After this so-called stimulated emission, there are two photons instead of one, both in the same state – a nice manifestation of the "bunching" Bose character of photons.

It was recognized in the 1920s that theoretically the process of stimulated emission could result in "negative absorption", that is, amplification, of radiation, but nobody had a good idea how to demonstrate this effect in practice.

New York, 1954

To achieve amplification of radiation via stimulated emission, it is necessary to have more atoms in the high-energy state than in the low-energy state. Otherwise, a photon hitting an atom will more likely just be absorbed than trigger stimulated emission, and there is no gain in radiation. This requirement for amplification is called "population inversion".

In 1951, Charles Townes had an idea how to create "population inversion" in an ensemble of ammonia molecules. The ammonia molecule comes with two states which are separated by an energy corresponding to microwave frequencies. A beam of ammonia molecules can be split into two in an inhomogeneous electric field, separating molecules in the higher and the lower energy states, respectively, with an arrangement similar to a Stern-Gerlach apparatus.

In April 1954, Townes and his students Jim Gordon and Herbert Zeiger at Columbia University piped a beam of ammonia molecules in the higher-energy state into a microwave cavity resonating at the frequency of the energy difference between the two states, and obtained "microwave amplification by stimulated emission of radiation" - this was the birth of the maser.

Townes soon started to think about ways how to extend the maser principle to infrared or optical frequencies. With graduate student Gordon Gould, he discussed arrangements of mirrors around the medium in which population inversion is created, replacing the microwave cavity. These mirrors make sure that a beam of light is going back and forth through the medium many times, thus being able to "collect" ever more photons every time it crosses the medium.

Gould realized that such an arrangement, for which he coined the term "laser", could create sharply focussed light beams of extreme intensity, which could be used for communication, as a tool, or as a weapon.

As soon as the concept of the "optical maser", as Townes continued to call it, was explained in detail in a paper written together with Arthur Schawlow, many groups embarked on a race to be the first to actually construct such a device.

Malibu, 1960

Theodore Maiman had received his doctorate in Physics from Stanford University in 1955 to take a job at the Hughes Research Laboratories, which moved to Malibu in 1960. At Hughes, Maiman had constructed masers using ruby crystals, and when he learned of the possibility of the laser, he convinced himself that it should be possible to build a laser using ruby as the "lasing" medium.

Ruby is, chemically speaking, a crystal of aluminum oxide doted with chromium ions. The chromium ions have several energy levels which can be excited by irradiation with light, two of which are metastable and can be used as the upper level of a lasing medium. The energy of the transition to the ground state corresponds to red light with a wavelength of 694 nm.

Maiman's idea was to take a rod of ruby with parallel faces, to coat these faces with silver to realize the mirrors, and to put the rod inside a helical flashlight tube. The flashlight then excites the chromium atoms and creates population inversion, and the spontaneous emission of one photon can trigger an avalanche of photons by stimulated emission.

On the afternoon of May 16, 1960, Maiman and his assistant Irnee D’Haenens saw for the first time directed beams of intense red light emerging from the ruby - they had realized the first laser.

Theodore Maiman holding the first laser. It consists of a small ruby crystal and a helical flashlight which serves to stimulate the chromium ions of the ruby, thus creating the population inversion necessary for laser action. The ends of the ruby rod have been coated with silver to mirror back and forth the light stemming from stimulated emission, thus producing sufficient gain. The whole device is placed in the small white casing. (Source)

Maiman is reported to have said that “A laser is a solution seeking a problem”, Gould's visions notwithstanding. I have no specific idea how fast the laser was used for commercial or industrial purposes, but it immediately grasped public imagination.

When the movie Goldfinger is released in 1964, James Bond has to face a huge laser, looking similar to a scaled-up version of Maiman's first tiny ruby device, and replacing the buzz saw of Ian Flemings original 1959 novel. As Auric Goldfinger explains:

l, too, have a new toy, but considerably more practical. You are looking at an industrial laser, which emits an extraordinary light, unknown in nature. It can project a spot on the moon. Or, at closer range, cut through solid metal. I will show you.

At the LaserFest website, you can find a nice description of the mechanism of the ruby laser, and a video with explanations by Theodore Maiman himself. Moroever, there is a long interview with Charles Townes on the history of the maser and the laser.

If you want to know more about the history of the laser, there are two books I can recommend:
  • The history of the laser, by Mario Bertolotti, actually tells much more than just the story of the laser: It starts back at the beginning of the 20th century with the early atom models and the puzzle of blackbody radiation, and traces the path to the laser via spectroscopy, magnetic resonance, and the maser.

  • Beam: the race to make the laser, by Jeff Hecht, focusses on the developments of the late 1950s and 1960, beginning with just two brief chapters on the early history of stimulated emission and the maser. If you get lost in between all the names, there is a list of dramatis personae at the end of the book which I, unfortunately, discovered only after reading the text.

If you have Feynman's lectures at hand, there is a discussion of Einstein's derivation of the blackbody spectrum using stimulated emission and the Einstein coefficients in Section 42-5 of Volume I, and the whole Chapter 9 of Volume III is devoted to explain the principle of the ammonia maser.

Bloggy Notes

First: As some of you (Steven,Phil) have noticed, we have turned on comment moderation for all posts older than 14 days. Blogger only allows such selective comment moderation since recently. I've tried it for some weeks and it saves me a lot of time and effort, thus I will keep it.

Thing is that the vast majority of comments on posts older than 2 weeks are spam comments. You will occasionally have noticed them appearing in the comment feed. They typically come in bulks of 5-10, sometimes several a day. With the old settings, we had to visit every post separately and delete them. With the comment moderation on, they now go into the moderation queue without appearing in the feed, and I can check the queue when I please and hit "delete all."

For you this brings the inconvenience that on posts older than 14 days you might have to wait for your comment to appear till I come around to publish it. Let me add that I get all comments by email, so while the risk is not zero that I miss one, it is small.

Second: The number of comments on this blog has steadily been increasing and it has reached a level where Stefan and I don't come around to adequately handling them. I made a count on two days last week, and I came up to more than 50 comments per day (including my own). This has finally convinced me to take the step I've been hesitating to take for several years now: I have disabled anonymous comments.

The reason is simply that I am sick of the all too common Web2.0 drive-by anonymity. More often than not, it's the analogue of dropping into my living room with a Mickey-Mouse mask, spitting on the floor and then running away. I have previously told you that yes, anonymity has its place, but it should not be used unnecessarily. However, in reality, almost all anonymous comments are anonymous simply for the reason of cowardice, because somebody finds it okay to bother me with what just went through their head but then doesn't want to be brought in connection with it. You all know who I am. If somebody feels like they have to utter words without thinking and waste my time, I at least want the crap to stick to them. I am also sick of complaining about it.

It is clear to to me that requiring a Blogger ID won't exactly prevent that problem, but at least it's a hurdle that I hope will improve things. Please note that most blogs meanwhile either require registration, or that you submit an email address with your comment. This is not the case at blogspot, which literally invites anonymity.

Practically, for you this means you can no longer post comments without a Blogger ID or an Open ID. This affects some of our more frequent commenters, George and Kay come to mind. You do not need to write a blog to get a blogger ID. With a Google-account it takes you like 30 seconds to get one. It is 100% spam free. I've had my Blogger account since more than 4 years and have not received one single spam mail/news/updates etc. The Open ID you get with any of the participating services, including Wordpress, Facebook and Flickr.

I hope that our readers will benefit from these decisions.